arXiv subjects

Stefan Leupold

Publications and source records attributed to Stefan Leupold.

At least 37 records · Page 2Linked to original sources

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.

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arXiv2018

Dispersion relation for hadronic light-by-light scattering: pion pole

The pion-pole contribution to hadronic light-by-light scattering in the anomalous magnetic moment of the muon $(g-2)_μ$ is fully determined by the doubly-virtual pion transition form factor. Although this crucial input quantity is, in principle, directly accessible in experiment, a complete measurement covering all kinematic regions relevant for $(g-2)_μ$ is not realistic in the foreseeable future. Here, we report in detail on a reconstruction from available data, both space- and time-like, using a dispersive representation that accounts for all the low-lying singularities, reproduces the correct high- and low-energy limits, and proves convenient for the evaluation of the $(g-2)_μ$ loop integral. We concentrate on the systematics of the fit to $e^+e^-\to 3π$ data, which are key in constraining the isoscalar dependence, as well as the matching to the asymptotic limits. In particular, we provide a detailed account of the pion transition form factor at low energies in the time- and space-like region, including the error estimates underlying our final result for the pion-pole contribution, $a_μ^{π^0\text{-pole}}=62.6^{+3.0}_{-2.5}\times 10^{-11}$, and demonstrate how forthcoming singly-virtual measurements will further reduce its uncertainty.

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arXiv2018

Pion-pole contribution to hadronic light-by-light scattering in the anomalous magnetic moment of the muon

The $π^0$ pole constitutes the lowest-lying singularity of the hadronic light-by-light (HLbL) tensor, and thus provides the leading contribution in a dispersive approach to HLbL scattering in the anomalous magnetic moment of the muon $(g-2)_μ$. It is unambiguously defined in terms of the doubly-virtual pion transition form factor, which in principle can be accessed in its entirety by experiment. We demonstrate that, in the absence of a direct measurement, the full space-like doubly-virtual form factor can be reconstructed very accurately based on existing data for $e^+e^-\to 3π$, $e^+e^-\to e^+e^-π^0$, and the $π^0\toγγ$ decay width. We derive a representation that incorporates all the low-lying singularities of the form factor, matches correctly onto the asymptotic behavior expected from perturbative QCD, and is suitable for the evaluation of the $(g-2)_μ$ loop integral. The resulting value, $a_μ^{π^0\text{-pole}}=62.6^{+3.0}_{-2.5}\times 10^{-11}$, for the first time, represents a complete data-driven determination of the pion-pole contribution with fully controlled uncertainty estimates. In particular, we show that already improved singly-virtual measurements alone would allow one to further reduce the uncertainty in $a_μ^{π^0\text{-pole}}$.

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arXiv2018

Radiative corrections to the $η^{(\prime)}$ Dalitz decays

We provide the complete set of radiative corrections to the Dalitz decays $η^{(\prime)}\to \ell^+\ell^-γ$ beyond the soft-photon approximation, i.e. over the whole range of the Dalitz plot and with no restrictions on the energy of a radiative photon. The corrections inevitably depend on the $η^{(\prime)}\toγ^*γ^{(*)}$ transition form factors. For the singly virtual transition form factor appearing e.g. in the bremsstrahlung correction, recent dispersive calculations are used. For the one-photon-irreducible contribution at the one-loop level (for the doubly virtual form factor), we use a vector-meson-dominance-inspired model while taking into account the $η$-$η^\prime$ mixing.

