Showing 1–50 of 163 results for author: Hammer, H -

An alternative scheme for pionless EFT: neutron-deuteron scattering in the doublet S-wave

Authors: M. Ebert, H. -W. Hammer, A. Rusetsky

Abstract: Using the effective-range expansion for the two-body amplitudes may generate spurious sub-threshold poles outside of the convergence range of the expansion. In the infinite volume, the emergence of such poles leads to the breakdown of unitarity in the three-body amplitude. We discuss the extension of our alternative subtraction scheme for including effective range corrections in pionless effective… ▽ More Using the effective-range expansion for the two-body amplitudes may generate spurious sub-threshold poles outside of the convergence range of the expansion. In the infinite volume, the emergence of such poles leads to the breakdown of unitarity in the three-body amplitude. We discuss the extension of our alternative subtraction scheme for including effective range corrections in pionless effective field theory for spinless bosons to nucleons. In particular, we consider the neutron-deuteron system in the doublet S-wave channel explicitly. △ Less

Submitted 18 August, 2023; originally announced August 2023.

Comments: 9 pages, 2 figures, REVTeX

Theory of Halo Nuclei

Authors: H. -W. Hammer

Abstract: Halo nuclei are characterized by a few weakly bound halo nucleons and a more tightly bound core. This separation of scales can be exploited in a few-body description of halo nuclei, since the detailed structure of the core is not resolved by the halo nucleons. We present an introduction to the effective (field) theory for low-energy properties of halo nuclei. The focus is on halos with S-wave inte… ▽ More Halo nuclei are characterized by a few weakly bound halo nucleons and a more tightly bound core. This separation of scales can be exploited in a few-body description of halo nuclei, since the detailed structure of the core is not resolved by the halo nucleons. We present an introduction to the effective (field) theory for low-energy properties of halo nuclei. The focus is on halos with S-wave interactions for which universal properties are most pronounced. The special role of the unitary limit is illustrated using the example of multineutron systems and the Efimov effect as a universal binding mechanism for halo nuclei. Connections to ultracold atoms and hadron physics are highlighted and extensions to higher partial waves, Coulomb forces and nuclear reactions are briefly touched upon. △ Less

Submitted 24 March, 2022; originally announced March 2022.

Comments: 30 pages, 5 figures, contribution to the "Handbook of Nuclear Physics", Springer, 2022, edited by I. Tanihata, H. Toki, and T. Kajino

An alternative scheme for effective range corrections in pionless EFT

Authors: M. Ebert, H. -W. Hammer, A. Rusetsky

Abstract: We discuss an alternative scheme for including effective range corrections in pionless effective field theory. The standard approach treats range terms as perturbative insertions in the T -matrix. In a finite volume this scheme can lead to singular behavior close to the unperturbed energies. We consider an alternative scheme that resums the effective range but expands the spurious pole of the T -m… ▽ More We discuss an alternative scheme for including effective range corrections in pionless effective field theory. The standard approach treats range terms as perturbative insertions in the T -matrix. In a finite volume this scheme can lead to singular behavior close to the unperturbed energies. We consider an alternative scheme that resums the effective range but expands the spurious pole of the T -matrix created by this resummation. We test this alternative expansion for several model potentials and observe good convergence. △ Less

Submitted 24 September, 2021; originally announced September 2021.

Nuclear Structure at the Crossroads

Authors: R. J. Furnstahl, H. -W. Hammer, A. Schwenk

Abstract: Steven Weinberg's seminal papers from 1990-92 initiated the use of effective field theories (EFTs) for nuclei. We summarize progress, priorities, and open questions for nuclear EFT developments based on the 2019 INT program "Nuclear Structure at the Crossroads." Steven Weinberg's seminal papers from 1990-92 initiated the use of effective field theories (EFTs) for nuclei. We summarize progress, priorities, and open questions for nuclear EFT developments based on the 2019 INT program "Nuclear Structure at the Crossroads." △ Less

Submitted 15 August, 2021; v1 submitted 1 July, 2021; originally announced July 2021.

Comments: 15 pages, Contribution to Special Issue: Celebrating 30 years of Steven Weinberg's papers on Nuclear Forces from Chiral Lagrangians; published version

Journal ref: Few Body Syst. 62, 72 (2021)

Impurities in a one-dimensional Bose gas: the flow equation approach

Authors: F. Brauneis, H. -W. Hammer, M. Lemeshko, A. G. Volosniev

Abstract: A few years ago, flow equations were introduced as a technique for calculating the ground-state energies of cold Bose gases with and without impurities. In this paper, we extend this approach to compute observables other than the energy. As an example, we calculate the densities, and phase fluctuations of one-dimensional Bose gases with one and two impurities. For a single mobile impurity, we use… ▽ More A few years ago, flow equations were introduced as a technique for calculating the ground-state energies of cold Bose gases with and without impurities. In this paper, we extend this approach to compute observables other than the energy. As an example, we calculate the densities, and phase fluctuations of one-dimensional Bose gases with one and two impurities. For a single mobile impurity, we use flow equations to validate the mean-field results obtained upon the Lee-Low-Pines transformation. We show that the mean-field approximation is accurate for all values of the boson-impurity interaction strength as long as the phase coherence length is much larger than the healing length of the condensate. For two static impurities, we calculate impurity-impurity interactions induced by the Bose gas. We find that leading order perturbation theory fails when boson-impurity interactions are stronger than boson-boson interactions. The mean-field approximation reproduces the flow equation results for all values of the boson-impurity interaction strength as long as boson-boson interactions are weak. △ Less

Submitted 4 August, 2021; v1 submitted 26 January, 2021; originally announced January 2021.

Comments: Version accepted for publication in SciPost Physics

Journal ref: SciPost Phys. 11, 008 (2021)

Simulating core excitation in breakup reactions of halo nuclei using an effective three-body force

Authors: P. Capel, D. R. Phillips, H. -W. Hammer

Abstract: We extend our previous calculation of the breakup of 11Be using Halo Effective Field Theory and the Dynamical Eikonal Approximation to include an effective 10Be-n-target force. The force is constructed to account for the virtual excitation of 10Be to its low-lying 2+ excited state. In the case of breakup on a 12C target this improves the description of the neutron-energy and angular spectra, espec… ▽ More We extend our previous calculation of the breakup of 11Be using Halo Effective Field Theory and the Dynamical Eikonal Approximation to include an effective 10Be-n-target force. The force is constructed to account for the virtual excitation of 10Be to its low-lying 2+ excited state. In the case of breakup on a 12C target this improves the description of the neutron-energy and angular spectra, especially in the vicinity of the 11Be 5/2+ state. By fine-tuning the range parameters of the three-body force, a reasonable description of data in the region of the 3/2+ 11Be state can also be obtained. This sensitivity to the three-body force's range results from the structure of the overlap integral that governs the 11Be s-to-d-state transitions induced by the three-body force. △ Less

Submitted 27 December, 2021; v1 submitted 13 August, 2020; originally announced August 2020.

Comments: Accepted for publication within Physics Letters B; 9 pages, 4 figures

Lifetime of the hypertriton

Authors: F. Hildenbrand, H. -W. Hammer

Abstract: We calculate the lifetime of the hypertriton as function of the $Λ$ separation energy $B_Λ$ in an effective field theory with $Λ$ and deuteron degrees of freedom. We also consider the impact of new measurements of the weak decay parameter of the $Λ$. While the sensitivity of the total width to $B_Λ$ is small, the partial widths for decays into individual final states and the experimentally measure… ▽ More We calculate the lifetime of the hypertriton as function of the $Λ$ separation energy $B_Λ$ in an effective field theory with $Λ$ and deuteron degrees of freedom. We also consider the impact of new measurements of the weak decay parameter of the $Λ$. While the sensitivity of the total width to $B_Λ$ is small, the partial widths for decays into individual final states and the experimentally measured ratio $R=Γ_{^3\textrm{He}}/\left(Γ_{^3 \text{He}}+Γ_{pd}\right)$ show a strong dependence. For the standard value $B_Λ=(0.13\pm 0.05)$ MeV, we find $R=0.37\pm 0.05$, which is in good agreement with past experimental studies and theoretical calculations. For the recent STAR value $B_Λ=(0.41\pm0.12\pm0.11)$ MeV, we obtain $R=0.57\pm 0.11$. △ Less

Submitted 10 December, 2020; v1 submitted 20 July, 2020; originally announced July 2020.

