arXiv subjects

Stefan Leupold

Publications and source records attributed to Stefan Leupold.

At least 19 recordsLinked to original sources

arXiv2026

Dispersive Analysis of $D$- and $B$-Meson Form Factors with Chiral and Heavy-Quark Constraints

We analyze the isovector vector form factors of $D$, $D^*$, $B$, and $B^*$ mesons at low energies. We employ all constraints due to chiral and heavy-quark symmetry, and include the physics of resonant pion-pion rescattering in a model-independent way, using dispersion theory. Special attention is paid to the analytic properties of these form factors, which include anomalous thresholds due to triangle diagrams that are located on the physical Riemann sheets in some of the form factors. We extract the couplings of the $ρ(770)$ resonance to all these heavy mesons by determining the appropriate pole residues.

hep-ph↗

arXiv2026

Hyperon non-leptonic decays in relativistic Chiral Perturbation Theory with resonances

Motivated by recent experimental advances in the corresponding measurements, non-leptonic hyperon decays are calculated, for the first time in a relativistic manner, in Chiral Perturbation Theory at next-to-leading order (NLO). On the one hand, relativistic loop corrections are computed explicitly based on the ground-state octet and decuplet fields. On the other hand, the NLO weak-transition low-energy constants are estimated by resonance saturation, inspired by the non-relativistic tree-level computation of Ref. [1]. In particular, the $1/2^-$ and the (excited) $1/2^+$ resonance octets are utilized. The remaining unknown parameters are fitted to the decay amplitudes. A good combined fit to both $s$- and $p$-wave amplitudes is achieved with the caveat of not being very tightly constrained. The role of the resonances is found to be crucial. Consequences for further investigations and open questions are addressed.

hep-ph↗

arXiv2025

Kinetic Mixing and Axial Charges in the Parity-Doublet Model

The standard parity doublet model with its mass-mixing mechanism fails to describe the axial charge $g_A$ of the nucleon. While $g_A = 1$ in the original Gell-Mann--Levy model, which reproduces the Adler-Bell-Jackiw anomaly of QCD, in the presence of a chirally invariant baryon mass the mass mixing leads to $g_A < 1 $ whereas phenomenologically it is about 1.28. We propose to remedy this problem by introducing kinetic-mixing terms corresponding to meson-baryon derivative couplings, similar in spirit to the two-mixing-angle scenario of the $η$-$η'$ mixing. This extended parity doublet model contains five parameters in the effective baryonic Lagrangian. Three of them can be determined by using the empirical results for the axial charge of the nucleon together with the masses of the nucleon and its parity partner, the $N^*(1535)$ resonance. We discuss various options how to determine the remaining parameters, touching upon the mass of both parity partners if the chiral condensate is put to zero; the mass of the nucleon in the chiral limit; and the values of meson-baryon coupling constants related to the decays of the resonance to pion-nucleon and sigma-nucleon.

hep-ph↗

arXiv2024

Electromagnetic isovector form factors of the transition from the $N^*(1520)$ to the nucleon

Dispersion theory is used to provide a model-independent low-energy representation of the three electromagnetic isovector transition form factors $N^{*}(1520)\to N$. At low energies the virtual photon couples dominantly to a pion pair. Taking the very well understood pion vector form factor and pion re-scattering into consideration, the determination of the transition form factors is traced back to the determination of pion-baryon scattering amplitudes. Their low-energy aspects are parametrized by baryon exchange, accounting for the main decay channels of the $N^*(1520)$. Short-distance physics is encoded in subtraction constants that are fitted to data on space-like form factors and hadronic decays. It is shown that a limitation in the determination of the subtraction constants lies in the fact that isovector form factors require sufficient information about the differences between protons and neutrons. In particular, this calls for improvements in the form factor extraction from the electroproduction of the $N^*(1520)$ on the neutron. Via the dispersion relations, space- and time-like regions are naturally connected from first principles. This allows to predict the time-like form factors that enter the Dalitz decays $N^*(1520)\to N e^- e^+$ and $N^*(1520)\to N μ^- μ^+$. Under the assumption of the dominance of the isovector over the isoscalar channel, the Dalitz decay distributions are predicted.

