## Haber on “Present status and future prospects for a Higgs boson discovery”

“The electroweak symmetry breaking dynamics of the Minimal Standard Model (MSM) employs a self-interacting complex doublet of scalar fields, which consists of four real degrees of freedom.  Three of this four degrees of freedom has been already observed in the experiments as the longitudinal components of the massive (electroweak) gauge bosons (the $W^\pm$ and $Z$ bosons). The fourth remaining scalar degree of freedom is predicted by the standard Higgs mechanism to remain in the physical spectrum as a CP-even neutral Higgs boson. Precision electroweak data favors a Higgs mass below 200 GeV/c², in which case the scalar self-interactions are weak.” In such a case, “the Standard Model is very likely embedded in a supersymmetric theory in order to stabilize the large gap between the electroweak and the Planck scales in a natural way. The minimal supersymmetric extension of the Standard Model (MSSM) employs two complex Higgs doublets, resulting in five physical scalar degrees of freedom.  In a large range of the MSSM parameter space, the properties of the lightest scalar of the MSSM are nearly indistinguishable from those of the SM Higgs boson.” Howard E. Haber (Santa Cruz Institute for Particle Physcs, University of California), “Present status and future prospects for a Higgs boson discovery at the Tevatron and LHC,” ArXiv, 4 Nov 2010.

Let us recall from John C. Baez, “Hypercharge and Weak Isospin,” May 12, 2003, that “in the Standard Model, the weak and electromagnetic forces are two aspects of the “electroweak force” described by the symmetry group SU(2)×U(1). The familiar concept of  “electric charge” Q is less fundamental than the concepts of “weak isospin” T (with 3 components transforming under SU(2) symmetry) and “hypercharge” Y (only 1 component transforming under U(1) symmetry), in fact,  $Q=T_3+Y/2$.”

Returning to Haber, “for an arbitrary Higgs sector” a consistent perturbation theory “requires that $(2T+1)^2-3Y^2=1$The simplest solutions are Higgs singlets $(T,Y)=(0,0)$ and hypercharge-one complex Higgs doublets $(T,Y)=(1/2,1)$.” In the first case,the (Minimal) “Standard Model Higgs Boson has a mass given by: $M_{H,SM}^2=v^2\,\lambda/2$, where $\lambda$ is the Higgs self-coupling parameter, whose value is unknown at present, hence the Standard Model Higgs mass is not predicted, and $v=2\,M_W/g=$ 246 GeV.” The Next to Minimal, Standard Model Higgs corresponds to a “two-Higgs-doublet model (2HDM) consisting of two hypercharge-one scalar doublets.” In this later case, “of the eight initial degrees of freedom, three correspond to the Goldstone bosons and five are physical: a charged Higgs pair, $H^\pm$ and three neutral scalars. If CP is conserved,” as in the Minimal SM Higgs, “the Higgs spectrum contains two CP-even scalars, $h^0$ and $H^0$, and a CP-odd scalar $A^0$.” Hence, appart from a CP-even Higgs boson, there are “a CP-odd Higgs boson” (in order to restore CP conservation in the Higgs sector), “and two charged Higgs bosons.” Obviously “more exotic Higgs sectors” are possible “allowing for doubly-charged Higgs bosons, etc.”

“The Higgs sector of the Minimal Supersymmetric extension of the Standard Model (MSSM) is a 2HDM, where the neutral components of the Higgs fields acquire vacuum expectation values (vevs) $v_u$ and $v_d$, with $v^2\equiv v_d^2+v_u^2={4 M_W^2/ g^2}=$ 246 GeV². The ratio of the two vevs is an important parameter of the model, $\tan\beta\equiv v_u/v_d$. The five physical Higgs particles consist of a charged Higgs pair $H^\pm$, one CP-odd scalar $A^0$, and two CP-even scalars $h^0$ and $H^0$.” The maximum allowed mass for $h^0$ depends on the mass of the superpartner of the top quark; assuming that the top-squark mass is no heavier than about 2 TeV, results in a mass smaller than 130 GeV; this upper bound is reached when $\tan\beta\gg 1$, in the so-called maximal mixing scenario.” Note also that “in many models with extended Higgs sectors, a parameter regime exists in which one Higgs boson is light (of order $M_Z$) and all other Higgs scalars are very heavy $(\gg M_Z$). The effective low-energy Higgs theory is precisely that of the SM Higgs boson.  This is called the decoupling limit.”

“The Tevatron will continue to take data through the end of 2011. In addition to an increased integrated luminosity, there is still room for some improvements in the Higgs search analysis. Although it is possible that evidence for the Higgs boson may emerge from future Tevatron running, the discovery of the Higgs boson and the identification of its properties are expected to take place at the LHC.  Once the Higgs boson is discovered, a program of Higgs physics at the LHC must address the following important questions: How many Higgs states are there? Assuming one Higgs-like state is discovered, is it a Higgs boson? Is it the SM Higgs boson? The measurement of Higgs boson properties will be critical in order to answer the last two questions: mass, width, CP-quantum numbers (is the Higgs sector CP-violating?); branching ratios and Higgs couplings; reconstructing the Higgs potential (Higgs self-couplings).”