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Hans-Werner Hammer

Publications and source records attributed to Hans-Werner Hammer.

At least 37 records · Page 2Linked to original sources
arXiv2024

Baryon Form Factors

We review the status of baryon form factors with a special focus on the nucleon electromagnetic form factors which are known best. First, we give an introduction into the dispersive analyses and emphasize the role of unitarity and analyticity in the construction of the isoscalar and isovector spectral functions. Second, we present the state of the art in our understanding of nucleon form factors and radii including reliable uncertainty estimates from bootstrap and Bayesian methods. Third, we discuss the physics of the time-like form factors and point out further issues to be addressed in this framework. Finally, we review the status of hyperon form factors and comment on the pion cloud.

hep-ph↗
arXiv2024

Lüscher equation with long-range forces

We derive the modified Lüscher equation in the presence of the long-range force caused by the exchange of a light particle. It is shown that the use of this equation enables one to circumvent the problems related to the strong partial-wave mixing and the t-channel sub-threshold singularities. It is also demonstrated that the present method is intrinsically linked to the so-called modified effective-range expansion (MERE) in the infinite volume. A detailed comparison with the two recently proposed alternative approaches is provided.

hep-lat↗
arXiv2023

Entanglement in few-nucleon scattering events

We investigate the spin entanglement in few-nucleon scattering processes involving nucleons and deuterons. For this purpose, we consider the entanglement power introduced by Beane et al. We analyze different entanglement entropies as a basis to define the entanglement power of the strong interaction and calculate the corresponding entanglement powers for proton-neutron, neutron-deuteron, proton-deuteron, and deuteron-deuteron scattering. For the latter two processes, we also take into account the modification from the Coulomb interaction. In contrast to proton-neutron scattering, no universal low-energy features are evident in the spin entanglement in neutron-deuteron, proton-deuteron, and deuteron-deuteron scattering.

nucl-th↗
arXiv2023

Pionic Final State Interactions and the Hypertriton Lifetime

We analyze the contribution of pionic final state interactions (FSI) in the weak decay of the hypertriton. Focusing on the $^3$He channel, we find a contribution of the pionic FSI of the order of $18\%$. Assuming a fixed value for the branching ratio $R_3$ for the decay width into $^3$He over the decay width into $^3$He and $pd$ final states, we find values for the hypertriton lifetime that are consistent with the world average as well as recent measurements by the ALICE Collaboration.

nucl-th↗
arXiv2023

Universality of $nn$ distributions of $s$-wave $2n$ halos and the unitary limit

We calculate neutron-neutron relative-energy distributions of $s$-wave two-neutron ($2n$) halo nuclei using Halo Effective Field Theory (Halo EFT) at leading order. At this order these systems are described by the $2n$ separation energy, the neutron-core ($nc$) virtual-state energy and the neutron-neutron ($nn$) scattering length. We focus on knockout reactions where the removal of the core is sudden, such that the final-state interactions are dominated by the $nn$ interaction. We consider the neutron relative-energy distribution for the nuclei $^{11}$Li, $^{14}$Be, $^{17}$B, $^{19}$B, and $^{22}$C. We show that the ground-state neutron momentum distributions of all these nuclei stem from a single curve, which can be obtained by taking both the neutron-core and neutron-neutron interaction to the unitary limit. This universal description can be extended to the final distribution measured in experiment by including $nn$ final-state interactions via the approximate technique of enhancement factors. For all the nuclei considered we find good agreement between the full leading-order Halo EFT calculation and the universal prediction obtained in this way. The universality of the ground-state momentum distribution in two-neutron Borromean halos can thus be tested by dividing the experimental results from sudden core knockout by the enhancement factor and comparing to the unitary-limit prediction.

nucl-th↗
arXiv2023

Emergence of a Bose polaron in a small ring threaded by the Aharonov-Bohm flux

The model of a ring threaded by the Aharonov-Bohm flux underlies our understanding of a coupling between gauge potentials and matter. The typical formulation of the model is based upon a single particle picture, and should be extended when interactions with other particles become relevant. Here, we illustrate such an extension for a particle in an Aharonov-Bohm ring subject to interactions with a weakly interacting Bose gas. We show that the ground state of the system can be described using the Bose polaron concept -- a particle dressed by interactions with a bosonic environment. We connect the energy spectrum to the effective mass of the polaron, and demonstrate how to change currents in the system by tuning boson-particle interactions. Our results suggest the Aharonov-Bohm ring as a platform for studying coherence and few- to many-body crossover of quasi-particles that arise from an impurity immersed in a medium.

