Gearing up for the next generation of LFV experiments, via on-shell methods

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.

Amplitude bases in generic EFTs

“…15 23 [15][23] M W 25 34 [14][15] [23], M W 13 45 [15][23] [24], M W 12 25 34 [15][34], M Z 15 24 [15][23] [34], M Z 12 45 [15][23] [34], M W 14 15 23 [25][34], M Z 15 24 [12][34] [35], 13 45 [15][34] 2|p 1 |2], 12 45 [12][45] 3|p 2 |3],…”

“…For instance, such methods have been applied to compute the anomalous dimension in generic EFTs [6][7][8][9][10][11][12][13][14], to understand the patterns of zeros in the one-loop anomalous JHEP08(2022)299 dimension matrix for dimension-six operators in the SMEFT [15][16][17] and Wilson coefficients when integrating out heavy modes [18], and the (non-)interference of tree-level SMEFT and SM amplitudes [19]. In the study of gravitational binary systems, scattering amplitude techniques allowed to compute the conservative two-body scattering dynamics up to O(G 4 ) in all orders in velocity [20][21][22][23][24][25][26][27][28][29][30], and to lower orders in G including spin effects [23,[31][32][33][34][35][36][37][38], tidal effects [39][40][41][42][43] and higher-derivative interactions [44,45].…”

“…In section 4, we work out explicitly three examples: the classification of D 2n F 4 operators in SU(N ) Yang-Mills theories, dimension-six interactions between (charged and uncharged) massive and massless vectors, and quadratic-in-spin (spin-)tidal interactions in gravity. Finally, in appendix A JHEP08(2022)299 The graph associate to the kinematic structures 23 31 3 [12] 2 [14][32] and 23 34 [13] [14][25] respectively.…”

“…Figure 1.The graph associate to the kinematic structures 23 313 [12] 2[14][32] and 23 34[13][14][25] respectively.…”

EFT matching from analyticity and unitarity

“…They helped uncovering positivity constraints [53][54][55], non-interferences between renormalisable and dimension-six amplitudes [56], and non-renormalisation theorems between higherdimensional operators [57][58][59][60][61]. They provided an alternative means of computing anomalous dimensions [62][63][64][65][66][67][68][69][70], of constructing SMEFT operator bases [71][72][73][74][75][76][77] as well as broken-phase massive amplitudes [78][79][80][81][82][83][84][85][86].…”