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arXiv2018

The relativistic chiral Lagrangian for decuplet and octet baryons at next-to-leading order

A complete and minimal relativistic Lagrangian is constructed at next-to-leading order for SU(3) chiral perturbation theory in the presence of baryon octet and baryon decuplet states. The Lagrangian has 13 terms for the pure decuplet sector, 6 terms for the transition sector from baryon octet to decuplet and (as already known from the literature) 16 terms for the pure octet sector. The minimal field content of 25 of these terms is meson-baryon four-point interactions. 3 terms give rise to the mass splitting for baryon octet and decuplet states, respectively. 2 terms give rise to overall mass shifts. 4 terms provide anomalous magnetic moments and a decuplet-to-octet magnetic transition moment. 1 term leads to an axial vector transition moment. It is shown that meson-baryon three-point coupling constants come in at leading order whereas no additional one appears in the minimal Lagrangian at next-to-leading order. Those low-energy constants that give rise to mass splitting and magnetic moments, respectively, are determined. Predictions are provided for radiative decays of decuplet to octet baryons.

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arXiv2018

Constraining P and CP violation in the main decay of the neutral Sigma hyperon

On general grounds based on quantum field theory the decay amplitude for $Σ^0 \to Λγ$ consists of a parity conserving magnetic and a parity violating electric dipole transition moment. Because of the subsequent self-analyzing weak decay of the $Λ$ hyperon the interference between magnetic and electric dipole transition moment leads to an asymmetry in the angular distribution. Comparing the decay distributions for the $Σ^0$ hyperon and its antiparticle gives access to possible C and CP violation. Based on flavor SU(3) symmetry the present upper limit on the neutron electric dipole moment can be translated to an upper limit for the angular asymmetry. It turns out to be far below any experimental resolution that one can expect in the foreseeable future. Thus any true observation of a CP violating angular asymmetry would constitute physics beyond the standard model, even if extended by a CP violating QCD theta-vacuum-angle term.

hep-ph↗

arXiv2018

Chiral-partner D mesons in a heat bath within QCD sum rules

Utilizing QCD sum rules, we extract the temperature dependences of the spectral properties of the pseudo-scalar and scalar D mesons regarded as chiral partners. Besides the masses also decay constants are analyzed as the D meson yields in heavy-ion collisions may be sensitive to their altered decay properties in an ambient strongly interacting medium. Our findings are ($i$) a decreasing scalar D meson mass for growing temperatures while its pseudo-scalar partner meson seems hardly affected, which is in qualitative agreement with hadronic model calculations; ($ii$) inferring an equally weak temperature dependence of the pseudo-scalar D meson decay properties the decreasing residua and decay constants of the scalar particle point towards partial chiral restoration. As a bonus of our analysis in the pseudo-scalar sector we determine the pseudo-scalar decay constant at vanishing temperature. Due to the connection to particular leptonic branching fractions this decay constant is of great interest allowing for the determination of the off-diagonal CKM matrix element $|V_{cd}|$ at zero temperature.

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arXiv2017

The nucleon as a test case to calculate vector-isovector form factors at low energies

Extending a recent suggestion for hyperon form factors to the nucleon case, dispersion theory is used to relate the low-energy vector-isovector form factors of the nucleon to the pion vector form factor. The additionally required input, i.e. the pion-nucleon scattering amplitudes are determined from relativistic next-to-leading-order (NLO) baryon chiral perturbation theory including the nucleons and optionally the Delta baryons. Two methods how to include pion rescattering are compared: (a) solving the Muskhelishvili-Omnes (MO) equation and (b) using an N/D approach. It turns out that the results differ strongly from each other. Furthermore the results are compared to a fully dispersive calculation of the (subthreshold) pion-nucleon amplitudes based on Roy-Steiner (RS) equations. In full agreement with the findings from the hyperon sector it turns out that the inclusion of Delta baryons is not an option but a necessity to obtain reasonable results. The magnetic isovector form factor depends strongly on a low-energy constant of the NLO Lagrangian. If it is adjusted such that the corresponding magnetic radius is reproduced, then the results for the corresponding pion-nucleon scattering amplitude (based on the MO equation) agree very well with the RS results. Also in the electric sector the Delta degrees of freedom are needed to obtain the correct order of magnitude for the isovector charge and the corresponding electric radius. Yet quantitative agreement is not achieved. If the subtraction constant that appears in the solution of the MO equation is not taken from nucleon+Delta chiral perturbation theory but adjusted such that the electric radius is reproduced, then one obtains also in this sector a pion-nucleon scattering amplitude that agrees well with the RS results.

