Beyond the Standard Model

Dec 4, 2018

With slides from Paris Sphicas 2015 Hadron Collider Summer School

Unanswered Questions

• With discovery of the Higgs, SM looks complete

• Aside from ν-mass (which can easily be accomodated) dataappears consistent with SM

• But, there are many unanswered questions:I What is Dark Matter?I Where did all the antimatter go?I Why is the EW scale so low (relative to Planck scale)?I Why 3 generations?I Do all the forces unify?

Answers to these questions lie outside the SM

The Hierarchy Problem

• Why is the EWK scale so low?

• Assume no new physics up to ascale Λ

I Suppose that scale isMPlanck

I Radiative corections forceHiggs mass up:mh ∼MPlanck

• Need “finetuned”cancellation betweendiagrams

• Can be solved by presence ofnew particles at TeV scale

I Tuning already ∼ 1% forΛ ∼ 10 TeV

Possible Solutions to the Hierarchy Problem

• Solution #1: a composite HiggsI Higgs a bound state (eg due to new extra strong interaction)

• Solution #2: Supersymmetry (SUSY)I Partner for every SM particle with spin that differs by 1

2

• Solution #3: “little Higgs”I Ultimate theory with scale well above EW scale with Higgs as

“pseudo goldstone boson.” Effective theory valide up to ∼ 10TeV or higher

• Solution #4: Extra DimensionsI Brings Planck scale down to EW scaleI Gravity propagates in all dimensions, SM in 3

All these solutions demand presence of new particles

Searching for New Physics

• Before LHC turn-on, SUSY was by far the most popular optionI Extension of Poincare group to include fermionic anticommuting

spinorsI Required by string theoryI Has natural Dark Matter candidateI Helps with unification of coupling constantsI Predicts a light higgs

• So far, SUSY has not been foundI Current limits rule out most of phase space for simplest model

• Encourages Broader range of searchesI New heavy quarksI New gauge bosonsI Long lived heavy particlesI Non-SUSY Dark Matter candidatesI Evidence for higher scale interactions via excesses from theory in

well defined EW measurements (eg WW scattering)

Will flash a few examples of non-SUSY searches (slides by Paris Sphicas)

and then talk about SUSY in more detail

SUSY can solve the some problems of SM

• Each SM particle gets a partnerdiffering in spin by 1/2

• Unification of forces possibleI SUSY changes running of

coupling constants

• Dark matter candidate exitsI Lightest neutral partner of

gauge bosons (or higgs)

• Little fine-tuning requiredI Cancellation of fermion

and sfermion loopsI SUSY particle masses

must not be too high forthis to work ( TeV)

Supersymmetry: Overview

Supersymmetry: The Particles

SUSY Breaking

• If SUSY was a good symmetry, the particles and sparticleswould have the same mass

• We have not seen selectrons, squarks, etc, so if they existtheir masses must be large

I SUSY must be a broken symmetry

• Not clear what mechanism breaks SUSY. Many possibilitiesI Phenomenology changes drastically depending on mechanism

for SUSY breakingI Breaking occurs in some “hidden sector” that does only

couples very weakly to “visible sector” of SM and SUSYparticles

Examples of SUSY Breaking Mechanisms

• Gravity-mediated SUSY breakingI Breaking via new particles at scale < F >:

msoft ∼< F > /MP

I Here < F > is the VEV of the hidden sectorI For MSUSY ∼ 1 TeV:

√F ∼ 1011 GeV

• Gauge-mediated SUSY breakingI Breaking via messenger particles

msoft ∼αa

4π

< F >

Mmess

I For MSUSY ∼ 1 TeV:√F ∼ 104 GeV if Mmess ∼

√F

I Also called “low-scale SUSY breaking”

SUSY and Proton Decay

• In a generic SUSY model, the proton would decay, edp→ e+π0

• Bound on proton lifetime τ > 5.8× 1029years (Super-K)

Need a mechanism to keep the proton stable

R-Parity

• Introduce a new quantum number called “R-parity”I R = +1 for all SM particlesI R = −1 for all SUSY particles

• Require R-parity be conservedI SUSY particles can only be produced in pairtsI SUSY particles must decay into an odd number of SUSY

particles, plus SM particlesI Lightest SUSY particle is stable and cannot decay

• This is a good candidate for Dark Matter

A “Typical” Sparticle Mass Spectrum

NB: This spectrum has already been ruled out by the LHC

How the SUSY particles develop their different masses

• Depends on SUSY breaking mechanism. This is one example.

