Lecture 8: BSMdauncey/DanielMaitreLectures/Lecture6.pdf · Phenomenology – Daniel Maître Grand...

Phenomenology – Daniel Maître

Phenomenology

Lecture 8: BSM

Daniel Maître

IPPP, Durham


Why BSM?

● Despite the success of the Standard model, there are some puzzles left:– Why is the top so much heavier than the electron?

– Why is Θ so small?

– Is there enough CP violation?

● We need masses for the neutrinos● What is dark matter?● What is dark energy?● What about gravity?


BSM

● New models usually include more particles● We can find them

– Direct production: By directly producing them in the colliders if they are light enough and they interact (enough) with the standard model

– Precision observables: By measuring their effect on precision observables through loop correction (where they can be off-shell if the energy is not sufficient to produce them) examples: g-2, EW precision measurements

– Rare decays: If there is a new interaction, even a weak one, new processes become allowed that are not allowed in the standard model, or are highly suppressed. Examples: Proton decay, neutrino mixing, rare B and Kaon decays...


BSM models

● There are a large number of BSM models● This may be due to the fact that it is easier to “cook up”

a model that it is to test it.● Since there is no (direct) experimental evidence for

BSM particles the game is to find models that are most undistinguishable from the SM.

● We can only cover a limited number of models and look at their experimental implications

● It is much better, when possible, to have model independent searches, so that they can be used for several models not just the one that is trendy at the moment of the measurement


BSM models

● Here are some models– GUT theories

– Technicolor

– SUSY

– Large extra dimensions

– Small extra dimensions

– Little Higgs Models

– ...


Grand unified Theories

● The basic idea is that the Standard model gauge group is a subgroup of a larger gauge symmetry group

● The simplest is SU(5), another example is SO(10)


SU(5)

● SU(3) has 32-1=8 generators, they correspond to the 8 gluons

● The quarks are in the fundamental representation of SU(3)

● SU(5) has 52-1=24 generators, which means that we have 24 gauge bosons– 8 gluons and 4 electroweak bosons

– So we get 12 new gauge boson


SU(5)

● Generators of SU(5)


SU(5)

● The right handed down type quarks and left handed leptons form a 5 representation of SU(5)

● The rest forms a 10 representation


Grand unified Theories

● 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)xU(1) symmetry is broken as before

● There are three problems with this theory:– The couplings don't meet at the GUT scale– Still need to explain why the GUT scale is higher than

the electroweak scale– Proton decay


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

● There are also other constraints from astrophysics and cosmology


Proton Decay

● Since in Grand Unified theories we have the X boson coupling quarks and leptons, they predict the decay of the proton

● The expected decay rate would be


Proton decay

● There are limits on the proton lifetime from water Čerenkov experiment.

● The decay of the proton will produce an electron which is travelling faster than the speed of light in water, which will cause Čerenkov radiation

● This can be detected as in a neutrino reactor● There are no evidence for such a decay and this gives a

lower limit on the lifetime of the proton of 1.6x1032 ● This translates into a lower limit on the mass of the X

boson of 1016-17 GeV, which is larger than preferred by coupling unification

● The proton decay gives limits on other models too.


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 Plank scale? (The plank scale is the scale at which gravity becomes strong)

● It is most common to discuss the technical hierarchy problem which is related to the Higgs mass

● As we have seen, masses get correction from higher orders


Hierarchy problem

● This gives a correction to the Higgs mass:

● We need to introduce an ultraviolet cut-off to regularize the integral

● This is because the Higgs is a scalar, otherwise the cut-off dependence is less severe


Hierarchy Problem

● So either the Higgs mass is at the Plank scale or there is a cancellation

of over 30 orders of magnitude to have a light Higgs

● This worries a lot of BSM theorists, however there are values of the Higgs boson mass for which the Standard model could be correct up to the Plank scale


SM validity

● The Higgs boson mass is

● There are two constrains on the mass:– We want the coupling to

stay perturbative,

– We want the vacuum to be stable, too small values of λ are not allowed

● There are values for which both are possible up to the Plank mass


Hierarchy problem

● Many models address the hierarchy “problem”– Technicolor

– Supersymmetry

– Extra dimensions

– Little Higgs models


Technicolor

● This is one of the oldest solutions to the hierarchy problem.

● The main idea is that as the problems in the theory come from having a fundamental scalar, a solution is not to have one.

