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arXiv · 1512.01544

$\theta$ dependence in $SU(3)$ Yang-Mills theory from analytic continuation

Claudio Bonati·Massimo D'Elia·Aurora Scapellato
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Abstract

We investigate the topological properties of the $SU(3)$ pure gauge theory by performing numerical simulations at imaginary values of the $\theta$ parameter. By monitoring the dependence of various cumulants of the topological charge distribution on the imaginary part of $\theta$ and exploiting analytic continuation, we determine the free energy density up to the sixth order order in $\theta$, $f(\theta,T) = f(0,T) + {1\over 2} \chi(T) \theta^2 (1 + b_2(T) \theta^2 + b_4(T) \theta^4 + O(\theta^6))$. That permits us to achieve determinations with improved accuracy, in particular for the higher order terms, with control over the continuum and the infinite volume extrapolations. We obtain $b_2=-0.0216(15)$ and $|b_4|\lesssim 4\times 10^{-4}$.

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Claudio Bonati, Massimo D'Elia, Aurora Scapellato. 2015-12-04. $\theta$ dependence in $SU(3)$ Yang-Mills theory from analytic continuation. https://doi.org/10.1103/physrevd.93.025028

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