Hitoshi Murayama (LBNL): "Higgs and Susy Higgs Studies at a Linear Collider"
An explicit question to draw out a response on these interlocked issues might be:
0. Suppose a Higgs is discovered with mass 110, 210 or 610 GeV. Discuss what we would learn with a 250 - 350 GeV collider, a 500 GeV machine? with 800 - 1000 GeV collider? How does the answer depend on the luminosity of the collider?
110 GeV: prove Higgsness: 50 fb-1 enough tau/b ratio: 50 fb-1 enough --> prove that Higgs is the source of both vector and fermion masses branching fraction measurements may tell that it is the MSSM Higgs at least 100 fb-1, up to mA=700 GeV with 1000 fb-1 needs to be redone with a lower lumi 210 GeV: verify WW/ZZ ratio: at 10% level with 50 fb-1 at 500 GeV ttbar H coupling: at 10% level with 50 fb-1 at 500 GeV can look for exotic decay modes 610 GeV: verify WW/ZZ ratio: at 15% level with 60 fb-1 at 1 TeV ttbar H coupling: at 10% level with 300 fb-1 at 1 TeV can look for exotic decay modes sensitivity should improve with 1.5 TeV machineIn WW/ZZ ratio, I assumed that the di-jet mass resolution is good enough to separate them in fully hadronic modes. Mixed modes in WW, ZZ had not been studied carefuly yet, even though they are obviously useful.
1. Much is made of the hints, from precision fits to LEP and other data, that the lightest Higgs is "just around the corner." What does this kind of analysis say about the mass of the lightest Higgs in a general, multi-doublet model? In technicolor models?
I agree that the precision EW bound on Higgs mass can be relaxed by assuming an additional operators from the cutoff (3 TeV?) with definite signs (Kolda and Hall, Phys. Lett. B459, 213 (1999), hep-ph/9904236). We do not know of explicit "nice" models which give rise to them, however. In technicolor models, it would be a fine-tuning between various constributions. I do not know the general predicition of multi-doublet models, but unlike fermions, these contributions decouple in the heavy mass limit.
2. How can we determine that a "Higgs" signal seen at a linear collider is truly the SM higgs with the required couplings to quarks, leptons, W and Z? In particular, can we understand if the "Higgs" gives mass to fermions and bosons, or to bosons only.
The spin/parity analysis and left-right asymmetry would prove that Higgs is produced by ZZH coupling. Simply the measurement of e+e- -> ZH rate determines the ZZH coupling. That answers if the coupling is truly that required to generate MZ. W coupling requires either H->ZZ and H->WW branching fraction measurements, or e+e- --> nu nubar H rate measurement. For fermion masses, measure H->ttbar branching fraction for heavy Higgs, H-> bbar/t ratio and e+e- --> ttbar H for light Higgs.
3. How can we distinguish experimentally between the SM Higgs and the lowest mass state in a more complex multi-doublet model such as Susy? Can we determine the number of Higgs multiplets in the theory? Can we verify the Susy character of the Higgs sector?
The most direct method is to produce additional Higgs states which can be done close to the kinematic limit. The branching fraction measurements could tell the SM and the MSSM apart even if the additional Higgs states are above threshold. If the measured ZZH coupling is less than that in the SM, it implies the existence of additional Higgs doublets. It would be impossible to determine the number of Higgs doublets in a model-independent way at any experimental facility, as one can always add new Higgs doublets with large *positive* mass-squared so that they decouple from the electroweak symmetry breaking mechanism. The relation between Higgs masses can verify the SUSY character of the Higgs sector, such as MH±2 = MA2 + MW2. Branching fractions of H0->ZZ and H0->hh, if both present, would be an even better test of the Higgs self-coupling which is given by the gauge coupling constant due to supersymmetry.
4. How would linear collider measurements extend the presumed LHC measurements in establishing the Higgs spin, parity fermion couplings and width? Do these measurements require operation of the collider in special (e.g. gamma gamma) modes? Do these measurements require use of the polarization of the electron beam (and positron beam)? How many operating energies are required? (We are trying to get a fix here on the integrated luminosity, hence time required to complete a reasonable set of measurements.)