● The model postulates a new set of gauge interactions: Technicolor, which acts on new technifermions.

● We think of this interaction as a copy of QCD, although different gauge groups have been considered.

● The technifermions form bound states, the lightest being technipions.


Technicolor

● By the Higgs mechanism these technipions give the longitudinal components of the W± and Z bosons, and hence generate the boson masses.

● Still need to find a way to give the fermions masses, called Extended Technicolor.

● It has proved hard to construct realistic models which are not already ruled out.

● For many years Technicolor fell out of fashion, however following the introduction of Little Higgs models there has been a resurgence of interest and the new walking Technicolor models look more promising.


Supersymmetry

● If there were a scalar loop in the Higgs propagator

● We would get a new contribution to the Higgs mass


Supersymmetry

● If there are two scalars for every fermion, with the same mass and then the quadratic dependence cancels.

● Theorists like to have symmetries to explain cancellations like this: Supersymmetry.⇒

● For every fermionic degree of freedom there is a 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 the up and down type quarks.


Supersymmetric particles

● All standard model bosons have 2 spin-half partners, called gauginos

SM particle Spin SUSY particle Spin

ElectronNeutrinoupdown

1/21/21/21/2

SelectronSneutrinoSupSdown

0000

Gluon 1 gluino 1/2

PhotonZHiggs

110

PhotinoZinoHiggsino

1/21/2 Neutralino1/2

W+H+

10

WinoHiggsino

1/2 Charginos1/2


Supersymmetry

● There are major two reasons, in addition to the solution of the hierarchy problem, to favour SUSY as an extension of the SM.

● Coleman-Mandula theorem– If we consider extensions to the Poincaré group any

new generators which transform as bosons (defined through commutation relations) lead to a trivial S-matrix, i.e. scattering only through discrete angles.

– Later Haag, Lopuszanski and Sohnius showed that SUSY is the only possible extension of the Poincaré group which doesn’t give a trivial S matrix.


Supersymmetry

● Susy coupling unification– In SUSY the additional SUSY particles change the running

of the coupling and allow the couplings to truly unify at the GUT scale

– This is not quite the case any more with the increasingly accurate experimental measurements of the strong coupling


Supersymmetry: R-parity

● The usual way a theory is constructed is to add new particles and/or symmetries (which lead to new interactions)

● We then consider all new terms in the Lagrangian that are allowed by the symmetries

● Doing this with supersymmetry leads to terms which violate baryon and lepton number and can cause proton decay


R-Parity

● The limits on the proton lifetime lead to a lower limit on the couplings of the supersymmetric particles involved in the proton decay process


R-Parity

● Model builders don't like small numbers either: we need to have a symmetry that explains why the couplings (or at least one of them) are zero

● Normally one uses R-parity:

● It is a discrete transformation● It is 1 for standard model particles and -1 for

SUSY particles● Other symmetries can be imposed


R-Parity

● It we impose it as a symmetry, all interaction terms allowed in the Lagrangian have to have parity 1

● So only vertices with an even number of SUSY particles are allowed

● It has two important consequences:– SUSY particle are only pair produced

– A SUSY particle can not decay in SM particles only, that means that the lightest supersymmetric particle (LSP) is stable. This is usually taken as a selling argument for SUSY as this LSP provides a candidate for dark matter


Supersymmetry

● Since we don't observe supersymmetric particles, supersymmetry has to be broken

● The phenomenology is quite different depending on the susy breaking scenario – Supergravity (SUGRA)

– Gauge mediation

– Anomaly mediation

● Main differences:– mass splitting between gluino and electroweak Gauginos;

– mass splitting of the squarks and sleptons;

– nature of the LSP


Supersymmetry


Flavour changing neutral current● In the Standard Model Flavour Changing Neutral Currents are

suppressed by the GIM (Glashow-Iliopoulos-Maiani) mechanism.● For example in kaon mixing

● And the rare kaon decays


GIM mechanism● The amplitude is proportional to two CKM matrix elements

● When we sum over the u-family quarks we are computing one element of the matrix

● But the CKM matrix is unitary so it has to vanish!


Flavour changing neutral current

● If we consider two generation for simplicity.● All the diagrams behave like

multiplied with a factor due to the Cabbibo angle● M is the largest mass left after the removal of 1 W

propagator, i.e.–

–


GIM mechanism

● This suppression is called the GIM (Glashow-Iliopoulos-Maiani) mechanism.