Comments: 17 pages, 9 figures, J=3/2 FSI added, typos corrected

Journal ref: Phys. Rev. C 102, 064002 (2020)

Reply to Comment on "Is a Trineutron Resonance Lower in Energy than a Tetraneutron Resonance?"

Authors: S. Gandolfi, H. -W. Hammer, P. Klos, J. E. Lynn, A. Schwenk

Abstract: We reply to a Comment on our Letter [Phys. Rev. Lett. 118, 232501 (2017), arXiv:1612.01502] by A. Deltuva and R. Lazauskas [Phys. Rev. Lett 123, 069201 (2019), arXiv:1904.00925]. We reply to a Comment on our Letter [Phys. Rev. Lett. 118, 232501 (2017), arXiv:1612.01502] by A. Deltuva and R. Lazauskas [Phys. Rev. Lett 123, 069201 (2019), arXiv:1904.00925]. △ Less

Submitted 19 August, 2019; originally announced August 2019.

Comments: 2 pages, published version

Journal ref: Phys. Rev. Lett. 123, 069202 (2019)

In-medium bound states of two bosonic impurities in a one-dimensional Fermi gas

Authors: D. Huber, H. -W. Hammer, A. G. Volosniev

Abstract: We investigate the ground-state energy of a one-dimensional Fermi gas with two bosonic impurities. We consider spinless fermions with no fermion-fermion interactions. The fermion-impurity and impurity-impurity interactions are modelled with Dirac delta functions. First, we study the case where impurity and fermions have equal masses, and the impurity-impurity two-body interaction is identical to t… ▽ More We investigate the ground-state energy of a one-dimensional Fermi gas with two bosonic impurities. We consider spinless fermions with no fermion-fermion interactions. The fermion-impurity and impurity-impurity interactions are modelled with Dirac delta functions. First, we study the case where impurity and fermions have equal masses, and the impurity-impurity two-body interaction is identical to the fermion-impurity interaction, such that the system is solvable with the Bethe ansatz. For attractive interactions, we find that the energy of the impurity-impurity subsystem is below the energy of the bound state that exists without the Fermi gas. We interpret this as a manifestation of attractive boson-boson interactions induced by the fermionic medium, and refer to the impurity-impurity subsystem as an in-medium bound state. For repulsive interactions, we find no in-medium bound states. Second, we construct an effective model to describe these interactions, and compare its predictions to the exact solution. We use this effective model to study non-integrable systems with unequal masses and/or potentials. We discuss parameter regimes for which impurity-impurity attraction induced by the Fermi gas can lead to the formation of in-medium bound states made of bosons that repel each other in the absence of the Fermi gas. △ Less

Submitted 17 December, 2019; v1 submitted 7 August, 2019; originally announced August 2019.

Comments: version accepted for publication in Physical Review Research

Journal ref: Phys. Rev. Research 1, 033177 (2019)

Nuclear effective field theory: status and perspectives

Authors: H. -W. Hammer, S. König, U. van Kolck

Abstract: The nuclear physics landscape has been redesigned as a sequence of effective field theories (EFTs) connected to the Standard Model through symmetries and lattice simulations of Quantum Chromodynamics (QCD). EFTs in this sequence are expansions around different low-energy limits of QCD, each with its own characteristics, scales, and ranges of applicability regarding energy and number of nucleons. W… ▽ More The nuclear physics landscape has been redesigned as a sequence of effective field theories (EFTs) connected to the Standard Model through symmetries and lattice simulations of Quantum Chromodynamics (QCD). EFTs in this sequence are expansions around different low-energy limits of QCD, each with its own characteristics, scales, and ranges of applicability regarding energy and number of nucleons. We review each of the three main nuclear EFTs -- Chiral, Pionless, Halo/Cluster -- highlighting their similarities, differences, and connections. In doing so, we survey the structural properties and reactions of nuclei that have been derived from the ab initio solution of the few- and many-body problem built upon EFT input. △ Less

Submitted 6 April, 2020; v1 submitted 28 June, 2019; originally announced June 2019.

Comments: 76 pages, 29 figures, version to appear in Rev. Mod. Phys

Journal ref: Rev. Mod. Phys. 92, 25004 (2020)

Momentum-space probability density of ${}^6$He in Halo Effective Field Theory

Authors: M. Göbel, H. -W. Hammer, C. Ji, D. R. Phillips

Abstract: We compute the momentum-space probability density of ${}^6$He at leading order in Halo EFT. In this framework, the ${}^6$He nucleus is treated as a three-body problem with a ${}^4$He core ($c$) and two valence neutrons ($n$). This requires the $nn$ and $nc$ t-matrices as well as a $cnn$ force as input in the Faddeev equations. Since the $nc$ t-matrix corresponds to an energy-dependent potential, w… ▽ More We compute the momentum-space probability density of ${}^6$He at leading order in Halo EFT. In this framework, the ${}^6$He nucleus is treated as a three-body problem with a ${}^4$He core ($c$) and two valence neutrons ($n$). This requires the $nn$ and $nc$ t-matrices as well as a $cnn$ force as input in the Faddeev equations. Since the $nc$ t-matrix corresponds to an energy-dependent potential, we consider the consequent modifications to the standard normalization and orthogonality conditions. We find that these are small for momenta within the domain of validity of Halo EFT. In this regime, the ${}^6$He probability density is regulator independent, provided the cutoff is significantly above the EFT breakdown scale. △ Less

Submitted 12 September, 2019; v1 submitted 15 April, 2019; originally announced April 2019.

Comments: 34 pages, 3 figures, version to appear in Few-Body Systems. Further explanations and discussions added, typos corrected, results unchanged

Journal ref: Few-Body Syst (2019) 60: 61

Three-Body Hypernuclei in Pionless Effective Field Theory

Authors: F. Hildenbrand, H. -W. Hammer

Abstract: We calculate the structure of three-body hypernuclei with $S=-1$ using pionless effective field theory at leading order in the isospin $I=0$ and $I=1$ sectors. In both sectors, three-body hypernuclei arise naturally from the Efimov effect and a three-body parameter is required at leading order. We apply our theory to the hypertriton and the hypothetical $Λnn$ bound state and calculate the correspo… ▽ More We calculate the structure of three-body hypernuclei with $S=-1$ using pionless effective field theory at leading order in the isospin $I=0$ and $I=1$ sectors. In both sectors, three-body hypernuclei arise naturally from the Efimov effect and a three-body parameter is required at leading order. We apply our theory to the hypertriton and the hypothetical $Λnn$ bound state and calculate the corresponding scaling factors. Moreover, we discuss constraints on the existence of the $Λnn$ bound state. In particular, we elucidate universal correlations between different observables and provide explicit calculations of wave functions and matter radii. △ Less

Submitted 15 July, 2020; v1 submitted 11 April, 2019; originally announced April 2019.

Comments: 26 pages, 13 figures, typos corrected, discussion of parameter space for Lambda_* extended, error in Figs. 5-7 and Lambda-d scattering length corrected, final version

Journal ref: Phys. Rev. C 100, 034002 (2019)

Universal physics of bound states of a few charged particles

Authors: C. H. Schmickler, H. -W. Hammer, A. G. Volosniev

Abstract: We study few-body bound states of charged particles subject to attractive zero-range/short-range plus repulsive Coulomb interparticle forces. The characteristic length scales of the system at zero energy are set by the Coulomb length scale $D$ and the Coulomb-modified effective range $r_{\mathrm{eff}}$. We study shallow bound states of charged particles with $D\gg r_{\mathrm{eff}}$ and show that t… ▽ More We study few-body bound states of charged particles subject to attractive zero-range/short-range plus repulsive Coulomb interparticle forces. The characteristic length scales of the system at zero energy are set by the Coulomb length scale $D$ and the Coulomb-modified effective range $r_{\mathrm{eff}}$. We study shallow bound states of charged particles with $D\gg r_{\mathrm{eff}}$ and show that these systems obey universal scaling laws different from neutral particles. An accurate description of these states requires both the Coulomb-modified scattering length and the effective range unless the Coulomb interaction is very weak ($D\to \infty$). Our findings are relevant for bound states whose spatial extent is significantly larger than the range of the attractive potential. These states enjoy universality -- their character is independent of the shape of the short-range potential. △ Less

Submitted 16 October, 2019; v1 submitted 1 April, 2019; originally announced April 2019.

