arXiv subjects

Ulf-G. Meißner

Publications and source records attributed to Ulf-G. Meißner.

At least 181 records · Page 10Linked to original sources

arXiv2021

Remarks on non-perturbative three--body dynamics and its application to the $KK\bar K$ system

A formalism is discussed that allows for a straightforward treatment of the relativistic three-body problem while keeping the correct analytic structure. In particular it is demonstrated that sacrificing covariance for analyticity can be justified by the hierarchy of different contributions in the spirit of an effective field theory. For definiteness the formalism is applied to the $KK\bar K$ system allowing for the emergence of the $a_0(980)$ and the $f_0(980)$ as hadronic molecules. For simplicity all inelastic channels are switched off.

hep-ph↗

arXiv2021

Hidden spin-isospin exchange symmetry

The strong interactions among nucleons have an approximate spin-isospin exchange symmetry that arises from the properties of quantum chromodynamics in the limit of many colors, $N_c$. However this large-$N_c$ symmetry is well hidden and reveals itself only when averaging over intrinsic spin orientations. Furthermore, the symmetry is obscured unless the momentum resolution scale is close to an optimal scale that we call $Λ_{{\rm large-}N_c}$. We show that the large-$N_c$ derivation requires a momentum resolution scale of $Λ_{{\rm large-}N_c} \sim 500$ MeV. We derive a set of spin-isospin exchange sum rules and discuss implications for the spectrum of $^{30}$P and applications to nuclear forces, nuclear structure calculations, and three-nucleon interactions.

nucl-th↗

arXiv2021

Constraints on the $Λ$-neutron interaction from charge symmetry breaking in the $\mathbf{^4_Λ\rm \bf He}$--$\mathbf{^4_Λ\rm \bf H}$ hypernuclei

We utilize the experimentally known difference of the $Λ$ separation energies of the mirror hypernuclei ${^4_Λ\rm He}$ and ${^4_Λ\rm H}$ to constrain the $Λ$-neutron interaction. We include the leading charge-symmetry breaking (CSB) interaction into our hyperon-nucleon interaction derived within chiral effective field theory at next-to-leading order. In particular, we determine the strength of the two arising CSB contact terms by a fit to the differences of the separation energies of these hypernuclei in the $0^+$ and $1^+$ states, respectively. By construction, the resulting interaction describes all low energy hyperon-nucleon scattering data, the hypertriton and the CSB in ${^4_Λ\rm He}$-${^4_Λ\rm H}$ accurately. This allows us to provide first predictions for the $Λ$n scattering lengths, based solely on available hypernuclear data.

nucl-th↗

arXiv2021

The axion-baryon coupling in SU(3) heavy baryon chiral perturbation theory

In the past, the axion-nucleon coupling has been calculated in the framework of SU(2) heavy baryon chiral perturbation theory up to third order in the chiral power counting. Here, we extend these earlier studies to the case of heavy baryon chiral perturbation theory with SU(3) flavor symmetry and derive the axion coupling to the full SU(3) baryon octet, showing that the axion also significantly couples to hyperons. As studies on dense nuclear matter suggest the possible existence of hyperons in stellar objects such as neutron stars, our results should have phenomenological implications related to the so-called axion window.

hep-ph↗

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

Wigner SU(4) symmetry, clustering, and the spectrum of $^{12}$C

We present lattice calculations of the low-lying spectrum of $^{12}$C using a simple nucleon-nucleon interaction that is independent of spin and isospin and therefore invariant under Wigner's SU(4) symmetry. We find strong signals for all excited states up to $\sim 15$~MeV above the ground state, and explore the structure of each state using a large variety of $α$ cluster and harmonic oscillator trial states, projected onto given irreducible representations of the cubic group. We are able to verify earlier findings for the $α$ clustering in the Hoyle state and the second $2^+$ state of $^{12}$C. The success of these calculations to describe the full low-lying energy spectrum using spin-independent interactions suggest that either the spin-orbit interactions are somewhat weak in the $^{12}$C system, or the effects of $α$ clustering are diminishing their influence. This is in agreement with previous findings from {\it ab initio} shell model calculations.

nucl-th↗

arXiv2021

A Neural Network Perturbation Theory Based on the Born Series

Deep Learning using the eponymous deep neural networks (DNNs) has become an attractive approach towards various data-based problems of theoretical physics in the past decade. There has been a clear trend to deeper architectures containing increasingly more powerful and involved layers. Contrarily, Taylor coefficients of DNNs still appear mainly in the light of interpretability studies, where they are computed at most to first order. However, especially in theoretical physics numerous problems benefit from accessing higher orders, as well. This gap motivates a general formulation of neural network (NN) Taylor expansions. Restricting our analysis to multilayer perceptrons (MLPs) and introducing quantities we refer to as propagators and vertices, both depending on the MLP's weights and biases, we establish a graph-theoretical approach. Similarly to Feynman rules in quantum field theories, we can systematically assign diagrams containing propagators and vertices to the corresponding partial derivative. Examining this approach for S-wave scattering lengths of shallow potentials, we observe NNs to adapt their derivatives mainly to the leading order of the target function's Taylor expansion. To circumvent this problem, we propose an iterative NN perturbation theory. During each iteration we eliminate the leading order, such that the next-to-leading order can be faithfully learned during the subsequent iteration. After performing two iterations, we find that the first- and second-order Born terms are correctly adapted during the respective iterations. Finally, we combine both results to find a proxy that acts as a machine-learned second-order Born approximation.