● Explains why

● The current experimental results are in good agreement with the SM.

● This often proves a problem in BSM physics as there are often new sources of FCNCs.


Flavour changing neutral current

● In SUSY theories the SUSY partners also give contributions to FCNCs.

● There are way to prevent FCNC in SUSY but it puts constraints on SUSY breaking


Extra dimensions● The idea is that we actually have more than 4 space-time

dimensions● String theories typically need an increased number of dimensions● The hierarchy problem can be solved (redefined?) in these

models in one of two ways.– There is an extra dimension with size 1mm.∼

● The Planck mass is then of order 1 TeV.● So there is no hierarchy problem, but need to explain the hierarchy in the sizes

of the dimensions.

– Small extra dimensions.● The extra dimension is warped.● The model has two branes.● We live on one and the other is at the Plank scale.● The Higgs VEV is suppressed by a warp factor, exp(−krc)


Kaluza-Klein Excitations● If we consider a scalar field in 5 dimensions

where

● If the fifth dimension is circular with radius R, we can expand the field in modes in the 5-th dimension

● The equation of motion becomes

● So we get a tower of states with mass splitting ~ 1/R^2


Extra dimensions

● In both small and large extra dimension models only gravity propagates in the bulk.

● So we get Kaluza-Klein excitations of the gravitons.● Large Extra Dimensions

– The mass splitting is small.

– All the gravitons contribute to a given process.

– Gives deviations from the SM prediction for SM processes.

● Small Extra Dimensions– The mass splitting is large.

– Gives resonant graviton production.

– The phenomenology is therefore very different.


Extra dimensions

● Another alternative is to let all the Standard Model fields 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 in 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.


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 ;

– 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, Z0, W± bosons and the top quark as well as extra Higgs bosons.

● The non-linear σ-model used for the high energy theory is similar to the low energy effective theory of pions which can be used to describe QCD, or is used in Technicolor models.

● This similarity with Technicolor models is one of the reasons for the resurgence of Technicolor models.


Little Higgs models

● The original Little Higgs models had problems with electroweak constraints.

● The solution is to introduce a discrete symmetry called T-parity, analogous to R-parity in SUSY models.

● This solves the problems with the precision electroweak data and provides a possible dark matter candidate.

● This model has a much larger particle content than the original Little Higgs model, and is more SUSY-like with a partner for each Standard Model particle.


g-2

● If you measure enough quantities some of them should disagree with the prediction by more the 1 sigma (about 1/3), and some by 2 sigma (4.6%) or 3 sigma (0.3%)

● This is why we define a discovery to be 5 sigma (6 × 10−5%).

● One quantity which recently showed such a deviation was the magnetic moment of the muon.

● The magnet moment of any fundamental fermion is defined as

● The Dirac equation predicts g = 2.


g-2● However there are quantum corrections.

● The problem is with the higher order corrections.● Quark loops in the photon propagator

● Low energy so can’t use perturbative QCD.


g-2

● Instead use the measured e+e− total cross section and the use the optical theorem.

● Gives an experimental error on the theoretical prediction.

● There can be corrections from BSM physics.


Rare B decays

● BSM physics can give additional contributions to rare B decays


B → μμ

● Two contributions (SM): Penguin & Box

● Both suppressed by ● The leptonic final state is easy to measure, there

are minor theoretical uncertainties● But: Huge background● Mass resolution paramount


B→μμ

● Recent result from CMS and LHCb


B→μμ

ArXiv:1204.5064


Finding new physics

● It seems that we have no striking signature of new physics at 8 TeV

● Still some hope for an “easy” discovery at 13 TeV● If not, it doesn't mean that there is no new physics,

but it is harder to pinpoint– Nastily hidden in parts of the phase space where we

are struggling to give a good simulation/calculation

– Can be feedback such as NP influencing the pdf fits, or the experimental control samples and conspire to hide it.


Speed dating with BSM model

● Questions to ask to avoid disappointments:– Are you compatible with the SM measurement?

– Sure? What about proton mass?

– Have you been checked for FCNC recently?

– How many free parameters do you have?

– ...

● Bonus:– Can you fix my g-2?

– Would you share your dark matter candidate with me?

– ...

Lecture 8: BSMdauncey/DanielMaitreLectures/Lecture6.pdf · Phenomenology – Daniel Maître Grand...

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