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Phenomenology

Lecture 6: Higgs

Daniel Maître

IPPP, Durham

Phenomenology - Daniel Maître The

● Very schematic, you have seen/will see it in SM lectures ● The SM contains -1 gauge and spin- 1/2 . ● Massless fields ensure:

– gauge invariance under SU(2)L × U(1)Y – renormalisability ● We could introduce 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 → 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 ?

● Consider W+W− → W+W− . ● In the high limit

● So that we have

Phenomenology - Daniel Maître Higgs mechanism

● This violate unitarity, so we need to do something ● If we add a scalar 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 we are forced to introduce a scalar interaction that couples to all 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 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% – pair: 0.23%

Phenomenology - Daniel Maître Higgs production channels

● Fusion ● -associated

0.13pb

19pb

● Higgs Strahlung ● Weak 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 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 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 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

● 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 . ● 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 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 ● 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