Particle physics – Beyond the standard model

Supersymmetry searches

Dr Sarah Williams


As a member of the ATLAS collaboration at CERN, Dr Williams’ research focuses on searches for new physics beyond the standard model, including models that predict extra spatial dimensions in the universe and those that could help explain what dark matter is made of. Her career in particle physics was seeded during her undergraduate degree in Natural Sciences at Cambridge. After her third year she was awarded a summer studentship at CERN which inspired her to do a PhD in High Energy Physics at Cambridge. After her PhD she moved to the Netherlands where she worked as a physics lecturer at Maastricht University, and continued her research on ATLAS as a member of Nikhef, the national institute for high energy physics in the Netherlands. She then returned to Cambridge in September 2016 and took up a fellowship in Physics at Murray Edwards College. In addition to her research she is also a college tutor and director of studies for physics.


Supersymmetry is arguably one of the most widely studies theories for Beyond-the-Standard-Model (BSM) physics, and has been searched for extensively at the Large Hadron Collider (LHC) at CERN. The talk explained the theoretical motivations behind the theory with a focus on its potential to solve the dark matter mystery. It also gave an overview of possible experimental signatures in colliders and summarised current constraints from the ATLAS collaboration. The lack of any discoveries of possible supersymmetric particles throughout run I and run II of the LHC have made many sceptical of the theory, so the talk highlighted the limitations of the current constraints and discussed interesting avenues for discovery in run III.

My notes from the lecture (if they don’t make sense then it is entirely my fault)


The LHC is now looking for physics beyond the standard model. There are reasons to expect new physics at the TeV scale. SUSY has the potential to solve the antimatter problem.

Shortcomings of the SM

1) It does not explain gravity.

2) There is a hierarchy problem. Why is the Higgs 125GeV

3) It does not explain dark matter

4) Neutrino mass and CP violation.


Bright bits show hot gases. The green lines show gravitational lensing contours.

The temperature profile of the bullet cluster gas suggests that the temperature is hottest near the centre of the lensing effect and drops towards the periphery.

Gravitational lensing studies of the bullet cluster 1E 0657-56 in Carina have recently been suggested to be the best evidence to date for the existence of that elusive hypothetical substance, dark matter. The object is a collision of two galaxy clusters and their associated hot interstellar gas. The most commonly cited graphic is the NASA composite image below.


The blue hues show the putative dark matter masses, separated from the visible mass in pink. The x-ray emitting hot gas is shown in red. The explanation given by NASA is that in this collision the dark matter and interstellar gas have separated, as is evidenced by the gravitational lensing profile of the cluster, which shows the largest lensing in the blue areas, separated from the hot gas and matter.

The cool points show the places where masses have not interacted.


A direct empirical proof of the existence of dark matter

Weakly interacting massive particles (WIMPs) are hypothetical particles that are thought to constitute dark matter. There exists no clear definition of a WIMP, but broadly, a WIMP is a new elementary particle which interacts via gravity and any other force (or forces), potentially not part of the standard model itself, which is as weak as or weaker than the weak nuclear force, but also non-vanishing in its strength. A WIMP must also have been produced thermally in the early Universe, similarly to the particles of the standard model according to Big Bang cosmology, and usually will constitute cold dark matter.

Because supersymmetric extensions of the standard model of particle physics readily predict a new particle with these properties, this apparent coincidence is known as the “WIMP miracle”, and a stable supersymmetric partner has long been a prime WIMP candidate.

Recent null results from direct-detection experiments along with the failure to produce evidence of supersymmetry in the Large Hadron Collider (LHC) experiment has cast doubt on the simplest WIMP hypothesis. Experimental efforts to detect WIMPs include the search for products of WIMP annihilation, including gamma rays, neutrinos and cosmic rays in nearby galaxies and galaxy clusters; direct detection experiments designed to measure the collision of WIMPs with nuclei in the laboratory, as well as attempts to directly produce WIMPs in colliders, such as the LHC.

The current conclusion is that wimps need to be much more massive than neutrinos in order to be a viable candidate for providing the dark matter content of the universe. The mass range of 100GeV/c2 to 1TeV/c2 seems to be appropriate for such candidates in most theories.

