3 The Standard Model of Electroweak Interactions
71
gauge theory is via the Higgs mechanism. The big remaining questions are about
the nature and the properties of the Higgs particle(s). The present experimental
information on the Higgs sector, is surprisingly limited and can be summarized in
a few lines, as follows. First, the relation M 2
W = M 2
Z cos 2 θ W , Eq. (3.55), modified
by small, computable radiative corrections, has been experimentally proven. This
relation means that the effective Higgs (be it fundamental or composite) is indeed
a weak isospin doublet. The Higgs particle has not been found but, in the SM, its
mass can well be larger than the present direct lower limit m H 114 GeV (at
95% c.l.) obtained from searches at LEP-2. The radiative corrections computed
in the SM when compared to the data on precision electroweak tests lead to a
clear indication for a light Higgs, not too far from the present lower bound. The
exact experimental upper limit for m H in the SM depends on the value of the top
quark mass m t . The CDF and D0 combined value after Run II is at present [8]
m t = 170.9 ± 1.8 GeV (it went down with respect to the value m t = 178 ±
4.3 GeV from Run I and also the experimental error is now sizably reduced). As
a consequence the present limit on m H is more stringent [8]: m H < 182 GeV (at
95% c.l., after including the information from the 114 GeV direct bound). On the
Higgs the LHC will address the following questions : one doublet, more doublets,
additional singlets? SM Higgs or SUSY Higgses? Fundamental or composite (of
fermions, of WW. . . )? Pseudo-Goldstone boson of an enlarged symmetry? A
manifestation of large extra dimensions (5th component of a gauge boson, an effect
of orbifolding or of boundary conditions. . . )? Or some combination of the above
or something so far unthought of? Here in the following we will summarize the
main properties of the SM Higgs that provide an essential basis for the planning
and the interpretation of the LHC Higgs programme. We start from the mass,
then the width and the branching ratios and, finally, the most important production
channels.
3.13.1 Theoretical Bounds on the SM Higgs Mass
It is well known [58–60] that in the SM with only one Higgs doublet a lower limit
on m H can be derived from the requirement of vacuum stability (or, in milder
form, of a moderate instability, compatible with the lifetime of the Universe [61]).
The limit is a function of m t and of the energy scale where the model breaks
down and new physics appears. The Higgs mass enters because it fixes the initial
value of the quartic Higgs coupling λ for its running up to the large scale .
Similarly an upper bound on m H (with mild dependence on m t ) is obtained, as
described in [62] and refs. therein, from the requirement that for λ no Landau pole
appears up to the scale , or in simpler terms, that the perturbative description
of the theory remains valid up to . We now briefly recall the derivation of these
limits.
The possible instability of the Higgs potential V [φ] is generated by the quantum
loop corrections to the classical expression of V [φ]. At large φ the derivative
71
gauge theory is via the Higgs mechanism. The big remaining questions are about
the nature and the properties of the Higgs particle(s). The present experimental
information on the Higgs sector, is surprisingly limited and can be summarized in
a few lines, as follows. First, the relation M 2
W = M 2
Z cos 2 θ W , Eq. (3.55), modified
by small, computable radiative corrections, has been experimentally proven. This
relation means that the effective Higgs (be it fundamental or composite) is indeed
a weak isospin doublet. The Higgs particle has not been found but, in the SM, its
mass can well be larger than the present direct lower limit m H 114 GeV (at
95% c.l.) obtained from searches at LEP-2. The radiative corrections computed
in the SM when compared to the data on precision electroweak tests lead to a
clear indication for a light Higgs, not too far from the present lower bound. The
exact experimental upper limit for m H in the SM depends on the value of the top
quark mass m t . The CDF and D0 combined value after Run II is at present [8]
m t = 170.9 ± 1.8 GeV (it went down with respect to the value m t = 178 ±
4.3 GeV from Run I and also the experimental error is now sizably reduced). As
a consequence the present limit on m H is more stringent [8]: m H < 182 GeV (at
95% c.l., after including the information from the 114 GeV direct bound). On the
Higgs the LHC will address the following questions : one doublet, more doublets,
additional singlets? SM Higgs or SUSY Higgses? Fundamental or composite (of
fermions, of WW. . . )? Pseudo-Goldstone boson of an enlarged symmetry? A
manifestation of large extra dimensions (5th component of a gauge boson, an effect
of orbifolding or of boundary conditions. . . )? Or some combination of the above
or something so far unthought of? Here in the following we will summarize the
main properties of the SM Higgs that provide an essential basis for the planning
and the interpretation of the LHC Higgs programme. We start from the mass,
then the width and the branching ratios and, finally, the most important production
channels.
3.13.1 Theoretical Bounds on the SM Higgs Mass
It is well known [58–60] that in the SM with only one Higgs doublet a lower limit
on m H can be derived from the requirement of vacuum stability (or, in milder
form, of a moderate instability, compatible with the lifetime of the Universe [61]).
The limit is a function of m t and of the energy scale where the model breaks
down and new physics appears. The Higgs mass enters because it fixes the initial
value of the quartic Higgs coupling λ for its running up to the large scale .
Similarly an upper bound on m H (with mild dependence on m t ) is obtained, as
described in [62] and refs. therein, from the requirement that for λ no Landau pole
appears up to the scale , or in simpler terms, that the perturbative description
of the theory remains valid up to . We now briefly recall the derivation of these
limits.
The possible instability of the Higgs potential V [φ] is generated by the quantum
loop corrections to the classical expression of V [φ]. At large φ the derivative