nucl-th↗

arXiv2024

Electromagnetic form factors of the transition from the Delta to the nucleon

The low-energy electromagnetic form factors of the $Δ$(1232)-to-nucleon transition are derived combining dispersion theory techniques and chiral perturbation theory. The form factors are expressed in terms of the well-understood pion vector form factor and pion-baryon scattering amplitudes. Nucleon and Delta exchange terms and contact terms constitute the input for these pion-baryon amplitudes. The framework is formulated for all form factors. When comparing to experimental data in the spacelike region of $e^- N \to e^- Δ$ scattering, the focus lies on the numerically dominant magnetic dipole transition form factor. Fitting two subtraction constants (one for the scattering amplitude, one for the form factor) yields a very good description of this dominant form factor up to photon virtualities of about 0.6 GeV. After determining the subtraction constants in the spacelike region and at the photon point, respectively, predictions for the timelike region of Dalitz decays $Δ\to N \, e^+ e^-$ are presented.

hep-ph↗

arXiv2023

Light quark mass dependence of nucleon electromagnetic form factors in dispersively modified chiral perturbation theory

The nucleon isovector electromagnetic form factors are calculated up to next-to-next-to-leading order by combining relativistic chiral perturbation theory (ChPT) of pion, nucleon, and $Δ$(1232) with dispersion theory. We specifically address the light-quark mass dependence of the form factors, achieving a good description of recent Lattice QCD results over a range of $Q^2 < 0.6$ GeV$^2$ and $M_π < 350$ MeV. For the Dirac form factor, the combination of ChPT and dispersion theory outperforms the pure dispersive and pure ChPT descriptions. For the Pauli form factor, the combined calculation leads to results comparable to the purely dispersive ones. The anomalous magnetic moment and the Dirac and Pauli radii are extracted.

hep-ph↗

arXiv2023

Goldberger-Treiman relation and Wu-type experiment in the decuplet sector

The leading-order chiral Lagrangian for the baryon octet and decuplet states coupled to Goldstone bosons and external sources contains six low-energy constants. Five of them are fairly well known from phenomenology, but the sixth one is practically unknown. This coupling constant provides the strength of the (p-wave) coupling of Goldstone bosons to decuplet states. Its size and even sign are under debate. Quark model and QCD for a large number of colors provide predictions, but some recent phenomenological analyses suggest even an opposite sign for the Delta-pion coupling. The Goldberger-Treiman relation connects this coupling constant to the axial charge of the Delta baryon. This suggests a Wu-type experiment to determine the unknown low-energy constant. While this is not feasible in the Delta sector because of the large hadronic width of the Delta, there is a flavor symmetry related process that is accessible: the weak semileptonic decay of the Omega baryon to a spin 3/2 cascade baryon. A broad research program is suggested that can pin down at least the rough size and the sign of the last unknown low-energy constant of the leading-order Lagrangian. It encompasses experimental measurements, in particular the forward-backward asymmetry of the semileptonic decay, together with a determination of the quark-mass dependences using lattice QCD for the narrow decuplet states and chiral perturbation theory to extrapolate to the Delta sector. Besides discussing the strategy of the research program, the present work provides a feasibility check based on a simple leading-order calculation.

hep-ph↗

arXiv2022

Estimates for rare three-body decays of the Omega baryon using chiral symmetry and the $ΔI = 1/2$ rule

