MSSM Higgs Mass
Encyclopedia
The MSSM Higgs Mass is a prediction of the Minimal Supersymmetric Standard Model
. Because the Higgs boson
has not yet been found, despite extensive searches, the MSSM has to go to great lengths to make the Higgs sufficiently heavy.
The mass of the lightest Higgs boson is set by the Higgs quartic coupling. Quartic couplings are not soft supersymmetry breaking parameters since they lead to a quadratic divergences to the Higgs mass. Furthermore, there are no supersymmetric parameters to make the Higgs mass a free parameter in the MSSM (though not in non-minimal extensions). This means that Higgs mass is a prediction of the MSSM. The Higgs boson was not found at LEP
II and the four experiments placed a lower limit on the Higgs mass of 114.4 GeV. This lower limit is significantly above where the MSSM would typically predict it to be, and while it does not rule out the MSSM, the non-discovery of the Higgs makes proponents of the MSSM nervous.
The only susy preserving operator that create a quartic coupling for the Higgs in the MSSM arise for the D-term
s of
the SU(2) and U(1) gauge sector and the magnitude of the quartic coupling is set by the size of the gauge couplings.
This leads to the prediction that the Standard Model-like Higgs mass (the scalar that couples approximately to the
vev) is limited to be less than the Z mass
.
Since supersymmetry is broken, there are radiative corrections to the quartic coupling that can increase the Higgs mass. These dominantly arise from the 'top sector'
where
is the top
mass and
is the mass of the top squark. This result can be interpreted as the RG running of the Higgs quartic coupling
from the scale of supersymmetry to the top mass — however since the top squark mass should be relatively close to the top mass, this is usually a fairly modest contribution and increases the Higgs mass to roughly the LEP II bound of 114 GeV before the top squark becomes too heavy.
Finally there is a contribution from the top squark A-terms
where
is a dimensionless number. This contributes an additional term to the Higgs mass at loop level, but is not logarithmically enhanced
by pushing
(known as 'maximal mixing') it is possible to push the Higgs mass to 125 GeV
without decoupling the top squark or adding new dynamics to the MSSM.
If the Higgs is found above 125 GeV (along with the other superparticles
) at the LHC, then this will strongly hint at new dynamics beyond the MSSM such as the 'Next to Minimal Supersymmetric Standard Model' (NMSSM
).
Minimal Supersymmetric Standard Model
The Minimal Supersymmetric Standard Model is the minimal extension to the Standard Model that realizes supersymmetry, although non-minimal extensions do exist. Supersymmetry pairs bosons with fermions; therefore every Standard Model particle has a partner that has yet to be discovered...
. Because the Higgs boson
Higgs boson
The Higgs boson is a hypothetical massive elementary particle that is predicted to exist by the Standard Model of particle physics. Its existence is postulated as a means of resolving inconsistencies in the Standard Model...
has not yet been found, despite extensive searches, the MSSM has to go to great lengths to make the Higgs sufficiently heavy.
The mass of the lightest Higgs boson is set by the Higgs quartic coupling. Quartic couplings are not soft supersymmetry breaking parameters since they lead to a quadratic divergences to the Higgs mass. Furthermore, there are no supersymmetric parameters to make the Higgs mass a free parameter in the MSSM (though not in non-minimal extensions). This means that Higgs mass is a prediction of the MSSM. The Higgs boson was not found at LEP
Large Electron-Positron Collider
The Large Electron–Positron Collider was one of the largest particle accelerators ever constructed.It was built at CERN, a multi-national centre for research in nuclear and particle physics near Geneva, Switzerland. LEP was a circular collider with a circumference of 27 kilometres built in a...
II and the four experiments placed a lower limit on the Higgs mass of 114.4 GeV. This lower limit is significantly above where the MSSM would typically predict it to be, and while it does not rule out the MSSM, the non-discovery of the Higgs makes proponents of the MSSM nervous.
The only susy preserving operator that create a quartic coupling for the Higgs in the MSSM arise for the D-term
D-term
In theoretical physics, one often analyzes theories with supersymmetry in which D-terms play an important role. In four dimensions, the minimal N=1 supersymmetry may be written using a superspace. This superspace involves four extra fermionic coordinates \theta^1,\theta^2,\bar\theta^1,\bar\theta^2,...
s of
the SU(2) and U(1) gauge sector and the magnitude of the quartic coupling is set by the size of the gauge couplings.
This leads to the prediction that the Standard Model-like Higgs mass (the scalar that couples approximately to the
vev) is limited to be less than the Z mass
.Since supersymmetry is broken, there are radiative corrections to the quartic coupling that can increase the Higgs mass. These dominantly arise from the 'top sector'
where
is the topTop quark
The top quark, also known as the t quark or truth quark, is an elementary particle and a fundamental constituent of matter. Like all quarks, the top quark is an elementary fermion with spin-, and experiences all four fundamental interactions: gravitation, electromagnetism, weak interactions, and...
mass and
is the mass of the top squark. This result can be interpreted as the RG running of the Higgs quartic couplingCoupling constant
In physics, a coupling constant, usually denoted g, is a number that determines the strength of an interaction. Usually the Lagrangian or the Hamiltonian of a system can be separated into a kinetic part and an interaction part...
from the scale of supersymmetry to the top mass — however since the top squark mass should be relatively close to the top mass, this is usually a fairly modest contribution and increases the Higgs mass to roughly the LEP II bound of 114 GeV before the top squark becomes too heavy.
Finally there is a contribution from the top squark A-terms
where
is a dimensionless number. This contributes an additional term to the Higgs mass at loop level, but is not logarithmically enhancedby pushing
(known as 'maximal mixing') it is possible to push the Higgs mass to 125 GeVwithout decoupling the top squark or adding new dynamics to the MSSM.
If the Higgs is found above 125 GeV (along with the other superparticles
Superpartner
In particle physics, a superpartner is a hypothetical elementary particle. Supersymmetry is one of the synergistic theories in current high-energy physics which predicts the existence of these "shadow" particles....
) at the LHC, then this will strongly hint at new dynamics beyond the MSSM such as the 'Next to Minimal Supersymmetric Standard Model' (NMSSM
NMSSM
In particle physics, NMSSM is an acronym for Next-to-Minimal Supersymmetric Standard Model. It is a supersymmetric extension to the Standard Model that adds an additional singlet chiral superfield to the MSSM and can be used to dynamically generate the \mu term, solving the mu problem.For review...
).