Effective field theory approach to lepton number violating τ decays

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We continue our endeavor to investigate lepton number violating (LNV) processes at low energies in the framework of effective field theory (EFT).In this work we study the LNV tau decays r+ → l-P+iP+j,where l =e,μ and P+i,j denote the lowest-lying charged pseudoscalars π+,K+.We analyze the dominant contributions in a series of EFTs from high to low energy scales,namely the standard model EFT (SMEFT),the low-energy EFT (LEFT),and the chiral perturbation theory (xPT).The decay branching ratios are expressed in terms of the Wilson coefficients of dimension-five and-seven operators in SMEFT and the hadronic low-energy constants.These Wilson coefficients involve the first and second generations of quarks and all generations of leptons;thus,they cannot be explored in low-energy processes such as nuclear neutrinoless double beta decay or LNV kaon decays.Unfortunately,the cur-rent experimental upper bounds on the branching ratios are too weak to set useful constraints on these coefficients.Alternatively,if we assume the new physics scale is larger than 1 TeV,the branching ratios are well below the cur-rent experimental bounds.We also estimate the hadronic uncertainties incurred in applying xPT to r decays by com-puting one-loop chiral logarithms and attempt to improve the convergence of chiral perturbation by employing dis-persion relations in the short-distance part of the decay amplitudes.
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