Comments: 8 pages, 6 figures, extended discussion, results unchanged, to appear in Phys. Lett. B

Journal ref: Phys. Lett. B 798, 135016 (2019)

More on the universal equation for Efimov states

Authors: M. Gattobigio, M. Göbel, H. -W. Hammer, A. Kievsky

Abstract: Efimov states are a sequence of shallow three-body bound states that arise when the two-body scattering length is much larger than the range of the interaction. The binding energies of these states are described as a function of the scattering length and one three-body parameter by a transcendental equation involving a universal function of one angular variable. We provide an accurate and convenie… ▽ More Efimov states are a sequence of shallow three-body bound states that arise when the two-body scattering length is much larger than the range of the interaction. The binding energies of these states are described as a function of the scattering length and one three-body parameter by a transcendental equation involving a universal function of one angular variable. We provide an accurate and convenient parametrization of this function. Moreover, we discuss the effective treatment of range corrections in the universal equation and compare with a strictly perturbative scheme. △ Less

Submitted 13 March, 2019; originally announced March 2019.

Comments: 13 pages, 5 figures

Journal ref: Few-Body Syst (2019) 60: 40

Efimov universality with Coulomb interaction

Authors: C. H. Schmickler, H. -W. Hammer, E. Hiyama

Abstract: The universal properties of charged particles are modified by the presence of a long-range Coulomb interaction. We investigate the modification of Efimov universality as a function of the Coulomb strength using the Gaussian expansion method. The resonant short-range interaction is described by Gaussian potentials to which a Coulomb potential is added. We calculate binding energies and root mean sq… ▽ More The universal properties of charged particles are modified by the presence of a long-range Coulomb interaction. We investigate the modification of Efimov universality as a function of the Coulomb strength using the Gaussian expansion method. The resonant short-range interaction is described by Gaussian potentials to which a Coulomb potential is added. We calculate binding energies and root mean square radii for the three- and four-body systems of charged particles and present our results in a generalised Efimov plot. We find that universal features can still be discerned for weak Coulomb interaction, but break down for strong Coulomb interaction. The root-mean-square radius plateaus at increasingly smaller values for strong Coulomb interaction and the probablity distributions of the states become more concentrated inside the Coulomb barrier. As an example, we apply our universal model to nuclei with an alpha-cluster substructure. Our results point to strong non-universal contributions in that sector. △ Less

Submitted 6 June, 2019; v1 submitted 11 January, 2019; originally announced January 2019.

Comments: 18 pages, 9 figures, final version (with small orthographical corrections)

Journal ref: Eur. Phys. J. A (2019) 55: 85

Neutron transfer reactions in halo effective field theory

Authors: M. Schmidt, L. Platter, H. -W. Hammer

Abstract: Direct reaction experiments provide a powerful tool to probe the structure of neutron-rich nuclei like beryllium-11. We use halo effective field theory to calculate the cross section of the deuteron-induced neutron transfer reaction ${}^{10}\text{Be}(\text{d},\,\text{p}){}^{11}\text{Be}$. The effective theory contains dynamical fields for the beryllium-10 core, the neutron, and the proton. In cont… ▽ More Direct reaction experiments provide a powerful tool to probe the structure of neutron-rich nuclei like beryllium-11. We use halo effective field theory to calculate the cross section of the deuteron-induced neutron transfer reaction ${}^{10}\text{Be}(\text{d},\,\text{p}){}^{11}\text{Be}$. The effective theory contains dynamical fields for the beryllium-10 core, the neutron, and the proton. In contrast, the deuteron and the beryllium-11 halo nucleus are generated dynamically from contact interactions using experimental and ab initio input. The reaction amplitude is constructed up to next-to-leading order in an expansion in the ratio of the length scales characterizing the core and the halo. The Coulomb repulsion between core and proton is treated perturbatively. Finally, we compare our results to cross-section data and other calculations. △ Less

Submitted 14 May, 2019; v1 submitted 21 December, 2018; originally announced December 2018.

Comments: 30 pages, 20 figures, published version with further details and minor typographic changes

Journal ref: Phys. Rev. C 99, 054611 (2019)

Dissecting reaction calculations using Halo EFT and ab initio input

Authors: P. Capel, D. R. Phillips, H. -W. Hammer

Abstract: We present a description of the break-up of halo nuclei in peripheral nuclear reactions by coupling a model of the projectile motivated by Halo Effective Field Theory with a fully dynamical treatment of the reaction using the Dynamical Eikonal Approximation. Our description of the halo system reproduces its long-range properties, i.e., binding energy and asymptotic normalization coefficients of bo… ▽ More We present a description of the break-up of halo nuclei in peripheral nuclear reactions by coupling a model of the projectile motivated by Halo Effective Field Theory with a fully dynamical treatment of the reaction using the Dynamical Eikonal Approximation. Our description of the halo system reproduces its long-range properties, i.e., binding energy and asymptotic normalization coefficients of bound states and phase shifts of continuum states. As an application we consider the break-up of 11Be in collisions on Pb and C targets. Taking the input for our Halo-EFT-inspired description of 11Be from a recent ab initio calculation of that system yields a good description of the Coulomb-dominated breakup on Pb at energies up to about 2 MeV, with the result essentially independent of the short-distance part of the halo wave function. However, the nuclear dominated break-up on C is more sensitive to short-range physics. The role of spectroscopic factors and possible extensions of our approach to include additional short-range mechanisms are also discussed. △ Less

Submitted 1 December, 2021; v1 submitted 7 June, 2018; originally announced June 2018.

Comments: Published within Phys. Rev. C. We have corrected a few typos, most importantly, the depth V_{s1/2}^{(2)} in Table I for the sole cutoff σ=2 fm has been corrected to its actual value +3MeV fm^{-2}

Journal ref: Phys. Rev. C 98, 034610 (2018)

Signatures of few-body resonances in finite volume

Authors: P. Klos, S. König, H. -W. Hammer, J. E. Lynn, A. Schwenk

Abstract: We study systems of bosons and fermions in finite periodic boxes and show how the existence and properties of few-body resonances can be extracted from studying the volume dependence of the calculated energy spectra. Using a plane-wave-based discrete variable representation to conveniently implement periodic boundary conditions, we establish that avoided level crossings occur in the spectra of up… ▽ More We study systems of bosons and fermions in finite periodic boxes and show how the existence and properties of few-body resonances can be extracted from studying the volume dependence of the calculated energy spectra. Using a plane-wave-based discrete variable representation to conveniently implement periodic boundary conditions, we establish that avoided level crossings occur in the spectra of up to four particles and can be linked to the existence of multi-body resonances. To benchmark our method we use two-body calculations, where resonance properties can be determined with other methods, as well as a three-boson model interaction known to generate a three-boson resonance state. Finding good agreement for these cases, we then predict three-body and four-body resonances for models using a shifted Gaussian potential. Our results establish few-body finite-volume calculations as a new tool to study few-body resonances. In particular, the approach can be used to study few-neutron systems, where such states have been conjectured to exist. △ Less

Submitted 29 September, 2018; v1 submitted 5 May, 2018; originally announced May 2018.

Comments: 13 pages, 10 figures, 2 tables, published version

Journal ref: Phys. Rev. C 98, 034004 (2018)

Electric structure of shallow D-wave states in Halo EFT

Authors: J. Braun, W. Elkamhawy, R. Roth, H. -W. Hammer

Abstract: We compute the electric form factors of one-neutron halo nuclei with shallow D-wave states up to next-to-leading order and the E2 transition from the S-wave to the D-wave state up to leading order in Halo Effective Field Theory (Halo EFT). The relevant degrees of freedom are the core and the halo neutron. The EFT expansion is carried out in powers of $R_{core}/R_{halo}$, where $R_{core}$ and… ▽ More We compute the electric form factors of one-neutron halo nuclei with shallow D-wave states up to next-to-leading order and the E2 transition from the S-wave to the D-wave state up to leading order in Halo Effective Field Theory (Halo EFT). The relevant degrees of freedom are the core and the halo neutron. The EFT expansion is carried out in powers of $R_{core}/R_{halo}$, where $R_{core}$ and $R_{halo}$ denote the length scales of the core and the halo, respectively. We propose a power counting scenario for weakly-bound states in one-neutron Halo EFT and discuss its implications for higher partial waves in terms of universality. The scenario is applied to the $\frac{5}{2}^+$ first excited state and the $\frac{1}{2}^+$ ground state of $^{15}\text{C}$. We obtain several universal correlations between electric observables and use data for the E2 transition $\frac{5}{2}^+\to \frac{1}{2}^+$ together with ab initio results from the No-Core Shell Model to predict the quadrupole moment. △ Less

Submitted 2 October, 2019; v1 submitted 6 March, 2018; originally announced March 2018.

