Abstract
Abstract The discovery or exclusion of the fundamental standard scalar is a hot topic, given the data of LEP, the Tevatron and the LHC, as well as the advanced status of the pertinent theoretical calculations. With the current statistics at the hadron colliders, the workhorse decay channel, at all relevant H masses, is H → W W, followed by W → ℓν, ℓ = e or μ. Using phase-space singularity techniques, we construct and study a plethora of “singularity variables” meant to facilitate the difficult tasks of separating signal and backgrounds and of measuring the mass of a putative signal. The simplest singularity variables are not invariant under boosts along the pp or $$ p\overline p $$ axes and the simulation of their distributions requires a good understanding of parton distribution functions, perhaps not a serious shortcoming during the boson hunting season. The derivation of longitudinally boost-invariant variables, which are functions of the four charged-lepton observables that share this invariance, is quite elaborate. But their use is simple and they are, in a kinematical sense, optimal.
Highlights
Narrow gaps, 131 GeV < MH < 453 GeV (ATLAS)
In mass intervals akin to the one implied by the quoted constraints CMS finds a 1.9σ excess of events — that could be an indication of a Higgs signal — at MH = 124 GeV and ATLAS a 2.5σ one at MH = 126 GeV [1,2,3,4]
The obvious problem with the H → W W channel is that MH cannot be reconstructed event by event, as a lot of information escapes detection with the unobserved neutrinos and, at a hadron collider, with the unobserved hadrons that exit “longitudinally” close to the beam pipe(s)
Summary
The simple example of single-W production is used in section 3 to clarify what singularity conditions and singularity variables are. It is a necessary intermediate step in the theoretical derivation, in section 6, of the general case with a boson which is not at rest. We analize MC-generated data in section 9 in the theoretical approximation of a Higgs boson made at rest. Our data analysis is not as thorough as the theoretical one, it is only meant to illustrate our points. It suffices to reach our conclusions, which, naturally, are drawn in the last section. A very formal but important step in our theoretical analysis is relegated to the appendix
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