## The Higgs Boson

The Standard Model has been tremendously successful over the last 30 years, despite being extensively tested in high energy particle colliders. On 4 July 2012 the European Laboratory for Particle Physics (CERN) reported that the last part of the Standard Model, **the Higgs boson**, had been discovered at the Large hadron Collider with a mass of around 125 GeV. This Higgs boson is a direct consequence of the *Higgs mechanism*, proposed by SUPA physicist Peter Higgs (right), which gives mass to the fundamental particles. This mechanism proposes a Higgs potential which respects the electroweak symmetry but has a vacuum state which does not.

The figure to the left displays the form of this potential (sometimes called the "Mexican hat"), with a raised hill in the centre with a moat all around. The distance from the centre point (the hill) describes the strength of the Higgs field while the height of the shape denotes the energy of a particular field configuration. Notice that the zero-field configuration sitting right on the top of the hill is unstable to small perturbations, so the system will fall into the lower energy state in the moat. This means that the natural (lowest energy) state of space (the vacuum) is not empty, but is permeated by the Higgs field. If this Higgs field is allowed to couple to particles, it will inhibit their motion, effectively giving them a mass. More technically, one point in the moat is chosen to be the vacuum state, and the symmetry is broken; it is this breaking of the symmetry which provides masses to the fundamental particles.

Peter Higgs was awarded the Nobel Prize for his work in December 2013.

# Research at Glasgow

Now that a particle looking like the Higgs boson has been discovered, it is necessary to prove that it is indeed the Higgs boson we expect by measuring its quantum numbers and couplings. In particular, we need to measure its spin to make sure it is spin-zero, its CP quantum numbers to ensure it is a scalar, and its couplings to other particles to check that they are proportional to the particles' mass.

Glasgow research has provided model independent methods for determining these quantum numbers and couplings so that we can definitively say whether or not any observed particle is the Higgs boson of the Standard Model. In particular, we have examined the decays of Higgs bosons to Z-boson pairs, and found that we can distinguish CP-even and CP-odd eigenstates. Distinguishing CP mixtures of the two is much harder, and work is ongoing to develop new measurements that can be used to definitively answer this question. We are also investigating methods for depermining how the Higgs boson couples to the W and Z bosons that mediate the weak interaction. Although we already have good indications that these couplings are of the correct form for the Z boson, it is much more challenging to make separate measurements for the coupling to the W boson.

In addition, making an accurate determination of the size of the couplings requires a precise knowledge of the relevant cross sections. Another strand of our research is to improve the reliability of these predictions, which are obtained using perturbative QCD. In this way the couplings may be extracted as accurately as possible from the observed data

# References

- Handbook of LHC Higgs Cross Sections: 3. Higgs Properties; S. Heinemeyer et al.; arXiv:1307.1347; Abstract, PDF, Citations.
- Next-to-Leading order Higgs + 2 jet production via gluon fusion; John M. Campbell, R. Keith Ellis, and Giulia Zanderighi; Eur. Phys. J. C13 (2000) 459; arXiv:hep-ph/0608194; Abstract, PDF, Citations.
- Identifying the Higgs spin and parity in decays to Z pairs; S.Y. Choi, D.J. Miller, M.M. Muhlleitner, and P.M. Zerwas; Phys. Lett. B553, 61 (2003); arXiv:hep-ph/0210077; Abstract, PDF, Citations.
- Measuring the spin of the Higgs boson; D.J. Miller, S.Y. Choi, B. Eberle, and M.M. Muhlleitner; Phys. Lett. B505, 149 (2001) [arXiv:hep-ph/0102023]; Abstract, PDF, Citations.
- Can the trilinear Higgs self-coupling be measured at future linear colliders?; D.J. Miller and S. Moretti; Eur. Phys. J. C13 (2000) 459 [arXiv:hep-ph/9906395]; Abstract, PDF, Citations.