Frontiers of particle physics II Jan 31 Precision tests of the Standard Model Steve Snow Feb 7 '' Feb 14 '' Feb 21 Matter-Antimatter asymmetry Stefan Soldner-Rembold Feb 28 '' Mar 7 '' Mar 14 Interactions of particles with matter Ian Duerdoth ----- Easter ------ One Interactions of particles with matter Three Beyond the Standard Model Brian Cox One Bank Holiday - no lecture

Course Outline Precision tests of the Standard Model “Precision tests” because the SM has already passed all of the simpler tests at today’s energies. Precision tests of the Standard Model Summary of the Standard Model. List of particles and vertices. Feynman diagrams and how they relate to a Lagrangian. Tree level diagrams and higher orders - equivalence to perturbative expansion. Diagrams = Amplitudes. Probability = A.A* . Memorise rules and practice drawing diagrams. Everything allowed will happen – small effects – precision. Input parameters: a=1/137.036003 from Quantum Hall effect. GF=1.16637w10-5 GeV-2 from muon lifetime. mZ=91.188 GeV from LEP. Low energy tests: muon and electron g-2. Sensitivity to SUSY. LEP. Z branching ratios. How they are measured. Particle ID by dE/dx. Heavy flavour tagging. LEP and SLC. Asymmetries; forward-backward, left-right, and t polarisation. How they are measured. Putting it all together in global fit. Overall c2 . Prediction of mH versus direct search for Higgs. Limits on SUSY and Z'. These slides and other material are at: http://hep.man.ac.uk/u/steve/fpp2.html

The Standard Model Particles leptons quarks e m t ne nm nt u c t d s b , Z, W+, W-, Higgs boson, gluon A Model not a Theory because many empirical patterns are built in to the model but not explained by it. The fermions are divided into leptons which feel only the electroweak force and quarks which feel both the EW and strong forces. Three generations with increasing mass. No special relation between generation 1 leptons and generation 1 quarks, etc. Strong and electromagnetic interactions preserve flavours. Weak interaction mixes quarks but not leptons. No unification of strong with electroweak.

The Standard Model Vertices g q g Q+ Q- W l , q nl ,q’ g Z f f g H g g Z W+,Z W-,Z W+,Z W-,Z H Q means charged, f means fermion , l means lepton , q means quark.

Feynman Diagrams For us For theorists Can be used at two levels: Given the list of particles and vertices which exist in a certain theory, (e.g. the SM) we can use FDs to find out all the processes which are allowed by the theory, and make rough estimates of their relative probability. Every vertex and particle corresponds to a term in the Lagrangian (the formulation of the theory which is the starting point for QFT calculations). FDs are used to organise the terms in a perturbative solution of the Lagrangian. There are rules for transforming any FDk into a probability amplitude, ak. As usual in the quantum world, the total amplitude for the transition from one state to another is the sum of the amplitudes of all the possible routes by which the transition can happen, A=Sak .The real probability of the transition is A.A* times flux and phase space factors. For us Anything which is not explicitly allowed is forbidden. For theorists This amplitude interference means that it is not easy to guess whether a small correction will increase or decrease or just change the phase of A.

More Rules By convention time is horizontal, space vertical. A right(left) arrow can be used to indicate a (anti-)fermion An incoming particle can be swapped for an outgoing anti-particle. Four-momentum, spin and charges (colour, electric) are conserved at each vertex, BUT Internal lines/particles can be virtual, i.e. they need not obey the usual relation of the particle’s rest mass m with its energy and momentum; E2 = p2 + m2 . External lines represent the particles which are actually observed; they must have the correct rest mass.

Semi-quantitative There are two features of the rules for transforming diagrams into amplitudes which we can use without going into the details: Each vertex is associated with a term which is related to the type of force involved. a.Q2 if the boson is a photon (~1/137 for Q=1) as if the boson is a gluon (~1/8 if the energy scale is large) if the boson is a W or Z the coupling is small, like a, within factors of sinqW The W couples equally strongly to all the fermion doublets en,mn,tn,ud’,cs’,tb’ whereas the Z coupling depends on the fermion charge. The coupling of the Higgs to any other particle is proportional to the particle’s mass Each virtual particle produces a “propagator” term which decreases the amplitude as the particle becomes more virtual, i.e. as m2 gets further from E2 – p2.

Tree level and higher a b c d f e If a process is allowed then you will always find that there are an infinite number of more complicated ways of achieving the same result. Here are just a few of the diagrams for e+ e - -> m+ m- . a b c d f e The lowest order or “tree level” diagram for e+ e - -> m+ m- . An extra photon in the final state makes this a different process from the theoretical point of view, i.e. does not interfere with a). But may it be indistinguishable in practice, if so it has to be taken into account. A higher order correction which can be significant and brings in the strong force. and e) are second order pure QED corrections. f) an electroweak correction.

Free parameters Any physics theory (except the ultimate one ?) has a number of parameters which can only come from experiment. The combination of theory with experimental parameters should then predict the result of any other experiment. For the standard model there are 18 parameters (assuming massless neutrinos). The choice of which experiments are used to define parameters and which ones test the theory is somewhat arbitrary. Conventionally, the most accurate experiments are used to set parameters. Note “most accurate” will change with time as technology advances. Four parameters of the CKM matrix aelectromagnetic and astrong The Fermi constant Three charged lepton masses Six quark masses The Z boson mass The Higgs mass

Mini-test To occupy you for 15 minutes over coffee. Which of the Feynman diagrams below is valid in the standard model. For those which are not, which rule do they break ?