hep-ph↗

arXiv2017

The electromagnetic Sigma-to-Lambda hyperon transition form factors at low energies

Using dispersion theory the low-energy electromagnetic form factors for the transition of a Sigma to a Lambda hyperon 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 optionally from the decuplet. Pion rescattering is again taken into account by dispersion theory. It turns out that the inclusion of decuplet baryons is not an option but a necessity to obtain reasonable results. The electric transition form factor remains very small in the whole low-energy region. The magnetic transition form factor depends strongly on one not very well determined low-energy constant of the NLO Lagrangian. One obtains reasonable predictive power if this low-energy constant is determined from a measurement of the magnetic transition radius. Such a measurement can be performed at the future Facility for Antiproton and Ion Research (FAIR).

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arXiv2016

Renormalisation of the low-energy constants of chiral perturbation theory from loops with dynamical vector mesons

Starting from a relativistic Lagrangian for pseudoscalar Goldstone bosons and vector mesons in the antisymmetric tensor representation, a one-loop calculation is performed to pin down the divergent structures that appear for the effective low-energy action at chiral orders Q^2 and Q^4. The corresponding renormalisation-scale dependences of all low-energy constants up to chiral order Q^4 are determined. Calculations are carried out for both the pseudoscalar octet and the pseudoscalar nonet, the latter in the framework of chiral perturbation theory in the limit of a large number of colours.

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arXiv2016

Contributions of loops with dynamical vector mesons to masses and decay constants of pseudoscalar mesons and their quark mass dependence

The contributions of one-loop diagrams with dynamical vector mesons to masses and decay constants of pseudoscalar mesons are determined. Hereby, a relativistic Lagrangian for both the pseudoscalar-meson octet and the vector-meson nonet is used. The vector mesons are given in the antisymmetric tensor representation. Both the differences between static and dynamical vector mesons and the differences between calculations with and without vector mesons are studied as functions of the light quark mass.

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arXiv2015

Two-Hadron Saturation for the Pseudoscalar-Vector-Vector Correlator and Phenomenological Applications

The pseudoscalar-vector-vector correlator is constructed using two meson multiplets in the vector and two in the pseudoscalar channel. The parameters are constrained by the operator product expansion at leading order where two or all three momenta are considered as large. Demanding in addition the Brodsky-Lepage limit one obtains (in the chiral limit) a pion-vector-vector correlator with only one free parameter. The singly virtual pion transition form factor and the decay width of omega to pion and photon are independent of this parameter and can serve as cross-checks of the results. The free parameter is determined from a fit of the omega-pion transition form factor. The resulting pion-vector-vector correlator is used to calculate the decay widths of omega to pion and dielectron and to pion and dimuon and finally the widths of the rare decay pion to dielectron and of the Dalitz decay pion to photon and dielectron. Incorporating radiative QED corrections the calculations of neutral-pion decays are compared to the KTeV results. We find a deviation of 2 sigma or less for the rare pion decay.

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arXiv2014

Dispersive analysis of the pion transition form factor

We analyze the pion transition form factor using dispersion theory. We calculate the singly-virtual form factor in the time-like region based on data for the $e^+e^-\to 3π$ cross section, generalizing previous studies on $ω,ϕ\to3π$ decays and $γπ\toππ$ scattering, and verify our result by comparing to $e^+e^-\toπ^0γ$ data. We perform the analytic continuation to the space-like region, predicting the poorly-constrained space-like transition form factor below 1 GeV, and extract the slope of the form factor at vanishing momentum transfer $a_π=(30.7\pm0.6)\times 10^{-3}$. We derive the dispersive formalism necessary for the extension of these results to the doubly-virtual case, as required for the pion-pole contribution to hadronic light-by-light scattering in the anomalous magnetic moment of the muon.