The Pursuit of Dark Matter at Colliders – An Overview

This article highlights the experimental and phenomenological development in collider dark matter searches of recent years and their connection with the wider field.

Simplified Models for Dark Matter Searches at the LHC

This document outlines a set of simplified models for dark matter and its interactions with Standard Model particles. It is intended to summarize the main characteristics that these simplified models have when applied to dark matter searches at the LHC, and to provide a number of useful expressions for reference. The list of models includes both s-channel and t-channel scenarios. For s-channel, spin-0 and spin-1 mediation is discussed, and also realizations where the Higgs particle provides a portal between the dark and visible sectors. The guiding principles underpinning the proposed simplified models are spelled out, and some suggestions for implementation are presented.

Any model must also satisfy astrophysical constraints including observed relic density

The presence of dark matter and its amount in the universe can be inferred from the variations of temperature in the early universe. This leftover amount of dark matter is called its “relic density”, and it amounts to about 27% of the matter-energy content of the universe.

The Planck 2015 result is WCDM = 0.1197 ± 0.0022

In 2018 the cold dark matter relic density WDMh2 = 0.1199 ± 0.0022, where h = 0.673 ± 0.098 is the present Hubble expansion rate in units of 100 km s−1 Mpc−1

SUSY invokes a symmetry between fermions and bosons. If no superpartners are observed there must be broken symmetry.

In particle physics, supersymmetry breaking is the process to obtain a seemingly non-supersymmetric physics from a supersymmetric theory which is a necessary step to reconcile supersymmetry with actual experiments. It is an example of spontaneous symmetry breaking. In supergravity, this results in a slightly modified counterpart of the Higgs mechanism where the gravitinos become massive.

Supersymmetry breaking occurs at supersymmetry breaking scale. The superpartners, whose mass would otherwise be equal to the mass of the regular particles in the absence of the SUSY breaking, become much heavier.

With SUSY the breaking mechanism is unknown. You need to introduce “soft” mass terms into theory

In theoretical physics, soft SUSY breaking is type of supersymmetry breaking that does not cause ultraviolet divergences to appear in scalar masses. These terms are relevant operators—i.e. operators whose coefficients have a positive dimension of mass—though there are some exceptions.

Even minimal extension to the standard model has 105 free parameters and contains 5 Higgs bosons.

We are still left with an unanswered question. How is SUSY broken?

Theoretical motivation for SUSY:

1) Looking for a dark matter candidate

2) Looking for gauge coupling unification

The standard model is a gauge theory, which means in part that the interactions are mediated by the exchange of (apparently) massless spin-1 gauge bosons.

In particle physics, a gauge boson is a force carrier, a bosonic particle that carries any of the fundamental interactions of nature, commonly called forces. Elementary particles, whose interactions are described by a gauge theory, interact with each other by the exchange of gauge bosons—usually as virtual particles.

All known gauge bosons have a spin of 1. Therefore, all known gauge bosons are vector bosons.

Gauge bosons are different from the other kinds of bosons: first, fundamental scalar bosons (the Higgs boson); second, mesons, which are composite bosons, made of quarks; third, larger composite, non-force-carrying bosons, such as certain atoms.

The Standard Model of particle physics recognizes four kinds of gauge bosons: photons, which carry the electromagnetic interaction; W and Z bosons, which carry the weak interaction; and gluons, which carry the strong interaction.

In physics, a coupling constant or gauge coupling parameter (or, more simply, a coupling), is a number that determines the strength of the force exerted in an interaction.

The coupling constant determines the strength of the interaction part with respect to the kinetic part, or between two sectors of the interaction part. For example, the electric charge of a particle is a coupling constant that characterizes an interaction with two charge-carrying fields and one photon field (hence the common Feynman diagram with two arrows and one wavy line). Since photons carry electromagnetism, this coupling determines how strongly electrons feel such a force, and has its value fixed by experiment.


A coupling plays an important role in dynamics. For example, one often sets up hierarchies of approximation based on the importance of various coupling constants. In the motion of a large lump of magnetized iron, the magnetic forces may be more important than the gravitational forces because of the relative magnitudes of the coupling constants. However, in classical mechanics, one usually makes these decisions directly by comparing forces.

