High precision renormalization of the flavour non-singlet Noether currents in lattice QCD with Wilson quarks

Dalla Brida, Mattia; Korzec, Tomasz; Sint, Stefan; Vilaseca, Pol

doi:10.1140/epjc/s10052-018-6514-5

High precision renormalization of the flavour non-singlet Noether currents in lattice QCD with Wilson quarks

Mattia Dalla Brida
(
- INFN, Milan Bicocca and
- Milan Bicocca U.
)
,
Tomasz Korzec
(
- Wuppertal U.
)
,
Stefan Sint
(
- Trinity Coll., Dublin
)
,
Pol Vilaseca
(
- INFN, Rome and
- Rome U.
)

Aug 28, 2018

43 pages

Published in:

Eur.Phys.J.C 79 (2019) 1, 23

Published: Jan 14, 2019

e-Print:

1808.09236 [hep-lat]

DOI:

10.1140/epjc/s10052-018-6514-5 (publication)

View in:

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Abstract: (Springer)

We determine the non-perturbatively renormalized axial current for

\hbox {O}(a)

improved lattice QCD with Wilson quarks. Our strategy is based on the chirally rotated Schrödinger functional and can be generalized to other finite (ratios of) renormalization constants which are traditionally obtained by imposing continuum chiral Ward identities as normalization conditions. Compared to the latter we achieve an error reduction by up to one order of magnitude. Our results have already enabled the setting of the scale for the

{N_{\mathrm{f}}}=2+1

CLS ensembles (Bruno et al. in Phys Rev D 95(7):074504. arXiv:1608.08900 , 2017) and are thus an essential ingredient for the recent

\alpha _s

determination by the ALPHA collaboration (Phys Rev Lett 119(10):102001. arXiv:1706.03821 , 2017). In this paper we shortly review the strategy and present our results for both

{N_{\mathrm{f}}}=2

and

{N_{\mathrm{f}}}=3

lattice QCD, where we match the

\beta

-values of the CLS gauge configurations. In addition to the axial current renormalization, we also present precise results for the renormalized local vector current.

Note:

43 pages, 11 figures. Added Appendix C containing fits to the final results for Z_{A,V}. Matches published version

Wilson fermions
Chiral symmetry
Lattice QCD
Non-perturbative renormalization
current: axial
quark: Wilson
current: renormalization
current: vector
Ward identity: chiral
quantum chromodynamics

References(56)

Figures(19)

[1]

Setting the scale for the CLS $2 + 1$ flavor ensembles

Mattia Bruno
(
- NIC, Zeuthen and
- DESY, Zeuthen and
- Brookhaven
)
,
Tomasz Korzec
(
- Wuppertal U.
)
,
Stefan Schaefer
(
- NIC, Zeuthen and
- DESY, Zeuthen
)

- Phys.Rev.D 95 (2017) 7, 074504
•
e-Print:
- 1608.08900
•
DOI:
- 10.1103/PhysRevD.95.074504

[2]

QCD Coupling from a Nonperturbative Determination of the Three-Flavor $\Lambda$ Parameter

ALPHA

Collaboration

•

Mattia Bruno
(
- Brookhaven Natl. Lab.
)

et al.

- Phys.Rev.Lett. 119 (2017) 10, 102001
•
e-Print:
- 1706.03821
•
DOI:
- 10.1103/PhysRevLett.119.102001

[3]

Confinement of Quarks

Kenneth G. Wilson
(
- Cornell U., LNS
)

- Phys.Rev.D 10 (1974) 2445-2459,
- In *Rebbi, C. ( Ed.): Lattice Gauge Theories and Monte Carlo Simulations*, 45-59. ( Phys. Rev. D10 ( 1974) 2445-2459) and Cornell Univ. Ithaca - CLNS-74-262 (74,REC.MAR.) 47p,
•
DOI:
- 10.1103/PhysRevD.10.2445