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

2. Outline Today Tomorrow Conclusions Why BSM Physics?
Where will we look for it?
What are the models
Tomorrow
Collider Signatures
Discovery channels
Determining the model
Conclusions
CTEQ 13th August

3. Why BSM Physics? The Standard Model has 19 free parameters:
3 gauge couplings, g1, g2, g3;
6 quark and 3 charged lepton masses;
The Higgs mass and vacuum expectation value (VEV);
3 mixing angles and 1 phase in the CKM matrix
the Q parameter of QCD.
Now need additional parameters to incorporate neutrino masses and mixing. I won’t talk much about neutrino masses as they don’t affect the collider physics.
CTEQ 13th August

4. Why BSM Physics What are the values of these parameters?
Why is the top quark so much heavier than the electron?
Why is the Q parameter so small?
Is there enough CP violation to explain why we are all here?
What about gravity?
These are all important questions.
No definite answers to any of them.
CTEQ 13th August

5. Where will we look for BSM Physics?
All models of BSM physics predict either new particles or differences from the Standard Model, otherwise they are pretty useless.
There are a number of ways of looking for BSM effects.
Collider experiments
If the theory contains new particles these should be produced in collider experiments and decay to give Standard Model particles.
Examples include: CDF, D0, ATLAS, CMS
CTEQ 13th August

6. Where will we look for BSM Physics?
Precision Experiments
Measure something predicted by the Standard Model to very high accuracy and compare the results with the prediction.
Examples include: LEP/SLD Z measurements, muon g-2
Rare Decays or Processes
Measure the cross section or decay rate for some process which the Standard Model predicts to be very small (or zero.)
Examples include:
Neutron EDM, Proton Decay, Neutrino mixing
Rare B decays and CP violation experiments (BELLE, BaBar, LHCB)
CTEQ 13th August

7. Where will we look for BSM Physics?
In many ways these approaches are complimentary.
Some effects, e.g. CP violation, are best studied by dedicated experiments.
However if the result of these experiments differs from the SM there should be new particles which are observable at collider experiments.
Given the focus of this school I’ll concentrate on collider experiments in these lectures, although I will mention some constraints from precision experiments and rare processes.
CTEQ 13th August

8. What are the Models?
There are a large number of models of BSM physics.
The number of models ≥ the number of model builders.
Given the lack of any experimental evidence of physics Beyond the Standard Model the field is driven by theoretical and ascetic arguments and unfortunately fashion.
I’ll try and give a brief review of the more promising models.
CTEQ 13th August

9. What are the Models? So there are as wide range of models
GUT theories
Technicolor
SUSY
Large Extra Dimensions
Small Extra Dimensions
Little Higgs Models
Unparticles ….
Depending on which model builder you talk to they may be almost fanatically in their belief in one of these models.
CTEQ 13th August

10. What are the Models?
What I’ll try and do is give a brief introduction to the models which are relevant for collider physics, concentrating on hadron colliders.
Tomorrow when we come to look at the implications of these models for collider physics I’ll take a pragmatic view and look at the models based on their properties rather than specific details.
CTEQ 13th August

11. GUTs
The first attempts to answer these questions were Grand Unified Theories (GUTs.)
The basic idea is that the Standard Model gauge group is the subgroup of some larger gauge symmetry.
The simplest group is SU(5), other examples include SO(10).
We’ll consider SU(5) as it’s the simplest example.
SU(5) has 24 generators g 24 gauge bosons:
8 gluons of the Standard Model;
4 Electroweak gauge bosons W±, Z0,g;
therefore there are 12 new gauge bosons, X±4/3, Y±1/3
CTEQ 13th August

12. GUTs
The right-handed down type quarks and left handed leptons form a representation of SU(5).
The rest of the particles form a 10
CTEQ 13th August

13. GUTs In this model there are two stages of symmetry breaking.
At the GUT scale the SU(5) symmetry is broken and the X and Y bosons get masses.
At the electroweak scale the symmetry is broken as before.
There are three problems with this theory:
the couplings don’t quite unify at the GUT scale;
why is the GUT scale higher than the electroweak scale;
proton decay.
CTEQ 13th August

14. Low Energy Constraints
There are many important constraints from low energy experiments on BSM physics.
The most important are:
Flavour Changing Neutral Currents;
Proton decay.
Often other constraints, e.g. from astrophysics and cosmology are imposed.
We’ll come back to those later.
CTEQ 13th August