• Assume Grand Unified (GUT) scale where all spin 0 sparticleshave one mass and all spin 1/2 sparticles has one mass

• Masses evolve with scale (use renormalization group equationsto calculate the running of the masses)

• Weakly coupled particles are the lightest

Additional Comments on SUSY Spectra

• As noted above, mass spectrum depends on SUSY breakingmechanisms

• Very different spectra for different SUSY breaking models

• Ususally (but not always) sleptons and gauginos are lighterthan squarks and gluinos

• The physical states are often mixtures of SM partnersI Eg: χ0 is a mixture of photino, zino and higgino

The Higgs in SUSY (MSSM)

• Two Higgs fields, one to give mass to the up-type particles and oneto give mass to the down-type particles

vu =< H0u > vd =< H0

d > tanβ = vu/vd

• There are 5 Higgs fields in this model

m2A0 = 2|µ|2 +m2

Hu+m2

Hd

m2h0,H0 =

1

2

(m2

A0 +m2Z ±

√(M2

A −m2Z)2 + 4m2

Zm2Z sin2(2β)

)m2

H± = m2A +m2

W

• At tree level mh0 < MZ | cos(2β)| which was ruled out at LEP

• But loop corrections lift the h0 mass, so SUSY can be consistent

with the LHC Higgs discovery (although much of the SUSY space is

excluded)

The Higgs in the MSSM

• Stop mass needs to be large tolift Higgs mass to 125 GeV

• But stop mass needs to be lowto avoid fine-tuning

• Impossible to get small fine

tuning without extending

MSSM

How do we search for SUSY?

• Precision measurements of SM ObservablesI Eg, g − 2 of the moun

• Enhancement in rare decaysI Eg µ→ eγ

• Direct production at collidersI Eg the LHC

Muon g − 2 and SUSY (I)

Muon g − 2 and SUSY (II)

Simplest interpretation in very constrained modelsThis model already ruled out by 125 GeV Higgs

Rare Decays: µ→ eγ

• Experimental limit from MEG at PSI BR < 1.2× 10−11

• Mu2e at FNAL plans improvement of 4 orders of magnitude

SUSY searches at the LHC

• Strong production of squarks and gluinos means rates arelarge (for moderate masses)

I In general, these sparticles have cascade decays until theyreach the LSP

• Weak production of sleptons and χ’s make them more difficultto find

I Often best found from the cascades of strongly producedparticles

I Otherwise, you need lot’s of integrated luminosity and goodbackground rejection

Strategy for SUSY Searches

• MSSM has 105 free parametersI Impossible to scan full parameter spaceI Many constrains from precision measurements, flavour

violation, baryon violation, etc

• Not sensible to choose random set of parametersI Use simplified well motivated “benchmark” models

• Ease comparison between experiments

• Try to make interpretation of data as model independent aspossible

Classic Searches: Missing ET

SUSY and Dark Matter

• SUSY models can provide DM candidatesI R-parity: Lighest SUSY particle (LSP) stableI In most models LSP is weakly interactingI Must be neutral to be DM candidate

• Strongly interacting SUSY particles heavier than LSPI Large production cross sectionsI Decay chains with LSP at the bottom

• Classic signature: missing momentum + many jets

Experimental Issues (I): Seeing the invisible

• DM particles will escape detector without being seen

• Signature is momentum imbalance

• Can only use transverse components of momentum (stuffalways goes down the beampipe)

• Often call missing-Et:

6 ET = −∑i

( ~pT )i

• Major sources of missing ET in SM are:I NeutrinosI Mismeasurement of hadronic jets

Experimental Issues (II): It’s the background, stupid

• Looking for small rate processes in environment where overallrate huge

• Must indentify signatures where signal stands out

• Must demonstrate that any potential signal is real

• Requires validation of background

Experimental Issues (III): You have to trigger first!

Example: Jets and Missing Et

What Next?

• Increased luminosity pushes limits upward

• Sensitivity to weakly produced particles much better withmore data

• Begin to study corners of phase space not accessible in genericsearches

• Searches for more Higgs Bosons

• Precison measurements of Higgs properties: possibledeviations from SM