Comments: 21 pages, 5 figures, improved presentation and discussion of uncertainties, some typos corrected

Journal ref: J. Phys. G 46, 115101 (2019)

Three-body spectrum in a finite volume: the role of cubic symmetry

Authors: M. Döring, H. -W. Hammer, M. Mai, J. -Y. Pang, A. Rusetsky, J. Wu

Abstract: The three-particle quantization condition is partially diagonalized in the center-of-mass frame by using cubic symmetry on the lattice. To this end, instead of spherical harmonics, the kernel of the Bethe-Salpeter equation for particle-dimer scattering is expanded in the basis functions of different irreducible representations of the octahedral group. Such a projection is of particular importance… ▽ More The three-particle quantization condition is partially diagonalized in the center-of-mass frame by using cubic symmetry on the lattice. To this end, instead of spherical harmonics, the kernel of the Bethe-Salpeter equation for particle-dimer scattering is expanded in the basis functions of different irreducible representations of the octahedral group. Such a projection is of particular importance for the three-body problem in the finite volume due to the occurrence of three-body singularities above breakup. Additionally, we study the numerical solution and properties of such a projected quantization condition in a simple model. It is shown that, for large volumes, these solutions allow for an instructive interpretation of the energy eigenvalues in terms of bound and scattering states. △ Less

Submitted 11 January, 2019; v1 submitted 9 February, 2018; originally announced February 2018.

Comments: 16 pages, 7 figures, supplemental material; version accepted by journal

Report number: JLAB-THY-18-2646

Journal ref: Phys. Rev. D 97, 114508 (2018)

Three particle quantization condition in a finite volume: 2. general formalism and the analysis of data

Authors: H. -W. Hammer, J. -Y. Pang, A. Rusetsky

Abstract: We derive the three-body quantization condition in a finite volume using an effective field theory in the particle-dimer picture. Moreover, we consider the extraction of physical observables from the lattice spectrum using the quantization condition. To illustrate the general framework, we calculate the volume-dependent three-particle spectrum in a simple model both below and above the three-parti… ▽ More We derive the three-body quantization condition in a finite volume using an effective field theory in the particle-dimer picture. Moreover, we consider the extraction of physical observables from the lattice spectrum using the quantization condition. To illustrate the general framework, we calculate the volume-dependent three-particle spectrum in a simple model both below and above the three-particle threshold. The relation to existing approaches is discussed in detail. △ Less

Submitted 7 July, 2017; originally announced July 2017.

Comments: 36 pages, 9 figures

Three-particle quantization condition in a finite volume: 1. The role of the three-particle force

Authors: H. -W. Hammer, J. -Y. Pang, A. Rusetsky

Abstract: Using non-relativistic effective Lagrangians in the particle-dimer picture, we rederive the expression for the energy shift of a loosely bound three-particle bound state of identical bosons in the unitary limit. The effective field theory formalism allows us to investigate the role of the three-particle force, which has not been taken into account in the earlier treatment of the problem. Moreover,… ▽ More Using non-relativistic effective Lagrangians in the particle-dimer picture, we rederive the expression for the energy shift of a loosely bound three-particle bound state of identical bosons in the unitary limit. The effective field theory formalism allows us to investigate the role of the three-particle force, which has not been taken into account in the earlier treatment of the problem. Moreover, we are able to relax the requirement of the unitary limit of infinite scattering length and demonstrate a smooth transition from the weakly bound three-particle state to a two-particle bound state of a particle and a deeply bound dimer. △ Less

Submitted 23 June, 2017; originally announced June 2017.

Comments: 24 pages, 3 figures

Flow equations for cold Bose gases

Authors: A. G. Volosniev, H. -W. Hammer

Abstract: We derive flow equations for cold atomic gases with one macroscopically populated energy level. The generator is chosen such that the ground state decouples from all other states in the system as the renormalization group flow progresses. We propose a self-consistent truncation scheme for the flow equations at the level of three-body operators and show how they can be used to calculate the ground… ▽ More We derive flow equations for cold atomic gases with one macroscopically populated energy level. The generator is chosen such that the ground state decouples from all other states in the system as the renormalization group flow progresses. We propose a self-consistent truncation scheme for the flow equations at the level of three-body operators and show how they can be used to calculate the ground state energy of a general $N$-body system. Moreover, we provide a general method to estimate the truncation error in the calculated energies. Finally, we test our scheme by benchmarking to the exactly solvable Lieb-Liniger model and find good agreement for weak and moderate interaction strengths. △ Less

Submitted 3 January, 2018; v1 submitted 8 May, 2017; originally announced May 2017.

Journal ref: New J. Phys. 19 113051 (2017)

Analytical approach to the Bose polaron problem in one dimension

Authors: A. G. Volosniev, H. -W. Hammer

Abstract: We discuss the ground state properties of a one-dimensional bosonic system doped with an impurity (the so-called Bose polaron problem). We introduce a formalism that allows us to calculate analytically the thermodynamic zero-temperature properties of this system with weak and moderate boson-boson interaction strengths for any boson-impurity interaction. Our approach is validated by comparing to ex… ▽ More We discuss the ground state properties of a one-dimensional bosonic system doped with an impurity (the so-called Bose polaron problem). We introduce a formalism that allows us to calculate analytically the thermodynamic zero-temperature properties of this system with weak and moderate boson-boson interaction strengths for any boson-impurity interaction. Our approach is validated by comparing to exact quantum Monte Carlo calculations. In addition, we test the method in finite size systems using numerical results based upon the similarity renormalization group. We argue that the introduced approach provides a simple analytical tool for studies of strongly interacting impurity problems in one dimension. △ Less

Submitted 25 September, 2017; v1 submitted 3 April, 2017; originally announced April 2017.

Comments: Version accepted for publication

Journal ref: PRA(R) 96, 031601 (2017)

Tetramer Bound States in Heteronuclear Systems

Authors: C. H. Schmickler, H. -W. Hammer, E. Hiyama

Abstract: We calculate the universal spectrum of trimer and tetramer states in heteronuclear mixtures of ultracold atoms with different masses in the vicinity of the heavy-light dimer threshold. To extract the energies, we solve the three- and four-body problem for simple two- and three-body potentials tuned to the universal region using the Gaussian expansion method. We focus on the case of one light parti… ▽ More We calculate the universal spectrum of trimer and tetramer states in heteronuclear mixtures of ultracold atoms with different masses in the vicinity of the heavy-light dimer threshold. To extract the energies, we solve the three- and four-body problem for simple two- and three-body potentials tuned to the universal region using the Gaussian expansion method. We focus on the case of one light particle of mass $m$ and two or three heavy bosons of mass $M$ with resonant heavy-light interactions. We find that trimer and tetramer cross into the heavy-light dimer threshold at almost the same point and that as the mass ratio $M/m$ decreases, the distance between the thresholds for trimer and tetramer states becomes smaller. We also comment on the possibility of observing exotic three-body states consisting of a dimer and two atoms in this region and compare with previous work. △ Less

Submitted 2 June, 2017; v1 submitted 3 March, 2017; originally announced March 2017.

