Critical hopping parameter in <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>O</mi><mo>(</mo><mi>a</mi><mo>)</mo><mn></mn></math></span> improved lattice QCD

H. Panagopoulos; Y. Proestos

doi:10.1103/PhysRevD.65.014511

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Critical hopping parameter in $O (a)$ improved lattice QCD

H. Panagopoulos^* and Y. Proestos^†

Department of Physics, University of Cyprus, P.O. Box 20537, Nicosia CY-1678, Cyprus

^*Email address: haris@ucy.ac.cy
^†Present address: Department of Physics, Ohio State University, Columbus, OH 43210. Email address: yiannis@mps.ohio-state.edu

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Phys. Rev. D 65, 014511 – Published 12 December, 2001

DOI: https://doi.org/10.1103/PhysRevD.65.014511

Abstract

We calculate the critical value of the hopping parameter, $κ_{c},$ in $O (a)$ improved lattice QCD, to two loops in perturbation theory. We employ the Sheikholeslami-Wohlert (clover) improved action for Wilson fermions. The quantity which we study is a typical case of a vacuum expectation value resulting in an additive renormalization; as such, it is characterized by a power (linear) divergence in the lattice spacing, and its calculation lies at the limits of applicability of perturbation theory. The dependence of our results on the number of colors N, the number of fermionic flavors, $N_{f},$ and the clover parameter $c_{SW}$ is shown explicitly. We compare our results with nonperturbative evaluations of $κ_{c}$ coming from Monte Carlo simulations.

References (15)

B. Sheikholeslami and R. Wohlert, Nucl. Phys. B259, 572 (1985).
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[c1] B. Sheikholeslami and R. Wohlert, Nucl. Phys. B259, 572 (1985).

[c2] E. Follana and H. Panagopoulos, Phys. Rev. D 63, 017501 (2001).

[c3] S. Caracciolo, A. Pelissetto, and A. Rago, Phys. Rev. D 64, 094506 (2001).

[c4] A. Bode, P. Weisz, and U. Wolff, Nucl. Phys. B576, 517 (2000).

[c5] C. Christou, A. Feo, H. Panagopoulos, and E. Vicari, Nucl. Phys. B525, 387 (1998).

[c6] A. Bode and H. Panagopoulos, “The three-loop $β$ -function of QCD with the clover action,” hep-lat/0110211.

[c7] M. Lüscher, S. Sint, R. Sommer, P. Weisz, and U. Wolff, Nucl. Phys. B491, 323 (1997).

[c8] UKQCD Collaboration, K. C. Bowler et al., Phys. Rev. D 62, 054506 (2000).

[c9] K. Jansen and R. Sommer, Nucl. Phys. B530, 185 (1998).

[c10] UKQCD Collaboration, C. R. Allton et al., hep-lat/0107021.

[c11] H. Panagopoulos and E. Vicari, Phys. Rev. D 58, 114501 (1998).

[c12] H. Panagopoulos and E. Vicari, Phys. Rev. D 59, 057503 (1999).

[c13] H. Panagopoulos and E. Vicari, Nucl. Phys. B (Proc. Suppl.) 83, 884 (2000).

[c14] G. Parisi, in High-Energy Physics—1980, XX International Conference, Madison, 1980, edited by L. Durand and L. G. Pondrom (AIP, New York, 1981).

[c15] G. P. Lepage and P. B. Mackenzie, Phys. Rev. D 48, 2250 (1993).

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Critical hopping parameter in O(a) improved lattice QCD

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Critical hopping parameter in $O (a)$ improved lattice QCD