Higgs spin parity can be determined from the production angles at LC. Only one operating energy is needed for this purpose, and 50 fb-1 is probably enough as long as the Higgs is well within the kinematic reach. LHC can presumably determine Higgs spin parity from the angular distributions and correlations if H -> ZZ-> 4l. If LHC sees H->gamma+gamma instead, spin 1 is excluded, and is probably spin 0, but will likely not distinguish scalar from pseudo-scalar. It may even be a techni-pion! But ttbarh production may help (Gunion and He, Phys.Rev.Lett. 76, 4468 (1996), hep-ph/9602226). Gamma gamma mode is not necessary for this purpose, but the linear polarization of photons in gamma gamma mode is useful to study the possible mixture of CP-odd component (Grzadkowski and Gunion, Phys.Lett. B294, 361 (1992), hep-ph/9206262).
5. Suppose we find a light Higgs and light charginos and neutralinos, but no other supersymmetric particles. Can we tell that the model is supersymmetric? Can we predict the masses of the other scalars?
If all charginos (both wino, higgsino) there, in principle one can show that the off-diagonal elements in the mass matrices are mW or mZ, which verifies SUSY (Feng, Peskin, HM, Tata, Phys.Rev. D52, 1418 (1995), hep-ph/9502260). If the chargino/neutrino are mostly gauginos and higgsino components heavy, one can show that the chargino is a pure SU(2) triplet state by the absence of the rate from the right-handed electron beam. This is not a proof of supersymetry, but is quite close. Then the rate from the left-handed electron beam determines the mass of the electron sneutrino up to 1 TeV range. This would predict the mass of the left-handed selectron by the D-term relation (Tsukamoto, Fujii, HM, Yamaguchi, Okada, Phys.Rev. D51, 3153 (1995)). But this doesn't prove SUSY until sneutrino is indeed found at the predicted mass.
6. Is it possible that we live in a supersymmetric world with the lightest higgs mass satisfying mh > 2 mN1 (the lightest neutalino)? If not ruled out, are there any observable decay modes of h? What would be the range of A masses, and could the A be observed at LEP, Tevatron or LHC? (or H or H+). Would such a scenario enhance the probability of observing the other susy particles? How would the Linear Collider detect such a light higgs whose decays are dominantly in to neutralino pairs?
It is still possible, because the lower bound on M1 is 30 GeV (as of 1999 PDG web update), which comes primarily from the bound on the chargino mass which is translated to the bound on M2 and further into M1 using the GUT relation. It is even more so if one drops the GUT relation. If h -> neutralino*2 open, it tends to dominate. No visible decay mode, unless the neutralino further decays into gamma+gravitino. Recoil mass spectrum still discovers Higgs without problem. No necessary correlation with A mass. No necessary correlation with other SUSY masses if neutralino = bino.
7. What are the backgrounds to be expected at the Linear Collider for the various Higgs signatures?
ZZ, WW, ttbar, WWZ, ttbarZ, enuW, nunuZ, eeWW, nnWW, nnWZ, enWZ.
8. What are the crucial experimental handles for isolating Higgs signals -- B tags, dijet mass resolutions, jet counting? How reliably are these understood at present? Do they depend critically upon unknown factors such as low energy particles from beam radiation or color radiation by quarks?
What counts is probably the overall performance rather than a single aspect. B-tags are certainly important, even though ALEPH-level detector would do just fine for discovery and many of the studies (see Janot, Hawaii). But ccbar/gg separation would require a vertex detector closer to the collision point (1 cm is the currently favored parameter) (see Battaglia, Sitges). Di-jet mass resolution is important if H->WW and H->ZZ need to be separated in fully hadronic modes (Miyamoto, Hawaii). Jet counting (I assume the granularity is being discussed) is important for ttbarZ, ttbarH final states, even though their reconstruction had been already demonstrated (Tauchi, Fujii, Miyamoto, Snowmass 1990). Low-energy particles from beam radiation are in principle important. Detectors need to be designed to minimize the overlap of mini-jet type events with real events, which may mean that a very fast time response is required to distinguish events from different bunches on a single train as already being discussed. However, 20% overlap probability was shown to be tolerable (Yamashita, Sitges) for Higgs studies.