Comments: 19 pages, 6 figures, final version, added some remarks and one reference and fixed notation

Journal ref: Phys. Rev. A 95, 052710 (2017)

Effective field theory description of halo nuclei

Authors: H. -W. Hammer, C. Ji, D. R. Phillips

Abstract: Nuclear halos emerge as new degrees of freedom near the neutron and proton driplines. They consist of a core and one or a few nucleons which spend most of their time in the classically-forbidden region outside the range of the interaction. Individual nucleons inside the core are thus unresolved in the halo configuration, and the low-energy effective interactions are short-range forces between the… ▽ More Nuclear halos emerge as new degrees of freedom near the neutron and proton driplines. They consist of a core and one or a few nucleons which spend most of their time in the classically-forbidden region outside the range of the interaction. Individual nucleons inside the core are thus unresolved in the halo configuration, and the low-energy effective interactions are short-range forces between the core and the valence nucleons. Similar phenomena occur in clusters of $^4$He atoms, cold atomic gases near a Feshbach resonance, and some exotic hadrons. In these weakly-bound quantum systems universal scaling laws for s-wave binding emerge that are independent of the details of the interaction. Effective field theory (EFT) exposes these correlations and permits the calculation of non-universal corrections to them due to short-distance effects, as well as the extension of these ideas to systems involving the Coulomb interaction and/or binding in higher angular-momentum channels. Halo nuclei exhibit all these features. Halo EFT, the EFT for halo nuclei, has been used to compute the properties of single-neutron, two-neutron, and single-proton halos of s-wave and p-wave type. This review summarizes these results for halo binding energies, radii, Coulomb dissociation, and radiative capture, as well as the connection of these properties to scattering parameters, thereby elucidating the universal correlations between all these observables. We also discuss how Halo EFT's encoding of the long-distance physics of halo nuclei can be used to check and extend ab initio calculations that include detailed modeling of their short-distance dynamics. △ Less

Submitted 5 November, 2017; v1 submitted 27 February, 2017; originally announced February 2017.

Comments: 104 pages, 31 figures. Topical Review for Journal of Physics G. v2 incorporates several modifications, particularly to the Introduction, in response to referee reports. It also corrects multiple typos in the original submission. It corresponds to the published version

Journal ref: J. Phys. G44, 103002 (2017)

Is a Trineutron Resonance Lower in Energy than a Tetraneutron Resonance?

Authors: S. Gandolfi, H. -W. Hammer, P. Klos, J. E. Lynn, A. Schwenk

Abstract: We present quantum Monte Carlo calculations of few-neutron systems confined in external potentials based on local chiral interactions at next-to-next-to-leading order in chiral effective field theory. The energy and radial densities for these systems are calculated in different external Woods-Saxon potentials. We assume that their extrapolation to zero external-potential depth provides a quantitat… ▽ More We present quantum Monte Carlo calculations of few-neutron systems confined in external potentials based on local chiral interactions at next-to-next-to-leading order in chiral effective field theory. The energy and radial densities for these systems are calculated in different external Woods-Saxon potentials. We assume that their extrapolation to zero external-potential depth provides a quantitative estimate of three- and four-neutron resonances. The validity of this assumption is demonstrated by benchmarking with an exact diagonalization in the two-body case. We find that the extrapolated trineutron resonance, as well as the energy for shallow well depths, is lower than the tetraneutron resonance energy. This suggests that a three-neutron resonance exists below a four-neutron resonance in nature and is potentially measurable. To confirm that the relative ordering of three- and four-neutron resonances is not an artifact of the external confinement, we test that the odd-even staggering in the helium isotopic chain is reproduced within this approach. Finally, we discuss similarities between our results and ultracold Fermi gases. △ Less

Submitted 13 June, 2017; v1 submitted 5 December, 2016; originally announced December 2016.

Comments: 6 pages, 5 figures, version compatible with published letter

Report number: LA-UR-16-29168

Journal ref: Phys. Rev. Lett. 118, 232501 (2017)

General aspects of effective field theories and few-body applications

Authors: H. -W. Hammer, Sebastian König

Abstract: Effective field theory provides a powerful framework to exploit a separation of scales in physical systems. In these lectures, we discuss some general aspects of effective field theories and their application to few-body physics. In particular, we consider an effective field theory for non-relativistic particles with resonant short-range interactions where certain parts of the interaction need to… ▽ More Effective field theory provides a powerful framework to exploit a separation of scales in physical systems. In these lectures, we discuss some general aspects of effective field theories and their application to few-body physics. In particular, we consider an effective field theory for non-relativistic particles with resonant short-range interactions where certain parts of the interaction need to be treated nonperturbatively. As an application, we discuss the so-called pionless effective field theory for low-energy nuclear physics. The extension to include long-range interactions mediated by photon and pion-exchange is also addressed. △ Less

Submitted 10 October, 2016; originally announced October 2016.

Comments: 46 pages, 16 figures. Lectures prepared for the ECT* Doctoral Training Program, "Computational Nuclear Physics", April 13 - May 22, 2015. Submitted to Lect. Notes Phys., "An advanced course in computational nuclear physics: Bridging the scales from quarks to neutron stars", M. Hjorth-Jensen, M. P. Lombardo, U. van Kolck, Editors

On the pi pi continuum in the nucleon form factors and the proton radius puzzle

Authors: M. Hoferichter, B. Kubis, J. Ruiz de Elvira, H. -W. Hammer, U. -G. Meißner

Abstract: We present an improved determination of the $ππ$ continuum contribution to the isovector spectral functions of the nucleon electromagnetic form factors. Our analysis includes the most up-to-date results for the $ππ\to\bar N N$ partial waves extracted from Roy-Steiner equations, consistent input for the pion vector form factor, and a thorough discussion of isospin-violating effects and uncertainty… ▽ More We present an improved determination of the $ππ$ continuum contribution to the isovector spectral functions of the nucleon electromagnetic form factors. Our analysis includes the most up-to-date results for the $ππ\to\bar N N$ partial waves extracted from Roy-Steiner equations, consistent input for the pion vector form factor, and a thorough discussion of isospin-violating effects and uncertainty estimates. As an application, we consider the $ππ$ contribution to the isovector electric and magnetic radii by means of sum rules, which, in combination with the accurately known neutron electric radius, are found to slightly prefer a small proton charge radius. △ Less

Submitted 11 November, 2016; v1 submitted 21 September, 2016; originally announced September 2016.

Comments: 10 pages, 3 figures, spectral functions included as supplementary material; journal version

Report number: INT-PUB-16-031

Nuclear Physics Around the Unitarity Limit

Authors: Sebastian König, Harald W. Grießhammer, H. -W. Hammer, U. van Kolck

Abstract: We argue that many features of the structure of nuclei emerge from a strictly perturbative expansion around the unitarity limit, where the two-nucleon S waves have bound states at zero energy. In this limit, the gross features of states in the nuclear chart are correlated to only one dimensionful parameter, which is related to the breaking of scale invariance to a discrete scaling symmetry and set… ▽ More We argue that many features of the structure of nuclei emerge from a strictly perturbative expansion around the unitarity limit, where the two-nucleon S waves have bound states at zero energy. In this limit, the gross features of states in the nuclear chart are correlated to only one dimensionful parameter, which is related to the breaking of scale invariance to a discrete scaling symmetry and set by the triton binding energy. Observables are moved to their physical values by small, perturbative corrections, much like in descriptions of the fine structure of atomic spectra. We provide evidence in favor of the conjecture that light, and possibly heavier, nuclei are bound weakly enough to be insensitive to the details of the interactions but strongly enough to be insensitive to the exact size of the two-nucleon system. △ Less

Submitted 16 May, 2017; v1 submitted 15 July, 2016; originally announced July 2016.

Comments: 6 pages, 3 figures, published version, rewritten for clarity

Report number: INT-PUB-16-019

Journal ref: Phys. Rev. Lett. 118, 202501 (2017)

Quantum Monte Carlo calculations of two neutrons in finite volume

Authors: P. Klos, J. E. Lynn, I. Tews, S. Gandolfi, A. Gezerlis, H. -W. Hammer, M. Hoferichter, A. Schwenk

Abstract: Ab initio calculations provide direct access to the properties of pure neutron systems that are challenging to study experimentally. In addition to their importance for fundamental physics, their properties are required as input for effective field theories of the strong interaction. In this work, we perform auxiliary-field diffusion Monte Carlo calculations of the ground and first excited state o… ▽ More Ab initio calculations provide direct access to the properties of pure neutron systems that are challenging to study experimentally. In addition to their importance for fundamental physics, their properties are required as input for effective field theories of the strong interaction. In this work, we perform auxiliary-field diffusion Monte Carlo calculations of the ground and first excited state of two neutrons in a finite box, considering a simple contact potential as well as chiral effective field theory interactions. We compare the results against exact diagonalizations and present a detailed analysis of the finite-volume effects, whose understanding is crucial for determining observables from the calculated energies. Using the Lüscher formula, we extract the low-energy S-wave scattering parameters from ground- and excited-state energies for different box sizes. △ Less

Submitted 24 November, 2016; v1 submitted 5 April, 2016; originally announced April 2016.

