Erratum to: Anomalous non-conservation of fermion/chiral number in Abelian gauge theories at finite temperature
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Springer
Received: July 7, 2020 Accepted: July 8, 2020 Published: July 29, 2020
Daniel G. Figueroaa and Mikhail Shaposhnikovb a
Theory Department, CERN, CH-1211 Geneve 23, Switzerland b Institute of Physics, Laboratory of Particle Physics and Cosmology, ´ Ecole Polytechnique F´ed´erale de Lausanne, CH-1015 Lausanne, Switzerland
E-mail: [email protected], [email protected] Erratum to: JHEP04(2018)026 ArXiv ePrint: 1707.09967
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP07(2020)217
JHEP07(2020)217
Erratum: Anomalous non-conservation of fermion/chiral number in Abelian gauge theories at finite temperature
(th)
Γdiff ' 4.1 · 10−5 log(17.6/e2 ) e6 B 2 .
(1)
Comparing the theoretical prediction eq. (1) [say for e2 = 1] with a re-analysis of the numerical diffusion rate Γdiff (by weighting the mean values of our data with the error ∆Γdiff , cf. eq. (4.8), and without assuming an enforcement of a fixed exponent in the scaling of Γ with e2 ), we obtain now in ref. [1] (num)
Γdiff
(th) Γdiff
e2 =1
= 11.2+6.9 −4.3 .
(2)
This computation reduces by a factor ∼ 5 − 6 our original claim in the discrepancy between theory and numerics: we still obtain that the numerically extracted rates are larger than the MHD counterpart by a factor O(10), but this factor is rather ∼ 11, instead of the originally claimed factor ∼ 58. The reduction from a factor ∼ 58 down to ∼ 11 is a combined effect of correcting a factor 2 in eq. (2.16) [this leads to a ratio ∼ 29] and a factor ∼ 2.6 when comparing the numerical result against the theoretical prediction eq. (1), instead of eq. (1.11) [this leads to the final ratio ∼ 11]. The errors in the new ratio are also larger, as we do not fix the scaling power of Γdiff with e2 , and hence the numerical fit we use now exhibits larger errors. If we enforce a scaling Γdiff ∝ e6 , as we did originally in the main text of the article, we still obtain a similar ratio 11.4+3.0 −2.4, albeit with smaller errors. Open Access. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
References [1] D.G. Figueroa, A. Florio and M. Shaposhnikov, Chiral charge dynamics in Abelian gauge theories at finite temperature, JHEP 10 (2019) 142 [arXiv:1904.11892] [INSPIRE]. [2] P.B. Arnold, G.D. Moore and L.G. Yaffe, Transport coefficients in high temperature gauge theories. 1. Leading log results, JHEP 11 (2000) 001 [hep-ph/0010177] [INSPIRE]. [3] P.B. Arnold, G.D. Moore and L.G. Yaffe, Transport coefficients in high temperature gauge theories. 2. Beyond leading log, JHEP 05 (2003) 051 [hep-ph/0302165] [INSPIRE].
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JHEP07(2020)217
To confront the numerical results of Γdiff with the analytical results from section 2.3, we originally considered the theoretical prediction for the diffusion rate given by eq. (2.17), which we re-wrote in eq. (4.25). However, we have more recently found
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