# Standard Model

## THE ANOMALOUS MAGNETIC MOMENT OF THE MUON

The anomalous magnetic moment of the muon, $(g_{\mu}-2)$, is among the most precise measured quantities in particle physics. Its nonzero value (e.g. $g_{\mu}\neq 0$) emerges purely out of quantum effects and tests our knowledge of particle physics. In particular, the current experimental value has reached a precision that requires accounting for all the known sectors of the Standard Model of particle physics when computing its theoretical value. In the past years, such an observable has attracted great attention due to the current discrepancy among the measured value and its theoretical prediction, that might point to the presence of new physics around the corner.

As a result, a large theory community with more than a hundred scientists worldwide gathered together under the “Muon g-2 Theory Initiative”, whose object was to improve the current theory estimate, in accordance to the unprecedented precision from the new experiment held at FermiLab that expects to release its first data in 2021. Scientists at IFAE have actively contributed to this effort. In particular, S. Peris has contributed to the current estimate of the lattice determination for the hadronic vacuum polarization contribution to $(g_{\mu}-2)$, while P. Masjuan and P. Sanchez-Puertas contributed to the current estimate of the hadronic light-by-light contribution. The global effort has crystallized in the publication of a whitepaper “The anomalous magnetic moment of the muon in the Standard Model” in 2020, where the people at IFAE also played an important role in the writing and coordination of the document.

## Simulating the expansion of the COVID-19 outbreak

In 2020, the project Simulating the expansion of the COVID-19 outbreak: a risk forecast tool considering socioeconomic and gender inequalities in Barcelona was awarded a “Premi de Recerca Científica Fons COVID de l’Ajuntament de Barcelona” grant with 72KEUR. Pere Masjuan is leading this project with the aim to develop a software tool to simulate COVID-19 spread by leveraging newly available demographic, mobility, and health data based on group theory techniques. Its main deliverable will consist of a user-friendly web interface for researchers to explore the determinants of the COVID-19 expansion with respect to socioeconomic and gender inequalities in Barcelona.

## Other activities in 2020

In 2020, the Standard Model and Flavour Physics subgroup of the IFAE Theory Group was involved in the following activities:

S.Peris: We combine ALEPH and OPAL results for the spectral distributions mea-sured in tau decays with (i)recent BaBar results and (ii) estimates of the contributions from other hadronic τau-decay modes obtained using CVC and electroproduction data, to obtain a new and more precise non-strange, inclusive vector, isovector spectral function. We use the resulting spectral function to determine the strong coupling at the tau mass scale, employing finite energy sum rules. Using the fixed-order perturbation theory (FOPT) prescription, we find $\alpha_s(m_\tau) = 0.3077\pm 0.0075$, which corresponds to the five-flavor result $\alpha_s(M_Z) = 0.1171\pm 0.0010$ at the Z mass. One of the more important systematic effects affecting lattice computations of the hadronic vacuum polarization contribution to the anomalous magneticmoment of the muon, $a^{HVP}_{\mu}$, is the distortion due to a finite spatial volume. In order to reach sub-percent precision, these effects need to be reliably estimated and corrected for, and one of the methods that has been employed for doing this is finite-volume chiral perturbation theory. In this paper, we argue that finite-volume corrections to $a^{HVP}_\mu$ can, in principle, be calculated at any given order inchiral perturbation theory. More precisely, once all low-energy constants needed to define the Effective Field Theory representation of $a^{HVP}_\mu$ in infinite volume are known to a given order, also the finite-volume corrections can be predicted to that order in the chiral expansion.

J. Matias: We have identified, for the first time, using the amplitude symmetry formalism a set of non-trivial relations among angular observables of the B–>D*lnu decay in absence of New Physics (NP) tensor contributions. These observables that were previously thought to be independent allowed us to construct an alternative way of measuring the longitudinal polarization fraction of the D*. This observable, recently measured by Belle, exhibits a disturbing high value that our alternative path, once measured, can confirm or dismiss. We have presented the the state-of-the-art of the b–>sll global fits including the most recent B–>K*μμ angular distribution data from LHCb. The result of our analysis including 180 observables showed that the data collected by LHCb corresponding to an integrated luminosity of 4.7 1/fb exhibits: a) a higher consistency arriving at significances above 6s in several NP hypothesis and b) confirmed the hints of RHC.
A. Pineda: We give the hyperasymptotic expansion of the energy of a static quarkantiquark pair with a precision that includes the eff ects of the subleading renormalon. The terminants associated to the fi rst and second renormalon are incorporated. From this analysis, we obtain accurate determinations of $\Lambda_{MS} (nf =3)= 338(12)$ MeV and $\alpha (Mz) = 0.1181(9)$ when fi tting to short-distance lattice data of the static energy. We give the hyperasymptotic expansion of the plaquette with a precision that includes the terminant associated to the leading renormalon. We use this analysis to give a determination of the gluon condensate in SU(3) pure gluodynamics that is independent of the scale and renormalization scheme used for the coupling constant: $<G^2>_{PV}(nf = 0) = 3.15(18) r_0^{-4}$.
R. Escribano: We have carried out a complete theoretical analysis of the $C$-conserving semileptonic decays $\eta^{(\prime)}\to\pi^0 l^+ l^-$ and $\eta^\prime\to\eta l^+ l^-$ ($l=e$ or $\mu$) within the framework of the Vector Meson Dominance model. The decay widths and dilepton energy spectra for the two $\eta\to\pi^0 l^+ l^-$ processes using this approach are compared and found to be in good agreement with previous published results. Theoretical predictions for the four $\eta^\prime\to\pi^0 l^+ l^-$ and $\eta^\prime\to\eta l^+ l^-$ processes are calculated and presented for the first time. We have presented an enhanced phenomenological model that includes isospin-symmetry breaking. The model is then constrasted with the most recent experimental data for the radiative transitions $VP\gamma$ ($V=\rho, \omega, \phi$ and $P=\pi^0, \eta, \eta^\prime$) and estimations for the mixing angles amongst the three pseudoscalar states with vanishing third-component of isospin are obtained. The current experimental uncertainties allow for isospin-symmetry violations with a confidence level of approximately $2.5\sigma$. We have analyzed the scalar and vector meson exchange contributions to the doubly radiative decays $\eta^{(\prime)}\to\pi^0\gamma\gamma$ and $\eta^\prime\to\eta\gamma\gamma$ within the linear sigma model and vector meson dominance frameworks, respectively. Predictions for the diphoton invariant mass spectra and the associated integrated branching ratios are given and compared with current available experimental data. While a satisfactory description of the shape of the $\eta\to\pi^0\gamma\gamma$ and $\eta^\prime\to\pi^0\gamma\gamma$ decay spectra is obtained, thus supporting the validity of the approach, the corresponding branching ratios cannot be reproduced simultaneously. A first theoretical prediction for the recently measured $\eta^\prime\to\eta\gamma\gamma$ by the BESIII Collaboration is also presented.
P. Sánchez: Participation in the writing of the whitepaper “The anomalous magnetic moment of the muon in the Standard Model”. The recommended value from the community includes the estimates from P. Masjuan and P. Sanchez Puertas for the pseudoscalar-poles contributions. Computation of the axial-vector mesons’ contributions to g-2 within resonance chiral theory (published in PRD) together with P. Roig. New paper (not published yet) with P. Masjuan and P. Roig about the role of axial-vector mesons and high-energies in g-2, that allows for a better understanding of current values as well as some seemingly conflicting results.