Comments: 11 pages, 8 figures

Report number: INT-PUB-16-010

Journal ref: Phys. Rev. C 94, 054005 (2016)

Two Cold Atoms in a Time-Dependent Harmonic Trap in One Dimension

Authors: M. Ebert, A. Volosniev, H. -W. Hammer

Abstract: We analyze the dynamics of two atoms with a short-ranged pair interaction in a one-dimensional harmonic trap with time-dependent frequency. Our analysis is focused on two representative cases: (i) a sudden change of the trapping frequency from one value to another, and (ii) a periodic trapping frequency. In case (i), the dynamics of the interacting and the corresponding non-interacting systems tur… ▽ More We analyze the dynamics of two atoms with a short-ranged pair interaction in a one-dimensional harmonic trap with time-dependent frequency. Our analysis is focused on two representative cases: (i) a sudden change of the trapping frequency from one value to another, and (ii) a periodic trapping frequency. In case (i), the dynamics of the interacting and the corresponding non-interacting systems turn out to be similar. In the second case, however, the interacting system can behave quite differently, especially close to parametric resonance. For instance, in the regions where such resonance occurs we find that the interaction can significantly reduce the rate of energy increase. The implications for applications of our findings to cool or heat the system are also dicussed. △ Less

Submitted 7 July, 2016; v1 submitted 21 December, 2015; originally announced December 2015.

Comments: Version accepted for publication in Annalen der Physik

Journal ref: Ann. Phys. (Berlin) 528, 693 (2016)

Effective Theory of 3H and 3He

Authors: Sebastian König, Harald W. Grießhammer, H. -W. Hammer, U. van Kolck

Abstract: We present a new perturbative expansion for pionless effective field theory with Coulomb interactions in which at leading order the spin-singlet nucleon-nucleon channels are taken in the unitarity limit. Presenting results up to next-to-leading order for the Phillips line and the neutron-deuteron doublet-channel phase shift, we find that a perturbative expansion in the inverse 1S0 scattering lengt… ▽ More We present a new perturbative expansion for pionless effective field theory with Coulomb interactions in which at leading order the spin-singlet nucleon-nucleon channels are taken in the unitarity limit. Presenting results up to next-to-leading order for the Phillips line and the neutron-deuteron doublet-channel phase shift, we find that a perturbative expansion in the inverse 1S0 scattering lengths converges rapidly. Using a new systematic treatment of the proton-proton sector that isolates the divergence due to one-photon exchange, we renormalize the corresponding contribution to the 3H-3He binding energy splitting and demonstrate that the Coulomb force in pionless EFT is a completely perturbative effect in the trinucleon bound-state regime. In our new expansion, the leading order is exactly isospin-symmetric. At next-to-leading order, we include isospin breaking via the Coulomb force and two-body scattering lengths, and find for the energy splitting (E_B(3He)-E_B(3H))^NLO = (-0.86 +/- 0.17) MeV. △ Less

Submitted 27 April, 2016; v1 submitted 20 August, 2015; originally announced August 2015.

Comments: 37 pages, 14 figures, published version

Journal ref: J. Phys. G: Nucl. Part. Phys. 43 (2016) 055106

Range corrections in Proton Halo Nuclei

Authors: Emil Ryberg, Christian Forssén, H. -W. Hammer, Lucas Platter

Abstract: We analyze the effects of finite-range corrections in halo effective field theory for S-wave proton halo nuclei. We calculate the charge radius to next-to-leading order and the astrophysical S-factor for low-energy proton capture to fifth order in the low-energy expansion. As an application, we confront our results with experimental data for the S-factor for proton capture on Oxygen-16 into the ex… ▽ More We analyze the effects of finite-range corrections in halo effective field theory for S-wave proton halo nuclei. We calculate the charge radius to next-to-leading order and the astrophysical S-factor for low-energy proton capture to fifth order in the low-energy expansion. As an application, we confront our results with experimental data for the S-factor for proton capture on Oxygen-16 into the excited $1/2^+$ state of Fluorine-17. Our low-energy theory is characterized by a systematic low-energy expansion, which can be used to quantify an energy-dependent model error to be utilized in data fitting. Finally, we show that the existence of proton halos is suppressed by the need for two fine tunings in the underlying theory. △ Less

Submitted 30 July, 2015; originally announced July 2015.

Comments: 30pages, 12 figures

Journal ref: Annals Phys, 367 (2016) 13-32

Simulation of Time-dependent Heisenberg Models in 1D

Authors: A. G. Volosniev, H. -W. Hammer, N. T. Zinner

Abstract: In this paper, we provide a theoretical analysis of strongly interacting quantum systems confined by a time-dependent external potential in one spatial dimension. We show that such systems can be used to simulate spin chains described by Heisenberg Hamiltonians in which the exchange coupling constants can be manipulated by time-dependent driving of the shape of the external confinement. As illustr… ▽ More In this paper, we provide a theoretical analysis of strongly interacting quantum systems confined by a time-dependent external potential in one spatial dimension. We show that such systems can be used to simulate spin chains described by Heisenberg Hamiltonians in which the exchange coupling constants can be manipulated by time-dependent driving of the shape of the external confinement. As illustrative examples, we consider a harmonic trapping potential with a variable frequency and an infinite square well potential with a time-dependent barrier in the middle. △ Less

Submitted 30 March, 2016; v1 submitted 1 July, 2015; originally announced July 2015.

Comments: Version accepted for publication in PRB

Journal ref: Phys. Rev. B 93, 094414 (2016)

New structures in the proton-antiproton system

Authors: I. T. Lorenz, H. -W. Hammer, U. -G. Meißner

Abstract: In the most recent measurements of the reaction $e^+e^- \rightarrow p\bar{p}$ by the BABAR collaboration, new structures have been found with unknown origin. We examine a possible relation of the most distinct peak to the recently observed $Φ(2170)$. Alternatively, we analyse possible explanations due to the nucleon$\,\barΔ$ and $Δ\barΔ$ thresholds. The latter could explain a periodicity found in… ▽ More In the most recent measurements of the reaction $e^+e^- \rightarrow p\bar{p}$ by the BABAR collaboration, new structures have been found with unknown origin. We examine a possible relation of the most distinct peak to the recently observed $Φ(2170)$. Alternatively, we analyse possible explanations due to the nucleon$\,\barΔ$ and $Δ\barΔ$ thresholds. The latter could explain a periodicity found in the data. △ Less

Submitted 7 June, 2015; originally announced June 2015.

Journal ref: Phys. Rev. D 92, 034018 (2015)

Limit Cycles from the Similarity Renormalization Group

Authors: P. Niemann, H. -W. Hammer

Abstract: We investigate renormalization group limit cycles within the similarity renormalization group (SRG) and discuss their signatures in the evolved interaction. A quantitative method to detect limit cycles in the interaction and to extract their period is proposed. Several SRG generators are compared regarding their suitability for this purpose. As a test case, we consider the limit cycle of the inver… ▽ More We investigate renormalization group limit cycles within the similarity renormalization group (SRG) and discuss their signatures in the evolved interaction. A quantitative method to detect limit cycles in the interaction and to extract their period is proposed. Several SRG generators are compared regarding their suitability for this purpose. As a test case, we consider the limit cycle of the inverse square potential. △ Less

Submitted 17 April, 2015; originally announced April 2015.

