Abstract
We present a diagrammatic formulation of recently-revived covariant functional approaches to one-loop matching from an ultraviolet (UV) theory to a low-energy effective field theory. Various terms following from a covariant derivative expansion (CDE) are represented by diagrams which, unlike conventional Feynman diagrams, involve gauge-covariant quantities and are thus dubbed “covariant diagrams.” The use of covariant diagrams helps organize and simplify one-loop matching calculations, which we illustrate with examples. Of particular interest is the derivation of UV model-independent universal results, which reduce matching calculations of specific UV models to applications of master formulas. We show how such derivation can be done in a more concise manner than the previous literature, and discuss how additional structures that are not directly captured by existing universal results, including mixed heavy-light loops, open covariant derivatives, and mixed statistics, can be easily accounted for.
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References
M.K. Gaillard, The Effective One Loop Lagrangian With Derivative Couplings, Nucl. Phys. B 268 (1986) 669 [INSPIRE].
L.-H. Chan, Derivative Expansion for the One Loop Effective Actions With Internal Symmetry, Phys. Rev. Lett. 57 (1986) 1199 [INSPIRE].
O. Cheyette, Effective Action for the Standard Model With Large Higgs Mass, Nucl. Phys. B 297 (1988) 183 [INSPIRE].
B. Henning, X. Lu and H. Murayama, How to use the Standard Model effective field theory, JHEP 01 (2016) 023 [arXiv:1412.1837] [INSPIRE].
C.-W. Chiang and R. Huo, Standard Model Effective Field Theory: Integrating out a Generic Scalar, JHEP 09 (2015) 152 [arXiv:1505.06334] [INSPIRE].
R. Huo, Standard Model Effective Field Theory: Integrating out Vector-Like Fermions, JHEP 09 (2015) 037 [arXiv:1506.00840] [INSPIRE].
R. Huo, Effective Field Theory of Integrating out Sfermions in the MSSM: Complete One-Loop Analysis, arXiv:1509.05942 [INSPIRE].
A. Drozd, J. Ellis, J. Quevillon and T. You, The Universal One-Loop Effective Action, JHEP 03 (2016) 180 [arXiv:1512.03003] [INSPIRE].
F. del Aguila, Z. Kunszt and J. Santiago, One-loop effective lagrangians after matching, Eur. Phys. J. C 76 (2016) 244 [arXiv:1602.00126] [INSPIRE].
M. Boggia, R. Gomez-Ambrosio and G. Passarino, Low energy behaviour of standard model extensions, JHEP 05 (2016) 162 [arXiv:1603.03660] [INSPIRE].
B. Henning, X. Lu and H. Murayama, One-loop Matching and Running with Covariant Derivative Expansion, arXiv:1604.01019 [INSPIRE].
S.A.R. Ellis, J. Quevillon, T. You and Z. Zhang, Mixed heavy-light matching in the Universal One-Loop Effective Action, Phys. Lett. B 762 (2016) 166 [arXiv:1604.02445] [INSPIRE].
J. Fuentes-Martin, J. Portoles and P. Ruiz-Femenia, Integrating out heavy particles with functional methods: a simplified framework, JHEP 09 (2016) 156 [arXiv:1607.02142] [INSPIRE].
S. Dittmaier and C. Grosse-Knetter, Deriving nondecoupling effects of heavy fields from the path integral: A heavy Higgs field in an SU(2) gauge theory, Phys. Rev. D 52 (1995) 7276 [hep-ph/9501285] [INSPIRE].
S. Dittmaier and C. Grosse-Knetter, Integrating out the standard Higgs field in the path integral, Nucl. Phys. B 459 (1996) 497 [hep-ph/9505266] [INSPIRE].
M. Beneke and V.A. Smirnov, Asymptotic expansion of Feynman integrals near threshold, Nucl. Phys. B 522 (1998) 321 [hep-ph/9711391] [INSPIRE].
V.A. Smirnov, Applied asymptotic expansions in momenta and masses, Springer Tracts Mod. Phys. 177 (2002) 1.
B. Jantzen, Foundation and generalization of the expansion by regions, JHEP 12 (2011) 076 [arXiv:1111.2589] [INSPIRE].
J. Santiago, One-loop effective Lagrangians after matching, talk at Planck 2016, Valencia, Spain, 23-27 May 2016.
M.E. Peskin and D.V. Schroeder, An Introduction to quantum field theory, Addison-Wesley, Reading, U.S.A. (1995).
L.F. Abbott, Introduction to the Background Field Method, Acta Phys. Polon. B 13 (1982) 33 [INSPIRE].
A. Pich, Effective field theory: Course, hep-ph/9806303 [INSPIRE].
M.S. Bilenky and A. Santamaria, One loop effective Lagrangian for a standard model with a heavy charged scalar singlet, Nucl. Phys. B 420 (1994) 47 [hep-ph/9310302] [INSPIRE].
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ArXiv ePrint: 1610.00710
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Zhang, Z. Covariant diagrams for one-loop matching. J. High Energ. Phys. 2017, 152 (2017). https://doi.org/10.1007/JHEP05(2017)152
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DOI: https://doi.org/10.1007/JHEP05(2017)152