Abstract
When matter fields are included in chiral perturbation theory, the nonvanishing mass in the chiral limit introduces a new energy scale so that the loop diagrams including such matter field propagators spoil the usual power counting. However, the power counting breaking terms can be absorbed into counterterms in the chiral Lagrangian. In this paper, we systematically derive these terms to leading one-loop order (next-to-next-to leading order in the chiral expansion) at once by calculating the generating functional using the path integral. They are then absorbed by counterterms in the next-to-leading order Lagrangian. The method can be extended to calculating power counting breaking terms for other matter fields.
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References
S. Weinberg, Phenomenological Lagrangians, Physica A 96 (1979) 327 [INSPIRE].
J. Gasser and H. Leutwyler, Chiral Perturbation Theory to One Loop, Annals Phys. 158 (1984) 142 [INSPIRE].
J. Gasser and H. Leutwyler, Chiral Perturbation Theory: Expansions in the Mass of the Strange Quark, Nucl. Phys. B 250 (1985) 465 [INSPIRE].
S.L. Adler, Axial vector vertex in spinor electrodynamics, Phys. Rev. 177 (1969) 2426 [INSPIRE].
G.A. Christos, Chiral Symmetry and the U(1) Problem, Phys. Rept. 116 (1984) 251 [INSPIRE].
J. Gasser, M.E. Sainio and A. Svarc, Nucleons with Chiral Loops, Nucl. Phys. B 307 (1988) 779 [INSPIRE].
A. Roessl, Pion kaon scattering near the threshold in chiral SU(2) perturbation theory, Nucl. Phys. B 555 (1999) 507 [hep-ph/9904230] [INSPIRE].
E.E. Jenkins and A.V. Manohar, Baryon chiral perturbation theory using a heavy fermion Lagrangian, Phys. Lett. B 255 (1991) 558 [INSPIRE].
V. Bernard, N. Kaiser, J. Kambor and U.-G. Meißner, Chiral structure of the nucleon, Nucl. Phys. B 388 (1992) 315 [INSPIRE].
T. Becher and H. Leutwyler, Baryon chiral perturbation theory in manifestly Lorentz invariant form, Eur. Phys. J. C 9 (1999) 643 [hep-ph/9901384] [INSPIRE].
T. Fuchs, J. Gegelia, G. Japaridze and S. Scherer, Renormalization of relativistic baryon chiral perturbation theory and power counting, Phys. Rev. D 68 (2003) 056005 [hep-ph/0302117] [INSPIRE].
V. Bernard, N. Kaiser and U.-G. Meißner, Chiral dynamics in nucleons and nuclei, Int. J. Mod. Phys. E 4 (1995) 193 [hep-ph/9501384] [INSPIRE].
V. Bernard, N. Kaiser, U.-G. Meißner and A. Schmidt, Aspects of nucleon Compton scattering, Z. Phys. A 348 (1994) 317 [hep-ph/9311354] [INSPIRE].
H.-B. Tang, A new approach to chiral perturbation theory for matter fields, hep-ph/9607436 [INSPIRE].
P.J. Ellis and H.-B. Tang, Pion nucleon scattering in a new approach to chiral perturbation theory, Phys. Rev. C 57 (1998) 3356 [hep-ph/9709354] [INSPIRE].
J. Gegelia, G.S. Japaridze and K.S. Turashvili, Calculation of loop integrals by dimensional counting, Theor. Math. Phys. 101 (1994) 1313 [INSPIRE].
F.-K. Guo, C. Hanhart and U.-G. Meißner, Interactions between heavy mesons and Goldstone bosons from chiral dynamics, Eur. Phys. J. A 40 (2009) 171 [arXiv:0901.1597] [INSPIRE].
D.-L. Yao, M.-L. Du, F.-K. Guo and U.-G. Meißner, One-loop analysis of the interactions between charmed mesons and Goldstone bosons, JHEP 11 (2015) 058 [arXiv:1502.05981] [INSPIRE].
M.-L. Du, F.-K. Guo and U.-G. Meißner, One-loop renormalization of the chiral Lagrangian for spinless matter fields in the SU(N) fundamental representation, arXiv:1607.00822 [INSPIRE].
G. Ecker, Chiral perturbation theory, Prog. Part. Nucl. Phys. 35 (1995) 1 [hep-ph/9501357] [INSPIRE].
J. Bijnens, Chiral perturbation theory beyond one loop, Prog. Part. Nucl. Phys. 58 (2007) 521 [hep-ph/0604043] [INSPIRE].
J. Wess and B. Zumino, Consequences of anomalous Ward identities, Phys. Lett. B 37 (1971) 95 [INSPIRE].
E. Witten, Current Algebra, Baryons and Quark Confinement, Nucl. Phys. B 223 (1983) 433 [INSPIRE].
R. Unterdorfer and G. Ecker, Generating functional for strong and nonleptonic weak interactions, JHEP 10 (2005) 017 [hep-ph/0507173] [INSPIRE].
M.R. Schindler, J. Gegelia and S. Scherer, Infrared and extended on mass shell renormalization of two loop diagrams, Nucl. Phys. B 682 (2004) 367 [hep-ph/0310207] [INSPIRE].
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ArXiv ePrint: 1609.06134
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Du, ML., Guo, FK. & Meißner, UG. Subtraction of power counting breaking terms in chiral perturbation theory: spinless matter fields. J. High Energ. Phys. 2016, 122 (2016). https://doi.org/10.1007/JHEP10(2016)122
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DOI: https://doi.org/10.1007/JHEP10(2016)122