Abstract
We present the renormalisation group running of the bosonic operators of the Standard Model effective field theory (SMEFT) by the Lepton Number Violating operators (LNVs) at 1-loop order up to \( \mathcal{O} \)(v4/Λ4), with v ∼ 246 GeV as the electroweak scale and Λ as the SMEFT cut-off. Using these relations with the positivity bounds on Wilson coefficients of ϕ4D4 class, we derive sign constraints on the Wilson coefficients of LNV operators, for models where ϕ4D4 operators do not appear at tree-level. We inspect these constraints for the LNV Wilson coefficients generated from matching the Type-I and III seesaw models to SMEFT up to dimension seven at tree-level. We also exhibit the unique bounds induced by the T-parameter on LNVs.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Super-Kamiokande collaboration, Evidence for oscillation of atmospheric neutrinos, Phys. Rev. Lett. 81 (1998) 1562 [hep-ex/9807003] [INSPIRE].
S. Weinberg, Baryon and Lepton Nonconserving Processes, Phys. Rev. Lett. 43 (1979) 1566 [INSPIRE].
I. Brivio and M. Trott, The Standard Model as an Effective Field Theory, Phys. Rept. 793 (2019) 1 [arXiv:1706.08945] [INSPIRE].
J. Ellis, C.W. Murphy, V. Sanz and T. You, Updated Global SMEFT Fit to Higgs, Diboson and Electroweak Data, JHEP 06 (2018) 146 [arXiv:1803.03252] [INSPIRE].
J. Ellis, H.-J. He and R.-Q. Xiao, Probing new physics in dimension-8 neutral gauge couplings at e+e− colliders, Sci. China Phys. Mech. Astron. 64 (2021) 221062 [arXiv:2008.04298] [INSPIRE].
Anisha, S. Das Bakshi, J. Chakrabortty and S.K. Patra, Connecting electroweak-scale observables to BSM physics through EFT and Bayesian statistics, Phys. Rev. D 103 (2021) 076007 [arXiv:2010.04088] [INSPIRE].
T. Corbett, A. Helset, A. Martin and M. Trott, EWPD in the SMEFT to dimension eight, JHEP 06 (2021) 076 [arXiv:2102.02819] [INSPIRE].
M. Chala and A. Titov, Neutrino masses in the Standard Model effective field theory, Phys. Rev. D 104 (2021) 035002 [arXiv:2104.08248] [INSPIRE].
Anisha et al., Effective limits on single scalar extensions in the light of recent LHC data, Phys. Rev. D 107 (2023) 055028 [arXiv:2111.05876] [INSPIRE].
C. Degrande, A basis of dimension-eight operators for anomalous neutral triple gauge boson interactions, JHEP 02 (2014) 101 [arXiv:1308.6323] [INSPIRE].
A. Azatov, R. Contino, C.S. Machado and F. Riva, Helicity selection rules and noninterference for BSM amplitudes, Phys. Rev. D 95 (2017) 065014 [arXiv:1607.05236] [INSPIRE].
Y.-C. Guo, Y.-Y. Wang, J.-C. Yang and C.-X. Yue, Constraints on anomalous quartic gauge couplings via Wγjj production at the LHC, Chin. Phys. C 44 (2020) 123105 [arXiv:2002.03326] [INSPIRE].
S. Alioli, R. Boughezal, E. Mereghetti and F. Petriello, Novel angular dependence in Drell-Yan lepton production via dimension-8 operators, Phys. Lett. B 809 (2020) 135703 [arXiv:2003.11615] [INSPIRE].
C.W. Murphy, Dimension-8 operators in the Standard Model Eective Field Theory, JHEP 10 (2020) 174 [arXiv:2005.00059] [INSPIRE].
N. Craig, M. Jiang, Y.-Y. Li and D. Sutherland, Loops and Trees in Generic EFTs, JHEP 08 (2020) 086 [arXiv:2001.00017] [INSPIRE].
S. Das Bakshi, J. Chakrabortty and M. Spannowsky, Classifying Standard Model Extensions Effectively with Precision Observables, Phys. Rev. D 103 (2021) 056019 [arXiv:2012.03839] [INSPIRE].
S.D. Bakshi et al., Landscaping CP-violating BSM scenarios, Nucl. Phys. B 975 (2022) 115676 [arXiv:2103.15861] [INSPIRE].
R. Contino et al., On the Validity of the Effective Field Theory Approach to SM Precision Tests, JHEP 07 (2016) 144 [arXiv:1604.06444] [INSPIRE].
J. Baglio et al., Validity of standard model EFT studies of VH and VV production at NLO, Phys. Rev. D 101 (2020) 115004 [arXiv:2003.07862] [INSPIRE].
