Speaker
Description
The chiral phase transition in QCD is frequently studied by either
locating the inflection point of a suitably renormalized order
parameter or the extrema of chiral susceptibilities as function of the
light quark masses. In the limit of vanishing light quark masses
their scaling behaviour is dominated by scaling functions and critical
exponents that are unique for a given universality class.
Generally properties of the relevant universality class, $\it i.e.$ the
$3$-$d$, $O(2)$ or $O(4)$ universality classes are used to extract the
chiral phase transition temperature at vanishing values of the chemical
potentials. No serious attempt exists so far, to extract the relevant
universal critical exponents directly from lattice QCD calculations.
In this talk, we will use properties of a renormalized chiral order
parameter $M$, obtained as a suitable difference of the 2-flavor light quark
chiral condensate $M_b$ and its susceptibility $\chi_b$ and given by $M = M_b - H \, \chi_b $ [1,2].
Similar to the related observable $H \,\chi_b/ M_b$, the improved order
parameter $M$ also is directly proportional to a scaling function. In addition
the latter has the advantage of eliminating additive UV divergences as well
as ${\cal O}(H)$ regular contributions.
In the scaling region the logarithm of the ratio of this
order parameter, evaluated for two different light quark masses, has a unique
crossing point as function of temperature. This crossing-point arises at
the chiral phase transition temperature $T_c$ and directly gives the value of
the critical exponent $\delta$ without any prior information regarding the
associated universality class of the phase transition.
We present first results from our numerical study of this order parameter
ratio on lattices with fixed temporal extent $N_\tau=8$. We discuss the
prospects for a parameter free determination of $T_c$ and $\delta$ in the chiral limit of (2+1)-flavor QCD.
References:
[1] L. Dini et al, Phys.Rev.D 105 (2022) 034510, arXiv:2111.12599
[2] H.-T. Ding et al, arXiv:2403.09390
