Abstract
Lepton Flavor Violating (LFV) observables such as μ → eγ, μ → 3e and μN → eN are among the best probes for new physics at the TeV scale. In the near future the bounds on these observables will improve by many orders of magnitude. In this work we use the SM EFT to understand the impact of these measurements. The precision reach is such that the interpretation of the bounds requires an analysis of the dimension-six operator mixing up to the two-loop level. Using on-shell amplitude techniques, which make transparent many selection rules, we classify and calculate the different operator mixing chains. At the leading order, on-shell techniques allow to calculate anomalous dimensions of SM EFT operators from the product of tree-level amplitudes, even for two-loop renormalization group mixings. We illustrate the importance of our EFT approach in models with extra vector-like fermions.
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References
L. Calibbi and G. Signorelli, Charged Lepton Flavour Violation: An Experimental and Theoretical Introduction, Riv. Nuovo Cim. 41 (2018) 71 [arXiv:1709.00294] [INSPIRE].
A. Baldini et al., A submission to the 2020 update of the European Strategy for Particle Physics on behalf of the COMET, MEG, Mu2e and Mu3e collaborations, arXiv:1812.06540 [INSPIRE].
S. Caron-Huot and M. Wilhelm, Renormalization group coefficients and the S-matrix, JHEP 12 (2016) 010 [arXiv:1607.06448] [INSPIRE].
J. Elias Miró, J. Ingoldby and M. Riembau, EFT anomalous dimensions from the S-matrix, JHEP 09 (2020) 163 [arXiv:2005.06983] [INSPIRE].
P. Baratella, C. Fernandez and A. Pomarol, Renormalization of Higher-Dimensional Operators from On-shell Amplitudes, Nucl. Phys. B 959 (2020) 115155 [arXiv:2005.07129] [INSPIRE].
M. Jiang, T. Ma and J. Shu, Renormalization Group Evolution from On-shell SMEFT, JHEP 01 (2021) 101 [arXiv:2005.10261] [INSPIRE].
Z. Bern, J. Parra-Martinez and E. Sawyer, Structure of two-loop SMEFT anomalous dimensions via on-shell methods, JHEP 10 (2020) 211 [arXiv:2005.12917] [INSPIRE].
P. Baratella, D. Haslehner, M. Ruhdorfer, J. Serra and A. Weiler, RG of GR from on-shell amplitudes, JHEP 03 (2022) 156 [arXiv:2109.06191] [INSPIRE].
M. Accettulli Huber and S. De Angelis, Standard Model EFTs via on-shell methods, JHEP 11 (2021) 221 [arXiv:2108.03669] [INSPIRE].
J. Elias-Miro, J.R. Espinosa and A. Pomarol, One-loop non-renormalization results in EFTs, Phys. Lett. B 747 (2015) 272 [arXiv:1412.7151] [INSPIRE].
C. Cheung and C.-H. Shen, Nonrenormalization Theorems without Supersymmetry, Phys. Rev. Lett. 115 (2015) 071601 [arXiv:1505.01844] [INSPIRE].
Z. Bern, J. Parra-Martinez and E. Sawyer, Nonrenormalization and Operator Mixing via On-Shell Methods, Phys. Rev. Lett. 124 (2020) 051601 [arXiv:1910.05831] [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].
M. Jiang, J. Shu, M.-L. Xiao and Y.-H. Zheng, Partial Wave Amplitude Basis and Selection Rules in Effective Field Theories, Phys. Rev. Lett. 126 (2021) 011601 [arXiv:2001.04481] [INSPIRE].
P. Baratella, C. Fernandez, B. von Harling and A. Pomarol, Anomalous Dimensions of Effective Theories from Partial Waves, JHEP 03 (2021) 287 [arXiv:2010.13809] [INSPIRE].
H.-L. Li, J. Shu, M.-L. Xiao and J.-H. Yu, Depicting the Landscape of Generic Effective Field Theories, arXiv:2012.11615 [INSPIRE].
J. Shu, M.-L. Xiao and Y.-H. Zheng, Constructing general partial waves and renormalization in EFT, arXiv:2111.08019 [INSPIRE].
Y. Shadmi and Y. Weiss, Effective Field Theory Amplitudes the On-Shell Way: Scalar and Vector Couplings to Gluons, JHEP 02 (2019) 165 [arXiv:1809.09644] [INSPIRE].
G. Durieux, T. Kitahara, Y. Shadmi and Y. Weiss, The electroweak effective field theory from on-shell amplitudes, JHEP 01 (2020) 119 [arXiv:1909.10551] [INSPIRE].
G. Durieux and C.S. Machado, Enumerating higher-dimensional operators with on-shell amplitudes, Phys. Rev. D 101 (2020) 095021 [arXiv:1912.08827] [INSPIRE].
Z.-Y. Dong, T. Ma and J. Shu, Constructing on-shell operator basis for all masses and spins, arXiv:2103.15837 [INSPIRE].
A. Crivellin, S. Najjari and J. Rosiek, Lepton Flavor Violation in the Standard Model with general Dimension-Six Operators, JHEP 04 (2014) 167 [arXiv:1312.0634] [INSPIRE].
G.M. Pruna and A. Signer, The μ → eγ decay in a systematic effective field theory approach with dimension 6 operators, JHEP 10 (2014) 014 [arXiv:1408.3565] [INSPIRE].