15. Proton Decay
Grand Unified theories predicts the decay of the proton via the exchange of X and Y bosons
Should go like
CTEQ 13th August

16. Proton Decay
Limits from water Cerenkov experiments give tP≥1.6x1032 years.
This means MX> GeV.
This is larger than preferred by simpler unification models.
Proton decay gives important limits on other models.
CTEQ 13th August

17. Hierarchy Problem
The vast majority of new physics models are motivated by considering the hierarchy problem.
Fundamentally this is the question
Why is the electroweak scale so much less than the GUT or Planck (where gravity becomes strong) scales?
This is often motivated by considering the so-called technical hierarchy problem.
CTEQ 13th August

18. Hierarchy Problem
If we look at the Higgs mass there are quantum corrections
This gives a correction to the Higgs mass
If we introduce an ultra-violet cut-off to regularize the integral
CTEQ 13th August

19. Hierarchy Problem
So either the Higgs mass is at the GUT/Planck scale or there is a cancellation
of over thirty orders of magnitude to have a light Higgs.
This worries a lot of BSM theorists, however there are values of the Higgs mass for which the Standard Model could be correct up to the Planck scale.
CTEQ 13th August

20. Hierarchy Problem Many solutions to the hierarchy have been proposed.
They come in and out of fashion and occasionally new ones are proposed.
I will consider four:
Technicolor;
Supersymmetry;
Extra Dimensions;
Little Higgs Models.
CTEQ 13th August

21. Technicolor
This is one of the oldest solutions to the hierarchy problem.
Main idea is that as the problems in the theory come from having a fundamental scalar, so don’t have one.
The model postulates a new set of gauge interaction, Technicolor, which acts on new technifermions.
The interaction is supposed to be like QCD.
The technifermions form bound states, the lightest being technipions.
CTEQ 13th August

22. Technicolor
By the Higgs mechanism these technipions give the longitudinal components of the W± and Z bosons, and hence generate the boson masses.
Still needs to find a way to give the fermions masses, called Extended Technicolor.
It has proven hard to construct realistic models which aren’t ruled out.
For many years Technicolor fell out of fashion however following the introduction of Little Higgs models there has been a resurgence and the new walking Technicolor models look more promising.
CTEQ 13th August

23. Supersymmetry
By far the most popular theory of new physics is supersymmetry.
If we consider a scalar loop in the Higgs propagator
There is a new contribution to the Higgs mass
CTEQ 13th August

24. Supersymmetry
If there are two scalars for every fermion, with the same mass and lS=|gf|2 the quadratic divergence cancels.
Theorists like to have symmetries to explain cancellations like this ⇒ Supersymmetry.
For every fermionic degree of freedom there is a corresponding bosonic degree of freedom:
All the SM fermions have two spin-0 partners;
All the SM gauge bosons have a spin-1/2 partner.
Need two Higgs doublets to give mass to both up and down type quarks.
CTEQ 13th August

25. SUSY Particles
The partners of the photon, Z and Higgs bosons mix, as to the partners of the charged Higgs boson and the W±.
CTEQ 13th August

26. Supersymmetry
In addition to the solution of the hierarchy problem there are other important reasons to favour SUSY as an extension of the Standard Model.
Coleman-Mandula theorem
Any extension to the Poincare group which has generators which transform as bosons leads to a trivial S matrix.
Haag, Lopuszanski and Sohnius showed that SUSY is the only possible extension of the Poincare group which doesn’t give a trivial S matrix.
CTEQ 13th August

27. Supersymmetry SUSY coupling unification
In SUSY GUTS the additional SUSY particles change the running of the couplings and allow the couplings to truly unify at the GUT scale.
CTEQ 13th August

28. R-parity
If we were to construct the Standard Model based on its symmetries then we must write down all the terms allowed by the symmetry.
If we do the same in SUSY we naturally get terms which do not conserve lepton and baryon number.
CTEQ 13th August

29. R-parity
Proton decay requires that both lepton and baryon number are violated.
The limits on the lifetime of the proton therefore leads to very stringent limits on the product of the couplings leading to proton decay.
CTEQ 13th August

