Nonperturbative renormalization and $O(a)$-improvement of the nonsinglet vector current with $N_f=2+1$ Wilson fermions and tree-level Symanzik improved gauge action - INSPIRE

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Nonperturbative renormalization and $O(a)$ -improvement of the nonsinglet vector current with $N_f=2+1$ Wilson fermions and tree-level Symanzik improved gauge action

Antoine Gerardin
(
- U. Mainz, PRISMA and
- Julich, NIC and
- DESY, Zeuthen
)
,
Tim Harris
(
)
,
Harvey B. Meyer
(
- U. Mainz, PRISMA and
- Julich, NIC and
- Helmholtz Inst., Mainz
)

Nov 20, 2018

17 pages

Published in:

Phys.Rev.D 99 (2019) 1, 014519

Published: Feb 1, 2019

e-Print:

1811.08209 [hep-lat]

DOI:

10.1103/PhysRevD.99.014519

Report number:

MITP/18-106

View in:

reference search61 citations

Citations per year

Abstract: (APS)

In calculating hadronic contributions to precision observables for tests of the Standard Model in lattice QCD, the electromagnetic current plays a central role. Using a Wilson action with O(a) improvement in QCD with Nf flavors, a counterterm must be added to the vector current in order for its on-shell matrix elements to be O(a) improved. In addition, the local vector current, which has support on one lattice site, must be renormalized. At O(a), the breaking of the SU(Nf) symmetry by the quark mass matrix leads to a mixing between the local currents of different quark flavors. We present a nonperturbative calculation of all the required improvement and renormalization constants needed for the local and the conserved electromagnetic current in QCD with Nf=2+1 O(a)-improved Wilson fermions and tree-level Symanzik improved gauge action, with the exception of one coefficient, which we show to be order g06 in lattice perturbation theory. The method is based on the vector and axial Ward identities imposed at finite lattice spacing and in the chiral limit. We make use of lattice ensembles generated as part of the coordinated lattice simulations initiative.

Note:

19 pages, 7 figures. Few typos corrected. Updated to match the published version

Lattice field theories, lattice QCD
current: vector
current: electromagnetic
quantum electrodynamics
fermion: Wilson
fermion: clover
perturbation theory: lattice
renormalization: nonperturbative
quark: flavor: 3
Ward identity: vector

References(25)

Figures(16)

[1]

Review of lattice results concerning low-energy particle physics

S. Aoki
(
- Kyoto U., Yukawa Inst., Kyoto
)
,
Y. Aoki
(
- KMI, Nagoya and
- RIKEN BNL
)
,
D. Becirevic
(
- Orsay, LPT
)
,
C. Bernard
(
- Washington U., St. Louis
)
,
T. Blum
(
- Connecticut U. and
- RIKEN BNL
)

et al.

- Eur.Phys.J.C 77 (2017) 2, 112
•
e-Print:
- 1607.00299
•
DOI:
- 10.1140/epjc/s10052-016-4509-7

[2]

Lattice QCD and the anomalous magnetic moment of the muon

Harvey B. Meyer
(
- U. Mainz, PRISMA
)
,
Hartmut Wittig
(
- U. Mainz, PRISMA
)

- Prog.Part.Nucl.Phys. 104 (2019) 46-96
•
e-Print:
- 1807.09370
•
DOI:
- 10.1016/j.ppnp.2018.09.001

[3]

Improved bilinears in lattice QCD with non-degenerate quarks

Tanmoy Bhattacharya
(
- Los Alamos
)
,
Rajan Gupta
(
- Los Alamos
)
,
Weonjong Lee
(
- Seoul Natl. U.
)
,
Stephen R. Sharpe
(
- Washington U., Seattle
)
,
Jackson M.S. Wu
(
- Washington U., Seattle
)

- Phys.Rev.D 73 (2006) 034504
•
e-Print:
- hep-lat/0511014
•
DOI:
- 10.1103/PhysRevD.73.034504

[4]

Nonperturbative O(a) improvement of the vector current

M. Guagnelli
(
- CERN
)
,
R. Sommer
(
- DESY, Zeuthen
)

- Nucl.Phys.B Proc.Suppl. 63 (1998) 886-888,
•
e-Print:
- hep-lat/9709088
•
DOI:
- 10.1016/S0920-5632(97)00930-4

[5]

Nonperturbative renormalization and improvement of the local vector current for quenched and unquenched Wilson fermions

QCDSF-UKQCD

Collaboration

•

T. Bakeyev
(
- Dubna, JINR
)

et al.