In many grand unified theories the three gauge couplings (electromagnetic, weak and strong) are predicted to meet at some high energy unification (GUT) scale MX, above which the three interactions are unified and GUT symmetry breaking can be ignored. By around 1990 the gauge couplings at MZ had been determined very precisely, allowing a test of this gauge coupling unification.

3) It could provide an elegant solution to the hierarchy problem

In theoretical physics, the hierarchy problem is the large discrepancy between aspects of the weak force and gravity. There is no scientific consensus on why, for example, the weak force is 1024 times stronger than gravity. More technically, the question is why the Higgs boson is so much lighter than the Planck mass (or the grand unification energy, or a heavy neutrino mass scale).

One proposed solution, popular amongst many physicists, is that one may solve the hierarchy problem via supersymmetry. Supersymmetry can explain how a tiny Higgs mass can be protected from quantum corrections. Supersymmetry removes the power-law divergences of the radiative corrections to the Higgs mass and solves the hierarchy problem as long as the supersymmetric particles are light enough to satisfy the Barbieri–Giudice criterion. This still leaves open the mu problem, however. Currently the tenets of supersymmetry are being tested at the LHC, although no evidence has been found so far for supersymmetry.

In theoretical physics, the μ problem is a problem of supersymmetric theories, concerned with understanding the parameters of the theory.

Points 1 and 2 provide theoretical motivations for SUSY even though the 125GeV Higgs puts the SUSY paradigm at risk.

Consequences of R-parity conservation in the collider

R-parity is a concept in particle physics. In the Minimal Supersymmetric Standard Model, baryon number and lepton number are no longer conserved by all of the renormalizable couplings in the theory. Since baryon number and lepton number conservation have been tested very precisely, these couplings need to be very small in order not to be in conflict with experimental data.

1) Sparticles are pair produced in collisions

2) All particles decay to SM and LSP, which is stable

In particle physics, the lightest supersymmetric particle (LSP) is the generic name given to the lightest of the additional hypothetical particles found in supersymmetric models.

3) The LSP escape the detector unnoticed – missing transverse momentum

Undiscovered particles in the MSSM:

The Minimal Supersymmetric Standard Model (MSSM) is an extension to the Standard Model that realizes supersymmetry. MSSM is the minimal supersymmetrical model as it considers only “the [minimum] number of new particle states and new interactions consistent with phenomenology”. Supersymmetry pairs bosons with fermions, so every Standard Model particle has a superpartner yet undiscovered. If we find these superparticles, it equates to discovering such particles as dark matter, could provide evidence for grand unification, and provide hints as to whether string theory describes nature.

Higgsino; squarks; sleptons; neutralinos; charginos (guaginos); charginos; gluinos

Experimental signatures of R-parity conserving models:

Ex 1; gluino pair – decays into hadronic jets

Ex 2: Stop pair (anti-top quarks) decays either leptonically or hadronically

In particle physics, a stop squark, is the superpartner of the top quark as predicted by supersymmetry (SUSY). It is a sfermion, which means it is a spin-0 boson (scalar boson). While the top quark is the heaviest known quark, the stop squark is actually often the lightest squark in many supersymmetry models.

The stop squark is a key ingredient of a wide range of SUSY models that address the hierarchy problem of the Standard Model (SM) in a natural way. A boson partner to the top quark would stabilize the Higgs boson mass against quadratically divergent quantum corrections, provided its mass is close to the electroweak symmetry breaking energy scale. If this was the case then the stop squark would be accessible at the Large Hadron Collider. In the generic R-parity conserving Minimal Supersymmetric Standard Model (MSSM) the scalar partners of right-handed and left-handed top quarks mix to form two stop mass eigenstates. Depending on the specific details of the SUSY model and the mass hierarchy of the sparticles, the stop might decay into a bottom quark and a chargino, with a subsequent decay of the chargino into the lightest neutralino (which is often the lightest supersymmetric particle).

Many searches for evidence of the stop squark have been performed by both the ATLAS and CMS experiments at the LHC but so far no signal has been discovered. In January 2019, the CMS Collaboration published findings excluding stop squarks with masses as large as 1230 GeV at 95% confidence level.