G.M. Pruna and A. Signer, Lepton-flavour violating decays in theories with dimension 6 operators, EPJ Web Conf. 118 (2016) 01031 [arXiv:1511.04421] [INSPIRE].
A. Crivellin, S. Davidson, G.M. Pruna and A. Signer, Renormalisation-group improved analysis of μ → e processes in a systematic effective-field-theory approach, JHEP 05 (2017) 117 [arXiv:1702.03020] [INSPIRE].
M. Ardu and S. Davidson, What is Leading Order for LFV in SMEFT?, JHEP 08 (2021) 002 [arXiv:2103.07212] [INSPIRE].
S. Davidson, Completeness and complementarity for μ → eγμ → \( e\overline{e}e \) and μA → eA, JHEP 02 (2021) 172 [arXiv:2010.00317] [INSPIRE].
S. Davidson, μ → eγ and matching at mW, Eur. Phys. J. C 76 (2016) 370 [arXiv:1601.07166] [INSPIRE].
A. Celis, V. Cirigliano and E. Passemar, Lepton flavor violation in the Higgs sector and the role of hadronic τ-lepton decays, Phys. Rev. D 89 (2014) 013008 [arXiv:1309.3564] [INSPIRE].
A. Celis, V. Cirigliano and E. Passemar, Model-discriminating power of lepton flavor violating τ decays, Phys. Rev. D 89 (2014) 095014 [arXiv:1403.5781] [INSPIRE].
T. Husek, K. Monsalvez-Pozo and J. Portoles, Lepton-flavour violation in hadronic tau decays and μ − τ conversion in nuclei, JHEP 01 (2021) 059 [arXiv:2009.10428] [INSPIRE].
V. Cirigliano, K. Fuyuto, C. Lee, E. Mereghetti and B. Yan, Charged Lepton Flavor Violation at the EIC, JHEP 03 (2021) 256 [arXiv:2102.06176] [INSPIRE].
MEG collaboration, Search for the lepton flavour violating decay μ+ → e+γ with the full dataset of the MEG experiment, Eur. Phys. J. C 76 (2016) 434 [arXiv:1605.05081] [INSPIRE].
SINDRUM collaboration, Search for the Decay μ+ → e+e+e−, Nucl. Phys. B 299 (1988) 1 [INSPIRE].
SINDRUM II collaboration, A Search for muon to electron conversion in muonic gold, Eur. Phys. J. C 47 (2006) 337 [INSPIRE].
ATLAS collaboration, Search for the Higgs boson decays H → ee and H → eμ in pp collisions at \( \sqrt{s} \) = 13 TeV with the ATLAS detector, Phys. Lett. B 801 (2020) 135148 [arXiv:1909.10235] [INSPIRE].
MEG II collaboration, The design of the MEG II experiment, Eur. Phys. J. C 78 (2018) 380 [arXiv:1801.04688] [INSPIRE].
A. Blondel et al., Research Proposal for an Experiment to Search for the Decay μ → eee, arXiv:1301.6113 [INSPIRE].
Mu2e collaboration, Mu2e Technical Design Report, arXiv:1501.05241 [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].
J. Elias-Miro, J.R. Espinosa, E. Masso and A. Pomarol, Higgs windows to new physics through d = 6 operators: constraints and one-loop anomalous dimensions, JHEP 11 (2013) 066 [arXiv:1308.1879] [INSPIRE].
Y. Kuno and Y. Okada, Muon decay and physics beyond the standard model, Rev. Mod. Phys. 73 (2001) 151 [hep-ph/9909265] [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].
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].
R. Britto, F. Cachazo and B. Feng, New recursion relations for tree amplitudes of gluons, Nucl. Phys. B 715 (2005) 499 [hep-th/0412308] [INSPIRE].
R. Britto, F. Cachazo, B. Feng and E. Witten, Direct proof of tree-level recursion relation in Yang-Mills theory, Phys. Rev. Lett. 94 (2005) 181602 [hep-th/0501052] [INSPIRE].
K. Risager, A Direct proof of the CSW rules, JHEP 12 (2005) 003 [hep-th/0508206] [INSPIRE].
R. Kitano, M. Koike and Y. Okada, Detailed calculation of lepton flavor violating muon electron conversion rate for various nuclei, Phys. Rev. D 66 (2002) 096002 [Erratum ibid. 76 (2007) 059902] [hep-ph/0203110] [INSPIRE].
W. Dekens, E.E. Jenkins, A.V. Manohar and P. Stoffer, Non-perturbative effects in μ → eγ, JHEP 01 (2019) 088 [arXiv:1810.05675] [INSPIRE].
A. Freitas, J. Lykken, S. Kell and S. Westhoff, Testing the Muon g-2 Anomaly at the LHC, JHEP 05 (2014) 145 [Erratum ibid. 09 (2014) 155] [arXiv:1402.7065] [INSPIRE].
C. Cornella, D.A. Faroughy, J. Fuentes-Martin, G. Isidori and M. Neubert, Reading the footprints of the B-meson flavor anomalies, JHEP 08 (2021) 050 [arXiv:2103.16558] [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].
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Miró, J.E., Fernandez, C., Gümüş, M.A. et al. Gearing up for the next generation of LFV experiments, via on-shell methods. J. High Energ. Phys. 2022, 126 (2022). https://doi.org/10.1007/JHEP06(2022)126
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DOI: https://doi.org/10.1007/JHEP06(2022)126