Comments: 11 pages, 6 figures

Real-Time Dynamics of an Impurity in an Ideal Bose Gas in a Trap

Authors: A. G. Volosniev, H. -W. Hammer, N. T. Zinner

Abstract: We investigate the behavior of a harmonically trapped system consisting of an impurity in a dilute ideal Bose gas after the boson-impurity interaction is suddenly switched on. As theoretical framework, we use a field theory approach in the space-time domain within the T-matrix approximation. We establish the form of the corresponding T-matrix and address the dynamical properties of the system. As… ▽ More We investigate the behavior of a harmonically trapped system consisting of an impurity in a dilute ideal Bose gas after the boson-impurity interaction is suddenly switched on. As theoretical framework, we use a field theory approach in the space-time domain within the T-matrix approximation. We establish the form of the corresponding T-matrix and address the dynamical properties of the system. As a numerical application, we consider a simple system of a weakly interacting impurity in one dimension where the interaction leads to oscillations of the impurity density. Moreover, we show that the amplitude of the oscillations can be driven by periodically switching the interaction on and off. △ Less

Submitted 17 August, 2015; v1 submitted 18 February, 2015; originally announced February 2015.

Comments: Version accepted for publication in PRA

Journal ref: Phys. Rev. A 92, 023623 (2015)

Remarks on the study of the X(3872) from Effective Field Theory with Pion-Exchange Interaction

Authors: V. Baru, E. Epelbaum, A. A. Filin, Feng-Kun Guo, H. -W. Hammer, C. Hanhart, Ulf-G. Meißner, A. V. Nefediev

Abstract: In a recent paper Phys.Rev.Lett. 111, 042002 (2013) (arXiv:1304.0846), the charmonium state X(3872) is studied in the framework of an effective field theory. In that work it is claimed that (i) the one-pion exchange (OPE) alone provides sufficient binding to produce the X as a shallow bound state at the $D^0\bar{D}^{*0}$ threshold, (ii) short-range dynamics (described by a contact interaction) pro… ▽ More In a recent paper Phys.Rev.Lett. 111, 042002 (2013) (arXiv:1304.0846), the charmonium state X(3872) is studied in the framework of an effective field theory. In that work it is claimed that (i) the one-pion exchange (OPE) alone provides sufficient binding to produce the X as a shallow bound state at the $D^0\bar{D}^{*0}$ threshold, (ii) short-range dynamics (described by a contact interaction) provides only moderate corrections to the OPE, and (iii) the X-pole disappears as the pion mass is increased slightly and therefore the X should not be seen on the lattice, away from the pion physical mass point, if it were a molecular state. In this paper we demonstrate that the results of Phys.Rev.Lett. 111, 042002 (2013) (arXiv:1304.0846) suffer from technical as well as conceptual problems and therefore do not support the conclusions drawn by the authors. △ Less

Submitted 13 January, 2015; originally announced January 2015.

Comments: LaTeX2e, 7 pages, 2 figures, to appear in Phys.Rev.D

Journal ref: Phys.Rev.D91:034002,2015

Ab initio lattice results for Fermi polarons in two dimensions

Authors: Shahin Bour, Dean Lee, H. -W. Hammer, Ulf-G. Meißner

Abstract: We investigate the attractive Fermi polaron problem in two dimensions using non-perturbative Monte Carlo simulations. We introduce a new Monte Carlo algorithm called the impurity lattice Monte Carlo method. This algorithm samples the path integral in a computationally efficient manner and has only small sign oscillations for systems with a single impurity. As a benchmark of the method, we calculat… ▽ More We investigate the attractive Fermi polaron problem in two dimensions using non-perturbative Monte Carlo simulations. We introduce a new Monte Carlo algorithm called the impurity lattice Monte Carlo method. This algorithm samples the path integral in a computationally efficient manner and has only small sign oscillations for systems with a single impurity. As a benchmark of the method, we calculate the universal polaron energy in three dimensions in the scale-invariant unitarity limit and find agreement with published results. We then present the first fully non-perturbative calculations of the polaron energy in two dimensions and density correlations between the impurity and majority particles in the limit of zero range interactions. We find evidence for a smooth crossover transition from fermionic quasiparticle to molecular state as a function of interaction strength. △ Less

Submitted 1 October, 2015; v1 submitted 28 December, 2014; originally announced December 2014.

Comments: Includes new results on density-density correlations. Final version as will appear in Phys. Rev. Lett

Journal ref: Phys. Rev. Lett. 115, 185301 (2015)

Theoretical Constraints and Systematic Effects in the Determination of the Proton Form Factors

Authors: I. T. Lorenz, Ulf-G. Meißner, H. -W. Hammer, Y. -B. Dong

Abstract: We calculate the two-photon exchange corrections to electron-proton scattering with nucleon and $Δ$ intermediate states. The results show a dependence on the elastic nucleon and nucleon-$Δ$-transition form factors used as input which leads to significant changes compared to previous calculations. We discuss the relevance of these corrections and apply them to the most recent and precise data set a… ▽ More We calculate the two-photon exchange corrections to electron-proton scattering with nucleon and $Δ$ intermediate states. The results show a dependence on the elastic nucleon and nucleon-$Δ$-transition form factors used as input which leads to significant changes compared to previous calculations. We discuss the relevance of these corrections and apply them to the most recent and precise data set and world data from electron-proton scattering. Using this, we show how the form factor extraction from these data is influenced by the subsequent inclusion of physical constraints. The determination of the proton charge radius from scattering data is shown to be dominated by the enforcement of a realistic spectral function. Additionally, the third Zemach moment from the resulting form factors is calculated. The obtained radius and Zemach moment are shown to be consistent with Lamb shift measurements in muonic hydrogen. △ Less

Submitted 20 January, 2015; v1 submitted 6 November, 2014; originally announced November 2014.

Comments: minor changes, added references, version to appear in PRD

Journal ref: Phys. Rev. D91 (2015) 014023

Constraining Low-Energy Proton Capture on Beryllium-7 through Charge Radius Measurements

Authors: Emil Ryberg, Christian Forssén, H. -W. Hammer, Lucas Platter

Abstract: In this paper, we point out that a measurement of the charge radius of Boron-8 provides indirect access to the S-factor for radiative proton capture on Beryllium-7 at low energies. We use leading-order halo effective field theory to explore this correlation and we give a relation between the charge radius and the S-factor. Furthermore, we present important technical aspects relevant to the renorma… ▽ More In this paper, we point out that a measurement of the charge radius of Boron-8 provides indirect access to the S-factor for radiative proton capture on Beryllium-7 at low energies. We use leading-order halo effective field theory to explore this correlation and we give a relation between the charge radius and the S-factor. Furthermore, we present important technical aspects relevant to the renormalization of pointlike P-wave interactions in the presence of a repulsive Coulomb interaction. △ Less

Submitted 29 October, 2014; v1 submitted 26 June, 2014; originally announced June 2014.

Comments: Accepted for publication in European Physical Journal A. 29 pages, 9 figures

Journal ref: Eur. Phys. J. A (2014) 50: 170

The proton-deuteron system in pionless EFT revisited

Authors: Sebastian König, Harald W. Grießhammer, H. -W. Hammer

Abstract: We provide a detailed discussion of the low-energy proton-deuteron system in pionless effective field theory, considering both the spin-quartet and doublet S-wave channels. Extending and amending our previous work on the subject, we calculate the 3He-3H binding energy difference both perturbatively (using properly normalized trinucleon wave functions) and non-perturbatively by resumming all O(alph… ▽ More We provide a detailed discussion of the low-energy proton-deuteron system in pionless effective field theory, considering both the spin-quartet and doublet S-wave channels. Extending and amending our previous work on the subject, we calculate the 3He-3H binding energy difference both perturbatively (using properly normalized trinucleon wave functions) and non-perturbatively by resumming all O(alpha) Coulomb diagrams in the doublet channel. Our nonperturbative result agrees well with a calculation that involves the full off-shell Coulomb T-matrix. Carefully examining the cutoff-dependence in the doublet channel, we present numerical evidence for a new three-nucleon counterterm being necessary at next-to-leading order if Coulomb effects are included. Indeed, such a term has recently been identified analytically. We furthermore make a case for a simplified Coulomb power counting that is consistent throughout the bound-state and scattering regimes. Finally, using a "partially screened" full off-shell Coulomb T-matrix, we investigate the importance of higher-order Coulomb corrections in low-energy quartet-channel scattering. △ Less

Submitted 21 January, 2015; v1 submitted 30 May, 2014; originally announced May 2014.

