Truncation of the operator-product expansion for the <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>〈</mi><mi>q</mi><mrow><mrow><mover><mrow><mi>q</mi></mrow><mrow><mi>¯</mi></mrow></mover></mrow></mrow><mi>〉</mi></math></span>-condensate component of the quark mass

V. Elias; T. Steele; M. D. Scadron; R. Tarrach

doi:10.1103/PhysRevD.34.3537

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Truncation of the operator-product expansion for the $〈 q \bar{q} 〉$ -condensate component of the quark mass

V. Elias and T. Steele

M. D. Scadron

R. Tarrach

Department of Applied Mathematics, University of Western Ontario, London, Ontario, Canada N6A5B9

Physics Department, University of Arizona, Tucson, Arizona 85721

Department de Física Teorica, Universitat Autonoma de Barcelona, Bellaterra, Barcelona, Spain

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Phys. Rev. D 34, 3537(R) – Published 1 December, 1986

DOI: https://doi.org/10.1103/PhysRevD.34.3537

Abstract

Quark-condensate contributions to $m_{dyn}$ , the quark mass generated by the dynamical breakdown of chiral symmetry, are shown to arise from only the first two terms of the operator-product expansion (OPE) for the appropriate $O (g^{2})$ nonperturbative vacuum expectation value. Since the $\frac{m}{| p |}$ expansion parameter of the OPE is unity on the gauge-invariant $p = m_{dyn}$ propagator pole, such truncation of OPE contributions is an essential support to the calculation of $m_{dyn}$ .

References (7)

H. D. Politzer, Nucl. Phys. B117, 397 (1976)
P. Pascual and E. de Rafael, Z. Phys. C 12, 127 (1982)
V. Elias, M. D. Scadron, and R. Tarrach, Phys. Lett. 162B, 176 (1985)
V. A. Fock, Phys. Z. Sowjetunion 12, 404 (1937) J. Schwinger, Particles and Fields (Addison-Wesley, New York, 1970) M. A. Shifman, Nucl. Phys. B173, 13 (1980) C. Cronstroem, Phys. Lett. 90B, 267 (1980) M. Dubikov and A. Smilga, Nucl. Phys. B185, 109 (1981)
P. Pascual and R. Tarrach, in QCD: Renormalization for the Practitioner, Lecture Notes in Physics, Vol. 194, edited by H. Araki, J. Ehlers, K. Hepp, J. Kippenhahn, H. A. Weidenmüller, and J. Zittartz (Springer, Berlin, 1984), pp. 168-172 and 179-184
V. Elias, M. D. Scadron, and R. Tarrach, Phys. Lett. 173B, 184 (1986)
V. Elias and M. D. Scadron, Phys. Rev. D 30, 647 (1984)

[c1] H. D. Politzer, Nucl. Phys. B117, 397 (1976)

[c2] P. Pascual and E. de Rafael, Z. Phys. C 12, 127 (1982)

[c3] V. Elias, M. D. Scadron, and R. Tarrach, Phys. Lett. 162B, 176 (1985)

[c4] V. A. Fock, Phys. Z. Sowjetunion 12, 404 (1937) J. Schwinger, Particles and Fields (Addison-Wesley, New York, 1970) M. A. Shifman, Nucl. Phys. B173, 13 (1980) C. Cronstroem, Phys. Lett. 90B, 267 (1980) M. Dubikov and A. Smilga, Nucl. Phys. B185, 109 (1981)

[c5] P. Pascual and R. Tarrach, in QCD: Renormalization for the Practitioner, Lecture Notes in Physics, Vol. 194, edited by H. Araki, J. Ehlers, K. Hepp, J. Kippenhahn, H. A. Weidenmüller, and J. Zittartz (Springer, Berlin, 1984), pp. 168-172 and 179-184

[c6] V. Elias, M. D. Scadron, and R. Tarrach, Phys. Lett. 173B, 184 (1986)

[c7] V. Elias and M. D. Scadron, Phys. Rev. D 30, 647 (1984)

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Truncation of the operator-product expansion for the $〈 q \bar{q} 〉$ -condensate component of the quark mass

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Truncation of the operator-product expansion for the 〈qq¯〉-condensate component of the quark mass

Abstract

References (7)

Truncation of the operator-product expansion for the $〈 q \bar{q} 〉$ -condensate component of the quark mass