Phenomenology Lecture 6: Higgs Daniel Maître IPPP, Durham Phenomenology - Daniel Maître The Higgs Mechanism ● Very schematic, you have seen/will see it in SM lectures ● The SM contains spin-1 gauge bosons and spin- 1/2 fermions. ● Massless fields ensure: – gauge invariance under SU(2)L × U(1)Y – renormalisability ● We could introduce mass terms “by hand” but this violates gauge invariance ● We add a complex doublet under SU(2) L Phenomenology - Daniel Maître Higgs Mechanism ● Couple it to the SM ● Add terms allowed by symmetry → potential ● We get a potential with infinitely many minima. ● If we expend around one of them we get – Vev which will give the mass to the fermions and massive gauge bosons – One radial and 3 circular modes – Circular modes become the longitudinal modes of the gauge bosons Phenomenology - Daniel Maître Higgs Mechanism ● From the new terms in the Lagrangian we get ● There are fixed relations between the mass and couplings to the Higgs scalar (the one component of it surviving) Phenomenology - Daniel Maître What if there is no Higgs boson? ● Consider W+W− → W+W− scattering. ● In the high energy limit ● So that we have Phenomenology - Daniel Maître Higgs mechanism ● This violate unitarity, so we need to do something ● If we add a scalar particle with coupling λ to the W ● We get a contribution ● Cancels the bad high energy behaviour if , i.e. the Higgs coupling. ● Repeat the argument for the Z boson and the fermions. Phenomenology - Daniel Maître Higgs mechanism ● Even if there was no Higgs boson we are forced to introduce a scalar interaction that couples to all particles proportional to their mass. ● There must be something Higgs-like in the theory! ● Now we know there is something that looks very much like the standard model Higgs, but we want to be sure! ● Width seem to be narrow → we can factorize production and decay Phenomenology - Daniel Maître Higgs signal ● The decay modes of the Higgs boson depends on its mass. ● It couples most to heavy particles (top,Z,W) ● This plot is mostly useful if you are looking for another Higgs... From the LHC Higgs cross section working group Phenomenology - Daniel Maître Higgs signal ● But now we know the mass of the Higgs boson ● So we know its (expected) branching ratios bb tautau – mumu B pair: 56% cc gg – gammagamma WW : 23% WW ZZ – Gg: 8.5% – τ τ : 6.25 – ZZ: 3% – Photon pair: 0.23% Phenomenology - Daniel Maître Higgs production channels ● Gluon Fusion ● Quark-associated 0.13pb 19pb ● Higgs Strahlung ● Weak Vector Boson Fusion (VBF) 0.69pb 0.41pb 1.57pb Phenomenology - Daniel Maître Higgs production channels ● The production channels also depend on the mass Phenomenology - Daniel Maître Higgs channels ● – Very good mass resolution – Small branching ratio – Challenges: resolution and pion rejection ● – Good resolution on mass peak ● – Larger cross section – No mass peak Phenomenology - Daniel Maître Higgs discovery ● The Higgs boson was discovered in the di-photon and ZZ channels, with some help from the WW channel Phenomenology - Daniel Maître Di-photon channel ● Looking for a bump ● Challenges are pion over a smooth conversion of photons background (use side- ● Diphoton mass bands subtraction) resolution: ~ 1GeV From arXiv:1307.1427 Phenomenology - Daniel Maître ZZ channel ● Very clean signal, ● Since all final state particles are observed, the mass resolution is very good ● But rate is low for a mass of 125 GeV From CMS Higgs Physics Results Phenomenology - Daniel Maître WW channel ● Provides a direct measurement of the coupling of the Higgs boson with the W ● No mass peak ● Consider transverse mass of leptons ● Lepton directions are correlated, which can be used to reduce the background Phenomenology - Daniel Maître From arXiv:1307.1427 ZH Strahlung ● It was long thought that this channel was hopeless because of the high background ● Consider highly boosted configuration ● The Higgs decay products (b pair) will be in a single “fat” jet ● Looking for a boosted Z and a fat jet ● Problem: the resolution was not good because of the underlying event contributions ● Need to use more information about the jet structure Phenomenology - Daniel Maître ZH Strahlung ● Undo the jet clustering until two jets remain with a small mass, we interpret these two jets as the jets from the b pair decay, and make sure their transverse momenta are not too different ● But the resolution is still poor due to Underlying event contribution ● Solution: filter the jet to keep only the hardest radiation. ● The two hardest jets have to be b-tagged Phenomenology - Daniel Maître ZH Strahlung ● reclustering with Cambridge-Aachen algorithm (only angle) From arXiv:0802.2470 Phenomenology - Daniel Maître Measuring the properties ● We define the signal strength as the ratio between the observed cross section and the standard model expectation ● One of the challenges is to separate VBF and gluon fusion channels Phenomenology - Daniel Maître Higgs signal strength Phenomenology - Daniel Maître Testing the coupling ● To test the coupling to the Higgs, introduce scaling factors for the coupling of the Higgs to the fermions and vector bosons From M. Duehrssen's YETI 2013 lecture Phenomenology - Daniel Maître Testing the coupling ● Try to fit the values of the scaling factors Phenomenology - Daniel Maître Testing the coupling ● Try to fit the values of the scaling factors Phenomenology - Daniel Maître Measuring spin ● Polar angle θ in the Collins-Soper frame (in the rest frame of the di- photon system, z axis is between the the first incoming momentum and – the second incoming momentum ) Phenomenology - Daniel Maître Measuring the spin ● Add more channels and obervables – H→WW→lνlν ● Transverse momentum of the lepton pair ● Invariant mass of the lepton pair ● Azimutal angle difference between the leptons – H→ZZ→4l ● Angles and invariant – Combine them in a Boosted Decision Tree ● Combine all channels Phenomenology - Daniel Maître Spin measurement Phenomenology - Daniel Maître CP measurement ● Different method at CMS From arXiv:1212.6639 Phenomenology - Daniel Maître Future ● Higgs self-coupling, needed to measure the higgs potential – Triple higgs vertex ● Only possible at high luminosity LHC – Quartic higgs vertex ● Probably not possible even at a high luminosity LHC Phenomenology - Daniel Maître.