Searcharxiv⌕ Search

arXiv subjects

Hans-Werner Hammer

Publications and source records attributed to Hans-Werner Hammer.

53 records · Page 3Linked to original sources
arXiv2022

Differential Cross Section Predictions for PRad-II from Dispersion Theory

We predict the differential cross sections for $e^-p$ and $e^+p$ elastic scattering in the PRad-\Rom{2} energy region. The prediction is based on form factors obtained in our previous high-precision analysis of space- and time-like data from dispersion theory and different sets of two-photon exchange corrections. We investigate the sensitivity of the cross sections to two-photon exchange effects and find that the differences between model calculations and phenomenological extractions of the two-photon corrections can not be resolved if the uncertainty in the form factors is taken into account.

hep-ph↗
arXiv2022

Interpretation of neutral charm mesons near threshold as unparticles

The existence of the $X(3872)$ resonance extremely close to the $D^{*0} \bar{D}^0$ threshold implies that neutral charm mesons have an approximate nonrelativistic conformal symmetry. Systems consisting of these mesons with small kinetic energies produced in a short-distance reaction are unparticles in the sense that they can be created by operators with definite scaling dimensions in a nonrelativistic conformal field theory. There is a scaling region in which their energy distribution has power-law behavior with an exponent determined by the scaling dimension of the operator. The unparticle associated with two neutral charm mesons produces a peak in the recoil momentum spectrum of $K^\pm$ in inclusive decays of $B^\pm$ that has been observed. The scaling dimensions of the unparticles associated with three neutral charm mesons are calculated. They can be determined experimentally by measuring the invariant mass distributions for $XD^0$ or $X D^{*0}$ in inclusive prompt production at the Large Hadron Collider.

hep-ph↗
arXiv2021

New insights into the nucleon's electromagnetic structure

We present a combined analysis of the electromagnetic form factors of the nucleon in the space- and timelike regions using dispersion theory. Our framework provides a consistent description of the experimental data over the full range of momentum transfer, in line with the strictures from analyticity and unitarity. The statistical uncertainties of the extracted form factors are estimated using the bootstrap method, while systematic errors are determined from variations of the spectral functions. We also perform a high-precision extraction of the nucleon radii and find good agreement with previous analyses of spacelike data alone. For the proton charge radius, we find $r_E^p = 0.840^{+0.003}_{-0.002}{}^{+0.002}_{-0.002}$~fm, where the first error is statistical and the second one is systematic. The Zemach radius and third moment are in agreement with Lamb shift measurements and hyperfine splittings. The combined data set of space- and timelike data disfavors a zero crossing of $μ_p G_E^p/G_M^p$ in the spacelike region. Finally, we discuss the status and perspectives of modulus and phase of the form factors in the timelike region in the context of future experiments as well as the onset of perturbative QCD.

hep-ph↗
arXiv2021

$\mathbfβ$-delayed proton emission from $\mathbf{^{11}}$Be in effective field theory

We calculate the rate of the rare decay $^{11}\text{Be}$ into $^{10}\text{Be} + p +e^- + \barν_e$ using Halo effective field theory, thereby describing the process of beta-delayed proton emission. We assume a shallow $1/2^+$ resonance in the $^{10}\text{Be}-p$ system with an energy consistent with a recent experiment by Ayyad et al. and obtain $b_p = 4.9_{-2.9}^{+5.6}\text{(exp.)}_{-0.8}^{+4.0}\text{(theo.)} \times 10^{-6}$ for the branching ratio of this decay, predicting a resonance width of $Γ_R = (9.0^{+4.8}_{-3.3}\text{(exp.)}^{+5.3}_{-2.2}\text{(theo.)})~\text{keV}$. Our calculation shows that the experimental branching ratio and resonance parameters of Ayyad et al. are consistent with each other. Moreover, we analyze the general impact of a resonance on the branching ratio and demonstrate that a wide range of combinations of resonance energies and widths can reproduce branching ratios of the correct order. Thus, no exotic mechanism (such as beyond the standard model physics) is needed to explain the experimental decay rate.

