<p>The low-energy electromagnetic form factors of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="normal">Δ</mi><mo stretchy="false">(</mo><mn>1232</mn><mo stretchy="false">)</mo></mrow></math>-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 <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>−</mo></msup><mi>N</mi><mo stretchy="false">→</mo><msup><mi>e</mi><mo>−</mo></msup><mi mathvariant="normal">Δ</mi></math> scattering, the focus lies on the numerically dominant magnetic dipole transition form factor. Fitting two subtraction constants (one for the scattering amplitude and 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 <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Δ</mi><mo stretchy="false">→</mo><mi>N</mi><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math> are presented.</p>

Thailand

Sweden

Moh Moh Aung

Stefan Leupold

United States

Elisabetta Perotti

Yupeng Yan

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

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 models and quantum chromodynamics (QCD) for a large number of colors provide predictions, but some recent phenomenological analyses even suggest 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 <math><mrow><mn>3</mn><mo>/</mo><mn>2</mn></mrow></math> 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.

Magnus Bertilsson

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

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 <math><mrow><mi>Δ</mi><mo>(</mo><mn>1232</mn><mo>)</mo></mrow></math> 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 <math><msup><mi>Q</mi><mn>2</mn></msup><mo>≲</mo><mn>0.6</mn><mtext> </mtext><mtext> </mtext><msup><mrow><mi>GeV</mi></mrow><mrow><mn>2</mn></mrow></msup></math> and <math><msub><mi>M</mi><mi>π</mi></msub><mo>≲</mo><mn>350</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>. 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.

Spain

Fernando Alvarado

Di An

Luis Alvarez-Ruso

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

In this paper, the existence of a massive dark photon, associated with a new gauge group is considered. The dark photon can be kinetically mixed with the photon. To study some applications, the thermo field dynamics formalism is used. Exploring the topological structure of this approach, the influence of dark photons on the Stefan–Boltzmann law and the Casimir effect at zero and finite temperature is calculated.

Brazil

V. Prata

A. Santos

Canada

Faqir Khanna

Stefan–Boltzmann law and Casimir effect for dark photons

We study rare three-body decays of the <math><mrow><mi>Ω</mi></mrow></math> 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 <math><msup><mi>Ω</mi><mo>−</mo></msup><mo>→</mo><mi>Ξ</mi><mi>π</mi><mi>π</mi></math> 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 nonrelativistic 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 <math><mrow><mi>Ω</mi></mrow></math> decays, which reaffirm the gap between theory and experiment. We point out that this discrepancy is closely tied to the <math><mi>Δ</mi><mi>I</mi><mo>=</mo><mn>1</mn><mo>/</mo><mn>2</mn></math> 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 <math><msup><mi>Ω</mi><mo>−</mo></msup><mo>→</mo><msup><mi>Ξ</mi><mn>0</mn></msup><msup><mi>μ</mi><mo>−</mo></msup><msub><mover><mi>ν</mi><mo>¯</mo></mover><mi>μ</mi></msub></math>. 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 <math><mrow><mi>Ω</mi></mrow></math> 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.

Cornelis J. G. Mommers

Estimates for rare three-body decays of the <math><mrow><mi>Ω</mi></mrow></math> baryon using chiral symmetry and the <math><mi>Δ</mi><mi>I</mi><mo>=</mo><mn>1</mn><mo>/</mo><mn>2</mn></math> rule

Nonleptonic two-body weak decays of baryons are an important tool to probe the combined charge conjugation–parity symmetry (<math><mi>C</mi><mi>P</mi></math>) violation. We explain why the decays of strange baryons provide complementary information to the decays of kaons. A model-independent parametrization of the nonleptonic decays of the <math><mi>Λ</mi></math> and <math><mi>Ξ</mi></math> 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 <math><mi>J</mi><mo>/</mo><mi>ψ</mi></math> factories with luminosity of <math><msup><mn>10</mn><mn>35</mn></msup><mtext> </mtext><mtext> </mtext><msup><mrow><mi>cm</mi></mrow><mrow><mo>−</mo><mn>2</mn></mrow></msup><mtext> </mtext><msup><mi>s</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math>. The copious production of spin-entangled hyperon-antihyperon pairs via the <math><mi>J</mi><mo>/</mo><mi>ψ</mi></math> 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 <math><mi>C</mi><mi>P</mi></math> tests. We show that by using a longitudinally polarized electron beam the statistical precision of the <math><mi>C</mi><mi>P</mi></math> 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 <math><mi>C</mi><mi>P</mi></math>-violation signal with a strength corresponding to the standard model predictions. Our conclusions should encourage more detailed feasibility studies, including optimization of the measurement methods and studies of systematic effects. Finally, our results call for an update of the theory predictions with increased precision.

