Standard Model

Mathias Jamin

The Standard Model of particle interactions is one of the major achievements of fundamental science. Within this framework a wide range of phenomena can be described to an impressive degree of accuracy. As a matter of fact, few are the branches of Physics where the predictive power of a theory has been tested to such a level of precision.

INTRODUCTION

The Standard Model (SM) subgroup of the IFAE theory division investigates the phenomenology of particle physics within the realms of the Standard Model. Even if physics going beyond the SM is expected, suggested for example by the presence of dark matter or neutrino masses, precise values of the fundamental SM parameters like couplings and masses are essential inputs for predictions within the SM, and beyond-SM physics should show up as clashes between those predictions and the experimental measurements.

The group investigates the phenomenology of particle physics within the realms of the standard model

In 2017, the Standard Model sub-group of the IFAE Theory Group was involved in the following activities: R. Escribano et al. introduced parametrisations of hadronic three-body $B$ and $D$ weak decay amplitudes that can be readily implemented in experimental analyses and are a sound alternative to the simplistic and widely used sum of Breit-Wigner type amplitudes, also known as the isobar model. These parametrizations can be particularly useful in the interpretation of CP asymmetries in the Dalitz plots. M. Jamin et al. investigated the behaviour of perturbative QCD series at high orders, both in the large-$\beta_0$ approximation and in full QCD by means of Borel representations of the series. J. Matias et al. studied deviations of Standard model predictions for the decay $B \to K^* \mu^+ \mu^-$ in the light of new experimental data. S. Peris et al. analysed hadronic contributions to the muon $g-2$ by means of chiral extrapolations and also extracted an ${\mathcal O}(p^6)$ chiral coupling from hadronic tau decay data. Finally, A. Pineda et al. investigated hyperfine splitting in muonic hydrogen and also the proton radius puzzle in the light of chiral perturbation theory.

Rare B decays

The Standard Model (SM) is an extremely successful effective theory that has passed all tests done in different accelerators up to recently. After the discovery of the SM Higgs and in absence of any real direct signal of New Physics since LHC is operative all the focus is now on indirect searches for New Physics. Flavour Physics having access to very high energy scales is at the frontier of this research. In particular rare B decays are now a cornerstone in our search for the fundamental theory.

This field of research has evolved from a Precision to a Discovery Era due to a set of coherent anomalies that have been detected recently. Before jumping on more or less contrived models the most difficult task is to provide a set of robust SM predictions for the relevant observables. In the case of the semileptonic B decays, where the anomalies are observed, this requires to include in all predictions the known factorizable and non-factorizable (in particular long-distance charm contributions with one soft gluon exchange) contributions. The second step is then to extract the information from those observables in a model independent way free from any model-building bias. This was implemented in a recent work [1] where the results of the most complete global fit were presented. We included 175 observables that governs the $b \to s \ell\ell$ transition: $B \to K^{*} \ell\ell$, $B_s \to \phi\mu^+\mu^-$ observables at large and low-recoil, radiative observables and observables sensitive to violation of lepton flavour universality (LFUV) like $R_K$, $R_{K^{*}}$ and $Q_{4,5}$ from LHCb, BELLE, ATLAS and CMS. The most relevant tensions observed up to now are: the observable $P_5^{\prime}$ from $B \to K^{*}\mu^+\mu^-$ that deviates near 3 sigma from the SM prediction in two adjacent bins [4,6] and [6,8], $R_K$ deviating 2.6$\sigma$ and $R_{K^{*}}$ in two bins with more than 2$\sigma$ tension in each of them, but also the low-recoil bins of the modes $B^{(0,+)} \to K^{* (0,+)} \mu^+\mu^-$ and $B_s \to \phi \mu^+\mu^-$ that deviate between 2.2 to 2.5$\sigma$ in different bins.