nucl-th↗
arXiv2021

Morphology of three-body quantum states from machine learning

The relative motion of three impenetrable particles on a ring, in our case two identical fermions and one impurity, is isomorphic to a triangular quantum billiard. Depending on the ratio $κ$ of the impurity and fermion masses, the billiards can be integrable or non-integrable (also referred to in the main text as chaotic). To set the stage, we first investigate the energy level distributions of the billiards as a function of $1/κ\in [0,1]$ and find no evidence of integrable cases beyond the limiting values $1/κ=1$ and $1/κ=0$. Then, we use machine learning tools to analyze properties of probability distributions of individual quantum states. We find that convolutional neural networks can correctly classify integrable and non-integrable states.The decisive features of the wave functions are the normalization and a large number of zero elements, corresponding to the existence of a nodal line. The network achieves typical accuracies of 97%, suggesting that machine learning tools can be used to analyze and classify the morphology of probability densities obtained in theory or experiment.

quant-ph↗
arXiv2021

Neutron-neutron scattering length from the $^6$He$(p,pα)nn$ reaction

We propose a novel method to measure the neutron-neutron scattering length using the $^{6}$He$(p,pα)nn$ reaction in inverse kinematics at high energies. The method is based on the final state interaction (FSI) between the neutrons after the sudden knockout of the $α$ particle. We show that the details of the neutron-neutron relative energy distribution allow for a precise extraction of the $s$-wave scattering length. We present the state-of-the-art in regard to the theory of this distribution. The distribution is calculated in two steps. First, we calculate the ground-state wave function of $^6$He as a $αn n$ three-body system. For this purpose we use Halo effective field theory (Halo EFT), which also provides uncertainty estimates for the results. We compare our results at this stage to model calculations done with the computer code FaCE. In a second step we determine the effects of the $nn$ FSI using the $nn$ t-matrix. We compare these FSI results to approximate FSI approaches based on standard FSI enhancement factors. While the final distribution is sensitive to the $nn$ scattering length, it depends only weakly on the effective range. Throughout we emphasize the impact of theoretical uncertainties on the neutron-neutron relative energy distribution, and discuss the extent to which those uncertainties limit the extraction of the neutron-neutron scattering length from the reaction $^{6}$He$(p,pα)nn$.

nucl-th↗
arXiv2021

Dispersion-theoretical analysis of the electromagnetic form factors of the nucleon: Past, present and future

We review the dispersion-theoretical analysis of the electromagnetic form factors of the nucleon. We emphasize in particular the role of unitarity and analyticity in the construction of the isoscalar and isovector spectral functions. We present new results on the extraction of the nucleon radii, the electric and magnetic form factors and the extraction of $ω$-meson couplings. All this is supplemented by a detailed calculation of the theoretical uncertainties, using bootstrap and Bayesian methods to pin down the statistical errors, while systematic errors are determined from variations of the spectral functions. We also discuss the physics of the time-like form factors and point out further issues to be addressed in this framework.

hep-ph↗
arXiv2021

High-precision determination of the electric and magnetic radius of the proton

Using dispersion theory with an improved description of the two-pion continuum based on the precise Roy-Steiner analysis of pion-nucleon scattering, we analyze recent data from electron-proton scattering. This allows for a high-precision determination of the electric and magnetic radius of the proton, $r_E = (0.838^{+0.005}_{-0.004}{}^{+0.004}_{-0.003})\,$fm and $r_M = (0.847\pm{0.004}\pm{0.004})\,$fm, where the first error refers to the fitting procedure using bootstrap and the data while the second one refers to the systematic uncertainty related to the underlying spectral functions.

hep-ph↗
arXiv2021

Unnuclear physics

We investigate a nonrelativistic version of Georgi's "unparticle physics." We define the unnucleus as a field in a nonrelativistic conformal field theory. Such a field is characterized by a mass and a conformal dimension. We then consider the formal problem of scatterings to a final state consisting of a particle and an unnucleus and show that the differential cross section, as a function of the recoil energy received by the particle, has a power-law singularity near the maximal recoil energy, where the power is determined by the conformal dimension of the unnucleus. We argue that unlike the relativistic unparticle, which remains a hypothetical object, the unnucleus is realized, to a good approximation, in nuclear reactions involving emission of a few neutrons, when the energy of the final-state neutrons in their center-of-mass frame lies in the range between about 0.1 MeV and 5 MeV. Combining this observation with the known universal properties of fermions at unitarity in a harmonic trap, we predict a power-law behavior of an inclusive cross section in this kinematic regime. We compare our predictions with previous effective field theory and model calculations of the $^6$He$(p,pα)2n$, $^3$H$(π^-,γ)3n$, and $^3$H$(μ^-,ν_μ)3n$ reactions and find excellent agreement.

