Abstract
We present SuperTracer, a Mathematica package aimed at facilitating the functional matching procedure for generic UV models. This package automates the most tedious parts of one-loop functional matching computations. Namely, the determination and evaluation of all relevant supertraces, including loop integration and Dirac algebra manipulations. The current version of SuperTracer also contains a limited set of output simplifications. However, a further reduction of the output to a minimal basis using Fierz identities, integration by parts, simplification of Dirac structures, and/or light field redefinitions might still be necessary. The code and example notebooks are publicly available at .1
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
W. Buchmüller and D. Wyler, Effective Lagrangian Analysis of New Interactions and Flavor Conservation, Nucl. Phys. B 268 (1986) 621 [INSPIRE].
B. Grzadkowski, M. Iskrzynski, M. Misiak and J. Rosiek, Dimension-Six Terms in the Standard Model Lagrangian, JHEP 10 (2010) 085 [arXiv:1008.4884] [INSPIRE].
E. E. Jenkins, A. V. Manohar and M. Trott, Renormalization Group Evolution of the Standard Model Dimension Six Operators I: Formalism and lambda Dependence, JHEP 10 (2013) 087 [arXiv:1308.2627] [INSPIRE].
E. E. Jenkins, A. V. Manohar and M. Trott, Renormalization Group Evolution of the Standard Model Dimension Six Operators II: Yukawa Dependence, JHEP 01 (2014) 035 [arXiv:1310.4838] [INSPIRE].
R. Alonso, E. E. Jenkins, A. V. Manohar and M. Trott, Renormalization Group Evolution of the Standard Model Dimension Six Operators III: Gauge Coupling Dependence and Phenomenology, JHEP 04 (2014) 159 [arXiv:1312.2014] [INSPIRE].
R. Alonso, H.-M. Chang, E. E. Jenkins, A. V. Manohar and B. Shotwell, Renormalization group evolution of dimension-six baryon number violating operators, Phys. Lett. B 734 (2014) 302 [arXiv:1405.0486] [INSPIRE].
E. E. Jenkins, A. V. Manohar and P. Stoffer, Low-Energy Effective Field Theory below the Electroweak Scale: Operators and Matching, JHEP 03 (2018) 016 [arXiv:1709.04486] [INSPIRE].
W. Dekens and P. Stoffer, Low-energy effective field theory below the electroweak scale: matching at one loop, JHEP 10 (2019) 197 [arXiv:1908.05295] [INSPIRE].
J. Aebischer, A. Crivellin, M. Fael and C. Greub, Matching of gauge invariant dimension-six operators for b → s and b → c transitions, JHEP 05 (2016) 037 [arXiv:1512.02830] [INSPIRE].
E. E. Jenkins, A. V. Manohar and P. Stoffer, Low-Energy Effective Field Theory below the Electroweak Scale: Anomalous Dimensions, JHEP 01 (2018) 084 [arXiv:1711.05270] [INSPIRE].
A. Celis, J. Fuentes-Martin, A. Vicente and J. Virto, DsixTools: The Standard Model Effective Field Theory Toolkit, Eur. Phys. J. C 77 (2017) 405 [arXiv:1704.04504] [INSPIRE].
J. Aebischer, J. Kumar and D. M. Straub, Wilson: a Python package for the running and matching of Wilson coefficients above and below the electroweak scale, Eur. Phys. J. C 78 (2018) 1026 [arXiv:1804.05033] [INSPIRE].
J. Fuentes-Martin, P. Ruiz-Femenia, A. Vicente and J. Virto, DsixTools 2.0: The Effective Field Theory Toolkit, Eur. Phys. J. C 81 (2021) 167 [arXiv:2010.16341] [INSPIRE].
J. C. Criado, MatchingTools: a Python library for symbolic effective field theory calculations, Comput. Phys. Commun. 227 (2018) 42 [arXiv:1710.06445] [INSPIRE].
J. Aebischer, M. Fael, A. Lenz, M. Spannowsky and J. Virto eds., Computing Tools for the SMEFT, in proceedings of the 1st Workshop on Tools for Low-Energy SMEFT Phenomenology (SMEFT-Tools 2019), Durham, U.K., 12–14 June 2019, arXiv:1910.11003 [INSPIRE].
B. Gripaios and D. Sutherland, DEFT: A program for operators in EFT, JHEP 01 (2019) 128 [arXiv:1807.07546] [INSPIRE].
J. C. Criado, BasisGen: automatic generation of operator bases, Eur. Phys. J. C 79 (2019) 256 [arXiv:1901.03501] [INSPIRE].
A. Dedes, M. Paraskevas, J. Rosiek, K. Suxho and L. Trifyllis, SmeftFR – Feynman rules generator for the Standard Model Effective Field Theory, Comput. Phys. Commun. 247 (2020) 106931 [arXiv:1904.03204] [INSPIRE].
N. P. Hartland et al., A Monte Carlo global analysis of the Standard Model Effective Field Theory: the top quark sector, JHEP 04 (2019) 100 [arXiv:1901.05965] [INSPIRE].
J. Aebischer, J. Kumar, P. Stangl and D. M. Straub, A Global Likelihood for Precision Constraints and Flavour Anomalies, Eur. Phys. J. C 79 (2019) 509 [arXiv:1810.07698] [INSPIRE].
D. van Dyk et al., EOS HEP program for Flavor Observables, (2016) https://eos.github.io.
D. M. Straub, flavio: a Python package for flavour and precision phenomenology in the Standard Model and beyond, arXiv:1810.08132 [INSPIRE].
I. Brivio, Y. Jiang and M. Trott, The SMEFTsim package, theory and tools, JHEP 12 (2017) 070 [arXiv:1709.06492] [INSPIRE].