G. Panico, A. Pomarol and M. Riembau, EFT approach to the electron Electric Dipole Moment at the two-loop level, JHEP 04 (2019) 090 [arXiv:1810.09413] [INSPIRE].
M. Ardu and S. Davidson, What is Leading Order for LFV in SMEFT?, JHEP 08 (2021) 002 [arXiv:2103.07212] [INSPIRE].
M. Chala, C. Krause and G. Nardini, Signals of the electroweak phase transition at colliders and gravitational wave observatories, JHEP 07 (2018) 062 [arXiv:1802.02168] [INSPIRE].
C. Hays, A. Martin, V. Sanz and J. Setford, On the impact of dimension-eight SMEFT operators on Higgs measurements, JHEP 02 (2019) 123 [arXiv:1808.00442] [INSPIRE].
C. Hays, A. Helset, A. Martin and M. Trott, Exact SMEFT formulation and expansion to \( \mathcal{O} \)(v4/Λ4), JHEP 11 (2020) 087 [arXiv:2007.00565] [INSPIRE].
J. Gu, L.-T. Wang and C. Zhang, Unambiguously Testing Positivity at Lepton Colliders, Phys. Rev. Lett. 129 (2022) 011805 [arXiv:2011.03055] [INSPIRE].
M. Chala, G. Guedes, M. Ramos and J. Santiago, Towards the renormalisation of the Standard Model effective field theory to dimension eight: Bosonic interactions I, SciPost Phys. 11 (2021) 065 [arXiv:2106.05291] [INSPIRE].
A. Helset, E.E. Jenkins and A.V. Manohar, Renormalization of the Standard Model Effective Field Theory from geometry, JHEP 02 (2023) 063 [arXiv:2212.03253] [INSPIRE].
M. Accettulli Huber and S. De Angelis, Standard Model EFTs via on-shell methods, JHEP 11 (2021) 221 [arXiv:2108.03669] [INSPIRE].
S. Das Bakshi, M. Chala, Á. Díaz-Carmona and G. Guedes, Towards the renormalisation of the Standard Model effective field theory to dimension eight: bosonic interactions II, Eur. Phys. J. Plus 137 (2022) 973 [arXiv:2205.03301] [INSPIRE].
A.J. R. Figueiredo, Neutrino masses from SUSY breaking in radiative seesaw models, Eur. Phys. J. C 75 (2015) 99 [arXiv:1406.0557] [INSPIRE].
S.S.C. Law and K.L. McDonald, The simplest models of radiative neutrino mass, Int. J. Mod. Phys. A 29 (2014) 1450064 [arXiv:1303.6384] [INSPIRE].
R. Adhikari and A. Raychaudhuri, Light neutrinos from massless texture and below TeV seesaw scale, Phys. Rev. D 84 (2011) 033002 [arXiv:1004.5111] [INSPIRE].
M. Mitra, G. Senjanovic and F. Vissani, Neutrinoless Double Beta Decay and Heavy Sterile Neutrinos, Nucl. Phys. B 856 (2012) 26 [arXiv:1108.0004] [INSPIRE].
Z. Dong et al., Baryon number violation at the LHC: the top option, Phys. Rev. D 85 (2012) 016006 [arXiv:1107.3805] [INSPIRE].
A. Adams et al., Causality, analyticity and an IR obstruction to UV completion, JHEP 10 (2006) 014 [hep-th/0602178] [INSPIRE].
C. Zhang and S.-Y. Zhou, Positivity bounds on vector boson scattering at the LHC, Phys. Rev. D 100 (2019) 095003 [arXiv:1808.00010] [INSPIRE].
Q. Bi, C. Zhang and S.-Y. Zhou, Positivity constraints on aQGC: carving out the physical parameter space, JHEP 06 (2019) 137 [arXiv:1902.08977] [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, Signs, spin, SMEFT: Sum rules at dimension six, Phys. Rev. D 105 (2022) 036006 [arXiv:2010.04723] [INSPIRE].
Q. Bonnefoy, E. Gendy and C. Grojean, Positivity bounds on Minimal Flavor Violation, JHEP 04 (2021) 115 [arXiv:2011.12855] [INSPIRE].
B. Bellazzini et al., Positive moments for scattering amplitudes, Phys. Rev. D 104 (2021) 036006 [arXiv:2011.00037] [INSPIRE].
M. Chala and J. Santiago, Positivity bounds in the standard model effective field theory beyond tree level, Phys. Rev. D 105 (2022) L111901 [arXiv:2110.01624] [INSPIRE].
X. Li, Positivity bounds at one-loop level: the Higgs sector, JHEP 05 (2023) 230 [arXiv:2212.12227] [INSPIRE].
J. de Blas et al., Electroweak precision constraints at present and future colliders, PoS ICHEP2016 (2017) 690 [arXiv:1611.05354] [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].