cs.LG↗

arXiv2021

Where is the lightest charmed scalar meson?

The lightest charmed scalar meson is known as the $D_0^*(2300)$, which is one of the earliest new hadron resonances observed at modern $B$ factories. We show here that the parameters assigned to the lightest scalar $D$-meson are in conflict with the precise LHCb data of the decay $B^-\to D^+ π^- π^-$. On the contrary, these data can be well described by an unitarized chiral amplitude containing a much lighter charmed scalar meson, the $D_0^*(2100)$. We also extract the low-energy $S$-wave $Dπ$ phase of the decay $B^-\to D^+ π^- π^-$ from the data in a model-independent way, and show that its difference from the $Dπ$ scattering phase shift can be traced back to an intermediate $ρ^-$ exchange. Our work highlights that an analysis of data consistent with chiral symmetry, unitarity, and analyticity is mandatory in order to extract the properties of the ground-state scalar mesons in the singly heavy sector correctly, in analogy to the light scalar mesons $f_0(500)$ and $K_0^*(700)$.

hep-ph↗

arXiv2021

Jülich-Bonn-Washington Model for Pion Electroproduction Multipoles

Pion electroproduction off the proton is analyzed in a new framework based on a general parametrization of transition amplitudes, including constraints from gauge invariance and threshold behavior. Data with energies $1.13~{\rm GeV}<W<1.6~{\rm GeV}$ and $Q^2$ below $6~{\rm GeV}^2$ are included. The model is an extension of the latest Jülich-Bonn solution incorporating constraints from pion-induced and photoproduction data. Performing large scale fits ($\sim10^5$ data) we find a set of solutions with $χ^2_{\rm dof}=1.69-1.81$ which allows us to assess the systematic uncertainty of the approach.

nucl-th↗

arXiv2021

Two-Meson Form Factors in Unitarized Chiral Perturbation Theory

We present a comprehensive analysis of form factors for two light pseudoscalar mesons induced by scalar, vector, and tensor quark operators. The theoretical framework is based on a combination of unitarized chiral perturbation theory and dispersion relations. The low-energy constants in chiral perturbation theory are fixed by a global fit to the available data of the two-meson scattering phase shifts. Each form factor derived from unitarized chiral perturbation theory is improved by iteratively applying a dispersion relation. This study updates the existing results in the literature and explores those that have not been systematically studied previously, in particular the two-meson tensor form factors within unitarized chiral perturbation theory. We also discuss the applications of these form factors as mandatory inputs for low-energy phenomena, such as the semi-leptonic decays $B_s\to π^+π^-\ell^+\ell^-$ and the $τ$ lepton decay $τ\rightarrowπ^{-}π^{0}ν_τ$, in searches for physics beyond the Standard Model.

hep-ph↗

arXiv2021

Chiral dynamics and S-wave contributions in $\bar B^0/D^0 \to π^{\pm}η l^{\mp} ν$ decays

In this work, we analyze the semi-leptonic decays $\bar B^0/D^0 \to (a_0(980)^{\pm}\toπ^{\pm}η) l^{\mp} ν$ within light-cone sum rules. The two and three-body light-cone distribution amplitudes (LCDAs) of the $B$ meson and the only available two-body LCDA of the $D$ meson are used. To include the finite-width effect of the $a_0(980)$, we use a scalar form factor to describe the final-state interaction between the $πη$ mesons, which was previously calculated within unitarized Chiral Perturbation Theory. The result for the decay branching fraction of the $D^0$ decay is in good agreement with that measured by the BESIII Collaboration, while the branching fraction of the $\bar B^0$ decay can be tested in future experiments.

