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Title: Nonperturbative renormalization of composite operators with overlap fermions

Abstract

We compute nonperturbatively the renormalization constants of composite operators on a quenched 16{sup 3}x28 lattice with lattice spacing a=0.20 fm for the overlap fermion by using the regularization-independent (RI) scheme. The quenched gauge configurations were generated with the Iwasaki action. We test the relations Z{sub A}=Z{sub V} and Z{sub S}=Z{sub P} and find that they agree well (less than 1%) above {mu}=1.6 GeV. We also perform a Renormalization Group (RG) analysis at the next-to-next-to-leading order and match the renormalization constants to the MS scheme. The wave function renormalization Z{sub {psi}} is determined from the vertex function of the axial current and Z{sub A} from the chiral Ward identity. Finally, we examine the finite quark mass behavior for the renormalization factors of the quark bilinear operators. We find that the (pa){sup 2} errors of the vertex functions are small and the quark mass dependence of the renormalization factors to be quite weak.

Authors:
 [1];  [2];  [3];  [4]; ; ; ;  [3];  [5]; ;  [6]
  1. Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University, Hangzhou 310027 (China)
  2. (Australia)
  3. Department of Physics and Astronomy, University of Kentucky, Lexington, Kentucky 40506 (United States)
  4. (United States)
  5. Center for Nuclear Studies, Department of Physics, George Washington University, Washington, D.C. 20052 (United States)
  6. Special Research Center for the Subatomic Structure of Matter and Department of Physics, University of Adelaide, Adelaide, SA 5005 (Australia)
Publication Date:
OSTI Identifier:
20774450
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. D, Particles Fields; Journal Volume: 72; Journal Issue: 11; Other Information: DOI: 10.1103/PhysRevD.72.114509; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ALGEBRAIC CURRENTS; CHIRALITY; GAUGE INVARIANCE; GEV RANGE; LATTICE FIELD THEORY; QUANTUM CHROMODYNAMICS; QUARKS; RENORMALIZATION; REST MASS; VERTEX FUNCTIONS; WARD IDENTITY; WAVE FUNCTIONS

