# Standard Model

## Rafel Escribano

## 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. The group consists of Profs. Rafel Escribano, Pere Masjuan, Joaquim Matias, Santi Peris and Antonio Pineda, the postdoc Dr. Pablo Sánchez-Puertas and the PhD students Cristian Alarcón, Marcel Algueró, Arul Prakash, Camilo Rojas and Emilio Royo. The group activities are mainly in the Standard Model and Flavour Physics.

## A FIRST UNIFIED EXPLANATION OF FOUR ANOMALIES

J. Matias and M. Algueró in collaboration with A. Crivellin and C. A. Manzari (Paul Shcerrer Institute, Switzerland) have proposed a simple model obtained from the SM by adding:

- Two heavy quarks which are vector-like ($Q$ and $D$) under the SM gauge group.
- A gauged $L_\mu-L_\tau$ symmetry resulting in a $Z^\prime$ boson.
- A neutral and a singly charged scalar, singlet under color and weak isospin, ($S$ and $\phi^+$) with $L_\mu-L_\tau$ charge $-1$.

This model can explain:

- The $Z\to b\bar b$ forward-backward asymmetry via the mixing of the vector-like quarks with the SM bottom quark.
- The Cabibbo Angle Anomaly via a positive definite shift in $G_F$ induced by the singly charged scalar.
- $\tau\to\mu\nu\nu/\tau\to e\nu\nu$ and $\tau\to\mu\nu\nu/\mu\to e\nu\nu$ via the box contributions involving the $Z^\prime$.
- Accounts for $b\to s\ell^+\ell^-$ data through a modified $Z$ coupling and a loop induced $Z^\prime$ effect without being in conflict with $B_s-\bar B_s$ mixing.

Therefore, this model describes data significantly better than the SM and constitutes the first unified explanation of all four anomalies. With new particles at the TeV scale, it provides interesting discovery potential for the (HE-) LHC and the FCC-hh but could also be indirectly verified through $Z$ pole observables by FCC-ee, ILC, CEPC or CLIC. Also BELLE II is sensitive to the $Z\to b\bar b$ asymmetry via $e^+e^-\to b\bar b$ measurements with polarized electron beams. Furthermore, precision measurements of $\tau$ decays at BELLE~II and of course the pattern predicted in $b\to s\ell^+\ell^-$ at the HL-LHC and BELLE~II could test the model.

## STRONG COUPLING FROM AN IMPROVED TAU VECTOR ISOVECTOR SPECTRAL FUNCTION

S. Peris in collaboration with D. Boito and M. V. Rodrigues (U. Sao Paulo, Brasil), M. Golterman and W. Schaaf (San Francisco State U., USA), and K. Maltman (York U., Canada) have combined ALEPH and OPAL results for the spectral distributions measured in $\tau\to\pi^-\pi^0\nu_\tau$, $\tau\to2\pi^-\pi^+\pi^0\nu_\tau$ and $\tau\to\pi^-3\pi^0\nu_\tau$ decays with

- recent BaBar results for the analogous $\tau\to K^- K^0\nu_\tau$ distribution and
- estimates of the contributions from other hadronic $\t$-decay modes obtained using CVC and electroproduction data,to obtain a new and more precise non-strange, inclusive vector, isovector spectral function.

The BaBar $K^- K^0$ and CVC/electroproduction results provide them with alternate, entirely data-based input for the contributions of all exclusive modes for which ALEPH and OPAL employed Monte-Carlo-based estimates. They used the resulting spectral function to determine $\alpha_s(m_\t)$, the strong coupling at the $\tau$ mass scale, employing finite energy sum rules. Using the fixed-order perturbation theory (FOPT) prescription, they 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. While they also provide an estimate using contour-improved perturbation theory (CIPT), they point out that the FOPT prescription is to be preferred for comparison with other $\alpha_s$ determinations employing the $\overline{{\rm MS}}$ scheme, especially given the inconsistency between CIPT and the standard operator product expansion recently pointed out in the literature. Additional experimental input on the dominant $2\pi$ and $4\pi$ modes would allow for further improvements to the current analysis. The present result for $\alpha_s(M_Z)$ together with former results by the same authors and the current PDG average are shown in the figure below.

## OTHER ACTIVITIES IN 2021

**R. Escribano**: We have computed the pole mass and the pole width of the Kaluza-Klein gluon, which appears in theories with a warped extra dimension as very broad resonances coupled to composite fermions, and compare these predictions with those obtained from the usual Breit-Wigner approximation. Comparing both approaches, along with the existing experimental data from ATLAS and CMS, for the $t\bar t$, $t\bar t W$, $t\bar t Z$, $t\bar t H$, and $t t \bar t \bar t$ channels, We have found differences between the two approaches of up to about 100%, highlighting that the effect of broad resonances can be dramatic on present, and mainly future, experimental searches. The channel $t t \bar t \bar t$ is particularly promising because the size of the cross-section signal is of the same order of magnitude as the Standard Model prediction, and future experimental analyses in this channel, especially for broad resonances, can shed light on the nature of possible physics beyond the Standard Model (see figure below).

**P. Masjuan**: We have applied Pad\’e Theory in estimating $B\to\pi$ and $B\to K$ form factors to extract a precise $V_{ub}$ CKM parameter, with proper error estimations rendering inclusive and exclusive $V_{ub}$ determinations in agreement. We have also studied missing higher orders in the massless scalar-current quark correlator, predicting the yet unknown six-loop coefficient of its imaginary part, related to $\Gamma(H\to b\bar b).

**J. Matias**: We have presented the most complete analysis of the $B\to K^+\pi^-l^+l^-$ decay including both $P$ and $S$-wave contributions from a theoretical and experimental point of view. We have not only determined the symmetries of both contributions but most importantly all the relations between observables that allow us to define a new complete basis. This provide us with a new handle on New Physics using the new $S$-wave observables. Using non-leptonic $B$ decays, we have constructed a new observable based on the ratio of longitudinal components of the $B_s\to VV$ vs $B_d\to VV$ decays, with $V$ a vector meson. We have opened a new research line by establishing a parallelism between this ratio and the semileptonic anomalies. We have discovered a tension of 2.6$sigma$ with our SM prediction in the newly constructed observable when the $V$ is a $K^{\star 0}$. Finally, we have identified the relevant EFT coefficients and discussed possible model building explanations.

**A. Pineda**: A state-of-the-art invited review clarifying the current situation of the proton radius puzzle has been written in collaboration with C. Peset and A. Tomalak. An invited review of a new method developed to describe the OPE with exponential precision and parametric control of the error has also been written.

**P. Sánchez-Puertas**: We have obtained estimates for the baryon form factor of charged pions arising from isospin-symmetry breaking in two phenomenological ways: from simple constituent quark models with unequal up and down quark masses, and from fitting to $e^+e^- \to \pi^+ \pi^-$ data. All our methods yield a positive $\pi^+$ baryon mean square radius of $(0.03-0.04~{\rm fm})^2$. Hence, a picture emerges where the outer region has a net baryon, and the inner region a net antibaryon density, both compensating each other such that the total baryon number is zero. For $\pi^-$ the effect is opposite.