The LHC offers a very detailed knowledge of how the Standard Model particles interact, but we know that this knowledge is incomplete. A number of experimental data and theoretical motivations point to the existence of new physics beyond the description of the Standard Model.  The recently discovered Higgs boson crowned a success of the SM and calls for further studies on this newly observed sector. In that context, the study of the Higgs boson and how it couples with the known particles of the Standard Model sets a clear, albeit ambitious, challenge for the experimental programme of any post-LHC machine.

To address the opportunities offered by proposed future colliders, the European Strategy for Particle Physics has formed a group to study in details the projected performance and possible searches. Following an intense period of work, during which they reviewed the design studies for these future machines, the group prepared a comprehensive report that largely informed discussions during the recent EPPSU meeting in Granada. Comparing possible measurements and searches linked to the Higgs boson at the different environment offered by circular and linear colliders has not been a trivial task. Things get more complicated as one has to take into account different theoretical considerations that enter these calculations and the projected performance for these machines.

A key aspect of the experimental programme of a post-LHC collider includes precision studies of Higgs couplings, self-couplings and its total width as well as the study of rare decays. Since these couplings are well defined in the framework of the Standard Model, small deviations could be a sign of new physics. However, in the absence of knowledge of the form that new physics can have we need to parametrize our ignorance in terms of continuous deformations of the Higgs boson couplings. Different assumptions allow to capture different classes of new physics dynamics which was one of the challenges faced in producing this report. Two other topics discussed in the report are the significant progress expected in future colliders include the sensitivity to new high-scale physics through loop corrections as well as very sensitive searches for CP violating effects.

The calculations are combined with the expected reach of the HL-LHC programme. To understand the potential of future machines both the κ-framework and EFT analysis are taken into account.The first offers a convenient exploration tool without requiring further computations than those included in the SM and can capture the dominant effects of well motivated new physics scenarios on a set of on-shell Higgs observables. However, the validity of this approach is limited if you want to put Higgs measurements in perspective and compare them to processes with different particle multiplicities or combined with measurements at different energy scales. This is where, the EFT proves to be a more powerful tool. First of all, it allows to exploit polarisation- and angular-dependent observables to which κ-analysis remains blind. Moreover, EFT probes the Higgs in the extreme kinematical regions relevant for colliders operating far above the weak scale, exploring the tails of kinematical distributions. In addition, EFT offers a consistent framework where predictions can be systematically improved via the inclusion of both higher loop corrections in the SM couplings and corrections from new physics can be encoded in operators of even higher dimensions. The report presents detailed comparisons basedon these two frameworks and the current design parameters of the proposed future colliders. The primary goal is to allow a clear and coherent comparison that can guide decisions for the future of the field.

Another crucial experimental challenge is the measurement of Higgs couplings with other known particles of the Standard Model. A future lepton collider could push precision measurements closer to the 1% threshold where a number of new physics theories can be studied. In that respected the proposed High-Energy upgrade of the LHC (HE-LHC) seems to offer small improvements compared to the planned High-Luminosity LHC (HL-LHC) which will boost the precision measurement of these couplings.

Sensitivity at 68% probability to deviations in the different effective Higgs couplings and aTGC from a global fit to the projections available at each future collider project. Results obtained within the SMEFT framework in the benchmark SMEFTND.

Sensitivity at 68% probability to deviations in the different EW couplings from a global fit to the projections available at each future collider project. Results obtained within the SMEFT framework in the benchmark SMEFTND. See the original report (Fig.4, p.22) for details and the discussion therein. 

Regarding the study of Higgs couplings to vector bosons, both CEPC and FCC-ee would be able to measure the effective H→ ZZ coupling with a precision of ∼ 0.3%. Following a 15 years programme at 365 GeV, the FCC-ee can bring the H→ ZZ coupling down to ∼ 0.2% thanks to the unprecedented luminosities of circular colliders. In the case of ILC, operating at 250 GeV a precision of ∼ 0.4−0.5% can be achieved while to reach the same precision as FCC-ee would require to double its energy up to 500 GeV and about 22 years of operation. CLIC could also offer a two-per mille accuracy of the Higgs couplings to vector bosons about a 23-year programme profiting also from its upgradability to higher energies up to 1.5 TeV.

