425
22.8. The Higgs sector
Like the preceding argument, this one does not say that m H must be less
than some fixed number. Rather, it says that if m H gets bigger than a certain
value, perturbation theory will fail, or ‘new physics’ will enter. It is, in fact,
curiously reminiscent of the original situation with the four-fermion current–
current interaction itself (compare (22.10) with (22.206)). Perhaps this is a
clue that we may eventually need to replace the Higgs phenomenology. At all
events, this line of reasoning seems to imply that the Higgs boson will either
be found at a mass well below 1 TeV, or else some electroweak interactions
will become effectively strong with new physical consequences. This ‘no lose’
situation provided powerful motivation for the construction of the LHC.
There is also an interesting lower bound on the Higgs mass, which is derived from the requirement of vacuum stability. If the Higgs mass is sufficiently lighter than the top quark mass, the top quark loop contribution to
the running of the quartic coupling λ(E) can cause the coupling to go negative at large energy scales (Cabibbo et al. 1979). This would imply that, at
such scales, the effective scalar potential of the Standard Model would be unbounded below at large absolute values of the field, and there would no longer
be a stable ground state (vacuum). This can be tolerated if the lifetime of the
metastable vacuum is less that the age of the Universe (see Isidori et al. 2001,
and references cited therein). A re-examination of the issue by Elias-Miro et
al. (2012) showed that the Standard Model vacuum would become unstable
at scales around the Planck mass, for m H < 130 GeV. For m H ∼ 125 GeV,
instability occurs at scales of order 10
10 GeV, but the lifetime is greater than
the age of the Universe. Of course, new physics may enter well before such a
scale. It is nevertheless intriguing that a Higgs mass in this region may have
implications for the physics of the early Universe.
We now consider some simple aspects of Higgs boson production and decay processes at collider energies, as predicted by the Standard Model, and
conclude with the experiments leading to the probable Higgs boson discovery
in 2012.
22.8.3 Higgs boson searches and the 2012 discovery
We begin by considering the main production and decay modes. The existing
lower bound on m H established at LEP (LEP 2003)
m H ≥ 114.4 GeV (95% Confidence Level)
(22.208)
already excluded many possibilities in both production and decay. Subsequent
searches were carried out at the hadron colliders. At both the Tevatron and
the LHC, the dominant parton-level production mechanism is ‘gluon fusion’
via an intermediate top quark loop as shown in figure 22.27 (Georgi et al.
1978, Glashow et al. 1978, Stange et al. 1994a,b). The intermediate t quark
dominates, because the Higgs couplings to fermions are proportional to the
fermion mass. Since the gluon probability distribution rises rapidly at small
√
x values, which are probed at larger collider energy s, the cross section for
22.8. The Higgs sector
Like the preceding argument, this one does not say that m H must be less
than some fixed number. Rather, it says that if m H gets bigger than a certain
value, perturbation theory will fail, or ‘new physics’ will enter. It is, in fact,
curiously reminiscent of the original situation with the four-fermion current–
current interaction itself (compare (22.10) with (22.206)). Perhaps this is a
clue that we may eventually need to replace the Higgs phenomenology. At all
events, this line of reasoning seems to imply that the Higgs boson will either
be found at a mass well below 1 TeV, or else some electroweak interactions
will become effectively strong with new physical consequences. This ‘no lose’
situation provided powerful motivation for the construction of the LHC.
There is also an interesting lower bound on the Higgs mass, which is derived from the requirement of vacuum stability. If the Higgs mass is sufficiently lighter than the top quark mass, the top quark loop contribution to
the running of the quartic coupling λ(E) can cause the coupling to go negative at large energy scales (Cabibbo et al. 1979). This would imply that, at
such scales, the effective scalar potential of the Standard Model would be unbounded below at large absolute values of the field, and there would no longer
be a stable ground state (vacuum). This can be tolerated if the lifetime of the
metastable vacuum is less that the age of the Universe (see Isidori et al. 2001,
and references cited therein). A re-examination of the issue by Elias-Miro et
al. (2012) showed that the Standard Model vacuum would become unstable
at scales around the Planck mass, for m H < 130 GeV. For m H ∼ 125 GeV,
instability occurs at scales of order 10
10 GeV, but the lifetime is greater than
the age of the Universe. Of course, new physics may enter well before such a
scale. It is nevertheless intriguing that a Higgs mass in this region may have
implications for the physics of the early Universe.
We now consider some simple aspects of Higgs boson production and decay processes at collider energies, as predicted by the Standard Model, and
conclude with the experiments leading to the probable Higgs boson discovery
in 2012.
22.8.3 Higgs boson searches and the 2012 discovery
We begin by considering the main production and decay modes. The existing
lower bound on m H established at LEP (LEP 2003)
m H ≥ 114.4 GeV (95% Confidence Level)
(22.208)
already excluded many possibilities in both production and decay. Subsequent
searches were carried out at the hadron colliders. At both the Tevatron and
the LHC, the dominant parton-level production mechanism is ‘gluon fusion’
via an intermediate top quark loop as shown in figure 22.27 (Georgi et al.
1978, Glashow et al. 1978, Stange et al. 1994a,b). The intermediate t quark
dominates, because the Higgs couplings to fermions are proportional to the
fermion mass. Since the gluon probability distribution rises rapidly at small
√
x values, which are probed at larger collider energy s, the cross section for