Abstract
In this paper, we investigate the high-energy behavior of two-point and three-point Green functions of the QCD chiral currents and densities using the framework of the operator product expansion in the chiral limit. In detail, we study the contributions of the quark, gluon, quark-gluon and four-quark condensates to all the relevant non-vanishing three-point correlators.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S.R. Coleman, J. Wess and B. Zumino, Structure of phenomenological Lagrangians. 1., Phys. Rev. 177 (1969) 2239 [INSPIRE].
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].
G. Ecker, J. Gasser, A. Pich and E. de Rafael, The Role of Resonances in Chiral Perturbation Theory, Nucl. Phys. B 321 (1989) 311 [INSPIRE].
V. Cirigliano, G. Ecker, M. Eidemuller, R. Kaiser, A. Pich and J. Portoles, Towards a consistent estimate of the chiral low-energy constants, Nucl. Phys. B 753 (2006) 139 [hep-ph/0603205] [INSPIRE].
K. Kampf, J. Novotny and J. Trnka, On different lagrangian formalisms for vector resonances within chiral perturbation theory, Eur. Phys. J. C 50 (2007) 385 [hep-ph/0608051] [INSPIRE].
P. Masjuan and S. Peris, A Rational approach to resonance saturation in large-Nc QCD, JHEP 05 (2007) 040 [arXiv:0704.1247] [INSPIRE].
L.S. Geng, E. Oset, J.R. Pelaez and L. Roca, Nature of the axial-vector mesons from their N(c) behavior within the chiral unitary approach, Eur. Phys. J. A 39 (2009) 81 [arXiv:0811.1941] [INSPIRE].
S.-Z. Jiang, Y. Zhang, C. Li and Q. Wang, Computation of the p6 order chiral Lagrangian coefficients, Phys. Rev. D 81 (2010) 014001 [arXiv:0907.5229] [INSPIRE].
K. Kampf and J. Novotny, Resonance saturation in the odd-intrinsic parity sector of low-energy QCD, Phys. Rev. D 84 (2011) 014036 [arXiv:1104.3137] [INSPIRE].
J. Nieves, A. Pich and E. Ruiz Arriola, Large-Nc Properties of the ρ and f0 (600) Mesons from Unitary Resonance Chiral Dynamics, Phys. Rev. D 84 (2011) 096002 [arXiv:1107.3247] [INSPIRE].
I.M. Nugent, T. Przedzinski, P. Roig, O. Shekhovtsova and Z. Was, Resonance chiral Lagrangian currents and experimental data for τ− → π−π−π+ντ, Phys. Rev. D 88 (2013) 093012 [arXiv:1310.1053] [INSPIRE].
P. Roig and J.J. Sanz Cillero, Consistent high-energy constraints in the anomalous QCD sector, Phys. Lett. B 733 (2014) 158 [arXiv:1312.6206] [INSPIRE].
H. Czyż, P. Kisza and S. Tracz, Modeling interactions of photons with pseudoscalar and vector mesons , Phys. Rev. D 97 (2018) 016006 [arXiv:1711.00820] [INSPIRE].
A. Guevara, P. Roig and J.J. Sanz-Cillero, Pseudoscalar pole light-by-light contributions to the muon (g − 2) in Resonance Chiral Theory, JHEP 06 (2018) 160 [arXiv:1803.08099] [INSPIRE].
I. Rosell, P. Ruiz-Femenia and J.J. Sanz-Cillero, Resonance saturation of the chiral couplings at NLO in 1/Nc, Phys. Rev. D 79 (2009) 076009 [arXiv:0903.2440] [INSPIRE].
J.J. Sanz-Cillero, Renormalization group equations in resonance chiral theory, Phys. Lett. B 681 (2009) 100 [arXiv:0905.3676] [INSPIRE].
K. Kampf, J. Novotny and J. Trnka, Renormalization and additional degrees of freedom within the chiral effective theory for spin-1 resonances, Phys. Rev. D 81 (2010) 116004 [arXiv:0912.5289] [INSPIRE].
A. Pich, I. Rosell and J.J. Sanz-Cillero, The vector form factor at the next-to-leading order in 1/NC: chiral couplings L9(μ) and C 88(μ) − C 90(μ), JHEP 02 (2011) 109 [arXiv:1011.5771] [INSPIRE].
C. Terschlüsen, B. Strandberg, S. Leupold and F. Eichstädt, Reactions with pions and vector mesons in the sector of odd intrinsic parity, Eur. Phys. J. A 49 (2013) 116 [arXiv:1305.1181] [INSPIRE].
P.C. Bruns, L. Greil and A. Schäfer, Chiral behavior of vector meson self energies, Phys. Rev. D 88 (2013) 114503 [arXiv:1309.3976] [INSPIRE].
