Precision physics with QCD

Abstract

Abstract. The four-loop determination of the strong coupling from fully inclusive observables is reviewed. Special attention is given to the low-energy measurement extracted from the hadronic τ decay width. A recent exhaustive analysis of the ALEPH data, exploring several complementary methodologies with very different sensitivities to inverse power corrections and duality violations, confirms the strong suppression of nonperturbative contributions to R τ . It gives the value α s (m 2 τ ) = 0.328 ± 0.013, which implies α s (M 2 Z ) = 0.1197 ± 0.0015. The excellent agreement with the direct measurement at the Z peak, α s (M 2 Z ) = 0.1196 ± 0.0030, provides a beautiful test of asymptotic freedom. Together with the most recent lattice average from FLAG and the NNLO determinations from e + e − , PDFs and collider data quoted by the PDG, these two inclusive determinations imply a world average value α s (M 2 Z ) = 0.1180 ± 0.0010.

On the importance of electroweak corrections for B anomalies

“…The latter point can be easily understood using the Fiertz identity (ν iL γ µ τ L ) ¯ L γ µ ν jL = (ν iL γ µ ν jL ) ¯ L γ µ τ L and remembering that the charged lepton current ¯ L γ µ τ L is protected from renormalization effects by the QED Ward identity which stems from the electric charge conservation. LFUV in τ → νν is described by the observables 48) and are experimentally tested at the few level [77] R τ /µ τ = 1.0022 ± 0.0030…”

Direct CP violation in ${K^0\to\pi\pi}$ : Standard Model Status

“…As shown in table 1, the Wilson coefficients have a sizeable sensitivity to the chosen scheme for γ 5 , which limits the currently achievable precision. The table illustrates also their variation with the input value of the strong coupling, which has been taken in the range α (n f =3) s (m τ ) = 0.325 ± 0.015 [17,145]. To generate CP-violating effects, the SM requires at least three fermion families so that the CKM matrix incorporates a measurable complex phase.…”

“…λ 0.22506 ± 0.00050 [17] A 0.811 ± 0.026 [17] ρ 0.124 ± 0.019 [17] η 0.356 ± 0.011 [17] α −1 (M 2 Z ) 128.947 ± 0.012 [201] α (n f =3) s (M τ ) 0.325 ± 0.015 [17,145]…”

Combined analysis of the decays $\tau \to KS \pi^- \nu_\tau$ and $\tau \to K^- \eta \nu_\tau$

“…As discussed in the earlier analyses, the data points corresponding to bins 5, 6 and 7 are difficult to bring into accord with the theoretical descriptions and have thus been excluded from the minimisation. 5 The first point has not been included either, since the centre of the bin lies below the K S π − production threshold. Following a suggestion from the experimentalists, as in the previous analyses we have furthermore excluded data corresponding to bin numbers larger than 90.…”

“…(3.2) we employ the results obtained by Belle in correspondence with the employed decay distribution data: (0.404 ± 0.013)% [9] as well as (1.58 ± 0.10) × 10 −4 [20], respectively. This may be compared to the averages by the Particle Data Group, 5 Still, including them in the fits would just increase the χ 2 with only irrelevant changes in the fit parameters. 6 Contrary to our previous analysis [18], in the present study we have not included the BaBar data [19].…”