Citation Formats

Zhang, J.B., Special Research Center for the Subatomic Structure of Matter and Department of Physics, University of Adelaide, Adelaide, SA 5005, Mathur, N., Jefferson Lab, 12000 Jefferson Avenue, Newport News, Virginia 23606, Dong, S.J., Draper, T., Horvath, I., Liu, K.F., Lee, F.X., Leinweber, D.B., and Williams, A.G.. Nonperturbative renormalization of composite operators with overlap fermions. United States: N. p., 2005. Web. doi:10.1103/PhysRevD.72.114509.
Zhang, J.B., Special Research Center for the Subatomic Structure of Matter and Department of Physics, University of Adelaide, Adelaide, SA 5005, Mathur, N., Jefferson Lab, 12000 Jefferson Avenue, Newport News, Virginia 23606, Dong, S.J., Draper, T., Horvath, I., Liu, K.F., Lee, F.X., Leinweber, D.B., & Williams, A.G.. Nonperturbative renormalization of composite operators with overlap fermions. United States. doi:10.1103/PhysRevD.72.114509.
Zhang, J.B., Special Research Center for the Subatomic Structure of Matter and Department of Physics, University of Adelaide, Adelaide, SA 5005, Mathur, N., Jefferson Lab, 12000 Jefferson Avenue, Newport News, Virginia 23606, Dong, S.J., Draper, T., Horvath, I., Liu, K.F., Lee, F.X., Leinweber, D.B., and Williams, A.G.. Thu . "Nonperturbative renormalization of composite operators with overlap fermions". United States. doi:10.1103/PhysRevD.72.114509.
@article{osti_20774450,
title = {Nonperturbative renormalization of composite operators with overlap fermions},
author = {Zhang, J.B. and Special Research Center for the Subatomic Structure of Matter and Department of Physics, University of Adelaide, Adelaide, SA 5005 and Mathur, N. and Jefferson Lab, 12000 Jefferson Avenue, Newport News, Virginia 23606 and Dong, S.J. and Draper, T. and Horvath, I. and Liu, K.F. and Lee, F.X. and Leinweber, D.B. and Williams, A.G.},
abstractNote = {We compute nonperturbatively the renormalization constants of composite operators on a quenched 16{sup 3}x28 lattice with lattice spacing a=0.20 fm for the overlap fermion by using the regularization-independent (RI) scheme. The quenched gauge configurations were generated with the Iwasaki action. We test the relations Z{sub A}=Z{sub V} and Z{sub S}=Z{sub P} and find that they agree well (less than 1%) above {mu}=1.6 GeV. We also perform a Renormalization Group (RG) analysis at the next-to-next-to-leading order and match the renormalization constants to the MS scheme. The wave function renormalization Z{sub {psi}} is determined from the vertex function of the axial current and Z{sub A} from the chiral Ward identity. Finally, we examine the finite quark mass behavior for the renormalization factors of the quark bilinear operators. We find that the (pa){sup 2} errors of the vertex functions are small and the quark mass dependence of the renormalization factors to be quite weak.},
doi = {10.1103/PhysRevD.72.114509},
journal = {Physical Review. D, Particles Fields},
number = 11,
volume = 72,
place = {United States},
year = {Thu Dec 01 00:00:00 EST 2005},
month = {Thu Dec 01 00:00:00 EST 2005}
}
  • We compute non-perturbatively the renormalization constants of composite operators on a quenched 16{sup 3} x 28 lattice with lattice spacing a = 0.20 fm for the overlap fermion by using the regularization independent (RI) scheme. The quenched gauge configurations were generated with the Iwasaki action. We test the relations Z{sub A} = Z{sub V} and Z{sub S} = Z{sub P} and find that they agree well (less than 1%) above {mu} = 1.6 GeV. We also perform a Renormalization Group (RG) analysis at the next-to-next-to-leading order and match the renormalization constants to the {ovr MS} scheme. The wave-function renormalization Z{submore » {psi}} is determined from the vertex function of the axial current and Z{sub A} from the chiral Ward identity. Finally, we examine the finite quark mass behavior for the renormalization factors of the quark bilinear operators. We find that the (pa){sup 2} errors of the vertex functions are small and the quark mass dependence of the renormalization factors to be quite weak.« less
  • Using the nonperturbative renormalization technique, we calculate the renormalization factors for quark bilinear operators made of overlap fermions on the lattice. The background gauge field is generated by the JLQCD and TWQCD Collaborations, including dynamical effects of two or 2+1 flavors of light quarks on a 16{sup 3}x32 or 16{sup 3}x48 lattice at lattice spacing around 0.1 fm. By reducing the quark mass close to the chiral limit, where the finite volume system enters the so-called {epsilon} regime, the unwanted effect of spontaneous chiral symmetry breaking on the renormalization factors is suppressed. On the lattices in the conventional p regime,more » this effect is precisely subtracted by separately calculating the contributions from the chiral condensate.« less
  • We present nonperturbative renormalization constants of fermionic bilinears on the lattice in the quenched approximation at {beta}=6.1 using an overlap [H. Neuberger, Phys. Lett. B 417, 141 (1998)] fermion action with hypercubic (HYP)-blocked links. We consider the effects of the exact zero modes of the Dirac operator and find they are important in calculating the renormalization constants of the scalar and pseudoscalar density. The results are given in the RI' and MS schemes and compared to perturbative calculations.
  • The renormalization of the most general dimension-six four-fermion operators without power subtractions is studied at one loop in lattice perturbation theory using overlap fermions. As expected, operators with different chirality do not mix among themselves and parity-conserving and parity-violating multiplets renormalize in the same way. The renormalization constants of unimproved and improved operators are also the same. These mixing factors are necessary to determine the physical matrix elements relevant to many phenomenological applications of weak interactions. The most important are the K{sup 0}-{bar K}{sup 0} and B{sup 0}-{bar B}{sup 0} mixings in the standard model and beyond, the {Delta}I=1/2 rulemore » and {epsilon}{prime}/{epsilon}.« less
  • We present a calculation of the renormalization coefficients of the quark bilinear operators and the K-K mixing parameter B{sub K}. The coefficients relating the bare lattice operators to those in the RI/MOM scheme are computed nonperturbatively and then matched perturbatively to the MS scheme. The coefficients are calculated on the RBC/UKQCD 2+1 flavor dynamical lattice configurations. Specifically we use a 16{sup 3}x32 lattice volume, the Iwasaki gauge action at {beta}=2.13 and domain wall fermions with L{sub s}=16.