C. Terschlüsen and S. Leupold, Renormalization of the low-energy constants of chiral perturbation theory from loops with dynamical vector mesons, Phys. Rev. D 94 (2016) 014021 [arXiv:1603.05524] [INSPIRE].
T. Kadavý, K. Kampf and J. Novotný, Three-point Green Functions of Chiral Currents in the Odd-intrinsic Parity Sector of QCD up to \( \mathcal{O} \)(p6), in preparation.
P. Masjuan, P. Roig and P. Sanchez-Puertas, A different viewpoint on the Hadronic light-by-light tensor short-distance constraints, arXiv:2005.11761 [INSPIRE].
B. Moussallam, Chiral sum rules for parameters of the order six Lagrangian in the W-Z sector and application to pi0, eta, eta-prime decays, Phys. Rev. D 51 (1995) 4939 [hep-ph/9407402] [INSPIRE].
M. Jamin and V. Mateu, OPE-R(chi)T matching at order αs: Hard gluonic corrections to three-point Green functions, JHEP 04 (2008) 040 [arXiv:0802.2669] [INSPIRE].
R. Mertig, M. Böhm and A. Denner, FEYN CALC: Computer algebraic calculation of Feynman amplitudes, Comput. Phys. Commun. 64 (1991) 345 [INSPIRE].
V. Shtabovenko, R. Mertig and F. Orellana, New Developments in FeynCalc 9.0, Comput. Phys. Commun. 207 (2016) 432 [arXiv:1601.01167] [INSPIRE].
H.H. Patel, Package-X: A Mathematica package for the analytic calculation of one-loop integrals, Comput. Phys. Commun. 197 (2015) 276 [arXiv:1503.01469] [INSPIRE].
H.H. Patel, Package-X 2.0: A Mathematica package for the analytic calculation of one-loop integrals, Comput. Phys. Commun. 218 (2017) 66 [arXiv:1612.00009] [INSPIRE].
D. Binosi, J. Collins, C. Kaufhold and L. Theussl, JaxoDraw: A Graphical user interface for drawing Feynman diagrams. Version 2.0 release notes, Comput. Phys. Commun. 180 (2009) 1709 [arXiv:0811.4113] [INSPIRE].
T. Kadavý, K. Kampf and J. Novotný, OPE of Green Functions of Chiral Tensor Currents, in preparation.
J.S. Schwinger, Field theory commutators, Phys. Rev. Lett. 3 (1959) 296 [INSPIRE].
D.J. Gross and R. Jackiw, Construction of covariant and gauge invariant t* products, Nucl. Phys. B 14 (1969) 269 [INSPIRE].
S.B. Treiman, R. Jackiw and D.J. Gross, Lectures on current algebra and its application, Princeton University Press (1972).
S. Pokorski, Gauge Field Theories, Cambridge University Press (2000).
V. Cirigliano, G. Ecker, M. Eidemuller, A. Pich and J. Portoles, The 〈VAP〉 Green function in the resonance region, Phys. Lett. B 596 (2004) 96 [hep-ph/0404004] [INSPIRE].
M. Knecht, S. Peris, M. Perrottet and E. de Rafael, New nonrenormalization theorems for anomalous three point functions, JHEP 03 (2004) 035 [hep-ph/0311100] [INSPIRE].
B. Moussallam, A Sum rule approach to the violation of Dashen’s theorem, Nucl. Phys. B 504 (1997) 381 [hep-ph/9701400] [INSPIRE].
M. Knecht and A. Nyffeler, Resonance estimates of O(p6) low-energy constants and QCD short distance constraints, Eur. Phys. J. C 21 (2001) 659 [hep-ph/0106034] [INSPIRE].
V. Cirigliano, G. Ecker, M. Eidemuller, R. Kaiser, A. Pich and J. Portoles, The 〈SPP〉 Green function and SU(3) breaking in Kℓ3 decays, JHEP 04 (2005) 006 [hep-ph/0503108] [INSPIRE].
P.D. Ruiz-Femenia, A. Pich and J. Portoles, Odd intrinsic parity processes within the resonance effective theory of QCD, JHEP 07 (2003) 003 [hep-ph/0306157] [INSPIRE].
L.-Y. Dai, J. Fuentes-Martín and J. Portolés, Scalar-involved three-point Green functions and their phenomenology, Phys. Rev. D 99 (2019) 114015 [arXiv:1902.10411] [INSPIRE].
K.G. Wilson, The Renormalization Group and Strong Interactions, Phys. Rev. D 3 (1971) 1818 [INSPIRE].
M.S. Dubovikov and A.V. Smilga, Analytical Properties of the Quark Polarization Operator in an External Selfdual Field, Nucl. Phys. B 185 (1981) 109 [INSPIRE].