- Phys.Lett.B 580 (2004) 197-208
•
e-Print:
- hep-lat/0305014
•
DOI:
- 10.1016/j.physletb.2003.11.050

[6]

Non-perturbative improvement of the vector current in Wilson lattice QCD

Tim Harris
(
- Helmholtz Inst., Mainz
)
,
Harvey B. Meyer
(
)

- Phys.Rev.D 92 (2015) 114503,
- Phys.Rev.D 99 (2019) 5, 059905 (erratum)
•
e-Print:
- 1506.05248
•
DOI:
- 10.1103/PhysRevD.92.114503

[7]

O(a) improved twisted mass lattice QCD

ALPHA

Collaboration

•

Roberto Frezzotti
(
- Milan Bicocca U. and
- CERN
)

et al.

- JHEP 07 (2001) 048
•
e-Print:
- hep-lat/0104014
•
DOI:
- 10.1088/1126-6708/2001/07/048

[8]

Chiral symmetry and O(a) improvement in lattice QCD

Martin Luscher
(
- DESY
)
,
Stefan Sint
(
- Munich, Max Planck Inst.
)
,
Rainer Sommer
(
- CERN
)
,
Peter Weisz
(
- Munich, Max Planck Inst.
)

- Nucl.Phys.B 478 (1996) 365-400
•
e-Print:
- hep-lat/9605038
•
DOI:
- 10.1016/0550-3213(96)00378-1

[9]

Chiral Symmetry on the Lattice with Wilson Fermions

Marco Bochicchio
(
- Rome U. and
- INFN, Rome
)
,
Luciano Maiani
(
- Rome U. and
- INFN, Rome
)
,
Guido Martinelli
(
- Frascati
)
,
Gian Carlo Rossi
(
- Rome U., Tor Vergata and
- INFN, Rome
)
,
Massimo Testa
(
- INFN, Rome
)

- Nucl.Phys.B 262 (1985) 331,
- Asia Pacific Conf.1987:439,
- Trieste Electroweak 1985:25
•
DOI:
- 10.1016/0550-3213(85)90290-1

[10]

Non-perturbative determination of improvement coefficients using coordinate space correlators in $N_f=2+1$ lattice QCD

Piotr Korcyl
(
- Regensburg U.
)
,
Gunnar S. Bali
(
- Regensburg U.
)

- Phys.Rev.D 95 (2017) 1, 014505
•
e-Print:
- 1607.07090
•
DOI:
- 10.1103/PhysRevD.95.014505

[11]

Nonperturbative renormalization of the axial current in $N_f = 3$ lattice QCD with Wilson fermions and a tree-level improved gauge action

John Bulava
(
- Trinity Coll., Dublin
)
,
Michele Della Morte
(
- Southern Denmark U., CP3-Origins and
- Valencia U., IFIC
)
,
Jochen Heitger
(
- Munster U., ITP
)
,
Christian Wittemeier
(
- Munster U., ITP
)

- Phys.Rev.D 93 (2016) 11, 114513
•
e-Print:
- 1604.05827
•
DOI:
- 10.1103/PhysRevD.93.114513

[12]

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.
)

- Eur.Phys.J.C 79 (2019) 1, 23
•
e-Print:
- 1808.09236
•
DOI:
- 10.1140/epjc/s10052-018-6514-5

[13]

Non-perturbative improvement of the axial current in $N_f$ =3 lattice QCD with Wilson fermions and tree-level improved gauge action

ALPHA

Collaboration

•

John Bulava
(
- Trinity Coll., Dublin
)

et al.

