We present a precise computation of the topological charge distribution in the $SU(3)$ Yang-Mills theory. It is carried out on the lattice with high statistics Monte Carlo simulations by employing the clover discretization of the field strength tensor combined with the Yang-Mills gradient flow. The flow equations are integrated numerically by a fourth-order structure-preserving Runge-Kutta method. We have performed simulations at four lattice spacings and several lattice sizes to remove with confidence the systematic errors in the second (topological susceptibility $\chi_t^\text{YM}$) and the fourth cumulant of the distribution. In the continuum we obtain the preliminary results $t_0^2\chi_t^\text{YM}=6.53(8)\times 10^{-4}$ and the ratio between the fourth and the second cumulant $R=0.233(45)$. Our results disfavour the $\theta$-behaviour of the vacuum energy predicted by dilute instanton models, while they are compatible with the expectation from the large-$N_c$ expansion.

Cè, M., Consonni, C., Engel, G., Giusti, L. (2015). Testing the Witten-Veneziano mechanism with the Yang-Mills gradient flow on the lattice. In The 32nd International Symposium on Lattice Field Theory (Lattice 2014) (pp.353) [10.22323/1.214.0353].

Testing the Witten-Veneziano mechanism with the Yang-Mills gradient flow on the lattice

Cè, Marco
;
Giusti, L
2015

Abstract

We present a precise computation of the topological charge distribution in the $SU(3)$ Yang-Mills theory. It is carried out on the lattice with high statistics Monte Carlo simulations by employing the clover discretization of the field strength tensor combined with the Yang-Mills gradient flow. The flow equations are integrated numerically by a fourth-order structure-preserving Runge-Kutta method. We have performed simulations at four lattice spacings and several lattice sizes to remove with confidence the systematic errors in the second (topological susceptibility $\chi_t^\text{YM}$) and the fourth cumulant of the distribution. In the continuum we obtain the preliminary results $t_0^2\chi_t^\text{YM}=6.53(8)\times 10^{-4}$ and the ratio between the fourth and the second cumulant $R=0.233(45)$. Our results disfavour the $\theta$-behaviour of the vacuum energy predicted by dilute instanton models, while they are compatible with the expectation from the large-$N_c$ expansion.
slide + paper
High Energy Physics - Lattice; High Energy Physics - Lattice; High Energy Physics - Theory
English
32nd International Symposium on Lattice Field Theory (Lattice 2014)
2014
The 32nd International Symposium on Lattice Field Theory (Lattice 2014)
2015
353
http://arxiv.org/abs/1410.8358v1
open
Cè, M., Consonni, C., Engel, G., Giusti, L. (2015). Testing the Witten-Veneziano mechanism with the Yang-Mills gradient flow on the lattice. In The 32nd International Symposium on Lattice Field Theory (Lattice 2014) (pp.353) [10.22323/1.214.0353].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/64582
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