hep-ph↗

arXiv2013

Reactions with pions and vector mesons in the sector of odd intrinsic parity

The Wess-Zumino-Witten structure is supplemented by a simple vector-meson Lagrangian where the vector mesons are described by antisymmetric tensor fields. With the ρ-ω-π coupling as the only parameter in the sector of odd intrinsic parity, i.e. without additional contact terms, one can achieve a proper description of the decay of an ω-meson into three pions, the single- and double-virtual pion transition form factor and the three-pion production in electron-positron collisions.

hep-ph↗

arXiv2013

Non-equilibrium photon production arising from the chiral mass shift

We investigate the photon emission arising from the shift of the quark/antiquark masses during the chiral phase transition in the early stage of ultrarelativistic heavy-ion collisions. As this mass shift leads to spontaneous creation of quark-antiquark pairs and thus contributes to the formation of the quark-gluon plasma, our investigations are relevant in the context of finite-lifetime effects on the photon emission from the latter. Earlier investigations on this topic by Boyanovsky et al. were plagued by a UV divergent contribution from the vacuum polarization and the non-integrability of the remaining contributions in the ultraviolet domain. In contrast to these investigations, we do not consider the photon number-density at finite times but for free asymptotic states obtained by an adiabatic switching of the electromagnetic interaction according to the Gell-Mann and Low theorem. This approach eliminates possible unphysical contributions from the vacuum polarization and renders the resulting photon spectra integrable in the ultraviolet domain. It is emphasized that the consideration of free asymptotic states is indeed crucial to obtain such physically reasonable results.

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arXiv2012

Off-equilibrium photon production during the chiral phase transition

In the early stage of ultrarelativistic heavy-ion collisions chiral symmetry is restored temporarily. During this so-called chiral phase transition, the quark masses change from their constituent to their bare values. This mass shift leads to the spontaneous non-perturbative creation of quark-antiquark pairs, which effectively contributes to the formation of the quark-gluon plasma. We investigate the photon production induced by this creation process. We provide an approach that eliminates possible unphysical contributions from the vacuum polarization and renders the resulting photon spectra integrable inthe ultraviolet domain. The off-equilibrium photon numbers are of quadratic order in the perturbative coupling constants while a thermal production is only of quartic order. Quantitatively, we find, however, that for the most physical mass-shift scenarios and for photon momenta larger than 1 GeV the off-equilibrium processes contribute less photons than the thermal processes.

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arXiv2012

Towards an effective field theory for vector mesons

The assumption that vector mesons dominate the interactions of hadrons with electromagnetism (vector-meson dominance - VMD) provides an important phenomenological concept. On the other hand, a clear microscopic derivation is still missing and there are cases where VMD drastically fails, e.g. for the omega transition form factor. In principle, effective field theories with their systematic expansion and power counting could provide a tool to assess the validity of VMD and more generally to describe the interactions of vector mesons at low energies. Though the systematic development is still in an infant stage we present here a Lagrangian for light pseudoscalar and vector mesons which is inspired by ideas from effective field theories. The Lagrangian is used to calculate electromagnetic meson form factors. It turns out that one can reproduce both the successes of VMD concerning the pion form factors and the deviations from VMD concerning the omega transition form factor.

hep-ph↗

arXiv2012

Nonequilibrium effects in dynamic symmetry breaking

We present a dynamic model based on the linear sigma model with constituent quarks that allows for studying the explicit propagation of fluctuations at a chiral critical point and a first-order phase transition. The coupled dynamics of the sigma field and the quarks is derived selfconsistently. Hereby, the sigma field evolves according to a semiclassical Langevin equation of motion, while the evolution of the quarks is described fluid dynamically in order to model the expansion of a hot fireball in heavy-ion collisions. Dissipative processes and fluctuations in the Langevin equation are allowed under the assumption of energy-momentum conservation of the coupled system. We study the evolution of the constituent quark masses in this nonequilibrium set up.

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