1. Beyond the Standard Model Physics
Peter Richardson
IPPP, Durham University and
CERN Theory Group
CTEQ 13th August

2. Outline Yesterday Today Conclusions Why BSM Physics?
Where will we look for it?
What are the models
Today
Collider Signatures
Discovery channels
Determining the model
Conclusions
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3. Generic BSM signatures
Before we go on and consider the signals of models of new physics in great detail it is worthwhile considering what we expect to see in general.
Most models of new physics predict either:
the existence of more particles than the Standard Model;
new operators which give deviations from the Standard Model predictions.
The signatures of the model depends on either:
how these particles are produced and decay;
the type of deviations expected.
CTEQ 13th August

4. Backgrounds
So I’m going to exclusively talk about signals, however getting the background right is essential.
In fact really for BSM physics the most important things at this school have been said by the other lecturers.
It’s important that the Standard Model processes and detectors are under control and that we have accurate Standard Model simulations.
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5. Deviations from the Standard Model
So there can be deviations from what is expected in the Standard Model due to:
due to compositeness;
exchanging towers of Kaluza-Klein gravitons in large extra dimension models;
unparticle exchange; …
Tends to give changes in the shapes of spectra.
Therefore in order to see a difference you need to know the shape of the Standard Model prediction.
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6. Example I: High-pT jets
One possible signal of compositeness is the production of high pT jets.
At one point there was a disagreement between theory and experiment at the Tevatron.
Not new physics but too little high-x gluon in the PDFs.
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7. Example II: Unparticles
Many models predict deviations in the Drell-Yan mass spectra.
For example in an unparticle model with the exchange of virtual spin-1 unparticles.
Cheung et. al. Phys.Rev.D76:055003,2007.
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8. Monojets
In some models either stable neutral particles can be produced recoiling against a jet.
Or a tower of KK gravitons in large extra dimension models.
Or unparticles. …
Gives a monojet signal.
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9. Monojets Many Standard Model electroweak backgrounds
CDF results taken from Fermilab wine and cheese seminar by K. Burkett.
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10. New Particle Production
In general there are two cases for models in which new particles are produced
The model has only a few new particles, often mainly produced as s-channel resonances:
Z-prime models;
Little Higgs;
Small extra dimensions.
The model has a large number of new particles:
SUSY;
UED;
Little Higgs with T-parity.
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11. Resonance Production
The easiest and cleanest signal in hadron collisions is the production of an s-channel resonance which decays to e+e- or m+m-.
Resonances in this and other channels are possible in:
Little Higgs models;
Z’ models;
UED;
Small Extra Dimensions.
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12. Example: Resonant Graviton Production
The best channel, e+e-, gives a reach of order 2 TeV depending on the cross section.
Other channels m+m-, gg, WW are possible.
If light enough the angular distribution of the decay products can be used to measure the spin of the resonance.
Allanach et. al.
JHEP 0009:019, 2000
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13. Hadronic Resonances A lot of models predict hadronic resonances.
Much more problematic due to the mass resolution.
Smears out narrow resonances and the QCD backgrounds are often huge.
Can do background subtraction but dealing with huge S/B ratios.
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14. SUSY-like models
Most of the other models are ‘SUSY’-like, i.e. they contain:
a partner of some kind for every Standard Model particle;
often some additional particles such as extra Higgs bosons;
a lightest new particle which is stable and a dark matter candidate.
As these are the most popular models I’ll spend most time on them.
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15. New Particle Production
A lot of new particles should be produced in these models.
While some particles may be stable, i.e. the decay length of the particle is such that the majority of the particles escape from the detector before decaying. In practice this happens for lifetimes greater than 10-7s.
However the majority of these particles decay to Standard Model particles.
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16. New Particle Production
Therefore we expect to see:
charged leptons;
missing transverse energy from stable neutral particles or neutrinos;
jet from quarks, perhaps with heavy bottom and charm quarks;
tau leptons;
Higgs production;
photons;
stable charged particles.
It’s worth noting that seeing an excess of these doesn’t necessarily tell us which model we’ve seen.
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17. New Particle Production
The archetypal model containing large numbers of new particles which may be accessible at the LHC is SUSY.
Other models are
UED
Little Higgs with T-parity
However in practice UED is mainly used as a straw-man model for studies trying to show that a potential excess is SUSY.
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18. The LHC Two statements which are commonly made are:
The LHC will discover the Higgs;
The LHC will discover low-energy SUSY if it exists.
The first is almost certainly true.
The second is only partially true.
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19. SUSY Production
In hadron collisions the strongly interacting particles are dominantly produced.
Therefore in SUSY squark and gluino production has the highest cross section.
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20. SUSY Decays These particles then decay in a number of ways.
Some of them have strong decays to other strongly interacting SUSY particles.
