Hadronic Paschen–Back effect

Abstract

We find a novel phenomenon induced by the interplay between a strong magnetic field and finite orbital angular momenta in hadronic systems, which is analogous to the Paschen-Back effect observed in the field of atomic physics. This effect allows the wave functions to drastically deform. We discuss anisotropic decay from the deformation as a possibility to measure the strength of the magnetic field in high-energy heavy-ion collisions , which has not been measured experimentally. As an example we investigate charmonia with a finite orbital angular momentum in a strong magnetic field. We calculate the mass spectra and mixing ratios. To obtain anisotropic wave functions, we apply the cylindrical Gaussian expansion method. There we use different extention parameters for the parallel and transverse directions to the magnetic field.

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.…”

“…In this review, we focus on phenomena in quarkonia under a magnetic field. The essence of qurkonium properties in a magnetic field can be well known within the constituent quark model with numerical approaches [17][18][19][20][21]. Although this model is a simplified model with constituent quark degrees of freedom, it can implement various quantum phenomena induced by a magnetic field.…”

Nucleon and Δ isobar in a strong magnetic field

“…This is called the PB effect. In fact, Iwasaki et al discussed the PB effect [55], when the strong magnetic field (∼ 10 19 G) is exerted on a charmonium system. They found a very interesting feature: The strong magnetic field induces mixing between S = 0 and S = 1 states.…”

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. [4][5][6][7][8][9] Under such environments, charmonia are created more quickly than other light hadrons, and they would be a good probe of magnetic fields.…”