Comments: 56 pages, 23 figures, published version with one nontrivial correction indicated by a footnote on p. 2

Journal ref: J. Phys. G: Nucl. Part. Phys. 42 (2015) 045101

Precision calculation of the quartet-channel p-d scattering length

Authors: Sebastian König, H. -W. Hammer

Abstract: We present a fully perturbative calculation of the quartet-channel proton--deuteron scattering length up to next-to-next-to-leading order in pionless effective field theory. We use a framework that consistently extracts the Coulomb-modified effective range function for a screened Coulomb potential in momentum space and allows for a clear linear extrapolation back to the physical limit without scre… ▽ More We present a fully perturbative calculation of the quartet-channel proton--deuteron scattering length up to next-to-next-to-leading order in pionless effective field theory. We use a framework that consistently extracts the Coulomb-modified effective range function for a screened Coulomb potential in momentum space and allows for a clear linear extrapolation back to the physical limit without screening. Our result of (10.9 +/- 0.4) fm agrees with older experimental determinations of this quantity but deviates from potential-model calculations and a more recent result from Black et al., which find larger values around 14 fm. As a possible resolution to this discrepancy, we discuss the scheme dependence of Coulomb subtractions in a three-body system. △ Less

Submitted 2 October, 2014; v1 submitted 9 December, 2013; originally announced December 2013.

Comments: 9 pages, 7 figures, published version

Journal ref: Phys. Rev. C 90, 034005 (2014)

Effective field theory for proton halo nuclei

Authors: Emil Ryberg, Christian Forssén, H. -W. Hammer, Lucas Platter

Abstract: We use halo effective field theory to analyze the universal features of proton halo nuclei bound due to a large S-wave scattering length. With a Lagrangian built from effective core and valence-proton fields, we derive a leading-order expression for the charge form factor. Within the same framework we also calculate the radiative proton capture cross section. Our general results at leading order a… ▽ More We use halo effective field theory to analyze the universal features of proton halo nuclei bound due to a large S-wave scattering length. With a Lagrangian built from effective core and valence-proton fields, we derive a leading-order expression for the charge form factor. Within the same framework we also calculate the radiative proton capture cross section. Our general results at leading order are applied to study the excited 1/2+ state of Fluorine-17, and we give results for the charge radius and the astrophysical S-factor. △ Less

Submitted 27 August, 2013; originally announced August 2013.

Comments: 13 pages, 5 figures

Journal ref: Phys. Rev. C 89, 014325 (2014)

Efimov Physics around the neutron rich Calcium-60 isotope

Authors: G. Hagen, P. Hagen, H. -W. Hammer, L. Platter

Abstract: We calculate the neutron-Calcium-60 S-wave scattering phase shifts using state of the art coupled-cluster theory combined with modern ab initio interactions derived from chiral effective theory. Effects of three-nucleon forces are included schematically as density dependent nucleon-nucleon interactions. This information is combined with halo effective field theory in order to investigate the Calci… ▽ More We calculate the neutron-Calcium-60 S-wave scattering phase shifts using state of the art coupled-cluster theory combined with modern ab initio interactions derived from chiral effective theory. Effects of three-nucleon forces are included schematically as density dependent nucleon-nucleon interactions. This information is combined with halo effective field theory in order to investigate the Calcium-60-neutron-neutron system. We predict correlations between different three-body observables and the two-neutron separation energy of Calcium-62. This provides evidence of Efimov physics along the Calcium isotope chain. Experimental key observables that facilitate a test of our findings are discussed. △ Less

Submitted 10 January, 2014; v1 submitted 16 June, 2013; originally announced June 2013.

Comments: 5 pages, 4 figures

Journal ref: Phys. Rev. Lett. 111 (2013) 132501

Charge form factors of two-neutron halo nuclei in halo EFT

Authors: P. Hagen, H. -W. Hammer, L. Platter

Abstract: We set up a formalism to calculate the charge form factors of two-neutron halo nuclei with S-wave neutron-core interactions in the framework of the halo effective field theory. The method is applied to some known and suspected halo nuclei. In particular, we calculate the form factors and charge radii relative to the core to leading order in the halo EFT and compare to experiments where they are av… ▽ More We set up a formalism to calculate the charge form factors of two-neutron halo nuclei with S-wave neutron-core interactions in the framework of the halo effective field theory. The method is applied to some known and suspected halo nuclei. In particular, we calculate the form factors and charge radii relative to the core to leading order in the halo EFT and compare to experiments where they are available. Moreover, we investigate the general dependence of the charge radius on the core mass and the one- and two-neutron separation energies. △ Less

Submitted 3 September, 2013; v1 submitted 24 April, 2013; originally announced April 2013.

Comments: 22 pages, 12 figures, final version to appear in EPJA

Journal ref: Eur. Phys. J. A49, 118 (2013)

Electromagnetic Structure of the Z_c(3900)

Authors: E. Wilbring, H. -W. Hammer, U. -G. Meißner

Abstract: The observation of the exotic quarkonium state Z_c(3900) by the BESIII and Belle collaborations supports the concept of hadronic molecules. Charmonium states interpreted as such molecules would be bound states of heavy particles with small binding energies. This motivates their description using an effective theory with contact interactions. In particular, we focus on the electromagnetic structure… ▽ More The observation of the exotic quarkonium state Z_c(3900) by the BESIII and Belle collaborations supports the concept of hadronic molecules. Charmonium states interpreted as such molecules would be bound states of heavy particles with small binding energies. This motivates their description using an effective theory with contact interactions. In particular, we focus on the electromagnetic structure of the charged state Z_c(3900). Using first experimental results concerning spin and parity, we interpret it as an S-wave molecule and calculate the form factors as well as charge and magnetic radii up to next-to-leading order. We also present first numerical estimations of some of these observables at leading order. △ Less

Submitted 3 September, 2013; v1 submitted 10 April, 2013; originally announced April 2013.

Comments: 5 pages, 4 figures, final version to appear in Phys. Lett. B

Journal ref: Phys. Lett. B726, 326 (2013)

Causality, universality, and effective field theory for van der Waals interactions

Authors: Serdar Elhatisari, Sebastian König, Dean Lee, H. -W. Hammer

Abstract: We analyze low-energy scattering for arbitrary short-range interactions plus an attractive 1/r^6 tail. We derive the constraints of causality and unitarity and find that the van der Waals length scale dominates over parameters characterizing the short-distance physics of the interaction. This separation of scales suggests a separate universality class for physics characterizing interactions with a… ▽ More We analyze low-energy scattering for arbitrary short-range interactions plus an attractive 1/r^6 tail. We derive the constraints of causality and unitarity and find that the van der Waals length scale dominates over parameters characterizing the short-distance physics of the interaction. This separation of scales suggests a separate universality class for physics characterizing interactions with an attractive 1/r^6 tail. We argue that a similar universality class exists for any attractive potential 1/r^{alpha} for alpha >= 2. We also discuss the extension to multi-channel systems near a magnetic Feshbach resonance. We discuss the implications for effective field theory with attractive singular power law tails. △ Less

Submitted 16 May, 2013; v1 submitted 21 March, 2013; originally announced March 2013.

Comments: 19 pages, 3 figures, version published in Phys. Rev. A

Journal ref: Phys. Rev. A 87, 052705 (2013)

Universal Relation for the Inelastic Two-Body Loss Rate

Authors: Eric Braaten, H. -W. Hammer

Abstract: Strongly-interacting systems consisting of particles that interact through a large scattering length satisfy universal relations that relate many of their central properties to the contact, which measures the number of pairs with small separations. We use the operator product expansion of quantum field theory to derive the universal relation for the inelastic 2-body loss rate. A simple universal r… ▽ More Strongly-interacting systems consisting of particles that interact through a large scattering length satisfy universal relations that relate many of their central properties to the contact, which measures the number of pairs with small separations. We use the operator product expansion of quantum field theory to derive the universal relation for the inelastic 2-body loss rate. A simple universal relation between the loss rate and the contact is obtained by truncating the expansion after the lowest dimension operator. We verify the universal relation explicitly by direct calculations in the low-density limit at nonzero temperature. This universal relation can be tested experimentally using ultracold quantum gases of atoms in hyperfine states that have an inelastic spin-relaxation channel. △ Less

Submitted 8 January, 2014; v1 submitted 22 February, 2013; originally announced February 2013.

Comments: 18 pages, no figures, published version

Journal ref: J.Phys.B:At.Mol.Opt.Phys.46:215203,2013