However the lightest squark/gluino can only decay weakly.
The gluino can only have weak decays with virtual squarks or via loop diagrams.
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21. SUSY Decays
This is the main production mechanism for the weakly interacting SUSY particles.
The decays of the squarks and gluinos will produce lots of quarks and antiquarks.
The weakly interacting SUSY particles will then decay giving more quarks and leptons.
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22. SUSY Decays
Eventually the lightest SUSY particle which is stable will be produced.
This behaves like a neutrino and gives missing transverse energy.
So the signal for SUSY is large numbers of jets and leptons with missing transverse energy.
This could however be the signal for many models containing new heavy particles.
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23. SUSY Searches All SUSY studies fall into two categories Search Studies
Designed to show SUSY can be discovered by looking a inclusive signatures and counting events.
Measurement Studies
Designed to show that some parameters of the model, usually masses, can be measured.
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24. General SUSY Signals
There’s a large reach looking for a number of high transverse momentum, pT, jets and missing transverse energy.
Taken from the CMS Physics TDR
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25. General SUSY Signals Or with additional leptons as well.
Taken from the CMS Physics TDR
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26. General SUSY signals
Also possible to have the production of Z and Higgs bosons and top quarks.
In many cases the tau lepton may be produced more often than the electron and muon.
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27. Measuring the Mass Scale
For events which have at least four jets and missing transverse energy.
The scale can be estimated using
This variable is strongly correlated with the mass of strongly interacting SUSY particles
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28. Measuring the Mass Scale
Can measure the squark/gluino mass to about 15%.
Taken from Phys.Lett. B498, 1 (2001.), D. Tovey.
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29. Discovering SUSY
The analyses we have just looked at are those that are used to claim the LHC will discover SUSY.
Is that what they tell us?
They don’t really discover SUSY.
What they see is the production of massive strongly interacting particles.
Doesn’t have to be SUSY, could be something else.
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30. Discovering SUSY
In order to claim that a signal is SUSY we would need to know more about it.
SUSY analyses tend to proceed by looking for characteristic decay chains and using these to measure the masses of the SUSY particles.
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31. SUSY Decay chains The two most common chains are Higgs production,
Lepton production, , perhaps via an intermediate slepton.
These are used as a starting point for mass measurements.
The masses of other particles can be measured by adding more leptons or jets and working up the decay chain.
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32. SUSY Mass Reconstruction
In many models the decay chain
exists.
The end-point of the dilepton mass distribution gives the mass difference of the neutralinos.
Use the leptons to measure the mass difference of the neutralinos.
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33. SUSY Mass Reconstruction
Most of these studies are essentially an exercise in relativistic kinematics.
For example if the decay is three body the endpoint is
If the decay has an intermediate slepton the endpoint is
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34. Deriving the end-points
These end-point results are always easiest to calculate in a specific frame. In this case the rest frame of the slepton is best.
In this frame the lepton frame the lepton from the neutralino decay has momentum.
The end-point occurs when the lepton produced in the decay is back-to-back with this
Summing the 4-momenta gives the end-point.
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35. SUSY Mass Reconstruction
Other information can be obtained by adding in more leptons and jets.
By adding a jet to this can measure more end-points in the lepton-q and lqq distributions.
This provides enough kinematic end-points to measure all the masses in the decay chain.
Most recent studies have made use of this.
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36. SUSY Mass Reconstruction
The mass of the LSP here is obtained to 14%, the slepton to 9%, the second neutralino to 8% and the squark to 5%.
The small errors on the heavier states are due to their larger masses. The dominant error is the overall scale.
Taken from Allanach et.al. JHEP 0009:004,2000.
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37. Other Masses It is also possible to reconstruct the gluino mass.
In some cases the heavier neutralino and chargino masses can be measured.
This all seems very promising.
Many masses can be measured and we have learnt a lot.
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38. Problems Would this enough to say we have discovered supersymmetry?
It strongly depends on specific decay chains being present.
Also in simulations we know what model was put in, unless someone has divine inspiration this won’t happen with data.
It’s not clear how this will effect things. There are a lot of hidden assumptions.
Doing a general analysis without these is very hard.
However once we seen something things may be clearer.
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39. Problems
Equally analysis techniques have changed a lot in recent years.
The top mass analysis of 10 years ago was very different to the approaches currently used.
There’s no telling what analysis techniques will be developed or applied to BSM signals during LHC running.
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40. Dark Matter
One of the hottest topics for some time has been the relation between cosmology, in particular dark matter, and collider experiments.
One aspect of this is using the relic density to constrain the SUSY parameter space.
Another is the idea that if we see SUSY this would tell us the mass of the dark matter and something about its interactions.
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41. Constraints
The most common additional assumptions are that the model must satisfy:
cosmological constraints from WMAP;
bgsg constraint;
g-2 constraint.