The results are classified in two groups according to the set of observables considered: i) the full fit including all observables with the most updated theoretical SM computations and ii) a subgroup of only the LFUV observables. The first fit points to the Wilson coefficient $C_9$ of the 4-fermion operator $O_{9\ell}=e^2/(16\pi^2) \left( \bar{s} \gamma_\mu P_L b \right) \left(\bar{\ell} \gamma^{\mu} \ell\right)$ with a best fit point of $C_9^{\rm NP}=-1.1$ disfavouring the SM hypothesis in front of this New Physics hypothesis by near 6$\sigma$, changing to a best fit point $C_9^{\rm NP}=-1.76$ and a significance of 4$\sigma$ if only LFUV observables are considered. Our analysis is done allowing for variations of one, two and six Wilson coefficients at a time. The result of the 2D analysis for ($C_9^{\rm NP}, C_{10}^{\rm NP}$) is shown in the plot. The 6D fit shows a pattern of all Wilson coefficients positive ($C_{10}^{\rm NP}$ and $C_9^\prime$) or zero but with significances below 2$\sigma$ while $C_9^{\rm NP}$ has a large negative destructive interference with the SM with a very high significance. The pull$_{SM}$ of this fit is now at 5$\sigma$ level from the previous 3.6$\sigma$.

The analysis finds the first signals of lepton flavour universality violation in flavour changing neutral transitions at the 3-4 sigma level

The main conclusions of this analysis are that we find first signals of lepton flavour universality violation in flavour changing neutral transitions at the 3-4$\sigma$ level depending on the hypothesis of New Physics tested and second, that we observe a substantial increase in the coherence among the different anomalies and tensions, specially between those of LFUV type (like $R_K$) and those governed only by the transition $b \to s \mu\mu$ (like $P_5^\prime$). The latter point put in crisis naive arguments based purely on hadronic uncertainties that tried to explain some of the anomalies in the framework of the SM.

Largest pulls	$\langle{P_5^\prime}\rangle^{[4,6]}$	$\langle{P_5^\prime}\rangle^{[6,8]}$	${\mathcal B}_{B_s \to \phi\mu^+\mu^-}^{[2,5]}$	${\mathcal B}_{B_s \to \phi\mu^+\mu^-}^{[5,8]}$	${\mathcal B}_{B^+ \to K^{*+}\mu^+\mu^-}^{[15,19]}$
Experiment	$-0.30 \pm 0.16$	$-0.51 \pm 0.12$	$ 0.77 \pm 0.14$	$0.96 \pm 0.15$	$1.60 \pm 0.32$
SM pred. Pull ($\sigma$)	$-0.82 \pm 0.08$ -2.9	$-0.94 \pm 0.08$ -2.9	$1.55 \pm 0.33$ +2.2	$1.88 \pm 0.39$ +2.2	$2.59 \pm 0.25$ +2.5
Pred. $C_{9\mu}^{\rm NP}=-1.76$ Pull ($\sigma$)	$-0.26\pm 0.12$ +0.2	$-0.52 \pm 0.15$ -0.1	$1.22 \pm 0.22$ +1.7	$1.37 \pm 0.25$ +1.4	$1.54 \pm 0.105$ -0.3

Largest pulls	$R_K^{[1,6]}$	$R_{K^*}^{[0.045,1.1]}$	$R_{K^*}^{[1.1,6]}$
Experiment	$0.745^{+0.097}_{-0.082}$	$0.66^{+0.113}_{-0.074}$	$0.685^{+0.122}_{-0.083}$
SM pred. Pull ($\sigma$)	$1.00 \pm 0.01$ +2.6	$0.92 \pm 0.02$ +2.3	$1.00 \pm 0.01$ +2.6
Pred. $C_{9\mu}^{\rm NP}=-1.76$ Pull ($\sigma$)	$0.69 \pm 0.01$ -0.7	$0.89 \pm 0.09$ +1.6	$0.83 \pm 0.14 $ +0.8

[1] “Patterns of New Physics in b → sl+l− transitions in the light of recent data”, Bernat Capdevila (Barcelona, IFAE), Andreas Crivellin (PSI, Villigen), S ́ebastien Descotes-Genon (Orsay, LPT), Joaquim Matias (Barcelona, Autonoma U. Barcelona, IFAE), Javier Virto (U. Bern, AEC). Published in JHEP 1801 (2018) 093