# Beyond the Standard Model

## Mariano Quirós

## There are a number of reasons, both theoretical (hierarchy problem, strong CP problem, flavor problem, the origin of matter-antimatter asymmetry,…) and experimental (Dark Matter…) why we believe that the Standard Model of strong and electroweak interactions cannot be the ultimate theory of particle interactions. This has motivated the development of theories beyond the Standard Model (BSM), which is the main task of the BSM subgroup of the IFAE Theory Group, and the experimental search of BSM physics, which in particular is being undertaken at the LHC.

## Introduction

The group consists of Profs. Alex Pomarol and Eduard Masso, the ICREA Research Professor Jose Ramon Espinosa, the SO postdoc Dr. Giuliano Panico and the IFAE researchers Dr. Oriol Pujolas and former ICREA Research Professor Mariano Quiros. The group activities are mainly in Beyond the Standard Model and Cosmology.

## Instability of the Higgs potential in the Standard Model

J.R. Espinosa studied some of the physics associated to the instability of the Higgs potential in the Standard Model.
The scale of this instability, determined as the Higgs field value at which the potential drops below the electroweak minimum, is about $10^{11}$ GeV. However, such a scale is unphysical as it is not gauge-invariant and suffers from a gauge-fixing uncertainty of up to two orders of magnitude.

In a work with Mathias Garny (CERN), Thomas Konstandin (DESY) and Antonio Riotto (U. Geneva) it was shown how, by subjecting the SM to several probes of the instability (adding higher order operators to the potential; letting the vacuum decay through critical bubbles; heating up the system to very high temperature; inflating it) and asking in each case physical questions, one is able to provide several gauge-invariant scales related with the Higgs potential instability. In another work, in collaboration with Davide Racco and Antonio Riotto.
Riotto (U. Geneva) it was shown that a cosmological signature of such instability could be dark matter in the form of primordial black holes (PBH) seeded by Higgs fluctuations during inflation. In such case, the existence of dark matter might not require physics beyond the Standard Model. The predicted spectrum of primordial black holes via this mechanism is shown in figure 1.

## Anomalous magnetic moment of the muon in extra dimensional theories

M. Quiros, in collaboration with Dr. E. Megias (Max-Planck Institute) and L. Salas (IFAE), studied the experimental value of the anomalous magnetic moment of the muon, which point towards new physics coupled non-universally to muons and electrons. Working in extra dimensional theories, which solve the electroweak hierarchy problem with a warped metric, strongly deformed with respect to the AdS$_5$ geometry at the infra-red brane we have proven that extra physics has to be introduced to describe the anomalous magnetic moment of the muon.

This job is done by a set of vector-like leptons, mixed with the physical muon through Yukawa interactions, and with a high degree of compositeness. The theory is consistent with all electroweak indirect, direct and theoretical constraints, the most sensitive ones being the modification of the $Z\mu\mu$ coupling, oblique observables and constraints on the stability of the electroweak minimum. They impose lower bounds on the compositeness and on the mass of the lightest vector-like lepton ($\gtrsim 270$ GeV). Vector-like leptons could be easily produced in Drell-Yan processes at the LHC and detected at $\sqrt{s}=13$ TeV.
Using the same setup M. Quiros, in collaboration with Dr. E. Megias and L. Salas, explored the limits on lepton-flavor universality (LFU) violation in theories where the hierarchy problem is solved by means of a warped extra dimension. In those theories LFU violation, in fermion interaction with Kaluza-Klein modes of gauge bosons, is provided $ab$ $initio$ when different flavor of fermions are differently localized along the extra dimension. As this fact arises from the mass pattern of quarks and leptons, LFU violation is natural in this class of theories. We analyze the experimental data pointing towards LFU violation,
as well as the most relevant electroweak and flavor observables, and the LFU tests in the $\mu/e$ and $\tau/\mu$ sectors. We find agreement with $R_{K^{(\ast)}}$ and $R_{D^{(\ast)}}$ data at 95% CL, provided the third generation left-handed fermions are composite ($0.14 < c_{b_L} < 0.28$ and $0.27 < c_{\tau_L} < 0.33$), and find the absolute limits $R_{K^{(\ast)}}\gtrsim 0.79$ and $R_{D^{(\ast)}}/R_{D^{(\ast)}}^{\rm SM}\lesssim 1.13$. Moreover we predict $\mathcal B( B\to K\nu\bar\nu)\gtrsim 1.14\times 10^{-5}$ at 95% CL, smaller than the present experimental upper bound but a few times larger than the Standard Model prediction. Bounds translate into an allowed region for the compositeness parameters of the left-handed bottom and tau as well as a region of the parameter $(V_{u_L}^*)_{32}/V_{cb}^{CKM}$ as it is shown in figure 2

## Collider phenomenology and Beyond the Standard Model physics

G. Panico has been working on different topics connected to collider phenomenology and Beyond the Standard Model physics. He followed three main research directions. One of them was focussed on the measurement of the Higgs trilinear self-coupling at the LHC and future colliders. In a series of two papers, he explored the sensitivity reach at the LHC and at future lepton colliders, showing how, through a global fit of the data, complementary information can be obtained from single- and double-Higgs production processes. A second research line was devoted to precision electroweak measurements at hadron colliders. He showed how an interplay between high-energy reach and a careful selection of

*clean*processes can allow us to perform competitive measurements that can match, as in several cases surpass, the precision obtained at LEP. In three papers, I considered several processes, including di-lepton and di-boson production channels. In the third research line he followed, he investigated the implication of the stringent measurements on electron and neutron electric dipole moments for top partners in composite Higgs theories. Current bounds allow to set exclusions in the TeV mass range, while near-future improvements will push the reach well above the 10 TeV scale.## Precision tests of the SM at the LHC

A. Pomarol, has shown that precision tests of the SM at the LHC are possible by measuring differential cross-sections at high invariant mass, exploiting in this way the growth with the energy of the corrections induced by new physics. Together with his collaborators they have classified the leading growing-with-energy effects in longitudinal diboson and associated Higgs production processes, providing the reach on these effects at the LHC and future colliders. Their method will allow to test of the SM electroweak sector at the per-mille level, in competition with LEP bounds.
They have studied strongly-coupled theories close to the conformal transition using holography, to understand the presence of light scalars as recent lattice simulations seem to suggest.
With Yuri Gershtein, they have analyzed the plethora of new LHC results to asses their impact on extra-dimensional models, to be published in the “Review of Particle Physics” (2017 Edition).