Perturbative renormalization factors and O(a{sup 2}) corrections for lattice four-fermion operators with improved fermion/gluon actions

Journal Article · Fri Apr 01 00:00:00 EDT 2011 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.83.074503· OSTI ID:21537729

Constantinou, Martha; Panagopoulos, Haralambos; Skouroupathis, Apostolos; Stylianou, Fotos ^[1]; Dimopoulos, Petros ^[2]; Frezzotti, Roberto ^[3]; Lubicz, Vittorio ^[4]

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1. Department of Physics, University of Cyprus, P.O. Box 20537, Nicosia CY-1678 (Cyprus)
2. Dipartimento di Fisica, Sapienza, Universita di Roma Piazzale A. Moro, I-00185 Rome (Italy)
3. Dipartimento di Fisica, Universita di Roma 'Tor Vergata' Via della Ricerca Scientifica 1, I-00133 Rome (Italy)
4. Dipartimento di Fisica, Universita Roma Tre Via della Vasca Navale 84, I-00146 Rome (Italy)

In this work we calculate the corrections to the amputated Green's functions of four-fermion operators, in 1-loop lattice perturbation theory. One of the novel aspects of our calculations is that they are carried out to second order in the lattice spacing, O(a{sup 2}). We employ the Wilson/clover action for massless fermions (also applicable for the twisted mass action in the chiral limit) and a family of Symanzik improved actions for gluons. Our calculations have been carried out in a general covariant gauge. Results have been obtained for several popular choices of values for the Symanzik coefficients (Plaquette, Tree-level Symanzik, Iwasaki, TILW and DBW2 action). While our Green's function calculations regard any pointlike four-fermion operators which do not mix with lower dimension ones, we pay particular attention to {Delta}F=2 operators, both parity conserving and parity violating (F stands for flavor: S, C, B). By appropriately projecting those bare Green's functions we compute the perturbative renormalization constants for a complete basis of four-fermion operators and we study their mixing pattern. For some of the actions considered here, even O(a{sup 0}) results did not exist in the literature to date. The correction terms which we calculate (along with our previous O(a{sup 2}) calculation of Z{sub {Psi}}[M. Constantinou, V. Lubicz, H. Panagopoulos, and F. Stylianou, J. High Energy Phys. 10 (2009) 064.][M. Constantinou, P. Dimopoulos, R. Frezzotti, G. Herdoiza, K. Jansen, V. Lubicz, H. Panagopoulos, G. C. Rossi, S. Simula, F. Stylianou, and A. Vladikas, J. High Energy Phys. 08 (2010) 068.][C. Alexandrou, M. Constantinou, T. Korzec, H. Panagopoulos, and F. Stylianou (unpublished).]) are essential ingredients for minimizing the lattice artifacts which are present in nonperturbative evaluations of renormalization constants with the RI{sup '}-MOM method. Our perturbative results, for the matrix elements of {Delta}F=2 operators and for the corresponding renormalization matrices, depend on a large number of parameters: coupling constant, number of colors, lattice spacing, external momentum, clover parameter, Symanzik coefficients, gauge parameter. To make these results most easily accessible to the reader, we have included them in the distribution package of this paper, as an ASCII file named: 4-fermi.m; the file is best perused as Mathematica input. The main results of this work have been applied to improve nonperturbative estimates of the B{sub K}-parameter in N{sub F}=2 twisted mass lattice QCD [M. Constantinou, P. Dimopoulos, R. Frezzotti, K. Jansen, V. Gimenez, V. Lubicz, F. Mescia, H. Panagopoulos, M. Papinutto, G. C. Rossi, S. Simula, A. Skouroupathis, F. Stylianou, and A. Vladikas, arXiv:1009.5606.].

• OSTI ID: 21537729
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 7 Vol. 83; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BOSONS
CHIRALITY
COMPOSITE MODELS
COMPUTERIZED SIMULATION
CONSTRUCTIVE FIELD THEORY
CORRECTIONS
COUPLING CONSTANTS
DISTRIBUTION
EVALUATION
FERMIONS
FIELD THEORIES
FLAVOR MODEL
FUNCTIONS
GLUONS
GREEN FUNCTION
LATTICE FIELD THEORY
MASS
MATHEMATICAL MODELS
MATRIX ELEMENTS
PARITY
PARTICLE MODELS
PARTICLE PROPERTIES
PERTURBATION THEORY
QUANTUM CHROMODYNAMICS
QUANTUM FIELD THEORY
QUARK MODEL
RENORMALIZATION
SIMULATION