Quarkonium radiative decays from the hadronic Paschen-Back effect

Abstract

We study the radiative (E1 and M1) decays of P-wave quarkonia in a strong magnetic field based on the Lagrangian of potential nonrelativistic QCD. To investigate their properties, we implement a polarized wave function basis justified in the Paschen-Back limit. In a magnetic field stronger than the spin-orbit coupling, the wave functions of the P-wave quarkonia are drastically deformed by the Hadronic Paschen-Back effect. Such deformation leads to the anisotropy of the direction of decays from the P-wave quarkonia. The analytic formulas for the radiative decay widths in the nonrelativistic limit are shown, and the qualitative decay properties are discussed.

Anisotropic string tensions and inversely magnetic catalyzed deconfinement from a dynamical AdS/QCD model

“…Moreover, our model could also be fruitful to study, now in a gravitationally consistent setting, the melting and transport properties of charmonia in magnetic fields, thereby improving upon [64,[95][96][97][98], see also [65,[99][100][101][102][103].…”

A review of quarkonia under strong magnetic fields

“…Some of their properties are confirmed also by QCD sum rules [22,23] and an effective Lagrangian [20,[22][23][24]. In particular, there are some characteristic phenomena: (i) the mixing between spin-singlet and spin-triplet eigenstates [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33], which originates from the Zeeman coupling of charm quarks, (ii) the Landau levels of charm quarks (or squeezing of spatial wave function), (iii) anisotropic (or modified) confinement potential [18,[34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49], and (iv) the motional Stark effect (or Lorentz ionization) in moving charmonia [17,18,26,31,50,51]. For other phenomenological studies, see Refs.…”

“…The HPBE is induced by magnetic fields comparable with the LS splitting of the hadron masses, so that the wave functions of Pwave quarkonia can be deformed even in relatively smaller magnetic fields than those of the S-wave quarkonia. One of the resultant phenomena is the anisotropic photon emission in radiative decays [21,30] such as χ c0,c1,c2 → J/ψγ. As other phenomena relating to the HPBE, the anisotropy in 3 Schematic picture of Landau levels of charm quarks.…”

Hadronic Paschen-Back effect in P-wave charmonia under strong magnetic fields

“…As an example of detectable effects from the HPBE, we discuss the electric-dipole (E1) radiative decays of the P-wave charmonia. 2,3 In the strong field limit, we consider the decay processes using the "polarized" basis with a fixed L z instead of the original quarkonium eigenstates. The wave function with L z = 0 has the factor of z, so that the radiative decay amplitude is proportional to sin α, where α is the angle between the directions of the magnetic field parallel to the z-axis and the photon momentum vector.…”

“…In these proceedings, we review the Hadronic Paschen-Back effect (HPBE) for P-wave charmonia, 2,3 which was first predicted in terms of the constituent quark model. 2 The heavy-ion collision experiments in Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC) can create strong magnetic fields which is theoretically expected that |eB| ∼ 0.1 GeV 2 and |eB| ∼ 1.0 GeV 2 , respectively.…”