Electroweak pseudo-observables and Z-boson form factors at two-loop accuracy

Abstract

We present Standard Model predictions for the complete set of phenomenologically relevant electroweak precision pseudo-observables related to the Zboson: the leptonic and bottom-quark effective weak mixing angles sin 2 θ eff , sin 2 θ b eff , the Z-boson partial decay widths Γ f , where f indicates any charged lepton, neutrino and quark flavor (except for the top quark), as well as the total Z decay width Γ Z , the branching ratios R , R c , R b , and the hadronic cross section σ 0 had . The input parameters are the masses M Z , M H and m t , and the couplings α s , α. The scheme dependence due to the choice of M W or its alternative G µ as a last input parameter is also discussed. Recent substantial technical progress in the calculation of Minkowskian massive higher-order Feynman integrals allows the calculation of the complete electroweak two-loop radiative corrections to all the observables mentioned. QCD contributions are included appropriately. Results are provided in terms of simple and convenient parameterization formulae whose coefficients have been determined from the full numerical multi-loop calculation. The size of the missing electroweak three-loop or QCD higher-order corrections is estimated. We briefly comment on the prospects for their calculation. Finally, direct predictions for the Zf f vector and axial-vector form-factors are given, including a discussion of separate order-by-order contributions.

Electroweak and QCD corrections to Z and W pole observables in the standard model EFT

“…A l 0.1465 ± 0.0033 [52] 0.1472 ± 0.0004 [49,53] A c 0.670 ± 0.027 0.6679 ± 0.0002 [49,53] A b 0.923 ± 0.020 0.92699 ± 0.00006 [49,53,54] A l,F B 0.0171 ± 0.0010 0.0162 ± 0.0001 [49,53] A b,F B 0.0992 ± 0.0016 0.1023 ± 0.0003 [49,53,54] A c,F B 0.0707 ± 0.0035 0.0737 ± 0.0003 [49,53] A l (SLD) 0.1513 ± 0.0021 [52] 0.1472 ± 0.0004 [49,53] sin 2 θ l,ef f 0.23179 ± 0.00035 [55] 0.23150 ± 0.00006 [49,53,54] M W (GeV) 80.379 ± 0.012 [56] 80.359 ± 0.006 [57,58] Γ W (GeV) 2.085 ± 0.042 [56] 2.0904 ± 0.0003 [59] Table III.…”

“…Corrections to this formula are of higher order and we do not include them [49]. Nonresonant contributions, such as photon exchange, box diagrams and 4-fermions interactions [34], are also not included because they do not contribute to the observables on the Z pole to O( 1 Λ 2 ).…”

Probing μτ flavor-violating solutions for the muon g − 2 anomaly at Belle II

“…The both features are distinctive and useful to distinguish the signal from the BG and we simply assume the BG is negligible after the selection of the signs at the first approximation. 6 We note that ALP and Z decay immediately for the nearly entire mass region even if we take a boost factor at the Belle II experiment into account. When ALP mass is very slightly larger than the sum of muon and tau masses, the lifetime can be long because of the JHEP09(2020)144…”

“…For example, if the τ decays into π + π − π + π 0 + missing, we require the all acceptance cut and applies the 4 = 0.9 4 for the efficiency factor. The multiplicity distribution for the whole signal events peaks around 6, which would already end up with 6 0.53. The resulting factor including the acceptance and the efficiency for the aforementioned µ ± µ ± τ ∓ τ ∓ events is in general about 25% for most of the cases.…”

QED challenges at FCC-ee precision measurements

“…Its precision goes far beyond what was needed at LEP, as seen for example in the recent study of the IFI contribution to A F B (M Z ± 3.5GeV), where the precision δA F B ≤ 10 −4 was verified using auxiliary calculations. However, for the FCC-ee experimental precision of asymmetries quoted in Table 1, the QED part of matrix element has to be upgraded to include the next orders, up to O(α 3 L 3 f ) in the CEEX matrix element, and EW corrections should be upgraded in the MC matrix element to the level of known complete O(α 2 ) corrections [88][89][90][91]. Needless to say, TAUOLA MC used in KKMC for τ lepton decays will require additional testing and development.…”