cond-mat.quant-gas↗
arXiv2023

Neutron Scattering off One-Neutron Halo Nuclei in Halo Effective Field Theory

Neutron scattering off neutron halos can provide important information about the internal structure of nuclei close to the neutron drip line. In this work, we use halo effective field theory to study the $s$-wave scattering of a neutron and the spin-parity $J^P=\frac{1}{2}^+$ one-neutron halo nuclei $^{11}\rm Be$, $^{15}\rm C$, and $^{19}\rm C$ at leading order. In the $J=1$ channel, the only inputs to the Faddeev equations are their one-neutron separation energies. In the $J=0$ channel, the neutron-neutron scattering length and the two-neutron separation energies of $\rm ^{12}Be$, $\rm ^{16}C$ and $\rm ^{20}C$ enter as well. The numerical results show that the total $s$-wave cross sections in the $J=1$ channel at threshold are of the order of a few barns. In the $J=0$ channel, these cross sections are of the order of a few barns for $n$-$^{11}\rm Be$ and $n$-$^{19}\rm C$ scattering, and about 60 $\rm mb$ for the $n$-$^{15}\rm C$ scattering. The appearance of a pole in $p\cotδ$ close to zero in all three cases indicates the existence of a virtual Efimov state close to threshold in each of the $^{12}\rm Be$, $^{16}\rm C$, and $^{20}\rm C$ systems. Observation of this pole would confirm the presence of Efimov physics in halo nuclei. The dependence of the results on the neutron-core scattering length is also studied.

nucl-th↗
arXiv2023

The electromagnetic Sigma-to-Lambda transition form factors with coupled-channel effects in the space-like region

Using dispersion theory, the electromagnetic Sigma-to-Lambda transition form factors are expressed as the product of the pion electromagnetic form factor and the $Σ\barΛ\toππ$ scattering amplitudes with the latter estimated from SU(3) chiral perturbation theory including the baryon decuplet as explicit degrees of freedom. The contribution of the $K\bar{K}$ channel is also taken into account and the $ππ$-$K\bar{K}$ coupled-channel effect is included by means of a two-channel Muskhelishvili-Omnès representation. It is found that the electric transition form factor shows a significant shift after the inclusion of the $K\bar{K}$ channel, while the magnetic transition form factor is only weakly affected. However, the $K\bar{K}$ effect on the electric form factor is obscured by the undetermined coupling $h_A$ in the three-flavor chiral Lagrangian. The error bands of the Sigma-to-Lambda transition form factors from the uncertainties of the couplings and low-energy constant in three-flavor chiral perturbation theory are estimated by a bootstrap sampling method.

hep-ph↗
arXiv2023

Point Production of a Nonrelativistic Unparticle Recoiling Against a Particle

A nonrelativistic unparticle can be defined as an excitation created by an operator with a definite scaling dimension in a nonrelativistic field theory with an approximate conformal symmetry. The point production rate of an unparticle has power-law dependence on its total energy with an exponent determined by its scaling dimension. We use the exact result for the 3-point function of primary operators in a nonrelativistic conformal field theory to derive the contribution to the point production rate of the unparticle from its decay into another unparticle recoiling against a particle. In the case where the conformal symmetry is broken by a large positive scattering length, we deduce the exponent of the energy in the point production rate of the loosely bound two-particle state recoiling against a particle with large relative momentum.

hep-th↗
arXiv2022

Weak decay of halo nuclei

We investigate the weak decay of one-neutron halo nuclei into the proton-core continuum, i.e., beta-delayed proton emission from the halo nucleus using a cluster effective field theory for halo nuclei. On the one hand, we calculate the direct decay into the continuum. On the other hand, we consider the case of resonant final state interactions between the proton and the core. We present our formalism and discuss the application to the decay of $^{11}$Be in detail. Moreover, we compare to recent experimental results for the branching ratio and resonance parameters. As another example, we consider the case of $^{19}$C and predict the branching ratio for beta-delayed proton emission.

nucl-th↗
arXiv2022

Dispersion-theoretical analysis of the electromagnetic form factors of the $Λ$ hyperon

The electromagnetic form factors of the $Λ$ hyperon in the time-like region are determined precisely through a dispersion-theoretical analysis of the world data for the cross section of the annihilation process $e^+e^-\to \barΛΛ$. The spectral function is represented by a superposition of narrow and broad vector meson poles. We test different scenarios for the spectral function and obtain a good description of the world data in the time-like region. The uncertainties in the extracted form factors are estimated by means of the bootstrap sampling method. The analytical continuation of the form factors to the space-like region introduces large errors due to the lack of data. When the electric $Λ$ radius from chiral perturbation theory is taken as a constraint, the magnetic radius is predicted as $r_M = 0.681 \pm 0.002$ fm. We also extract various vector meson to baryon coupling constants.

hep-ph↗
arXiv2022

Final-state interactions and spin structure in $E1$ breakup of $^11$Li in Halo EFT