L. Lehman, Extending the Standard Model Effective Field Theory with the Complete Set of Dimension-7 Operators, Phys. Rev. D 90 (2014) 125023 [arXiv:1410.4193] [INSPIRE].
V. Gherardi, D. Marzocca and E. Venturini, Matching scalar leptoquarks to the SMEFT at one loop, JHEP 07 (2020) 225 [Erratum ibid. 01 (2021) 006] [arXiv:2003.12525] [INSPIRE].
M. Chala, Á. Díaz-Carmona and G. Guedes, A Green’s basis for the bosonic SMEFT to dimension 8, JHEP 05 (2022) 138 [arXiv:2112.12724] [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].
H.-L. Li et al., Complete set of dimension-eight operators in the standard model effective field theory, Phys. Rev. D 104 (2021) 015026 [arXiv:2005.00008] [INSPIRE].
Z. Ren and J.-H. Yu, A Complete Set of the Dimension-8 Green’s Basis Operators in the Standard Model Effective Field Theory, arXiv:2211.01420 [INSPIRE].
S. Davidson, M. Gorbahn and M. Leak, Majorana neutrino masses in the renormalization group equations for lepton flavor violation, Phys. Rev. D 98 (2018) 095014 [arXiv:1807.04283] [INSPIRE].
A. Alloul et al., FeynRules 2.0 — A complete toolbox for tree-level phenomenology, Comput. Phys. Commun. 185 (2014) 2250 [arXiv:1310.1921] [INSPIRE].
T. Hahn and M. Perez-Victoria, Automatized one loop calculations in four-dimensions and D-dimensions, Comput. Phys. Commun. 118 (1999) 153 [hep-ph/9807565] [INSPIRE].
T. Hahn, Generating Feynman diagrams and amplitudes with FeynArts 3, Comput. Phys. Commun. 140 (2001) 418 [hep-ph/0012260] [INSPIRE].
A. Carmona, A. Lazopoulos, P. Olgoso and J. Santiago, Matchmakereft: automated tree-level and one-loop matching, SciPost Phys. 12 (2022) 198 [arXiv:2112.10787] [INSPIRE].
R.N. Mohapatra and G. Senjanovic, Neutrino Mass and Spontaneous Parity Nonconservation, Phys. Rev. Lett. 44 (1980) 912 [INSPIRE].
M. Malinsky, J.C. Romao and J.W.F. Valle, Novel supersymmetric SO(10) seesaw mechanism, Phys. Rev. Lett. 95 (2005) 161801 [hep-ph/0506296] [INSPIRE].
Y. Du, X.-X. Li and J.-H. Yu, Neutrino seesaw models at one-loop matching: discrimination by effective operators, JHEP 09 (2022) 207 [arXiv:2201.04646] [INSPIRE].
A. Loureiro et al., On The Upper Bound of Neutrino Masses from Combined Cosmological Observations and Particle Physics Experiments, Phys. Rev. Lett. 123 (2019) 081301 [arXiv:1811.02578] [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].
P.H. Chankowski and Z. Pluciennik, Renormalization group equations for seesaw neutrino masses, Phys. Lett. B 316 (1993) 312 [hep-ph/9306333] [INSPIRE].
K.S. Babu, C.N. Leung and J.T. Pantaleone, Renormalization of the neutrino mass operator, Phys. Lett. B 319 (1993) 191 [hep-ph/9309223] [INSPIRE].
S. Antusch et al., Neutrino mass operator renormalization revisited, Phys. Lett. B 519 (2001) 238 [hep-ph/0108005] [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 et al., Renormalization group evolution of dimension-six baryon number violating operators, Phys. Lett. B 734 (2014) 302 [arXiv:1405.0486] [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].
Acknowledgments
We thank Mikael Chala for the suggestions and discussions. We also thank José Santiago and Pablo Olgoso for help with MatchMakerEFT [56], and Guilherme Guedes, Anisha and Maria Ramos for comments on the manuscript. This work is partly supported by SRA (Spain) under Grant No. PID2019-106087GB-C21 / 10.13039/501100011033 and PID2021-128396NB-100; by the Junta de Andalucía (Spain) under Grants No. FQM- 101, A-FQM-467-UGR18, and P18-FR-4314 (FEDER). ADC is also supported by the Spanish MINECO under the FPI programme.
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: 2301.07151
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
Bakshi, S.D., Díaz-Carmona, Á. Renormalisation of SMEFT bosonic interactions up to dimension eight by LNV operators. J. High Energ. Phys. 2023, 123 (2023). https://doi.org/10.1007/JHEP06(2023)123
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP06(2023)123