Effect of inverse magnetic catalysis on conserved charge fluctuations in hadron resonance gas model

The effect of inverse magnetic catalysis (IMC) has been observed on the conserved charge fluctuations and the correlations along the chemical freeze-out curve in a hadron resonance gas model. The fluctuations and the correlations have been compared with and without charge conservations. The charge conservation plays an important role in the calculation of the fluctuations at nonzero magnetic field and for the fluctuations in the strange charge at zero magnetic field. The charge conservation diminishes the correlations $\chi_{BS}$ and $\chi_{QB}$, but enhances the correlation $\chi_{QS}$. The baryonic fluctuations (2nd order) at $B = 0.25$ ${GeV}^2$ increases more than two times compared to $B = 0$ at higher $\mu_{B}$. The fluctuations have been compared at nonzero magnetic field along the freeze-out curve i.e along fitted parameters of the chemical freeze-out temperature and chemical potentials, with the fluctuations at nonzero magnetic field along the freeze-out curve with the IMC effect, and the results are very different with the IMC effect. This is clearly seen in the products of different moments ${{\sigma}^2}/{M}$ and $S\sigma$ of net-kaon distribution.

Hadron resonance gas model in presence of magnetic field • The basic features of the physical system created at the time of chemical freeze-out in heavy ion collisions are well described in terms of the hadron resonance gas (HRG) model.
• The grand partition function defined for each hadron species i as • V is the volume of the system, is the spin degeneracy factor.
is the chemical potential • Conservation laws : net S=0 and B/Q =2.52 • All the thermodynamic quantities like pressure, energy density and entropy density etc. can be derived from this partition function.
Now in presence of external magnetic field along z-axis • Landau quantization of energy levels for charged particle takes place along the plane perpendicular to the magnetic field.
• Energy is given by • n is the Landau level goes from 0 to ∞ • The grand partition function in presence of magnetic field is given by ( ) • The system exhibits magnetic catalysis at zero temperature where the chiral condensate increases in external magnetic field.
• Lattice QCD exhibits IMC effect at finite temperature in external magnetic field. The chiral condensate decreases and the critical temperature decreases.
• The IMC effect might be due to the decrease in interaction strength in presence of magnetic field. This decrease of interaction strength is consistent with asymptotic freedom of QCD if the relevant scale • Since the critical temperature decreases in presence of magnetic field, the chemical freezeout curve should correspond to a lower temperature in Tplane.
• The universal chemical freezeout curve is determined from the condition E/N = ε/n ~ 1 GeV.
chemical freezeout curve determined by E/N ≈ 1GeV with and without charge conservation. Solid line without electric charge and strangeness conservation. The dotted line is with charge conservation.
Due to IMC effect, the chemical freezeout temperature decreases in presence of nonzero magnetic field with charge conservation.
At higher and nonzero B, the chemical freezeout curve is pushed to higher temperature because there are more baryons, particularly more protons at This argees with the chemical freezeout curve at zero B.
However, at nonzero B, the chemical freezeout curve does not match with these fitted parameters.  117, 102301 (2016) Charge conservation diminishes the fluctuations along the freezeout curve.

Dominant contribution to
comes from k ± χ S Dominant cont. comes from proton and neutron at zero B. At nonzero B, Δ ± cont. is very large compared to proton.
Experimentally measured moments such as mean (M ), standard deviation (σ ), skewness (S ) and kurtosis (κ ) of conserved charges are used to characterize the shape of charge distribution.
IMC effect is observed in HRG with charge conservation.
At B=0, charge conservation does not play a role in the fluctuations along the freezeout curve for the conserved charges of electric charge and baryon number.
But charge conservation play an important role for strange charge at B=0. Charge conservation diminishes the fluctuations in strange charge at B=0 compared to the fluctuations without charge conservation.
For nonzero B, charge conservation play a very important role. If there is no charge conservation at nonzero B, then the fluctuations increase by a huge amount compared to zero B.
IMC effect is clearly observed in products of net kaon moment.

Thank you
Estimation of magnetic field in rel. heavy ion collisions • Magnetic field is produced due to valence charges of the colliding nuclei.
• This magnetic field decreases with time • However, rapidly decreasing magnetic field produces induced current in the Plasma and magnetic field of similar magnitude can be obtained from this induced current and sustain for longer time.
3 rd order susceptibility of conserved charges