Abstract
We construct a complete basis of dimension-8 operators in the Low-Energy Effective Field Theory below the Electroweak Scale (LEFT). We find there are 35058 dimension-8 operators in the LEFT for two generations of up-type quarks and three generations of down-type quarks, charged leptons, and left-handed neutrinos. The existence of this operator basis is a necessary prerequisite for matching to the Standard Model Effective Field Theory at the dimension-8 level.
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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].
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].
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].
Y. Liao, X.-D. Ma and Q.-Y. Wang, Extending low energy effective field theory with a complete set of dimension-7 operators, JHEP 08 (2020) 162 [arXiv:2005.08013] [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].
B. Henning, X. Lu, T. Melia and H. Murayama, 2, 84, 30, 993, 560, 15456, 11962, 261485, . . .: higher dimension operators in the SM EFT, JHEP 08 (2017) 016 [Erratum ibid. 09 (2019) 019] [arXiv:1512.03433] [INSPIRE].
Y. Liao and X.-D. Ma, Renormalization group evolution of dimension-seven baryon- and lepton-number-violating operators, JHEP 11 (2016) 043 [arXiv:1607.07309] [INSPIRE].
Y. Liao and X.-D. Ma, Renormalization group evolution of dimension-seven operators in Standard Model effective field theory and relevant phenomenology, JHEP 03 (2019) 179 [arXiv:1901.10302] [INSPIRE].
C. W. Murphy, Dimension-8 operators in the Standard Model effective field theory, JHEP 10 (2020) 174 [arXiv:2005.00059] [INSPIRE].
H.-L. Li, Z. Ren, J. Shu, M.-L. Xiao, J.-H. Yu and Y.-H. Zheng, Complete set of dimension-8 operators in the Standard Model effective field theory, arXiv:2005.00008 [INSPIRE].
H.-L. Li, Z. Ren, M.-L. Xiao, J.-H. Yu and Y.-H. Zheng, Complete set of dimension-9 operators in the Standard Model effective field theory, arXiv:2007.07899 [INSPIRE].
Y. Liao and X.-D. Ma, An explicit construction of the dimension-9 operator basis in the Standard Model effective field theory, JHEP 11 (2020) 152 [arXiv:2007.08125] [INSPIRE].
V. Bernard, M. Oertel, E. Passemar and J. Stern, \( {K}_{\mu 3}^L \) decay: a stringent test of right-handed quark currents, Phys. Lett. B 638 (2006) 480 [hep-ph/0603202] [INSPIRE].
V. Cirigliano, J. Jenkins and M. Gonzalez-Alonso, Semileptonic decays of light quarks beyond the Standard Model, Nucl. Phys. B 830 (2010) 95 [arXiv:0908.1754] [INSPIRE].
R. Alonso, B. Grinstein and J. Martin Camalich, Lepton universality violation and lepton flavor conservation in B-meson decays, JHEP 10 (2015) 184 [arXiv:1505.05164] [INSPIRE].
G. N. Remmen and N. L. Rodd, Consistency of the Standard Model effective field theory, JHEP 12 (2019) 032 [arXiv:1908.09845] [INSPIRE].
G. N. Remmen and N. L. Rodd, Flavor constraints from unitarity and analyticity, Phys. Rev. Lett. 125 (2020) 081601 [arXiv:2004.02885] [INSPIRE].
E. d. S. Almeida, O. J. P. Éboli and M. C. Gonzalez-Garcia, Unitarity constraints on anomalous quartic couplings, Phys. Rev. D 101 (2020) 113003 [arXiv:2004.05174] [INSPIRE].
C. Zhang and S.-Y. Zhou, Convex geometry perspective on the (Standard Model) effective field theory space, Phys. Rev. Lett. 125 (2020) 201601 [arXiv:2005.03047] [INSPIRE].
B. Fuks, Y. Liu, C. Zhang and S.-Y. Zhou, Positivity in electron-positron scattering: testing the axiomatic quantum field theory principles and probing the existence of UV states, Chin. Phys. C 45 (2021) 023108 [arXiv:2009.02212] [INSPIRE].
K. Yamashita, C. Zhang and S.-Y. Zhou, Elastic positivity vs extremal positivity bounds in SMEFT: a case study in transversal electroweak gauge-boson scatterings, JHEP 01 (2021) 095 [arXiv:2009.04490] [INSPIRE].
G. N. Remmen and N. L. Rodd, Signs, spin, SMEFT: positivity at dimension six, arXiv:2010.04723 [INSPIRE].
B. Bellazzini, J. Elias Miró, R. Rattazzi, M. Riembau and F. Riva, Positive moments for scattering amplitudes, arXiv:2011.00037 [INSPIRE].
J. Gu, L.-T. Wang and C. Zhang, An unambiguous test of positivity at lepton colliders, arXiv:2011.03055 [INSPIRE].
Q. Bonnefoy, E. Gendy and C. Grojean, Positivity bounds on minimal flavor violation, arXiv:2011.12855 [INSPIRE].
E. E. Jenkins and A. V. Manohar, Algebraic structure of lepton and quark flavor invariants and CP-violation, JHEP 10 (2009) 094 [arXiv:0907.4763] [INSPIRE].
A. Hanany, E. E. Jenkins, A. V. Manohar and G. Torri, Hilbert series for flavor invariants of the Standard Model, JHEP 03 (2011) 096 [arXiv:1010.3161] [INSPIRE].
L. Lehman and A. Martin, Hilbert series for constructing Lagrangians: expanding the phenomenologist’s toolbox, Phys. Rev. D 91 (2015) 105014 [arXiv:1503.07537] [INSPIRE].
L. Lehman and A. Martin, Low-derivative operators of the Standard Model effective field theory via Hilbert series methods, JHEP 02 (2016) 081 [arXiv:1510.00372] [INSPIRE].
R. M. Fonseca, The Sym2Int program: going from symmetries to interactions, J. Phys. Conf. Ser. 873 (2017) 012045 [arXiv:1703.05221] [INSPIRE].
B. Henning, X. Lu, T. Melia and H. Murayama, Operator bases, S-matrices, and their partition functions, JHEP 10 (2017) 199 [arXiv:1706.08520] [INSPIRE].
A. Kobach, Baryon number, lepton number, and operator dimension in the Standard Model, Phys. Lett. B 758 (2016) 455 [arXiv:1604.05726] [INSPIRE].
A. Helset and A. Kobach, Baryon number, lepton number, and operator dimension in the SMEFT with flavor symmetries, Phys. Lett. B 800 (2020) 135132 [arXiv:1909.05853] [INSPIRE].
H.-L. Li, Z. Ren, M.-L. Xiao, J.-H. Yu and Y.-H. Zheng, Low energy effective field theory operator basis at d ≤ 9, arXiv:2012.09188 [INSPIRE].
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Murphy, C.W. Low-Energy Effective Field Theory below the Electroweak Scale: dimension-8 operators. J. High Energ. Phys. 2021, 101 (2021). https://doi.org/10.1007/JHEP04(2021)101
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DOI: https://doi.org/10.1007/JHEP04(2021)101