Charmonium spectroscopy in strong magnetic fields by QCD sum rules:S-wave ground states

Abstract

We investigate quarkonium mass spectra in external constant magnetic fields by using QCD sum rules. We first discuss a general framework of QCD sum rules necessary for properly extracting meson spectra from current correlators computed in the presence of strong magnetic fields, that is, a consistent treatment of mixing effects caused in the mesonic degrees of freedom. We then implement operator product expansions for pseudoscalar and vector heavy-quark current correlators by taking into account external constant magnetic fields as operators, and obtain mass shifts of the lowestlying bound states ηc and J/ψ in the static limit with their vanishing spatial momenta. Comparing results from QCD sum rules with those from hadronic effective theories, we find that the dominant origin of mass shifts comes from a mixing between ηc and J/ψ with a longitudinal spin polarization, accompanied by other subdominant effects such as mixing with higher excited states and continua.

Determination of the properties of vector mesons in external magnetic field by quenched SU(3) lattice QCD

“…The correlation functions of the vector fermionic currents for the charged mesons in the coordinate space 14) where…”

“…Then the magnetic field was introduced in two flavor lattice QCD simulation [3] and used as the probe of QCD properties [4]. The energies of hadrons in magnetic fields have been calculated on the lattice [5][6][7][8], in theoretical models [9][10][11][12][13] and in the framework of the QCD sum rules [14,15]. The notion of the hadron polarizability was initially JHEP09(2017)142 discussed in [16,17].…”

Dmesons in a magnetic field

“…Recently, we have extended the framework of QCDSR, applying it to charmonium spectroscopy in magnetic fields [40,41], where the effects of magnetic fields were implemented both on the OPE side and the phenomenological side. Investigating the roles of magnetically induced terms on the phenomenological side, we have constructed a spectral Ansatz that takes into account the mixing effects between η c and J/ψ induced by a magnetic field.…”

Screening masses in strong external magnetic fields

“…[12,13] for recent reviews. As regards the effects more directly related to color interactions, various studies have considered the possible influence of an external magnetic field on the static quark-antiquark potential [14][15][16][17][18][19], which has been clarified by recent lattice results [20,21], and might have consequences relevant to the spectrum of heavy quark bound states [22][23][24][25][26][27][28][29][30][31][32]. At zero temperature, the potential becomes anisotropic and the string tension σ is larger (smaller) in the direction orthogonal (parallel) to the magnetic field B [20,21]; at finite T , in particular in the region right below the pseudocritical temperature T c , the magnetic field induces a general suppression of σ [21], leading to an early onset of deconfinement, in agreement with the observed dependence of T c on B [33][34][35] In this paper we extend the study to the region of temperatures above T c , in order to investigate the effects of a magnetic background on the interactions between heavy quarks in the Quark-Gluon Plasma.…”