We present our calculation of electromagnetic effects, induced by the spectator charge on Feynman-$x_F$ distributions of charged pions in peripheral $Pb+Pb$ collisions at CERN SPS energies, including realistic initial space-time-momentum conditions for pion emission. The calculation is performed in the framework of our simplified implementation of the fire-streak model, adopted to the production of both $π^-$ and $π^+$ mesons. Isospin effects are included to take into account the asymmetry in production of $π^+$ and $π^-$ at high rapidity. A comparison to a simpler model from the literature is made. We obtain a good description of the NA49 data on the $x_F$- and $p_T$-dependence of the ratio of cross sections $π^+/π^-$. The experimental data favors short times ($0.5<τ<2$~fm/$c$) for fast pion creation in the local fire-streak rest frame. The possibility of the expansion of the spectators is considered in our calculation, and its influence on the electromagnetic effect observed for the $π^+/π^-$ ratio is discussed. In addition we discuss the relation between anisotropic flow and the electromagnetic distortion of $π^+/π^-$ ratios, and study the influence of transverse expansion of fire streaks as well as their vorticity on this distortion. In this latter study we find that inclusion of rotation of fire streaks in our model gives a satisfactory description of the rapidity dependence of pion directed flow. We conclude that {our implementation of the} fire-streak model, which properly describes the centrality dependence of $π^-$ rapidity spectra at CERN SPS energies, also provides a quantitative description of the electromagnetic effect on the $π^+/π^-$ ratio as a function of $x_F$.
The Covariant Spectator Theory is applied to the description of quarks and the pion. The dressed quark mass function is calculated dynamically in Minkowski space and used in the calculation of the pion electromagnetic form factor. The effects of the mass function on the pion form factor and the different quark-pole contributions to the triangle diagram are analyzed.
The electromagnetic effects on charged pion ($π^+,π^-$) spectra provide new, independent information on the space-time evolution of the ultrarelativistic heavy ion collision. The spectator life time and its excitation energy may also be of importance for the understanding of the space-time evolution of the participant zone. This paper gives an overview of our coordinated effort to understand the interplay between electromagnetic phenomena and processes related to the fragmentation of the spectator system at forward rapidity in peripheral $Pb$+$Pb$ collisions at top CERN SPS energies. Our study…
Generalized transverse momentum dependent parton distributions (GTMDs), as mother funtions of transverse momentum dependent parton distributions (TMDs) and generalized parton distributions (GPDs), encode the most general parton structure of hadrons. We calculate four twist-two time reversal odd GTMDs of pion in a scalar spectator model. We study the dependence of GTMDs on the longitudinal momentum fraction $x$ carried by the active quark and the transverse momentum $|\vec k_T|$ for different values of skewness $ξ$ defined as the longitudinal momentum transferred to the proton as well as the to…
The formation of charged pion condensate under parallel electromagnetic fields is studied within the two-flavor Nambu--Jona-Lasinio model. The technique of Schwinger proper time method is extended to explore the quantity locating in the off-diagonal flavor space, i.e., charged pion. We obtain the associated effective potential as a function of the strength of the electromagnetic fields and find out that it contains a sextic term which possibly induce weakly first order phase transition. Dependence of pion condensation on model parameters is investigated.
We report on ongoing work to determine the pion-cloud contribution to the electromagnetic $N\rightarrowΔ$ transition form factors. The starting point is an $SU(6)$ spin-flavor symmetric constituent-quark model with instantaneous confinement that is augmented by dynamical pions which couple directly to the quarks. This system is treated in a relativistically invariant way within the framework of point-form quantum mechanics using a multichannel formulation. The first step is to determine the electromagnetic form factors of the bare particles that consist only of three quarks. These form factors…
We present our calculation of electromagnetic effects, induced by the spectator charge on Feynman-$x_F$ distributions of charged pions in peripheral $Pb+Pb$ collisions at CERN SPS energies, including realistic initial space-time-momentum conditions for pion emission. The calculation is performed in the framework of a specific implementation of the fire-streak model, adopted to the production of both $π^-$ and $π^+$ mesons. Isospin effects are included to take into account the asymmetry in production of $π^+$ and $π^-$ at high rapidity. A comparison to a simplified model from the literature is …
We revisit the connection between generalized parton distributions in impact parameter space and T-odd effects in single spin asymmetries of the semi-inclusive deep inelastic process. We show that nontrivial relations can be established only under very specific conditions, typically realized only in models that describe hadrons as two-body bound systems and involving a helicity-conserving coupling between the gauge boson and the spectator system. Examples of these models are the the scalar-diquark spectator model or the quark-target model for the nucleon, and relativistic models for the pion a…
We consider exclusive two-pion production in antiproton-deuteron interactions at the beam momenta around 10 GeV/c in the kinematics with large momentum transfer in the underlying hard process $\bar p n \to π^- π^0$. The calculations are performed taking into account the antiproton and pion soft rescattering on the spectator proton in the framework of the generalized eikonal approximation. We focus on the color transparency effect that is modeled by introducing the dependence of rescattering amplitudes on the relative position of the struck and spectator nucleons along the momentum of a fast pa…
The electromagnetic form factor of proton is studied following our previous calculation of the anomalous magnetic moment. The non-perturbative term is incorporated to correct the $Q^2$ dependence.
We construct analytic (3+1)-dimensional inhomogeneous and topologically non-trivial pion systems using chiral perturbation theory. We discuss the effect of isospin asymmetry with vanishing electromagnetic interactions as well as some particular configurations with non-vanishing electromagnetic interactions. The inhomogeneous configurations of the pion fields are characterized by a non-vanishing topological charge that can be identified with baryons surrounded by a cloud of pions. This system supports a topologically protected persistent superflow. When the electromagnetic field is turned on th…