Poland

Nora Salone

Patrik Adlarson

China

Varvara Batozskaya

Andrzej Kupsc

Indonesia

Jusak Tandean

Study of <math><mi>C</mi><mi>P</mi></math> violation in hyperon decays at super-charm-tau factories with a polarized electron beam

We investigate the weak decays of <math><msubsup><mover><mi>B</mi><mo>¯</mo></mover><mi>s</mi><mn>0</mn></msubsup></math> and <math><msub><mi>Λ</mi><mi>b</mi></msub></math> to charm hadrons based on the dynamical supersymmetry between the <math><mover><mi>s</mi><mo>¯</mo></mover></math> quark and the <math><mi>u</mi><mi>d</mi></math> diquark. We derive a new sum rule relating the decay rates of the processes <math><mrow><msubsup><mrow><mover><mrow><mi>B</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mi>s</mi></mrow><mrow><mn>0</mn></mrow></msubsup><mo>→</mo><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow><mrow><mo>+</mo></mrow></msubsup><msup><mrow><mi>P</mi></mrow><mrow><mo>−</mo></mrow></msup></mrow></math>, <math><mrow><msubsup><mrow><mover><mrow><mi>B</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mi>s</mi></mrow><mrow><mn>0</mn></mrow></msubsup><mo>→</mo><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow><mrow><mo>*</mo><mo>+</mo></mrow></msubsup><msup><mrow><mi>P</mi></mrow><mrow><mo>−</mo></mrow></msup></mrow></math>, and <math><msub><mi>Λ</mi><mi>b</mi></msub><mo>→</mo><msub><mi>Λ</mi><mi>c</mi></msub><msup><mi>P</mi><mo>−</mo></msup></math>, where <math><msup><mi>P</mi><mo>−</mo></msup></math> is a negatively charged meson, such as <math><msup><mi>π</mi><mo>−</mo></msup></math> and <math><msup><mi>K</mi><mo>−</mo></msup></math>. It is found that the observed decay rates satisfy the sum rule very well. This implies that the supersymmetry between the <math><mover><mi>s</mi><mo>¯</mo></mover></math> quark and the <math><mi>u</mi><mi>d</mi></math> diquark is also seen in the wave functions of the heavy hadrons and suggests that the <math><mi>u</mi><mi>d</mi></math> diquark can be regarded as a valid effective constituent for heavy hadrons.

Japan

Taiju Amano

Daisuke Jido

Sum rule for the partial decay rates of bottom hadrons based on the dynamical supersymmetry of the <math><mover><mi>s</mi><mo>¯</mo></mover></math> quark and the <math><mi>u</mi><mi>d</mi></math> diquark

The Dirac field, spin 1/2 particles, is investigated in phase space. The Dirac propagator is defined. The Thermo Field Dynamics (TFD) formalism is used to introduce finite temperature. The energy-momentum tensor is calculated at finite temperature. The Stefan-Boltzmann law is established, and the Casimir effect is calculated for the Dirac field in phase space at zero and finite temperature. A comparative analysis with these results in standard quantum mechanics space is realized.

S.C. Ulhoa

R.G.G. Amorim

J.S. da Cruz Filho

A.F. Santos

F.C. Khanna

Spin-1/2 Particles in Phase Space: Casimir Effect and Stefan-Boltzmann Law at Finite Temperature

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 $$\varSigma ^0\rightarrow \varLambda e^+e^-$$ <math><mrow><msup><mi>Σ</mi><mn>0</mn></msup><mo>→</mo><mi>Λ</mi><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>-</mo></msup></mrow></math> . 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.

Tomáš Husek

Radiative corrections for the decay $$\varSigma ^0\rightarrow \varLambda e^+e^-$$ <math><mrow><msup><mi>Σ</mi><mn>0</mn></msup><mo>→</mo><mi>Λ</mi><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>-</mo></msup></mrow></math>

The three electromagnetic form factors for the transition from a <math><mrow><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>+</mo></msup><mspace width="4pt"></mspace><msup><mi>Σ</mi><mo>*</mo></msup></mrow></math> hyperon to the ground-state <math><mi>Λ</mi></math> hyperon are studied. At low energies, combinations of the transition form factors can be deduced from Dalitz decays of the <math><msup><mi>Σ</mi><mo>*</mo></msup></math> hyperon to <math><mi>Λ</mi></math> 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 <math><mi>Λ</mi></math>. 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 such 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 transition form factors are related to decay distributions and differential cross sections. Using dispersion theory, the low-energy electromagnetic form factors for the <math><msup><mi>Σ</mi><mo>*</mo></msup></math>-to-<math><mi>Λ</mi></math> transition are related to the pion vector form factor. The additionally required input, i.e., the two-pion–<math><msup><mi>Σ</mi><mo>*</mo></msup></math>–<math><mi>Λ</mi></math> amplitudes, is 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 <math><mrow><msup><mi>Σ</mi><mo>*</mo></msup><mo>→</mo><mi>Λ</mi><mi>γ</mi></mrow></math> decay width. Pion rescattering is taken into account by using dispersion theory and solving a Muskhelishvili-Omnès 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.

Olov Junker

Timea Vitos

Electromagnetic form factors of the transition from the spin-3/2 <math><mi>Σ</mi></math> to the <math><mi>Λ</mi></math> hyperon