The Post Higgs Era & The Electron Positron Colliders

18th September 2017

Cross sections of the Higgs signal and major standard model backgrounds at electron-positron colliders (Left) and proton colliders (right).

For half a century, the development of the particle physics is characterized by the completion and experimental validation of the Standard Model, one of the most successful physics models that mankind have ever constructed. The Standard Model, with its simple and beautiful mathematical structure, explains and predicts almost all the phenomena we observed in collider experiments. In 2012, the Standard Model reaches the summit of its success by the discovery of the Higgs boson, the last missing piece of the Standard Model particle spectrum. This historic event opens a new era, the Post Higgs era, of the particle physics. 

Despites its enormous success, the SM can hardly be regarded as a satisfactory theory. These unsatisfactory include a series of coincidences within the SM, and the incapability to explain lots of the observed, or anticipated physics phenomena. The latter includes the famous Baryon-Asymmetry, the dark matter and dark energy, the non-vanishing neutrino masses, and, to some extend, the unification between gravity and gauge interactions. These coincidences could be well represented by the naturalness/hierarchy problem (the mass of Higgs is unnaturally small comparing to the Planck mass scale), and the vacuum stability problems, which predicts our universe is in a meta-stable vacuum that will eventually decay into the true vacuum with catastrophic, huge energy releases. In one word, it’s well believed there must be profound, fundamental physics laws underlying the SM, to explain all the questions concerning the SM. The exploration towards these unknown fundamental physics laws certainly becomes the priority for particle physics in the Post Higgs era. 

New physics laws could be tagged by either direct search at the High energy frontier (via the production of particles beyond the SM) or the precision measurements (via searching for deviations from the SM predictions). Being the origin of mass in the SM, the Higgs boson is responsible, or at least correlated with most of these unsatisfactory or says SM defects. Therefore, the Higgs boson can actually served as an excellent probe for the precision measurement. That’s why the precision measurement of the Higgs boson is a key physics objective for both the on-going LHC Higgs studies and the proposals of high-precision Higgs factories in the future. 

The LHC is a very powerful Higgs factory, which already produced Millions of Higgs bosons, while roughly two orders of magnitudes more Higgs bosons are anticipated in the HL-LHC program. However, the precision of Higgs boson measurements at the LHC/HL-LHC are limited by the huge QCD background. The QCD background is so strong that one Higgs event is produced in roughly 10 Billion proton-proton collisions. Meanwhile, the physics event at LHC is usually overlapped with tens or even hundreds of pile-up events, therefore, only the Higgs events with clear, for most of the time pre-defined final states could be identified and recorded. The typical event reconstruction efficiency at the proton collider is roughly at per mille level. Therefore, the ultimate precisions of the Higgs boson measurements, characterized by the signal strength measurements, are limited to the relative accuracies at 10% level. Meanwhile, the requirement of pre-defined final states makes the interpretation of experimental data always model dependent. 

The electron positron colliders measure the Higgs boson at a completely different collision environment, and bring the essential information on top of the proton colliders. First of all, the electron positron colliders are much clearer than the proton colliders. The typical ratio between the event rates of the Higgs signal and the inclusive SM background is roughly at 10-2 to 10-3 level. In fact, the event rate is so low that all the physics events at an electron positron collider could in principle be recorded and analyzed, which makes the searching for unexpected Higgs decay modes – clear signals of the new physics laws – much easier than at LHC. Secondly, the initial condition of the electron positron collider is well defined and adjustable. The SM backgrounds are usually well understood and could be easily studied. Thirdly, a significant portion of the Higgs boson are generated from the Higgsstrahlung (ZH) event at the electron positron collider – which allows a model-independent determination of the g(HZZ) coupling, the Higgs boson width and the other couplings between Higgs boson and its decay final states. 

Fig 1, the cross sections of the Higgs signal and major standard model backgrounds at electron-positron colliders (Left) and proton colliders (right)

For these very reasons, many different electron positron facilities have been proposed and studied in details, including the linear colliders (ILC[1] and CLIC[2]) and circular colliders (FCC[3] and CEPC[4]). Giving a typical anticipated luminosity of the future electron positron colliders, the total yields of the Higgs boson is of the order of one million. Therefore, the absolute Higgs couplings could be determined to percentage or per mille level accuracy, which is roughly one order of magnitude better than that of HL-LHC. In addition, electron positron colliders, especially the circular colliders, also produce lots of W and Z bosons, which could be well used for the precision SM and EW measurements. Dedicated studies shows that, the precisions of SM/EW measurements could be improved significantly – by at least one order of magnitude at circular colliders – with respect to our nowadays’ precision. 

In one word, the discovery of the Higgs boson strongly promotes the electron positron collider proposals, which could improve the precision of Higgs properties by one order of magnitude with respect to the HL-LHC, and also significantly improve the precision of EW measurements. Such precision will reveal the physics landscape in TeV or even higher energy scale, and strongly enhance our understanding towards the physics laws underlying the SM. In this sense, the electron positron collider(s), is not only a nature choice, but also a must for the Post Higgs Era particle physics exploration.