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Phenomenology Lecture 8 Phenomenology Lecture 8: BSM Daniel Maître IPPP, Durham Phenomenology – Daniel Maître 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? Phenomenology – Daniel Maître 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... Phenomenology – Daniel Maître 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 Phenomenology – Daniel Maître BSM models ● Here are some models – GUT theories – Technicolor – SUSY – Large extra dimensions – Small extra dimensions – Little Higgs Models – ... Phenomenology – Daniel Maître 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) Phenomenology – Daniel Maître 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 Phenomenology – Daniel Maître SU(5) ● Generators of SU(5) Phenomenology – Daniel Maître 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 Phenomenology – Daniel Maître 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 Phenomenology – Daniel Maître 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 Phenomenology – Daniel Maître 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 Phenomenology – Daniel Maître 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. Phenomenology – Daniel Maître 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 Phenomenology – Daniel Maître 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 Phenomenology – Daniel Maître 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 Phenomenology – Daniel Maître 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 Phenomenology – Daniel Maître Hierarchy problem ● Many models address the hierarchy “problem” – Technicolor – Supersymmetry – Extra dimensions – Little Higgs models Phenomenology – Daniel Maître 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. Phenomenology – Daniel Maître 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. Phenomenology – Daniel Maître Supersymmetry ● If there were a scalar loop in the Higgs propagator ● We would get a new contribution to the Higgs mass Phenomenology – Daniel Maître 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. Phenomenology – Daniel Maître Supersymmetric particles ● All standard model bosons have 2 spin-half partners, called gauginos SM particle Spin SUSY particle Spin Electron 1/2 Selectron 0 Neutrino 1/2 Sneutrino 0 up 1/2 Sup 0 down 1/2 Sdown 0 Gluon 1 gluino 1/2 Photon 1 Photino 1/2 Z 1 Zino 1/2 Neutralino Higgs 0 Higgsino 1/2 W+ 1 Wino 1/2 Charginos H+ 0 Higgsino 1/2 Phenomenology – Daniel Maître 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. Phenomenology – Daniel Maître 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 Phenomenology – Daniel Maître 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 Phenomenology – Daniel Maître 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 Phenomenology – Daniel Maître 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 Phenomenology – Daniel Maître 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.
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