Weak mixing angle in the Thomson limit

Abstract

We present a calculation of the weak mixing angle in the MS renormalization scheme which is relevant for experiments performed at very low energies or momentum transfers. We include higher orders in the perturbative QCD expansion, as well as updated phenomenological and theoretical input, and obtain the result sin 2θ W (0) = 0.23868(5)(2) for the reference valuesα s (M Z ) = 0.1182 andm c (m c ) = 1.272 GeV. The first quoted error is from the current Standard Model evaluation of the mixing angle at the Z boson mass scale. The second error represents the theoretical and parametric uncertainties induced by the evolution to the Thomson limit and is discussed in detail.

Coherent elastic neutrino-nucleus scattering at the European Spallation Source

“…In our calculations, the weak mixing angle has been set to its value at zero momentum transfer sin 2 θ w = 0.23867, following Refs. [128,129]. As for the form factors, most of them are readily available from Ref.…”

Global fits of the SM parameters

“…Figure 4: Renormalization group evolution (running) of the weak mixing angle (updated from Ref. [38]).…”

“…The Q i are the electric charges, while the γ i are constants depending on the field type [43]. For quarks, K i is proportional to the color factor N C = 3 and contains QCD corrections up to and including O(α 4 s ) [38], while for both leptons and bosons K i = N C = 1. The terms involving σ arise due to QCD annihilation (singlet) diagrams with purely gluonic sub-diagrams.…”

“…GeV)), and then use the renormalization group equation[37,38] -more precisely the anomalous dimension of the photon field -which depends on the strong coupling α s , and the charm and bottom quark MS masses,m c andm b . The results (for the on-shell definition of α) are,α −1 (M Z ) = 128.947 ± 0.012 [34],(5.1) α −1 (M Z ) = 128.958 ± 0.016 [35], (5.2) α −1 (M Z ) = 128.946 ± 0.015 [36], (5.3) α −1 (M Z ) = 128.949 ± 0.010 [38], (5.4)…”

Reduced uncertainty of the axial γZ -box diagram correction to the proton’s weak charge

“…The precision measurement of s 2 W ≡ sin 2 θ W , where θ W is the Standard Model (SM) weak mixing angle, in parity-violating (PV) electron scattering serves as a powerful tool to test the SM and search for physics beyond it. Since the energy dependence of s 2 W is very precisely predicted within the SM [1], any significant deviation from it would be an indication of Beyond Standard Model (BSM) physics. Polarized elastic ep scattering in the limit of vanishing beam energy E and momentum transfer t, probes the so-called weak charge of the proton,…”