Ex. 3: Chargino – neutralino pair production with decays into leptons

All “simplified models” rely on assumptions

Should not be taken as absolute limits on the masses of SUSY particles

Cross-section for SUSY production

In everyday speech, “cross section” refers to a slice of an object. A particle physicist might use the word this way, but more often it is used to mean the probability that two particles will collide and react in a certain way. For instance, when CMS physicists measure the “proton-proton to top-antitop” cross section, they are counting how many top-antitop pairs were created when a given number of protons were fired at each other.

Why use “cross section” when alternatives like “probability” and “reaction rate” exist? Cross section is independent of the intensity and focus of the particle beams, so cross section numbers measured at one accelerator can be directly compared with numbers measured at another, regardless of how powerful the accelerators are. Arrows are arrows, no matter how many of them are fired into the sky.

Early calculations led to the theoretical production of squarks and gluinos

If SUSY is realized in nature and the scalar quarks and/or the gluino are in the kinematic reach of the (HL-)LHC, it is expected that these strongly interacting particles are eventually produced and studied. On the other hand, SUSY particles that interact only via the electroweak force, i.e., the charginos, neutralinos, and scalar leptons, have a much smaller production cross section at the LHC.

At a (future) e+e collider charginos, neutralinos and sleptons, depending on their masses and the available centre-of-mass energy, could be produced and analysed in detail.

The ATLAS experiment has an extensive search program for third generation SUSY particles. These proceedings present new results that are interpreted in two simplified SUSY scenarios stemming from assumptions made regarding the mass spectrum: gluino-mediated and direct production of stops and sbottoms. Gauginos and third generation squarks/sleptons are relevant.

In supersymmetry theories of particle physics, a gaugino is the hypothetical fermionic supersymmetric field quantum (superpartner) of a gauge field, as predicted by gauge theory combined with supersymmetry.

  • The gluino is the superpartner of the gluon, and hence carries colour charge.
  • The gravitino  is the supersymmetric partner of the graviton.
  • Three winos  are the superpartners of the W bosons of the SU(2)Lgauge fields.
  • The bino is the superpartner of the U(1) gauge field corresponding to weak hypercharge.

Sometimes the term “electroweakinos” is used to refer to winos and binos and on occasion also higgsinos.

LHC ATLAS is a multipurpose experiment, but it can be “messy”

ATLAS (A Toroidal LHC ApparatuS) is one of the seven particle detector experiments constructed at the Large Hadron Collider (LHC), a particle accelerator at CERN (the European Organization for Nuclear Research) in Switzerland. The experiment is designed to take advantage of the unprecedented energy available at the LHC and observe phenomena that involve highly massive particles which were not observable using earlier lower-energy accelerators.


Linear accelerator 2 (Linac 2) is the starting point for the protons used in experiments at CERN.

The proton source is a bottle of hydrogen gas at one end of Linac 2. The hydrogen is passed through an electric field to strip off its electrons, leaving only protons to enter the accelerator. By the time they reach the other end, the protons have reached the energy of 50 MeV and gained 5% in mass. They then enter the Proton Synchrotron Booster, the next step in CERN’s accelerator chain, which takes them to a higher energy.

The proton beams are pulsed from the hydrogen bottle for up to 100 microseconds per pulse. The pulses are repeated again and again until enough protons are produced.

Linac 2 started up in 1978, when it replaced Linac 1. It was originally built to allow higher intensity beams for the accelerators that follow it in CERN’s accelerator complex. Linac 2 will be replaced by Linac 4 in 2020.

What does a proton-proton “collision” look like?


A Higgs particle is produced in a proton-proton collision at centre, and decays to two photons (particles of light, indicated by green towers) in an LHC detector. Tracks emerging from centre are from remnants of the two protons.

There are 1011 protons in each of the two bunches that collide with each other

ATLAS data-taking

Recent ATLAS Higgs coupling results


Searching for new physics in ATLAS

Electroweak SUSY searches in 21 final states. Need to select signal events whilst supressing backgrounds


Search for electroweak production of charginos and sleptons decaying in final states with two leptons and missing transverse momentum in s√=13 TeV pp collisions using the ATLAS detector.

Search for an excess of events with 2 leptons

No significant signs of electroweak SUSY

Is SUSY dead?

Dark matter interpretations of ATLAS searches for the electroweak production of supersymmetric particles in √s = 8 TeV proton-proton collisions

If we relax assumptions entering our simplified models then the constraints are often weaker (2016)

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