G. Uhlrich, F. Mahmoudi and A. Arbey, MARTY – Modern ARtificial Theoretical phYsicist: A C++ framework automating symbolic calculations Beyond the Standard Model, Comput. Phys. Commun. 264 (2021) 107928 [arXiv:2011.02478] [INSPIRE].
S. Das Bakshi, J. Chakrabortty and S. K. Patra, CoDEx: Wilson coefficient calculator connecting SMEFT to UV theory, Eur. Phys. J. C 79 (2019) 21 [arXiv:1808.04403] [INSPIRE].
J. de Blas, J. C. Criado, M. Pérez-Victoria and J. Santiago, Effective description of general extensions of the Standard Model: the complete tree-level dictionary, JHEP 03 (2018) 109 [arXiv:1711.10391] [INSPIRE].
M. Krämer, B. Summ and A. Voigt, Completing the scalar and fermionic Universal One-Loop Effective Action, JHEP 01 (2020) 079 [arXiv:1908.04798] [INSPIRE].
A. Angelescu and P. Huang, Integrating Out New Fermions at One Loop, JHEP 01 (2021) 049 [arXiv:2006.16532] [INSPIRE].
S. A. R. Ellis, J. Quevillon, P. N. H. Vuong, T. You and Z. Zhang, The Fermionic Universal One-Loop Effective Action, JHEP 11 (2020) 078 [arXiv:2006.16260] [INSPIRE].
C. Anastasiou, A. Carmona, A. Lazopoulos and J. Santiago, in preparation.
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].
L.-H. Chan, Effective Action Expansion in Perturbation Theory, Phys. Rev. Lett. 54 (1985) 1222 [Erratum ibid. 56 (1986) 404] [INSPIRE].
C. M. Fraser, Calculation of Higher Derivative Terms in the One Loop Effective Lagrangian, Z. Phys. C 28 (1985) 101 [INSPIRE].
I. J. R. Aitchison and C. M. Fraser, Fermion Loop Contribution to Skyrmion Stability, Phys. Lett. B 146 (1984) 63 [INSPIRE].
I. J. R. Aitchison and C. M. Fraser, Derivative Expansions of Fermion Determinants: Anomaly Induced Vertices, Goldstone-Wilczek Currents and Skyrme Terms, Phys. Rev. D 31 (1985) 2605 [INSPIRE].
I. J. R. Aitchison and C. M. Fraser, Trouble With Boson Loops in Skyrmion Physics, Phys. Rev. D 32 (1985) 2190 [INSPIRE].
O. Cheyette, Derivative Expansion of the Effective Action, Phys. Rev. Lett. 55 (1985) 2394 [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].
B. Henning, X. Lu and H. Murayama, How to use the Standard Model effective field theory, JHEP 01 (2016) 023 [arXiv:1412.1837] [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, JHEP 01 (2018) 123 [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].
Z. Zhang, Covariant diagrams for one-loop matching, JHEP 05 (2017) 152 [arXiv:1610.00710] [INSPIRE].
S. A. R. Ellis, J. Quevillon, T. You and Z. Zhang, Extending the Universal One-Loop Effective Action: Heavy-Light Coefficients, JHEP 08 (2017) 054 [arXiv:1706.07765] [INSPIRE].
B. Summ and A. Voigt, Extending the Universal One-Loop Effective Action by Regularization Scheme Translating Operators, JHEP 08 (2018) 026 [arXiv:1806.05171] [INSPIRE].
T. Cohen, M. Freytsis and X. Lu, Functional Methods for Heavy Quark Effective Theory, JHEP 06 (2020) 164 [arXiv:1912.08814] [INSPIRE].
T. Cohen, X. Lu and Z. Zhang, Functional Prescription for EFT Matching, JHEP 02 (2021) 228 [arXiv:2011.02484] [INSPIRE].
T. Cohen, X. Lu and Z. Zhang, STrEAMlining EFT Matching, arXiv:2012.07851 [INSPIRE].
M. Beneke and V. A. Smirnov, Asymptotic expansion of Feynman integrals near threshold, Nucl. Phys. B 522 (1998) 321 [hep-ph/9711391] [INSPIRE].
B. Jantzen, Foundation and generalization of the expansion by regions, JHEP 12 (2011) 076 [arXiv:1111.2589] [INSPIRE].
R. D. Ball, Chiral Gauge Theory, Phys. Rept. 182 (1989) 1 [INSPIRE].
F. Jegerlehner, Facts of life with gamma(5), Eur. Phys. J. C 18 (2001) 673 [hep-th/0005255] [INSPIRE].
M. S. Chanowitz, M. Furman and I. Hinchliffe, The Axial Current in Dimensional Regularization, Nucl. Phys. B 159 (1979) 225 [INSPIRE].
L. N. Mihaila, J. Salomon and M. Steinhauser, Renormalization constants and β-functions for the gauge couplings of the Standard Model to three-loop order, Phys. Rev. D 86 (2012) 096008 [arXiv:1208.3357] [INSPIRE].
J. Fuentes-Martin, M. König, J. Pagès, A. E. Thomsen and F. Wilsch, in preparation.
V. Gherardi, D. Marzocca and E. Venturini, Matching scalar leptoquarks to the SMEFT at one loop, JHEP 07 (2020) 225 [Erratum JHEP 01 (2021) 006] [arXiv:2003.12525] [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: 2012.08506
1https://gitlab.com/supertracer/supertracer.
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
Fuentes-Martín, J., König, M., Pagès, J. et al. SuperTracer: a calculator of functional supertraces for one-loop EFT matching. J. High Energ. Phys. 2021, 281 (2021). https://doi.org/10.1007/JHEP04(2021)281
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP04(2021)281