Reduced Hadronic Uncertainty in the Determination of Vud

Abstract

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...

Study of Two-Photon Exchange via the Beam Transverse Single Spin Asymmetry in Electron-Proton Elastic Scattering at Forward Angles over a Wide Energy Range

“…The hadronic uncertainty of the forward γZ-box correction has recently raised a significant interest [28][29][30][31][32][33][34][35][36][37][38][39][40] in the context of a precision determination of the weak mixing angle with parity-violating electron scattering [41,42]. Similarly, recent works on reducing hadronic and nuclear uncertainties of the γWbox correction [43][44][45][46][47] prove central in extracting the V ud element of the Cabibbo-Kobayashi-Maskawa (CKM) matrix and testing the CKM unitarity, a sensitive probe of the SM extensions [48]. Experimental observables explicitly sensitive to the TPE mechanism are instrumental in developing a dispersion-theoretical framework for TPE.The lepton-proton scattering amplitude in presence of TPE can be parameterized in terms of six generalized form factorsG E (Q 2 , ε),G M (Q 2 , ε) andF i (Q 2 , ε), i = 3, ..., 6 [49], where Q 2 is the negative four-momentum transfer squared, and ε = (1 + 2(1 + Q 2 4M 2 ) tan 2 θ 2 ) −1 , with M and θ being the nucleon mass and the lepton scattering angle, respectively.…”

Light gauge boson interpretation for (g − 2)μ and the KL→ π0 + (invisible) anomaly at the J-PARC KOTO experiment

“…The unitarity condition still hold in the 5 × 5 CKM matrix, but it would be violated in the 3 × 3 block of CKM, that can be tested by current precision measurements of CKM elements, for example the deviation from unity should be less than O(10 −3 ) under current measurements on 1st row of CKM, i.e. |V ud | 2 + |V cd | 2 + |V td | 2 = 0.9983(4) [53]. Figure 3: The diagrams which contribute to dsX FCNC process with X gauge boson coupled to a heavy vector-like quark Q (model I).…”

Toward a First-Principles Calculation of Electroweak Box Diagrams

“…Among various electroweak radiative corrections, the axial γW -boson box contribution ◻ V A γW contains a significant sensitivity to low-energy hadronic effects, and is a dominant source of the total theoretical uncertainty [2]. The recent dispersive analysis [3,4] reduced this uncertainty by a factor of 2 comparing to the previous study by Marciano and Sirlin [5], and the updated result of V ud raised a 4 standard-deviation tension with the first-row CKM unitarity (barring possibly underestimated nuclear effects: see Ref. [4,6]).…”

“…The main difference between those works is the use of inclusive neutrino and antineutrino scattering data that Refs. [3,4] used to estimate the contribution of the intermediate momenta inside the γW loop integral, 0.1 GeV 2 ≲ Q 2 ≲ 1 GeV 2 , prone to nonperturbative hadronic effects. To further improve the determination of V ud , it requires either better-quality experimental input or the direct, precise lattice QCD calculations of the γW -box contribution.…”

“…According to current algebra [2], it is this spin-independent term that gives rise to the hadron structure-dependent contribution and dominates the uncertainty in the theoretical prediction. Using T 3 as input, the axial γW -box correction to the tree-level amplitude is given as [3]…”