- Nucl.Phys.B 896 (2015) 555-568
•
e-Print:
- 1502.04999
•
DOI:
- 10.1016/j.nuclphysb.2015.05.003

[14]

The Running coupling from the QCD Schrodinger functional: A One loop analysis

Stefan Sint
(
- Munich, Max Planck Inst.
)
,
Rainer Sommer
(
- CERN
)

- Nucl.Phys.B 465 (1996) 71-98
•
e-Print:
- hep-lat/9508012
•
DOI:
- 10.1016/0550-3213(96)00020-X

[15]

Computation of the improvement coefficient c(SW) to one loop with improved gluon actions

- Nucl.Phys.B 540 (1999) 501-519
•
e-Print:
- hep-lat/9808007
•
DOI:
- 10.1016/S0550-3213(98)00742-1

[16]

Perturbative calculation of improvement coefficients to O(g**2a) for bilinear quark operators in lattice QCD

Yusuke Taniguchi
(
- Tsukuba U.
)
,
Akira Ukawa
(
- Tsukuba U.
)

- Phys.Rev.D 58 (1998) 114503
•
e-Print:
- hep-lat/9806015
•
DOI:
- 10.1103/PhysRevD.58.114503

[17]

Simulation of QCD with N $_{f} =$ 2 $+$ 1 flavors of non-perturbatively improved Wilson fermions

Mattia Bruno
(
- DESY, Zeuthen and
- NIC, Zeuthen
)
,
Dalibor Djukanovic
(
- Helmholtz Inst., Mainz
)
,
Georg P. Engel
(
- INFN, Milan Bicocca and
- Milan Bicocca U.
)
,
Anthony Francis
(
- Helmholtz Inst., Mainz
)
,
Gregorio Herdoiza
(
- Madrid, Autonoma U. and
- Madrid, IFT
)

et al.

- JHEP 02 (2015) 043
•
e-Print:
- 1411.3982
•
DOI:
- 10.1007/JHEP02(2015)043

[18]

Lattice QCD with open boundary conditions and twisted-mass reweighting

Martin Luscher
(
- CERN
)
,
Stefan Schaefer
(
- CERN
)

- Comput.Phys.Commun. 184 (2013) 519-528
•
e-Print:
- 1206.2809
•
DOI:
- 10.1016/j.cpc.2012.10.003

[19]

Improvement of $N_f$ = 3 lattice QCD with Wilson fermions and tree-level improved gauge action

John Bulava
(
- CERN and
- Trinity Coll., Dublin
)
,
Stefan Schaefer
(
- CERN
)

- Nucl.Phys.B 874 (2013) 188-197
•
e-Print:
- 1304.7093
•
DOI:
- 10.1016/j.nuclphysb.2013.05.019

[20]

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

[21]

Practical all-to-all propagators for lattice QCD

Justin Foley
(
- Trinity Coll., Dublin
)
,
K. Jimmy Juge
(
- Trinity Coll., Dublin
)
,
Alan O'Cais
(
- Trinity Coll., Dublin
)
,
Mike Peardon
(
- Trinity Coll., Dublin
)
,
Sinead M. Ryan
(
- Trinity Coll., Dublin
)

et al.

- Comput.Phys.Commun. 172 (2005) 145-162
•
e-Print:
- hep-lat/0505023
•
DOI:
- 10.1016/j.cpc.2005.06.008

[22]

Lattice simulations with $N_f=2+1$ improved Wilson fermions at a fixed strange quark mass

RQCD

Collaboration

•

Gunnar S. Bali
(
- Regensburg U. and
- TIFR, Mumbai, Dept. Theor. Phys.
)

et al.

- Phys.Rev.D 94 (2016) 7, 074501
•
e-Print:
- 1606.09039
•
DOI:
- 10.1103/PhysRevD.94.074501

[23]

Mass-improvement of the vector current in three-flavor QCD

Patrick Fritzsch
(
- CERN
)

- JHEP 06 (2018) 015
•
e-Print:
- 1805.07401
•
DOI:
- 10.1007/JHEP06(2018)015

[24]

private communication

P. Korcyl
,
G.S. Bali

[25]

Non-perturbative determination of $c_V, Z_V$ and $Z_S/Z_P$ in $N_f=3$ lattice QCD

Jochen Heitger
(
- Munster U., ITP
)
,
Fabian Joswig
(
- Munster U., ITP
)
,
Anastassios Vladikas
(
- INFN, Rome2 and
- Rome U., Tor Vergata
)
,
Christian Wittemeier
(
- Munster U., ITP
)

- EPJ Web Conf. 175 (2018) 10004
•
e-Print:
- 1711.03924
•
DOI:
- 10.1051/epjconf/201817510004