Higgs physics theory aspects experimental approaches Monika Jurcovicova Department of Nuclear Physics, Comenius University Bratislava H f ~ m f.

Higgs physics

theory aspects

experimental approaches

Monika Jurcovicova

Department of Nuclear Physics, Comenius University Bratislava

H f

~ mf

f

Reasons for Higgs

• the presence of mass terms for gauge fields

destroys the gauge invariance of Lagrangian

• no problem for gluons and photons

• serious problem for W, Z0

• problems with origin of fermion masses

Spontaneous Symmetry Breaking

• way to generate particle masses

• opposite of putting them by hand into Lagrangian

basic idea: -- there is a simple world consisting just of scalar particles described by -- where so not a usual mass term -- ground state (vacuum) is not there are 2 minima

)4/12/1()(2/1 4222 L

0,02 0

/, 2 vv

-v v

V

Spontaneous Symmetry Breaking

• perturbative calculations involve expansions around classical minimum or one of them has to be chosen ( )

• then the reflection symmetry of Lagrangian is broken

• the mass is revealed:

v vv

)()( xvx

constvvL 43222 4/1)(2/1

22 22 vm

The Higgs mechanism • spontaneous breaking of a local gauge symmetry

(simplest U(1) gauge symmetry)• procedure: add the Higgs potential to Lagrangian

translate the field to a true ground state• obtained particle spectrum: 1 Higgs field with mass

1 massive vector A - desired 1 massless Goldstone boson

- unwanted• with a special choice of gauge the unwanted Goldstone boson

becomes longitudinal polarization of the massive vector the Higgs mechanism has avoided massless particles

The EW Weinberg-Salam model• formulation of Higgs mechanism:

– W, Z0 - become massive

– photon remains massless

– SU(2) x U(1) gauge symmetry must be an isospin doublet

– special choice of vacuum

– U(1)em symmetry with generator remains unbroken => the photon remains massless

– W, Z0 masses:

0

1,2

1,

2

1with

0

2

1 3

YTT

v

23 YTQ

, 2

1gvMW

, 2

1 22 gggvM Z

WZ

W

M

M cos

Fermion masses

• the fermion mass term is excluded from the original Lagrangian by gauge invariance

• the same doublet which generates W, Z0 masses is sufficient to give masses to leptons and quarks

• however: the value of mass is not predicted - just parameters of the theory

• nevertheless: the Higgs coupling to fermions is proportional to their masses

this can be tested

Theory summary

• the existence of the Higgs field has 3 main consequences:– W, Z0 acquire masses in the ratio

– there are quanta of the Higgs field, called Higgs bosons

– fermions acquire masses

• deficiencies of the theory– fermion masses are not predicted

– the mass of the Higgs boson itself is not predicted either

WZW MM cos

What do we know today about

• mass not predicted by theory except that mH < 1000 GeV

• from direct searches at LEP mH > 114.4 GeV

• indirect limits from fit of SM to data from LEP, Tevatron (mW, mtop)

• Best fit (minimum χ2): mH=

81 +52-33 GeV

• mH < 193 GeV 95% C.L.

Higgs decays

• mH < 130 GeV: H dominates

• mH 130 GeV : H WW(*), ZZ(*) dominate

• important: H , H ZZ 4, HWW , etc.

H f

~ mf

f

bb

H

• select events with 2 photons with pT ~50

• measure energy and direction of each photon

• calculate invariant mass of photon pair: mγγ= ((E1+ E2 )2 -(p1+ p2 )2 )1/2

• plot the mγγ spectrum - Higgs should appear as a peak at mH

HW*

W*

W*

mH 150 GeV

Main backgrounds of H • γγ production:

irreducible (i.e. same final state as signal)

• γ jet + jet jet production where one/two jets fake photons : reducibleq

q

g

g

q

g

(s)

0q

)( Hjj

~ 108

) (

)(

H

60 m ~ 100 GeV

H ZZ(*) 4

• “gold-plated” channel for Higgs discovery at LHC

• select events with 4 high-pT leptons (excluded): e+e- e+e-, e+e-

• require at least one lepton pair consistent with Z mass

• plot 4 invariant mass distribution :

H Z(*)

Z

e,

e,

e, mZ

120 mH < 700 GeV

222 )( i

ii

i pEm

Higgs should appear as a peak at mH

Backgrounds of H ZZ(*) 4

• irreducible pp ZZ (*) 4

• reducible X 4l tt

t , t W

b

X 4l bZb g

g

b

b

Z

Both reducible rejected by asking:

-- m ~ mZ

-- leptons are isolated -- leptons come from interaction vertex ( B lifetime : ~ 1.5 ps leptons from B produced at 1 mm from vertex)

How can one claim a discovery

• Signal significancepeak width due to detectorresolution

m

B

S

N

N S

NS= number of signal eventsNB= number of background events

in peakregion

if S > 5 : signal is larger than 5x error of background probability that background fluctuates up by more than 5is 10-7

discovery

2 critical parameters to maximize S

• detector resolution S ~ 1 /m

detector with better resolution has larger probability to find signal (Note: only valid if H << m. If Higgs is broad, detector resolution is not relevant.)

• integrated luminosity S ~ L numbers of events increase with luminosity

Summary on Higgs at LHC

• LHC can discover Higgs over full mass range with S > 5 in < 2 years

• detector performance is crucial in most cases

• discovery faster for larger masses

• whole mass range can be excluded at 95% C.L. after 1 month of running

What about the Tevatron

• for mH ~ 115 GeV Tevatron needs:

• 2 fb-1 for 95% C.L. in 2003-2004 ?

• 5 fb-1 for 3σ observation in 2004-2005 ?

• 15 fb-1 for 5σ discovery end 2007-beg 2008 ? Discovery possible up to mH ~120 GeV

Conclusions

• Standard Model Higgs can be discovered:– at the Tevatron up to mH ~120 GeV

– at the LHC over the full mass region up to mH ~1 TeV final word about SM Higgs mechanism

• if SM Higgs is not found before/at LHC, then alternative methods for generation of masses will have to be found