Turning now to the Higgs couplings to fermions, a similar pattern of improvements is observed for couplings to bottom quark and τ lepton. The top quark Yukawa is not directly accessible for lepton colliders running below the ttH threshold that can be accessed with the high-energy runs of the lepton machines. ILC at 500 GeV can reach a precision ∼ 6-7% that can be brought to 3% by pushing the energy to 550 GeV and a similar projection exists for CLIC operating at 1.5 TeV. It should be noted though that a possible future 100 TeV proton collider (FCC-hh) coupled with precise measurements of the Z to top/antitop coupling at FCC-ee could bring the precision for this measurement down to 1%. The report notes that a number of Higgs couplings, mainly those associated to rare decays, remain statistically limited above the 1% threshold and only the combination with a high-luminosity proton machine could bring all the main Higgs couplings below 1%.

It should be noted that a precise measurement of the mass of the Higgs boson is needed also needed to improve the accuracy of these measurements. Future accelerators are expected to substantially improve the precision of the Higgs mass measurement. It is important to combine precise measurements of the Higgs couplings with equally precise measurements of the Higgs mass, to the level of 10 MeV which is possible at 240/250 GeV lepton colliders. Moreover, in the SM, the width of a 125 GeV H boson is predicted to be around 4 MeV, i.e. three orders of magnitude smaller than that of the weak bosons and of the top quark. It is therefore very challenging to measure it directly. All methods considered so far at colliders are in fact indirect and model dependent to various degrees. Three methods have been proposed at the LHC, and are considered for future hadron colliders while lepton colliders could also provide complementary results allowing to extract the total width of the Higgs boson with a mild model dependence (based on the measurements of the inclusive cross section of the ZH process).

Another top priority for future colliders is the measurement of the Higgs potential. This would allow to search for sizeable departures from the SM form and understand the role of the Higgs field in the spontaneous breaking of the electroweak symmetry and consequently the generation of the masses of all the Standard Model particles. Unfortunately the measurement of the Higgs potential depends on a number of theoretical considerations that are extensively discussed in the report. A robust analysis requires to be able to disentangle a variation due to a modified Higgs self-interaction from variations due other deformations of the Standard Model which proves to be a daunting challenge. Several of the proposed post-LHC colliders will reach a sensitivity of order 20%, thus establishing the existence of the self-interaction at 5σ. Even more remarkable, CLIC3000 can reach a sensitivity of 10% and FCChh bring it down to 5%, where one could start probing the size of the quantum corrections to the Higgs potential directly.

Another interesting topic concerns the Higgs boson rare decays as they can provide access to Higgs couplings which are expected to be small and thus have not yet been directly probed. For example, if we observe an enhanced rate in processes that are predicted to be rare in the SM this could be a signal of new physics at play. The ability of future colliders to explore these rare decays depends mainly on the number of Higgs bosons produced and the available statistics. Another way in which new physics could manifest in the study of rare decays is through peculiar signatures of final states. Finally, the Higgs boson could also decay to invisible particles that could be good Dark Matter candidates. The proposed lepton colliders improve the sensitivity by about a factor 10 compared to HL-LHC while a 100 TeV energy-frontier machine improves it by another order of magnitude and will probe values below that of the SM. In that front, high-energy hadron colliders are more sensitive and will allow direct searches for DM candidates.

Furthermore, searching for non-zero CP-odd components in the interaction of the Higgs with the other SM particles could shed light to the strong CP problem, offering the missing additional sources for CP violation to explain the apparent imbalance between matter and antimatter. Searches for this extra source of CP violation focus on ttH at hadron colliders and on ttH and tH final states at lepton colliders, respectively. For example, by studying distributions in ttH, the HL-LHC will be able to exclude a CP-odd Higgs at 95%CL with about 200 fb−1 of integrated luminosity. CLIC 1.5 TeV foresees to measure the mixing angle for the top quark, αt ttH¯ to better than 15◦ while FCC-ee offers a precision of 1.9% on αt. The most promising direct probe of CP violation in fermionic Higgs decays is the τ+τ− decay channel that benefits from a relatively large branching fraction. Accessing the CP violating phase requires a measurement of the linear polarisations of both τ leptons and the azimuthal angle between them.

In conclusion the report details a wealth of useful data, comparing different types of searches around the Higgs in future colliders. It places the Higgs measurements in perspective with other new physics studies at future colliders while offering a comprehensive overview of precision studies of the Higgs boson as a guaranteed deliverable of any future collider facility. The dedicated effort to make this comparison has been acknowledged during the Granada meeting and this document will inform the final drafting session setting the priorities for the next post-LHC collider.

Read the full report:  https://arxiv.org/pdf/1905.03764.pdf