Transcript Document

Beyond the Standard
Model Physics
Peter Richardson
IPPP, Durham University and
CERN Theory Group
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Outline
• Today
– Why BSM Physics?
– Where will we look for it?
– What are the models
• Tomorrow
– Collider Signatures
– Discovery channels
– Determining the model
• Conclusions
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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.
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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.
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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
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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)
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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.
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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.
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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.
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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.
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GUTs
• The first attempts to answer these questions were
Grand Unified Theories (GUTs.)
• The basic idea is that the Standard Model gauge
group SU (3)c  SU (2)L U (1)Y 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
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GUTs
• The right-handed down type quarks and left
handed leptons form a 5 representation of
SU(5).
• The rest of the particles form a 10
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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 SU (2) L U (1)Y
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.
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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.
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Proton Decay
• Grand Unified theories predicts the decay of
the proton via the exchange of X and Y
bosons
• Should go like ( p   e )
0 
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M X4
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Proton Decay
• Limits from water Cerenkov experiments give
tP≥1.6x1032 years.
• This means MX>1016-17GeV.
• This is larger than preferred by simpler
unification models.
• Proton decay gives important limits on other
models.
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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 socalled technical hierarchy problem.
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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
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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.
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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:
–
–
–
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Technicolor;
Supersymmetry;
Extra Dimensions;
Little Higgs Models.
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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.
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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.
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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
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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.
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SUSY Particles
• The partners of the photon, Z and Higgs bosons mix,
as to the partners of the charged Higgs boson and
the W±.
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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.
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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.
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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.
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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.
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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).
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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.
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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.
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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.
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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
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Flavour Changing Neutral Currents
• If we consider two generations for simplicity
the diagrams go like
1 m m
2
2
MW M
2
u
2
c
• 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+mdand mc for K0Lggg.
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Flavour Changing Neutral Currents
• This suppression is called the GIM
mechanism.
• Explains why (K0Lgm+m-) is 2x10-5(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.
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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.
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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.
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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.
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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.
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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.
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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 2loop.
• True LSP almost massless gravitino.
• Lightest superpartner is unstable and decays to the
gravitino.

• Can be neutral, e.g. 1,0 or charged t1.
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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
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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
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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
2
M Planck
~ M n  2 Rn
• 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.
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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.
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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
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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.
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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.
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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.
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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.
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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.
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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.
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Unparticles
• Leads to an effective theory
d BZ  dU
U
C L
U
M
k
U
OSM OU
– 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.
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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.
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