We analyze the conventional perturbative treatment of sphaleron-induced baryon number washout relevant for electroweak baryogenesis and show that it is not gauge-independent due to the failure of consistently implementing the Nielsen identities order-by-order in perturbation theory. We provide a gauge-independent criterion for baryon number preservation in place of the conventional (gauge-dependent) criterion needed for successful electroweak baryogenesis. We also review the arguments leading to the preservation criterion and analyze several sources of theoretical uncertainties in obtaining a numerical bound. In various beyond the standard model scenarios, a realistic perturbative treatment will likely require knowledge of the complete two-loop finite temperature effective potential and the one-loop sphaleron rate.

We analyze the universal radiative correction ∆ V R to neutron and superallowed nuclear β decay by expressing the hadronic γW -box contribution in terms of a dispersion relation, which we identify as an integral over the first Nachtmann moment of the γW interference structure function F (0) 3 . By connecting the needed input to existing data on neutrino and antineutrino scattering, we obtain an updated value of ∆ V R = 0.02467 (22), wherein the hadronic uncertainty is reduced. Assuming other Standard Model theoretical calculations and experimental measurements remain unchanged, we obtain an updated value of |V ud | = 0.97366(15), raising tension with the first row CKM unitarity constraint. We comment on ways current and future experiments can provide input to our dispersive analysis.The unitarity test of the Cabibbo-Kobayashi-Maskawa (CKM) matrix serves as one of the most important precision tests of the Standard Model. In particular, tests of first-row CKM unitarity |V ud | 2 + |V us | 2 + |V ub | 2 = 1 receive the most attention since these matrix elements are known with highest precision, all with comparable uncertainties. The good agreement with unitarity [1] serves as a powerful tool to constrain New Physics scenarios.Currently, the most precise determination of |V ud | comes from measurements of half-lives of superallowed 0 + → 0 + nuclear β decays with a precision of 10 −4 [2]. At tree-level, these decays are mediated by the vector part of the weak charged current only, which is protected against renormalization by strong interactions due to conserved vector current (CVC), making the extraction of |V ud | relatively clean. Beyond tree-level, however, electroweak radiative corrections (EWRC) involving the axial current are not protected, and lead to a hadronic uncertainty that dominates the error in the determination of |V ud |.The master formula relating the CKM matrix element |V ud | to the superallowed nuclear β decay half-life is [2]:where the nucleus-independent Ft-value is obtained from the experimentally measured f t-value by absorbing all nuclear-dependent corrections, and where ∆ V R represents the nucleus-independent EWRC. Currently, an average of the 14 best measured half-lives yields an extraordinarily precise value of Ft = 3072.27(72) s. A similar master formula exists for free neutron β decay [3] depending additionally on the axial-to-vector nucleon coupling ratio λ = g A /g V , and is free of nuclear-structure uncertainties. But the much larger experimental errors in the measurement of its lifetime and the ratio λ [4] makes it less competitive in the extraction of |V ud |. Regardless, if first-row CKM unitarity is to be tested at a higher level of precision, improvement in the theoretical estimate of ∆ V R by reducing hadronic uncertainties is essential. The best determination of ∆ V R = 0.02361(38) was obtained in 2006 by Marciano and Sirlin [5] (in the following, we refer to their work as [MS]). They were able to reduce the hadronic uncertainty by a factor of 2 over their earlier calculatio...

Package-X, a Mathematica package for the analytic computation of one-loop integrals dimensionally regulated near 4 spacetime dimensions is described. Package-X computes arbitrarily high rank tensor integrals with up to three propagators, and gives compact expressions of UV divergent, IR divergent, and finite parts for any kinematic configuration involving real-valued external invariants and internal masses. Output expressions can be readily evaluated numerically and manipulated symbolically with built-in Mathematica functions. Emphasis is on evaluation speed, on readability of results, and especially on user-friendliness. Also included is a routine to compute traces of products of Dirac matrices, and a collection of projectors to facilitate the computation of fermion form factors at one-loop. The package is intended to be used both as a research tool and as an educational tool. Program summaryProgram title: Package-X Program obtainable from:

We analyze the one-loop vacuum stability and perturbativity bounds on a singlet extension of the Standard Model (SM) scalar sector containing a scalar dark matter candidate. We show that the presence of the singlet-doublet quartic interaction relaxes the vacuum stability lower bound on the SM Higgs mass as a function of the cutoff and lowers the corresponding upper bound based on perturbativity considerations. We also find that vacuum stability requirements may place a lower bound on the singlet dark matter mass for given singlet quartic self coupling, leading to restrictions on the parameter space consistent with the observed relic density. We argue that discovery of a light singlet scalar dark matter particle could provide indirect information on the singlet quartic self-coupling.