We study rare three-body decays of the Omega baryon using SU(3) chiral perturbation theory, the successful effective field theory of quantum chromodynamics at low energies. At leading order, we calculate the branching fractions of the decay $Ω^- \to Ξππ$ for all possible combinations of pions. For one channel we find an order-of-magnitude discrepancy between theory and experiment. This tension is known to exist in the non-relativistic limit, and we confirm that it remains in the relativistic calculation. Fairly independent of the values of the low-energy constants we establish lower limits for the branching fractions of these three-body Omega decays, which reaffirm the gap between theory and experiment. We point out that this discrepancy is closely tied to the $ΔI =1/2$ selection rule. In turn, this means that the three-body decays constitute an interesting tool to scrutinize the selection rule. Using next-to-leading order calculations we also provide predictions for the decay $Ω^- \to Ξ^0 μ^- \barν_μ$. We show that fully-differential distributions will provide access to low-energy constants needed in the axial-vector transitions from a decuplet to octet baryon. Since data for all of these rare three-body Omega decays are scarce (fully differential data are nonexistent), we recommend that they be remeasured at running and upcoming experiments, such as BESIII, LHCb, Belle-II, and PANDA.

hep-ph↗

arXiv2022

Study of CP violation in hyperon decays at Super Charm-Tau Factories with a polarized electron beam

Non-leptonic two-body weak decays of baryons are an important tool to probe the combined charge-conjugation--parity symmetry (CP) violation. We explain why the decays of strange baryons provide complementary information to the decays of kaons. A model-independent parameterization of the non-leptonic decays of the $Λ$- and $Ξ$-baryons is reviewed, and the amplitudes are updated according to the latest experimental input. We demonstrate the potential of performing precision tests in strange baryon decays at the next generation electron-positron $J/ψ$ factories with luminosity of $10^{35}$ cm$^{-2}$s$^{-1}$. The copious production of spin-entangled hyperon-antihyperon pairs via the $J/ψ$ resonance allows for a direct comparison of the baryon and antibaryon decay properties. Using analytic approximations and numerical calculations, we study the quantitative impact of spin correlations and polarization in such CP tests. We show that by using a longitudinally-polarized electron beam, the statistical precision of the CP tests can be significantly improved compared to the experiments without polarized beams. Furthermore, we map out further directions for possible improvements, like analysis of incompletely reconstructed events or a combination of the isospin related processes. Altogether, these methods are promising for the observation of a statistically significant CP-violation signal with a strength corresponding to the standard model predictions. Our conclusions should encourage more detailed feasibility studies, including optimisation of the measurement methods and studies of systematic effects. Finally, our results call for an update of the theory predictions with increased precision.

hep-ph↗

arXiv2022

Sum rule for the partial decay rates of bottom hadrons based on the dynamical supersymmetry of the $\bar s$ quark and the $ud$ diquark

We investigate the weak decays of $\bar B_{s}^{0}$ and $Λ_{b}$ to charm hadrons based on the dynamical supersymmetry between the $\bar s$ quark and the $ud$ diquark. We derive a new sum rule relating the decay rates of the processes $\bar B_{s}^{0} \to D_{s}^{+} P^{-}$, $\bar B_{s}^{0} \to D_{s}^{*+} P^{-}$ and $Λ_{b} \to Λ_{c} P^{-}$, where $P^{-}$ is a negatively charged meson, such as $π^{-}$ and $K^{-}$. It is found that the observed decay rates satisfy the sum rule very well. This implies that the supersymmetry between the $\bar s$ quark and the $ud$ diquark is also seen in the wavefunctions of the heavy hadrons and suggests that the $ud$ diquark can be regarded as a valid effective constituent for heavy hadrons.

hep-ph↗

arXiv2021

Spacelike zero crossings and timelike phases in the electromagnetic form factors of vector mesons

