The Higgs Boson

The Standard Model of Particle Physics and the Higgs boson

In the Standard Model (SM) of electro-weak (EW) and strong interactions, there are four types of gauge vector bosons (gluon, photon, W and Z) and twelve types of fermions (six quarks and six leptons). The vectors bosons are force carriers. Photon is the carrier of the QED interaction. The W, Z bosons are the carriers of the weak interaction and the gluons are the carriers of the strong interaction. Fermions (quarks and leptons) are organized in three families. These particles have been observed experimentally. At present, all the data obtained from the many experiments in particle physics are in agreement with the Standard Model. In the Standard Model, there is one particle, the Higgs boson, that is responsible for giving masses to all the particles. In this sense, the Higgs particle occupies a unique position.

 

The weak interaction operates differently on left-handed fermions than it does for right-handed fermions. While left-handed fermions act as weak isodoublets, right-handed fermions are weak isosinglets. In other words, left-handed fermions transform under the weak interaction, but right-handed fermions don't.  One can write down a version of the Standard Model Lagrangian in which all gauge bosons and the fermions are massless. This Lagrangian would preserve gauge invariance. However, while gluons and photons are known to be massless, experimental evidence that weak bosons and fermions are massive is overwhelming. When introducing mass-related terms the Lagrangian would no longer be invariant under weak isospin transformations and it would violate gauge invariance. It is easy to see how introducing massive weak bosons would be a problem when one considers the analogous situation in QED. One can argue that the theory of QED forbids the photon to be massive. While the presence of fermion mass terms is not a problem for the strong interaction it is a fundamental problem for the electro-weak sector. One can visualize this problem by considering a left-handed fermion. If the fermion is massless then it will remain left-handed in all reference frames. In this case the fermion field will transform under the weak interaction equally in all reference frames. However, if the fermion is massive one can perform a Lorentz transformation such that the fermion becomes right-handed. As a result, depending on the reference frame the fermion field would transform under the weak interaction differently. The introduction of spontaneous electro-weak symmetry breaking is intended to reconcile weak boson and fermion masses with gauge invariance. This leads to a massive particle with spin 0, a scalar, typically referred to as the Higgs boson.

 

The ideas of spontaneous symmetry breaking were introduced into particle physics from condense matter physics. Imagine a Mexican-hat potential, as depicted in the graph, such that its minimum is not at (0,0). The ball will inevitably settle at a lower energy level. As a result, the local symmetry is spontaneously broken. In the context of the Standard Model Lagrangian this mechanism leads to spontaneous breaking of the electro-weak symmetry and the generation of at least one scalar boson.

Now the Standard Model Lagrangian respects gauge invariance. The graph below summarizes interactions between particles in the Standard Model, including the presence of a Higgs boson. The lines that start and end on the same particle indicate self-interactions.

 

When it comes to defining the experimental strategy for searches of the Higgs boson several theoretical inputs are necessary: the Higgs boson width, decay products and production mechanisms. The CMS and ATLAS detectors have been designed to a significant degree according to these theoretical inputs and within the context of inclusive analyses. Therefore the properties and features of these decays play a central role. The probability of a particle to decay into other particles depends on the couplings between these particles and it is expressed in the form of partial decay widths. The sum of all partial decay widths yield the total width of the particle. The plots below display the branching of the Standard Model Higgs boson to known particles as a function of the mass.

 

The Table given below gives the values of the branching fractions of the Standard Model Higgs boson with a mass of 125 GeV to known particles. The errors correspond to current level of theory uncertainties and are expressed in terms of fractional deviations in percent. The total width is given in MeV.

 

The Standard Model Higgs boson is produced at the LHC via several mechanisms. These are determined by the way the Higgs boson couples to SM particles. The figure below displays the LO diagrams Feynmann diagrams of the leading production mechanisms in proton-proton collisions. Shown are four main production mechanisms (from left to right): gluon-gluon fusion, vector boson fusion, associated production with weak bosons (Z,W) and associated production with top quarks.

 

The plot below gives the cross sections in pb for the production of the Standard Model Higgs boson in proton-proton collisions. Results are given for center of mass energy of 8 TeV. The bands correspond to the current level of theoretical uncertainty in the calculation.

 

On July 4th 2012 the ATLAS and CMS collaboration provided first strong evidence of a new particle consistent with a consistent with a scalar boson with a mass about 125 GeV. Analysis of data taken after have further confirmed this finding. Analyses by the ATLAS and CMS collaborations indicate that the newly observed particle is consistent with the hypothesis of the scalar boson in the SM within the accuracy provided by the available data.

Current efforts of the Wits-ATLAS group to understand the nature of the new boson

With the accuracy provided by the data analyzed so far by the ATLAS and CMS collaborations the observed new boson seems consistent with the Higgs boson in the Standard Model. However, a lot of work in coming years will go into verifying if indeed this is true. This entails the following endeavors:

Our group currently has sustained efforts in the following decay channels:

Our group is also involved in contributing to the phenomenology and preparation for the exploration of the new boson in future accelerators: e-p and e+e-.

Join us in the exploration of the new boson!


Wits HEP Group, School of Physics,
University of the Witwatersrand,
1 Jan Smuts Ave, Johannesburg, South Africa
Telephone: +27 11 717 6848
Fax: +27 11 717 6879