QCD effective potential with strongU(1)emmagnetic fields

Abstract

We derive the analytic expression for the one-loop SU (N c ) QCD effective potential including N f flavor quarks which nonlinearly interact with the chromomagnetic background field and the external U (1) em magnetic field. After the renormalization of couplings and fields, we obtain the correct one-loop β functions of both QCD and QED, and the resulting effective potential satisfies the renormalization group equation. We investigate the effect of the magnetic field on the QCD vacuum by using the effective potential, in particular for the color SU (3) case with the three flavors (u, d, s). Our result shows that the chromomagnetic field prefers to be parallel to the external magnetic field. Furthermore, quark loop contributions to the effective potential with the magnetic field enhance gluonic contributions, and then the chromomagnetic condensate increases with an increasing magnetic field. This result supports the recent observed gluonic magnetic catalysis at zero-temperature in lattice QCD. *

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

“…The spectral density ρ J (s) is often assumed to have a perturbative continuum ImΠ J pert (s)/π and a single pole at the ground-state mass δ(s − m 2 pole ). This ansatz works sufficiently well when the ground-state pole is well separated from a threshold of continuum as only the low-energy structure is important for the exponential sum rule (20) owing to the exponential suppression of the higher energy part of the spectral density by the Borel transformation. Thus, this simple ansatz works well for the tightly bound ground-state charmonia.…”

“…In our present analysis, we include the terms up to the dimension-4 scalar gluon condensate as in Eq. (33) since recent studies have shown that effects of external magnetic fields on the gluon condensate is sufficiently small as briefly discussed below [19,20]. A summary of the Wilson coefficients is available in Refs.…”

“…While the light-quark condensates in magnetic fields at zero temperature and density have been known to increase by a mechanism called "magnetic catalysis" [11,16], a similar growth of a gluon condensate at zero temperature and density was recently observed in both lattice QCD and analytic studies [19,20]. Modification of a gluon condensate should be small, since external magnetic fields do not directly couple to gluons, but indirectly through sea quarks.…”

“…Analysis of the Borel window in the exponential sum rule (20) is simpler and can be done in a more systematic way than those with the moment sum rule containing two parameters Q 2 and n. Note also that the Wilson coefficients are transformed to be suppressed by a factorial of the operator dimension 1/(d/2 − 1)!, and thus the convergence of the OPE is improved. Therefore, we will use the exponential sum rule (20) in subsequent sections.…”

“…Motivated by formation of strong electromagnetic fields in neutron stars/magnetars [3,4] and ultrarelativistic heavy-ion collisions at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC) [5][6][7][8], a number of lattice QCD simulations and analytic calculations have shown that strong magnetic fields modify properties of QCD vacuum such as quark condensates [5,[9][10][11][12][13][14][15][16][17][18] and gluon condensates [19,20], and consequently modify even phase structures [15,19,[21][22][23] and hadron properties [5,9,[24][25][26][27][28][29][30][31][32][33][34][35]. One of the remarkable findings is a discrepancy between meson spectra obtained from a hadronic effective model calculation and a lattice QCD simulation in strong magnetic fields [26,27].…”