Some form factors of ground-state hadrons with spin might show a zero crossing at spacelike momenta of electron-hadron scattering. In the timelike region of hadron-antihadron production by electron-positron collisions the form factors become complex. When the hadrons decay, the relative phases between form factors can be measured by the angular distributions of their decay products. Using analyticity and the QCD high-energy limits for constraint-free form factors and for helicity amplitudes, we show how a single zero crossing in the spacelike region is related to the high-energy limit of the phase in the timelike region. Theoretical predictions for such zero crossings can therefore be tested by experimental measurements, e.g. by Belle II, in the high-energy timelike region. In the present work, this line of reasoning is applied to vector mesons.

hep-ph↗

arXiv2021

Electromagnetic transition form factors and Dalitz decays of hyperons

Dalitz decays of a hyperon resonance to a ground-state hyperon and an electron-positron pair can give access to some information about the composite structure of hyperons. We present expressions for the multi-differential decay rates in terms of general transition form factors for spin-parity combinations J^P = 1/2^+/-, 3/2^+/- of the hyperon resonance. Even if the spin of the initial hyperon resonance is not measured, the self-analyzing weak decay of the "final" ground-state hyperon contains information about the relative phase between combinations of transition form factors. This relative phase is non-vanishing because of the unstable nature of the hyperon resonance. If all form factor combinations in the differential decay formulae are replaced by their respective values at the photon point, one obtains a QED type approximation, which might be interpreted as characterizing hypothetical hyperons with point-like structure. We compare the QED type approximation to a more realistic form factor scenario for the lowest-lying singly-strange hyperon resonances. In this way we explore which accuracy in the measurements of the differential Dalitz decay rates is required in order to distinguish the composite-structure case from the pointlike case. Based on the QED type approximation we obtain as a by-product a rough prediction for the ratio between the Dalitz decay width and the corresponding photon decay width.

hep-ph↗

arXiv2020

Radiative corrections for the decay $Σ^0\toΛe^+e^-$

Electromagnetic form factors serve to explore the intrinsic structure of nucleons and their strangeness partners. With electron scattering at low energies the electromagnetic moments and radii of nucleons can be deduced. The corresponding experiments for hyperons are limited because of the unstable nature of the hyperons. Only for one process this turns to an advantage: the decay of the neutral Sigma hyperon to a Lambda hyperon and a real or virtual photon. Due to limited phase space the effects caused by the Sigma-to-Lambda transition form factors compete with the QED radiative corrections for the decay $Σ^0\toΛe^+e^-$. These QED corrections are addressed in the present work, evaluated beyond the soft-photon approximation, i.e., over the whole range of the Dalitz plot and with no restrictions on the energy of the radiative photon.

hep-ph↗

arXiv2019

The electromagnetic form factors of the transition from the spin-3/2 Sigma to the Lambda hyperon

The three electromagnetic form factors for the transition from a 3/2+ Sigma* hyperon to the ground-state Lambda hyperon are studied. At low energies, combinations of the transition form factors can be deduced from Dalitz decays of the Sigma* hyperon to Lambda plus an electron-positron pair. It is pointed out how more information can be obtained with the help of the self-analyzing weak decay of the Lambda. In particular it is shown that these transition form factors are complex quantities already in this kinematical region. Such measurements are feasible at hyperon factories as for instance the Facility for Antiproton and Ion Research (FAIR). At higher energies, the transition form factors can be measured in electron-positron collisions. The pertinent relations between the transition form factors and the decay distributions and differential cross sections are presented. Using dispersion theory, the low-energy electromagnetic form factors for the Sigma*-to-Lambda transition are related to the pion vector form factor. The additionally required input, i.e. the two-pion - Sigma* - Lambda amplitudes are determined from relativistic next-to-leading-order (NLO) baryon chiral perturbation theory including the baryons from the octet and the decuplet. A poorly known NLO parameter is fixed to the experimental value of the Sigma* to Lambda-gamma decay width. Pion rescattering is taken into account by dispersion theory solving a Muskhelishvili-Omnes equation. Subtracted and unsubtracted dispersion relations are discussed. However, in view of the fact that the transition form factors are complex quantities, the current data situation does not allow for a full determination of the subtraction constants. To reduce the number of free parameters, unsubtracted dispersion relations are used to make predictions for the transition form factors in the low-energy space- and timelike regions.