30. R-parity
Only natural way for this to happen is if some symmetry requires that one or both couplings are zero.
Normally a symmetry R-parity is introduced which forbids both terms.
Rp = (-1)3B+L+2S
Rp=+1 Standard Model Particle
Rp= -1 SUSY particles
Alternatively symmetries can be imposed which only forbid the lepton or baryon number violating terms.
This has important consequences which we’ll discuss tomorrow.
Simplest SUSY extension of the Standard Model has Rp conservation and is called the Minimal Supersymmetric Standard Model (MSSM).
CTEQ 13th August

31. R-parity
The multiplicative conservation of R-parity has two important consequences:
SUSY particles are only pair produced;
The lightest SUSY particle is stable, and therefore must be neutral on cosmological grounds. It is therefore a good dark matter candidate.
CTEQ 13th August

32. The m-problem and the NMSSM
Many theorists worry about the m-term in the superpotential which couples the two Higgs doublets.
This is because as m has the dimensions of mass and is not protected by a symmetry from being at the GUT scale.
The solution is to replace the m term with an additional singlet Higgs field which couples to the two Higgs doublets.
The m term is then generated when it develops a VEV.
The NMSSM has cosmological problems with domain walls due to the self-coupling of the new singlet field.
There are a lot of different models on the market with different additional symmetries to prevent this.
CTEQ 13th August

33. SUSY Breaking So far I haven’t dealt with the biggest problem in SUSY.
Supersymmetry requires that the SUSY particles have the same mass as their Standard Model partner and we ain’t seen them.
SUSY must therefore be a broken symmetry.
It needs to be broken in such a way that the Higgs mass doesn’t depend quadratically on the cut-off, called Soft SUSY breaking.
Introduces over 120 parameters into the model.
CTEQ 13th August

34. Flavour Changing Neutral Currents
In the Standard Model Flavour Changing Neutral currents are suppressed by the GIM mechanism.
Let’s consider kaon mixing
And rare kaon decays
CTEQ 13th August

35. Flavour Changing Neutral Currents
If we consider two generations for simplicity the diagrams go like
Times a factor due to the Cabbibo angle.
M is the largest mass left after removing 1 W propagator, i.e MW for mixing and K0Lgm+m-dand mc for K0Lggg.
CTEQ 13th August

36. Flavour Changing Neutral Currents
This suppression is called the GIM mechanism.
Explains why G(K0Lgm+m-) is 2x10-5G(K0Lggg).
The current experimental results are in good agreement with the Standard Model.
This often proves a problem in BSM physics as there are often new sources of FCNCs.
CTEQ 13th August

37. Flavour Changing Neutral Currents
In SUSY theories the SUSY partners also give contributions to the FCNCs.
Here the diagrams are proportional to the mass difference of the squarks.
CTEQ 13th August

38. Flavour Changing Neutral Currents
Provided the SUSY breaking masses are flavour independent not a problem, as the mass differences are the same as in the SM.
Also not a problem if no flavour mixing in the model.
However, in general these things are possible and need to be considered.
CTEQ 13th August

39. SUSY Breaking What are these parameters?
SUSY breaking masses for the scalars;
SUSY breaking masses for the gauginos;
A terms which mix three scalars;
Mixing angles and CP violating phase.
Need a model of where these parameters come from in order to do any experimental studies.
CTEQ 13th August

40. SUSY Breaking
Instead use models which predict these parameters from physics at higher energy scales.
In all these models SUSY is broken in a hidden sector .
The models differ in how this breaking is transmitted to the visible sector.
CTEQ 13th August

41. SUGRA SUSY breaking is transmitted via gravity.
All the scalar masses (M0) are unified at the GUT scale.
All the gaugino masses (M1/2) are unified at the GUT scale.
Universal A terms.
Use the known value of the Z mass to constrain the m term, leaves tanb=v1/v2 and the sign of m as parameters.
Five parameters give the mass spectrum: M0, M1/2, tanb, sgnm, A.
CTEQ 13th August

42. GMSB
Solves the flavour-changing neutral current problem by using gauge fields to transmit the SUSY breaking.
Messenger particles, X, transmit the SUSY breaking.
The simplest choice is a complete SU(5) 5 or 10 plet to preserve the GUT symmetry.
Fundamental SUSY breaking scale ≤1010 GeV.
Gaugino masses occur at 1-loop, scalar masses at 2-loop.
True LSP almost massless gravitino.
Lightest superpartner is unstable and decays to the gravitino.
Can be neutral, e.g. , or charged .
CTEQ 13th August

