# Standard Model

## Joaquim Matias

## The Standard Model (SM) of particle interactions is one of the major achievements of fundamental science, recently validated also with the discovery of the Higgs boson. It is the most successful theory and for many years it has been probed and systematically confirmed in collider experiments, with tensions showing up only temporarily in isolated channels. However, in recent years a consistent picture of tensions has emerged in interrelated channels in the flavour sector.

## Introduction

The Standard Model and Flavour Physics subgroup of the IFAE theory division investigates the phenomenology of particle physics and its flavour sector within the realms of the Standard Model. The identification of any beyond the SM signal requires first a precise evaluation of the fundamental parameters of the SM to get accurate SM predictions to confront with experimental measurements.

## Summary of the 2019 activities

In 2019, the Standard Model and Flavour Physics subgroup of the IFAE Theory Group was involved in the following activities:

S. Peris have been focused in a reanalysis of the determination of alpha_s from tau decays. The novelty of this analysis is the inclusion of Duality Violation effects together with a self-consistent treatment of the OPE. The result of this is a systematic shift downwards of the central value plus a more reliable assessment of the error, which brings the result more in line with the world average. He also studied different aspects of the lattice determination of the Hadronic Vacuum Polarization contribution to the muon g-2, which is currently showing a $\sim 3 \sigma$ deviation between experiment and the result in the SM.

A. Pineda constructed expressions of the OPE of a given observable that carefully disentangle truncated sums of the perturbative series in powers of alpha from the non-perturbative (NP) corrections. This splitting is done with NP power accuracy. Analytic control of the error is achieved and the organization of the different terms is done along a super/hyper-asymptotic expansion.

J. Matias focused on the theoretical predictions for the relevant rare B decay observables contributing to a model-independent analysis of b->sll transitions. A coherent set of deviations with respect to the SM have been observed in recent years in these transitions, so called B-Flavour anomalies. Two were the main outcomes of the analysis: on the one hand, the identification of new emerging scenarios of New Physics that favour the presence of right handed currents and on the other, by removing one implicit hypothesis in current analysis, show that a combination of Lepton Flavour Universality Violating (LFUV) with LFU Conserving New Physics provides a better description of data. The predictions in the SM and beyond of new LFUV observables were also discussed.

R. Escribano analysed the rare, doubly radiative decays eta(‘)—>pi0gammagamma and eta’—>etagammagamma in terms of scalar and vector meson exchange contributions. Their predictions for the decays eta(‘)—>pi0gammagamma show a satisfactory agreement with the experimental values reported by the A2, Crystall Ball and BESIII collaborations, thus supporting the validity of their approach. They also provide a first prediction for the non yet measured invariant mass spectrum of the decay eta’—>etagammagamma whose integrated branching ratio seems to be in agreement with the recent BESIII reported measurement.

## Hyperasymptotic approximation to the operator product expansion

The operator product expansion (OPE) of an observable for large $Q^2$ is organized as a double expansion in powers of $\alpha$ and $e^{-\frac{2\pi}{\beta_0\alpha}}$. The different terms of the OPE are then organized as series of powers of $\alpha$ $\times$ powers of $e^{-d\frac{2\pi}{\beta_0\alpha}}$. The leading term of this expansion is standard perturbation theory.

All these series are asymptotic, and, therefore, ill defined. One can only give a numerical meaning to them after the sum of the series is regulated. This has to be done in a consistent way for all terms of the OPE, as the ambiguities of the different asymptotic series of the OPE are related. On top of that the knowledge of the perturbative series is limited introducing errors that have not been quantified this far.

Cesar Ayala, Xabier Lobregat and Antonio Pineda generalize the ideas of hyperasymptotic expansions originally developed in the context of ordinary differential equations to the case of quantum field theories where, in particular, one has to deal with the problem of the scheme and scale dependence of the coupling constant. Using these techniques they can find approximate expressions for the regulated series with well defined (and analytic) expressions for the error. The power of this method is illustrated in Fig. 1 using the static potential in the large $\beta_0$ approximation . The outcome is that the hyperasymptotic expansion is perfectly convergent, the precision is very high (exponential) and the prediction for the error works very well.

One can apply these analyses to more physical cases, like to determination of the top mass. In this case Cesar Ayala, Xabier Lobregat and Antonio Pineda were able to assess that the present theoretical uncertainty in the relation between the MS top mass (fixing this to be 163 GeV) and the top pole mass regulated using the PV prescription, is 28 MeV, quite small indeed.