nucl-th↗
arXiv2019

Three-body losses of a polarized Fermi gas near a p-wave Feshbach resonance in effective field theory

We study three-body recombination of fully spin-polarized ${}^6$Li atoms that are interacting resonantly in relative p-waves. Motivated by a recent experiment, we focus on negative scattering volumes where three atoms recombine into a deep dimer and another atom. We calculate the three-body recombination rate using a Faddeev equation derived from effective field theory. In particular, we study the magnetic field and temperature dependences of the loss rate and use the recombination data to determine the effective range of the p-wave atom-atom interaction. We also predict the existence of a shallow three-body bound state that manifests itself as a prominent feature in the energy-dependent three-body recombination rate.

cond-mat.quant-gas↗
arXiv2018

Halo structure of $^{17}$C

$^{17}$C has three states below the $^{16}$C + $n$ threshold with quantum numbers $J^P=3/2^+,1/2^+,5/2^+$. These states have relatively small neutron separation energies compared to the neutron separation and excitation energies of $^{16}$C. This separation of scales motivates our investigation of $^{17}$C in a Halo effective field theory (Halo EFT) with a $^{16}$C core and a valence neutron as degrees of freedom. We discuss various properties of the three states such as electric radii, magnetic moments, electromagnetic transition rates and capture cross sections. In particular, we give predictions for the charge radius and the magnetic moment of the $1/2^+$ state and for neutron capture on $^{16}$C into this state. Furthermore, we discuss the predictive power of the Halo EFT approach for the $3/2^+$ and $5/2^+$ states which are described by a neutron in a $D$-wave relative to the core.

nucl-th↗
arXiv2016

Open Effective Field Theories from Highly Inelastic Reactions

The loss of particles due to highly inelastic reactions has previously been taken into account in effective field theories for low-energy particles by adding local anti-Hermitian terms to the effective Hamiltonian. An additional modification is required in the time evolution equation for the density matrix of a multi-particle system. An effective density matrix can be defined by tracing over states containing high-momentum particles produced by the highly inelastic reactions and by a time average that eliminates short-time correlations. The effective density matrix satisfies the Lindblad equation, with local Lindblad operators that are determined by the anti-Hermitian terms in the effective Hamiltonian.

hep-ph↗
arXiv2016

Trimer and Tetramer Bound States in Heteronuclear Systems

The Efimov effect in heteronuclear cold atomic systems is experimentally more easily accessible than the Efimov effect for identical atoms, because of the potentially smaller scaling factor. We focus on the case of two or three heavy identical bosons and another atom. The former case was recently observed in a mixture of 133Cs and 6Li atoms. We employ the Gaussian Expansion Method as developed by Hiyama, Kino et al.. This is a variational method that uses Gaussians that are distributed geometrically over a chosen range. Supplemental calculations are performed using the Skorniakov-Ter-Martirosian equation. Blume et al. previously investigated the scaling properties of heteronuclear systems in the unitary limit and at the three-body breakup threshold. We have completed this picture by calculating the behaviour on the positive scattering length side of the Efimov plot, focussing on the dimer threshold.

cond-mat.quant-gas↗
arXiv2016

Electric Properties of One-Neutron Halo Nuclei in Halo EFT

We exploit the separation of scales in weakly-bound nuclei to compute E2 transitions and electric form factors in a Halo EFT framework. 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 halo, respectively. We include the strong $s$-wave and $d$-wave interactions by introducing dimer fields. The dimer propagators are regulated by employing the power divergence subtraction scheme and matched to the effective range expansion in the respective channel.Electromagnetic interactions are included via minimal substitution in the Lagrangian. We demonstrate that, depending on the observable and respective partial wave, additional local gauge-invariant operators contribute in LO, NLO and higher orders.

nucl-th↗
arXiv2011

Efimov physics from a renormalization group perspective

We discuss the physics of the Efimov effect from a renormalization group viewpoint using the concept of limit cycles. Furthermore, we discuss recent experiments providing evidence for the Efimov effect in ultracold gases and its relevance for nuclear systems.

nucl-th↗
arXiv2008

Modern Theory of Nuclear Forces

Effective field theory allows for a systematic and model-independent derivation of the forces between nucleons in harmony with the symmetries of Quantum Chromodynamics. We review the foundations of this approach and discuss its application for light nuclei at various resolution scales. The extension of this approach to many-body systems is briefly sketched.

nucl-th↗