### Speaker

Dr
Kenji Morita
(Frankfurt Institute for Advanced Studies)

### Description

Statistical fluctuations of the net baryon number and electric charge
have been regarded as an excellent diagnostic tool of the chiral phase
transition in QCD and in heavy ion collisions [1]. While
the second order cumulant exhibits divergence at the critical endpoint,
the higher order cumulants can reveal remnants of the $O(4)$ criticality
at the chiral crossover [2].
We will discuss criticality in the probability distribution of
conserved charges close to the chiral transition.
We calculate the probability distribution of the net baryon number
$P(N_B)$ in the chiral quark-meson model within the functional renormalization
group method, and compare its properties to the non-critical
Skellam function [3,4].
We will show, that the ratio of $P(N_B)$ to the Skellam distribution
exhibits a characteristic narrowing which is due to remnants of the $O(4)$ chiral transition [4].
We will apply the
above analysis to the experimental data measured by STAR
collaboration, and show that STAR data taken at the most central events
exhibit a similar narrowing as found in the model calculations [4].
We will indicate a relevant reference distribution for the net electric charge fluctuations. We show that the binomial and negative binomial
distribution cannot account for the characteristic behavior seen in
the chiral transition, and that due to quantum statistics and multi-charged
particle contribution, the Skellam distribution is also not a correct baseline for the recent STAR data on fluctuations of the electric charge [4].
[1] M. Stephanov, K. Rajagopal, E. Shuryak,
Phys. Rev. Lett. **81**, 4816 (1998).
[2] B. Friman, F. Karsch, K. Redlich, V. Skokov,
Eur. Phys. J. C **71**, 1694 (2011).
[3] K. Morita, B. Friman, K. Redlich, V. Skokov,
Phys. Rev. C **88**, 034903 (2013).
[4] K. Morita, B. Friman, K. Redlich, in preparation.

### Primary author

Dr
Kenji Morita
(Frankfurt Institute for Advanced Studies)

### Co-authors

Bengt Friman
(GSI)
Prof.
Krzysztof Redlich
(University of Wroclaw)