W. Hubschmid and S. Mallik, Operator expansion at short distance in QCD, Nucl. Phys. B 207 (1982) 29 [INSPIRE].
M.A. Shifman, A.I. Vainshtein and V.I. Zakharov, QCD and Resonance Physics. Theoretical Foundations, Nucl. Phys. B 147 (1979) 385 [INSPIRE].
J. Govaerts, L.J. Reinders, F. de Viron and J. Weyers, L = 1 Mesons and the Four Quark Condensates in QCD Sum Rules, Nucl. Phys. B 283 (1987) 706 [INSPIRE].
L.J. Reinders, H. Rubinstein and S. Yazaki, Hadron Properties from QCD Sum Rules, Phys. Rept. 127 (1985) 1 [INSPIRE].
V. Fock, Proper time in classical and quantum mechanics, Phys. Z. Sowjetunion 12 (1937) 404 [INSPIRE].
J.S. Schwinger, On gauge invariance and vacuum polarization, Phys. Rev. 82 (1951) 664 [INSPIRE].
S. Narison, QCD as a Theory of Hadrons: From Partons to Confinement, Camb. Monogr. Part. Phys. Nucl. Phys. Cosmol. 17 (2007) 1 [hep-ph/0205006] [INSPIRE].
V. Elias, T.G. Steele and M.D. Scadron, \( q\overline{q} \) and Higher Dimensional Condensate Contributions to the Nonperturbative Quark Mass, Phys. Rev. D 38 (1988) 1584 [INSPIRE].
P. Pascual and R. Tarrach, QCD: renormalization for the practitioner, Lect. Notes Phys. 194 (1984) 1 [INSPIRE].
V. Elias, T.G. Steele, M.D. Scadron and R. Tarrach, Truncation of the Operator Product Expansion for the \( \left\langle q\overline{q}\right\rangle \) Condensate Component of the Quark Mass, Phys. Rev. D 34 (1986) 3537 [INSPIRE].
V. Elias, M. Scadron and R. Tarrach, Gauge Independence of Subleading Contributions to the Operator Product Pole Mass, Phys. Lett. B 173 (1986) 184 [INSPIRE].
B.L. Ioffe, V.S. Fadin and L.N. Lipatov, Quantum chromodynamics: Perturbative and nonperturbative aspects, Camb. Monogr. Part. Phys. Nucl. Phys. Cosmol. 30 (2010) 1 [INSPIRE].
E. Bagan, M.R. Ahmady, V. Elias and T.G. Steele, Equivalence of plane wave and coordinate space techniques in the operator product expansion, Z. Phys. C 61 (1994) 157 [INSPIRE].
G. ’t Hooft and M.J.G. Veltman, Scalar One Loop Integrals, Nucl. Phys. B 153 (1979) 365 [INSPIRE].
S.L. Adler, Axial vector vertex in spinor electrodynamics, Phys. Rev. 177 (1969) 2426 [INSPIRE].
J.S. Bell and R. Jackiw, A PCAC puzzle: π0 → γγ in the σ model, Nuovo Cim. A 60 (1969) 47 [INSPIRE].
C. Corianò, N. Irges and S. Morelli, Stuckelberg axions and the effective action of anomalous Abelian models. 1. A Unitarity analysis of the Higgs-axion mixing, JHEP 07 (2007) 008 [hep-ph/0701010] [INSPIRE].
R. Armillis, C. Corianò, L. Delle Rose and M. Guzzi, Anomalous U(1) Models in Four and Five Dimensions and their Anomaly Poles, JHEP 12 (2009) 029 [arXiv:0905.0865] [INSPIRE].
V. Mateu and J. Portoles, Form-factors in radiative pion decay, Eur. Phys. J. C 52 (2007) 325 [arXiv:0706.1039] [INSPIRE].
V.A. Novikov, M.A. Shifman, A.I. Vainshtein and V.I. Zakharov, Calculations in External Fields in Quantum Chromodynamics. Technical Review, Fortsch. Phys. 32 (1984) 585 [INSPIRE].
B.L. Ioffe and A.V. Smilga, Meson Widths and Form-Factors at Intermediate Momentum Transfer in Nonperturbative QCD, Nucl. Phys. B 216 (1983) 373 [INSPIRE].
S.N. Nikolaev and A.V. Radyushkin, Method for Computing Higher Gluonic Power Corrections to QCD Charmonium Sum Rules, Phys. Lett. B 110 (1982) 476 [Erratum ibid. 116 (1982) 469] [INSPIRE].
M. Knecht, On some short-distance properties of the fourth-rank hadronic vacuum polarization tensor and the anomalous magnetic moment of the muon, JHEP 08 (2020) 056 [arXiv:2005.09929] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2006.13006
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Kadavý, T., Kampf, K. & Novotný, J. OPE of Green functions of chiral currents. J. High Energ. Phys. 2020, 142 (2020). https://doi.org/10.1007/JHEP10(2020)142
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2020)142