Lecture 6: Higgsdauncey/DanielMaitreLectures/Lecture4.pdf · Phenomenology - Daniel Maître Measuring the spin Add more channels and obervables – H→WW→lνlν Transverse momentum

Phenomenology - Daniel Maître

Phenomenology

Lecture 6: Higgs

Daniel Maître

IPPP, Durham


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


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 tothe fermions and massive gauge bosons

– One radial and 3 circular modes

– Circular modes become thelongitudinal modes of the gaugebosons


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)


What if there is no Higgs boson?

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

● So that we have


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.


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


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


Higgs signal

● But now we know the mass of the Higgs boson

● So we know its (expected) branching ratios– B pair: 56%

– WW : 23%

– Gg: 8.5%

– τ τ : 6.25

– ZZ: 3%

– Photon pair: 0.23%

bb

tautau

mumu

cc

gg

gammagamma

WW

ZZ


Higgs production channels

● Gluon Fusion ● Quark-associated

● Weak Vector Boson Fusion (VBF)

● Higgs Strahlung

19pb

0.13pb

0.69pb0.41pb 1.57pb


Higgs production channels

● The production channels also depend on the mass


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


Higgs discovery

● The Higgs boson was discovered in the di-photon and ZZ channels, with some help from the WW channel


Di-photon channel

● Looking for a bump over a smooth background (use side-bands subtraction)

● Challenges are pion conversion of photons

● Diphoton mass resolution: ~ 1GeV

From arXiv:1307.1427


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


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



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


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


ZH Strahlung

● reclustering with Cambridge-Aachen algorithm (only angle)



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


Higgs signal strength


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



● Try to fit the values of the scaling factors



● Try to fit the values of the scaling factors


● 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 )

Measuring spin


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


Spin measurement


CP measurement

● Different method at CMS



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

Documents

Lecture 6: Higgsdauncey/DanielMaitreLectures/Lecture4.pdf · Phenomenology - Daniel Maître Measuring the spin Add more channels and obervables – H→WW→lνlν Transverse momentum