H
f
f
~ mf
Higgs physics
theory aspects
experimental approaches
Monika Jurcovicova
Department of Nuclear Physics, Comenius University Bratislava
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
2
2 2
4
described by L  1/ 2(  )  (1/ 2   1/ 4  )
-- where  2 0 ,   0 so not a usual mass term
-- ground state (vacuum) is not   0
V
there are 2 minima    v , v    2 / 
-v
v
f
Spontaneous Symmetry Breaking
• perturbative calculations involve expansions around
classical minimum   v or    v
one of them has to be chosen (   v )
• then the reflection symmetry of Lagrangian is broken
• the mass is revealed:
 ( x)  v   ( x)
L  1 / 2(  )2   v 2 2   v 31 / 4  4  const
m  2 v 2   2 2
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
 

 0 
•  must be an isospin doublet   

– special choice of vacuum
1  0
1
1
  with T  , T 3   , Y  1

2
2
2 v
Y
– U(1)em symmetry with generator Q  T 3 
2
=> the photon remains massless
1

0
– W , Z masses: M W  v g ,
2
MZ 
1
v g g 2 g  2 ,
2
remains unbroken
MW
 cosW
MZ
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 M W M Z  cosW
– 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
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
H
f
f
~ mf
• mH < 130 GeV:
H  bb dominates
• mH  130 GeV : H
 WW(*), ZZ(*)
dominate
• important: H ,
H  ZZ  4,
HWW , etc.
H  
H

W*
W*
W*
mH  150 GeV

• 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
Main backgrounds of H  
• γγ production:
irreducible (i.e. same
final state as signal)
q

q
g

g
• γ jet + jet jet
production where
one/two jets fake
photons : reducible

q


 ( )
 60 m ~ 100 GeV
 ( H   )
g
q
p0
 jj
~ 108
 ( H   )
 (s)
H
(*)
ZZ 
4
H
e, 
Z(*)
e, 
Z
120  mH < 700 GeV
mZ
e, 
• “gold-plated” channel for Higgs discovery at LHC
• select events with 4 high-pT leptons (t excluded):
e+e- e+e-,  , e+e- 
• require at least one lepton pair consistent with Z
mass
 2
2
2
• plot 4 invariant mass distribution : m   Ei  ( pi )
i
Higgs should appear as a peak at mH
i
Backgrounds of H  ZZ(*)  4 
• irreducible
pp  ZZ (*)  4
• reducible t , t
tt  4l  X

W
b

Zb b  4l  X
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)
g
b


Z
g
b

How can one claim a discovery
peak width
due
to detector
resolution
• Signal significance
NS
S
NB
NS= number of signal events
NB= number of background
events
in peak
region
if S > 5 :
m
signal is larger than 5x error of background
probability that background fluctuates up by
more than 5 is 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 GH << 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