We calculate the $E1$ breakup of the $2n$ halo nucleus $^{11}$Li in Halo Effective Field Theory (Halo EFT) at leading order. In Halo EFT, $^{11}$Li is treated as a three-body system of a $^{9}$Li core and two neutrons. We present a detailed investigation of final-state interactions (FSI) in the neutron-neutron $(nn)$ and neutron-core $(nc)$ channels. We employ Moller operators to formulate an expansion scheme that satisfies the non-energy-weighted cluster sum rule and successively includes higher-order terms in the multiple-scattering series for the FSI. Computing the $E1$ strength up to third order in this scheme, we observe apparent convergence and good agreement with experiment. The neutron-neutron FSI is by far the most important contribution and largely determines the maximum value of the $E1$ distribution. However, inclusion of $nc$ FSI does shift the peak position to slightly lower energies. Moreover, we investigate the sensitivity of the $E1$ response to the spin structure of the neutron-${}^9$Li interaction. We contrast results for an interaction that is the same in the spin-1 and spin-2 channels with one that is only operative in the spin-2 channel, and find that good agreement with experimental data is only obtained if the interaction is present in both spin channels. The latter case is shown to be equivalent to a calculation in which the spin of $^9$Li is neglected.

nucl-th↗
arXiv2022

Three-body resonances in pionless effective field theory

We investigate the appearance of resonances in three-body systems using pionless effective field theory at leading order. The Faddeev equation is analytically continued to the unphysical sheet adjacent to the positive real energy axis using a contour rotation. We consider both, the three-boson system and the three-neutron system. For the former, we calculate the trajectory of Borromean three-body Efimov states turning into resonances as they cross the three-body threshold. For the latter, we find no sign of three-body resonances or virtual states at leading order. This result is validated by exploring the level structure of three-body states in a finite volume approach.

nucl-th↗
arXiv2022

Halo EFT for $^{31}$Ne in a spherical formalism

We calculate the electromagnetic properties of the deformed one-neutron halo candidate $^{31}$Ne using Halo Effective Field Theory (Halo EFT). In this framework, $^{31}$Ne is bound via a resonant $P$-wave interaction between the $^{30}$Ne core and the valence neutron. We set up a spherical formalism for $^{31}$Ne in order to calculate the electromagnetic form factors and the E1-breakup strength distribution into the $^{30}$Ne-neutron continuum at leading order in Halo EFT. The associated uncertainties are estimated according to our power counting. In particular, we assume that the deformation of the $^{30}$Ne core enters at next-to-leading order. It can be accounted for by including the $J^P=2^+$ excited state of $^{30}$Ne as an explicit field in the effective Lagrangian.

nucl-th↗
arXiv2022

Artificial atoms from cold bosons in one dimension

We investigate the ground-state properties of weakly repulsive one-dimensional bosons in the presence of an attractive zero-range impurity potential. First, we derive mean-field solutions to the problem on a finite ring for the two asymptotic cases: (i) all bosons are bound to the impurity and (ii) all bosons are in a scattering state. Moreover, we derive the critical line that separates these regimes in the parameter space. In the thermodynamic limit, this critical line determines the maximum number of bosons that can be bound by the impurity potential, forming an artificial atom. Second, we validate the mean-field results using the flow equation approach and the multi-layer multi-configuration time-dependent Hartree method for atomic mixtures. While beyond-mean-field effects destroy long-range order in the Bose gas, the critical boson number is unaffected. Our findings are important for understanding such artificial atoms in low-density Bose gases with static and mobile impurities.

cond-mat.quant-gas↗
arXiv2022

Spurious poles in a finite volume

Using 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 inconsistencies in the three-body equations, e.g., to the breakdown of unitarity. We investigate the effect of the spurious poles on the three-body quantization condition in a finite volume and show that it leads to a peculiar dependence of the energy levels on the box size $L$. Furthermore, within a simple model, it is demonstrated that the procedure for the removal of these poles, which was recently proposed in Ref.[1] in the infinite volume, can be adapted to the finite-volume calculations. The structure of the exact energy levels is reproduced with an accuracy that systematically improves order by order in the EFT expansion.

hep-lat↗
arXiv2022

Magnetic impurity in a one-dimensional few-fermion system

We present a numerical analysis of spin-$\frac{1}{2}$ fermions in a one-dimensional harmonic potential in the presence of a magnetic point-like impurity at the center of the trap. The model represents a few-body analogue of a magnetic impurity in the vicinity of an $s$-wave superconductor. Already for a few particles we find a ground-state level crossing between sectors with different fermion parities. We interpret this crossing as a few-body precursor of a quantum phase transition, which occurs when the impurity `breaks' a Cooper pair. This picture is further corroborated by analyzing density-density correlations in momentum space. Finally, we discuss how the system may be realized with existing cold-atoms platforms.

cond-mat.quant-gas↗