hep-ph↗

arXiv2019

Low-energy axial-vector transitions from decuplet to octet baryons

Axial-vector transitions of decuplet to octet baryons are parametrized at low energies guided by a complete and minimal chiral Lagrangian up to next-to-leading order. It is pointed out that beyond the well-known leading-order term, there is only one contribution at next-to-leading order. This contribution is flavor symmetric. Therefore the corresponding low-energy constant can be determined in any strangeness sector. As functions of this low-energy constant, we calculate the decay widths and Dalitz distributions for the decays of decuplet baryons to octet baryons, pions, and photons and for the weak decay of the Omega baryon to a cascade baryon, an electron, and an anti-neutrino.

hep-ph↗

arXiv2019

Towards solving the proton spin puzzle

The fact that the spins of the quarks in the proton, as measured in deep inelastic lepton scattering, only add up to about 30$\%$ of the spin of the proton is still not understood after 30 years. We show that our newly developed model for the quark and gluon momentum distributions in the proton, based on quantum fluctuations of the proton into baryon-meson pairs convoluted with Gaussian momentum distributions of partons in hadrons, can essentially reproduce the data on the proton spin structure function $g_1^P(x)$ and the associated spin asymmetry. A further improved description of the data is achieved by also including the relativistic correction of the Melosh transformation to the light-front formalism used in deep inelastic scattering. However, this does not fully resolve the spin puzzle, including also the neutron spin structure and the spin sum rules. These aspects can also be accounted for by our few-parameter model if the conventional SU(6) flavor-spin symmetry is broken, giving new information on the non-perturbative bound-state nucleon.

hep-ph↗

arXiv2019

Nucleon parton distributions from hadronic quantum fluctuations

A physical model is presented for the non-perturbative parton distributions in the nucleon. This is based on quantum fluctuations of the nucleon into baryon-meson pairs convoluted with Gaussian momentum distributions of partons in hadrons. The hadronic fluctuations, here developed in terms of hadronic chiral perturbation theory, occur with high probability and generate sea quarks as well as dynamical effects also for valence quarks and gluons. The resulting parton momentum distributions $f(x,Q_0^2)$ at low momentum transfers are evolved with conventional DGLAP equations from perturbative QCD to larger scales. This provides parton density functions $f(x,Q^2)$ for the gluon and all quark flavors with only five physics-motivated parameters. By tuning these parameters, experimental data on deep inelastic structure functions can be reproduced and interpreted. The contribution to sea quarks from hadronic fluctuations explains the observed asymmetry between $\bar{u}$ and $\bar{d}$ in the proton. The strange-quark sea is strongly suppressed at low $Q^2$, as observed.

hep-ph↗

arXiv2019

Polarization observables in $e^+e^-$ annihilation to a baryon-antibaryon pair

Using the helicity formalism of Jacob and Wick we derive spin density matrices of baryon antibaryon pairs produced in $e^+e^-$ annihilation. We consider the production of pairs with spins $1/2+\overline{1/2}$, $1/2+\overline{3/2}$ (+c.c.) and $3/2+\overline{3/2}$. We provide modular expressions to include chains of weak hadronic two-body decays of the produced hyperons. The expressions are suitable for the analysis of high statistics data from $J/ψ$ and $ψ(2S)$ decays at $e^+e^-$ colliders, by fits to the fully differential angular distributions of the measured particles. We illustrate the method by examples, such as the inclusive measurement of the $e^+e^-\toψ(2S)\toΩ^-\barΩ^+$ process where one decay chain $Ω^-\toΛK^-$ followed by $Λ\to pπ^-$ is considered. Finally we show that the inclusive angular distributions can be used to test spin assignment of the produced baryons.

hep-ph↗