Conserved vector current in QCD-like theories and the gradient flow
- PDF / 787,154 Bytes
- 41 Pages / 595.276 x 841.89 pts (A4) Page_size
- 56 Downloads / 173 Views
Springer
Received: July 16, 2020 Accepted: September 4, 2020 Published: October 6, 2020
Marco Boersa and Elisabetta Pallantea,b a
Van Swinderen Institute for Particle Physics and Gravity, University of Groningen, 9747 AG, The Netherlands b Nikhef, Science Park, Amsterdam, The Netherlands
E-mail: [email protected], [email protected] Abstract: We present analytical results for the Euclidean 2-point correlator of the flavorsinglet vector current evolved by the gradient flow at next-to-leading order (O(g 2 )) in perturbatively massless QCD-like theories. We show that the evolved 2-point correlator requires multiplicative renormalization, in contrast to the nonevolved case, and confirm, in agreement with other results in the literature, that such renormalization ought to be identified with a universal renormalization of the evolved elementary fermion field in all evolved fermion-bilinear currents, whereas the gauge coupling renormalizes as usual. We explicitly derive the asymptotic solution of the Callan-Symanzik equation for the connected √ 2-point correlators of these evolved currents in the limit of small gradient-flow time t, at fixed separation |x − y|. Incidentally, this computation determines the leading coefficient of the small-time expansion (STE) for the evolved currents in terms of their local nonevolved counterpart. Our computation also implies that, in the evolved case, conservation of the vector current, hence transversality of the corresponding 2-point correlator, is no longer related to the nonrenormalization, in contrast to the nonevolved case. Indeed, for small flow time the evolved vector current is conserved up to O(t) softly violating effects, despite its t-dependent nonvanishing anomalous dimension. Keywords: Lattice QCD, Perturbative QCD, Renormalization Group ArXiv ePrint: 2007.02121
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP10(2020)034
JHEP10(2020)034
Conserved vector current in QCD-like theories and the gradient flow
Contents 1
2 The 2.1 2.2 2.3
3 4 5 7
gradient flow in QCD-like theories Solutions of the gradient-flow equations Free propagators The vector current evolved by the gradient flow
3 The 1-point correlator h∂µ JµV (t, x)i evolved by the gradient flow 3.1 Leading order, O(g 0 ) 3.2 Next-to-leading order, O(g 2 )
8 9 10
4 The 2-point vector correlator in massless QCD-like theories 4.1 Solution of the Callan-Symanzik equation 4.2 Leading order, O(g 0 ) and next-to-leading order, O(g 2 )
12 12 14
5 The 2-point vector correlator evolved by the gradient flow 5.1 Leading order, O(g 0 ) 5.2 Next-to-leading order, O(g 2 ) 5.2.1 Type I contribution 5.2.2 Type II contribution 5.2.3 Type III contribution 5.2.4 Type IV contribution 5.3 Total UV divergence at O(g 2 ) 5.3.1 Including the gradient-flow renormalization factor, Zχ 5.4 STE of the evolved currents from their 2-point correlators
15 16 18 18 19 19 20 21 22 23
6 Current conservation and renormalization 6.1 Nonevolved case: conservation implies nonrenormalization 6.2 Evolved case: c
Data Loading...