Opinions on how much weight to give to these constraints varies.
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42. Cosmological Constraints
Brown has a charged LSP.
Pink favoured by g-2.
Green excluded by b to sg
Cyan favoured by older cosmological constraints.
Blue by the WMAP results.
Taken from Phys.Lett.B565, 176 Ellis et.al.
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43. Cosmological Constraints
Some people would argue that we want the model to be consistent with all the limits.
Others, myself included, would argue that many of the things constrained by these limits do not have a major impact on the collider signals.
Often they depend on masses of say the heavier Higgs in (co)-annihilation diagrams which does not have a major effect on the collider signals.
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44. Measuring BSM Properties
If its there the LHC should see TeV scale physics in a number of models.
Once we have seen evidence of such physics we will need more accurate measurements to determine what it is.
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45. Measuring the Spin
Due to the couplings there are significant spin correlations in the quark-lepton mass distribution.
This is best seen by looking at the end-point of the mass distribution.
This configuration is favoured if the neutralino decays to a positive lepton and disfavoured for a negative lepton.
Spin 1 q e-
Spin 0 q e+
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46. Measuring the Spin
The problem is that this asymmetry vanishes if we can’t distinguish between quarks and antiquarks.
However the LHC produces more squarks than antisquarks because there are more incoming quarks.
Gives a measurable charge asymmetry
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47. Measuring the Spin With spin correlations Without spin correlations
Taken from Barr hep-ph/
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48. Measuring the Spin A similar decay chain exists in the UED model.
Used as a straw-man for SUSY.
The particle spins are different, as are the couplings, leads to different correlations.
Taken from
Smillie and Webber
JHEP 0608:055,2006
Red UED, dashed SUSY,
dotted phase space
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49. SUSY Variants
So I’ve talked a lot about the MSSM, or in reality the SUGRA model.
There are variants of the SUSY model which are interesting:
GMSB can give a stau which is stable on collider time-scales;
Split SUSY models in which the scalars are very heavy give interesting signals;
R-parity models in which the LSP decays.
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50. Split SUSY In the Split SUSY model the scalars are very heavy.
Leads to a gluino which is stable on collider timescales.
The gluino hadronizes giving heavy hadrons which contain the gluino.
When the gluino hadronizes it will form either
Glueball-like state
Mesonic state
Baryonic state
General opinion is that
Rg is the lightest state
Rqqq is unlikely to be directly produced.
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51. Split SUSY The R-hadron can be neutral or charged
Charged R-hadron production
Signal much like stable weakly interacting particles.
R-hadron looks like a muon but deposits more energy in the calorimeter.
Neutral R-hadron production
Some energy loss in calorimeter
Monojet type signals
The charge of the R-hadron will change due to interactions in the detector.
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52. R-parity Violation
The most challenging option is that baryon number is violated, leads to the decay of the LSP to 3 quarks.
As the coloured sparticles are dominantly produced the jet multiplicities are large.
For small baryon number violating couplings two LSP’s will be produced.
Look for events with 8-10 jets and some leptons from other SUSY decays.
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53. Baryon Number Violation
In order to extract the signal have to look at the distribution in the (jjj,jjjll) plane.
The jjjll distribution is the mass of the second neutralino.
As before the masses of other particles, here the squark and the slepton can be reconstructed by adding more jets or leptons.
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54. Black Holes
One of the more interesting recent ideas is that extra dimensional black holes could be produced in colliders.
There has been a lot of theoretical, and mainly experimental, interest.
There are a lot of claims about.
Certainly if black holes are produced they will decay to give spectacular events.
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55. Black Hole Event
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56. Black Holes
It is claimed that by measuring the spectrum of the decay products the temperature, and hence number of extra-dimensions can be measured.
There are a lot of experimental and theoretical uncertainties involved.
These make it very difficult to measure the temperature and number of extra-dimensions.
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57. Simulations
So as this is a joint CTEQ/MCnet school I thought I’d say something about the simulation of BSM signals.
My own view is that simulation of the Standard Model backgrounds is the most important thing.
Until we see something
However a lot of work has gone into providing high quality simulations of BSM signals in many models.
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58. Simulations
There are a number of tools available CompHEP, CalcHEP, MadGraph, SHERPA which can calculate the matrix elements for a range of BSM models.
Simulation of a lot of models in FORTRAN HERWIG and PYTHIA.
Sophisticated simulation of spin correlations in FORTRAN HERWIG and Herwig++.
The new generation of tools makes adding new models much easier.
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59. Summary
We are on the brink of what will hopefully be very exciting times.
I’ve been working on these things for more than 10 years, and others for much longer, without any experimental evidence.
With the start of the LHC that will hopefully change in the next few years.
Perhaps one of the models I’ve discuss will really be true in nature or perhaps something we haven’t even thought of.
CTEQ 13th August