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

$g$-factor and static quadrupole moment of $^{135}$Pr, $^{105}$Pd, and $^{187}$Au in wobbling motion

The $g$-factor and static quadrupole moment of the nuclides $^{135}$Pr, $^{105}$Pd, and $^{187}$Au in the wobbling motion are investigated in the particle-rotor model as functions of the total spin $I$. The $g$-factor of $^{105}\mathrm{Pd}$ increases with increasing $I$, due to the negative gyromagnetic ratio of a neutron valence-neutron. This behavior is in contrast to the decreasing $g$-factor of the other two nuclides, $^{135}$Pr and $^{187}$Au, which feature a valence-proton. The static quadrupole moment $Q$ depends on all three expectation values of the total angular momentum. It is smaller in the yrast band than in the wobbling band for the transverse wobblers $^{135}$Pr and $^{105}$Pd, while larger for the longitudinal wobbler $^{187}$Au.

nucl-th↗

arXiv2021

The $Λ(1405)$ in resummed chiral effective field theory

We study the unitarized meson-baryon scattering amplitude at leading order in the strangeness $S=-1$ sector using time-ordered perturbation theory for a manifestly Lorentz-invariant formulation of chiral effective field theory. By solving the coupled-channel integral equations with the full off-shell dependence of the effective potential and applying subtractive renormalization, we analyze the renormalized scattering amplitudes and obtain the two-pole structure of the $Λ(1405)$ resonance. We also point out the necessity of including higher-order terms.

hep-ph↗

arXiv2021

Implications of an increased $Λ$-separation energy of the hypertriton

Stimulated by recent indications that the binding energy of the hypertriton could be significantly larger than so far assumed, requirements of a more strongly bound $^3_Λ{\rm H}$ state for the hyperon-nucleon interaction and consequences for the binding energies of $A=4,5$ and $7$ hypernuclei are investigated. As basis a $YN$ potential derived at next-to-leading order in chiral effective field theory is employed, Faddeev and Yakubovsky equations are solved to obtain the corresponding $3$- and $4$-body binding energies, respectively, and the Jacobi no-core shell model is used for $^5_Λ$He and $^7_Λ$Li. It is found that the spin-singlet $Λp$ interaction would have to be much more attractive which can be, however, accommodated within the bounds set by the available $Λp$ scattering data. The binding energies of the $^4_Λ{\rm He}$ hypernucleus are predicted to be closer to the empirical values than for $YN$ interactions that produce a more weakly bound $^3_Λ{\rm H}$. The quality of the description of the separation energy and excitation spectrum for $^7_Λ$Li remains essentially unchanged.

nucl-th↗

arXiv2020

Light nuclei with semilocal momentum-space regularized chiral interactions up to third order

We present a systematic investigation of few-nucleon systems and light nuclei using the current LENPIC interactions comprising semilocal momentum-space regularized two- and three-nucleon forces up to third chiral order (N$^2$LO). Following our earlier study utilizing the coordinate-space regularized interactions, the two low-energy constants entering the three-body force are determined from the triton binding energy and the differential cross section minimum in elastic nucleon-deuteron scattering. Predictions are made for selected observables in elastic nucleon-deuteron scattering and in the deuteron breakup reactions, for properties of the $A=3$ and $A=4$ nuclei, and for spectra of $p$-shell nuclei up to $A = 16$. A comprehensive error analysis is performed including an estimation of correlated truncation uncertainties for nuclear spectra. The obtained predictions are generally found to agree with experimental data within errors. Similar to the coordinate-space regularized chiral interactions at the same order, a systematic overbinding of heavier nuclei is observed, which sets in for $A \sim 10$ and increases with $A$.

nucl-th↗

arXiv2020

Jacobi no-core shell model for $p$-shell hypernuclei

We extend the recently developed Jacobi no-core shell model to hypernuclei. Based on the coefficients of fractional parentage for ordinary nuclei, we define a basis where the hyperon is the spectator particle. We then formulate transition coefficients to states that single out a hyperon-nucleon pair which allow us to implement a hypernuclear many-baryon Hamiltonian for $p$-shell hypernuclei. As a first application, we use the basis states and the transition coefficients to calculate the ground states of $^{4}_Λ$He, $^{4}_Λ$H, $^{5}_Λ$He, $^{6}_Λ$He, $^{6}_Λ$Li, and $^{7}_Λ$Li and, additionally, the first excited states of $^{4}_Λ$He, $^{4}_Λ$H, and $^{7}_Λ$Li. In order to obtain converged results, we employ the similarity renormalization group (SRG) to soften the nucleon-nucleon and hyperon-nucleon interactions. Although the dependence on this evolution of the Hamiltonian is significant, we show that a strong correlation of the results can be used to identify preferred SRG parameters. This allows for meaningful predictions of hypernuclear binding and excitation energies. The transition coefficients will be made publicly available as HDF5 data files.

nucl-th↗

arXiv2020

Strong CP violation in spin-1/2 singly charmed baryons

We report on the calculation of the CP-violating form factor $F_3$ and the corresponding electric dipole moment for charmed baryons in the spin-1/2 sector generated by the QCD $θ$-term. We work in the framework of covariant baryon chiral perturbation theory within the extended-on-mass-shell renormalization scheme up to next-to-leading order in the chiral expansion.

hep-ph↗