43. AMSB The superconformal anomaly is always present.
Predicts sparticle masses in terms of M3/2.
Simplest version predicts tachyonic particles.
Need another SUSY breaking mechanism to get a realistic spectrum.
E.g. add universal scalar masses, (M0)
The model has 4 parameters M0 , M3/2 , tanb , and sgnm.
In this model the lightest chargino is almost degenerate with the lightest neutralino
CTEQ 13th August

44. SUSY Spectrum The mass spectrum is different in the models.
Gives different collider signals which are worth studying.
Different splittings between the weakly and strongly interacting states.
Different nature of the LSP
CTEQ 13th August

45. Extra Dimensions
Many theorists believe there are more than 4 dimensions.
The hierarchy problem can be solved (redefined?) in these models in one of two ways.
There are extra dimensions with size ~1mm
The Planck mass is then of order 1 TeV
So no hierarchy problem, but need to explain the hierarchy in the sizes of the dimensions.
CTEQ 13th August

46. Extra Dimensions Small Extra Dimensions The extra dimension is warped.
The model has at least two branes.
We live on one and the other is at the Planck scale.
The Higgs VEV is suppressed by a warp factor.
CTEQ 13th August

47. Kaluza-Klein Excitations
If we consider the simplest example of a scalar field in 5 dimensions
Where
If the 5-th dimension is circular
The eqn of motion becomes.
Tower of states with mass splitting ~1/R2
CTEQ 13th August

48. Extra Dimensions
In both the small and large extra dimension models only gravity propagates in the bulk.
There we can Kaluza-Klein excitations of the graviton.
Large Extra Dimensions
The mass splitting is small.
All the gravitons contribute to a given process.
Small Extra Dimensions
The mass splitting is large.
Get resonant graviton production.
The phenomenology is therefore very different.
CTEQ 13th August

49. Universal Extra Dimensions
Another alternative is to let all the Standard Model field propagate in the bulk, Universal Extra Dimensions.
All the particles have Kaluza-Klein excitations.
It is possible to have a Kaluza-Klein parity, like R-parity is SUSY.
The most studied model has one extra dimension and a similar particle content to SUSY, apart from the spins.
Also some 6-dimensional models.
CTEQ 13th August

50. Little Higgs Models The main ideas of Little Higgs models are
The Higgs fields are Goldstone bosons associated with breaking a global symmetry at a high scale Ls;
The Higgs fields acquire a mass and become pseudo-Goldstone bosons via symmetry breaking at the electroweak scale
The Higgs fields remain light as they are protected by the approximate global symmetry.
The model has heavy partners for the photon, Z and W bosons and the top quark as well as extra Higgs bosons.
CTEQ 13th August

51. Little Higgs Models
The non-linear s-model used for the high energy theory is similar to low energy effective theory of pions which can be used to describe QCD, or is used in Technicolor models.
So there are some similarities between Little Higgs and Tecnicolor models which is the main reason for the resurgence of Technicolor models.
CTEQ 13th August

52. Little Higgs Models
The original Little Higgs models had problems with electroweak constraints.
Solution is to introduce a discrete symmetry called T-parity, analogous to R-parity.
Solves the problems with precision data and provides a possible dark matter candidate.
Has a much larger particle content than the original Little Higgs model, SUSY-like.
CTEQ 13th August

53. Unparticles Based on an idea of Georgi, hep-ph/0703260.
Introduce a new sector at a high energy scale with a non-trivial IR fixed point.
Interacts with the Standard Model via the exchange of particles with a large mass scale.
CTEQ 13th August

54. Unparticles Leads to an effective theory
dU is the scaling dimension of the unparticle operator OU;
MU is the mass scale for the exchanged particles;
OSM is the Standard Model operator;
dBZ is the dimension of the operator in the high energy theory;
k gives the correct overall dimension of the term.
CTEQ 13th August

55. Summary
In today’s lecture I’ve tried to give a summary of the more popular models of physics Beyond the Standard Model.
We’ve looked at the basic ideas and motivations for these models.
Tomorrow we’ll take a more pragmatic view and look at the signals at the LHC.
CTEQ 13th August