## Did we scr** up all the Higgs branching ratios ? May 27, 2008

Posted by dorigo in news, physics, science.
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An interesting paper (hep-ph/0804.1753) appeared in the arxiv last month, but I was late in noticing it. Have you ? It is titled “Higgs-dependent Yukawa couplings“, authors G.F. Giudice -formerly Padova University- and O.Lebedev. It seems that as we get closer to the time when the Large hadron collider (LHC) will be turned on at the CERN laboratories, phenomenological papers based on LHC signatures pop up like mushrooms after a September shower.

The idea of the study is not easy to explain to outsiders, but I want to keep this post simple enough -I have drifted a bit too much toward technicalities because of the PPC 2008 conference last week- and I will not go in the details. Besides, the paper is very clear, so whomever wants more information is encouraged to click the link above.

Basically the authors imagine that the pattern of masses we observe for quarks and leptons -which range from sub-electron volt for neutrinos (their masses are in fact not yet known precisely, but they are surely less than that tiny value), to 172.6 billion electron volts for the top quark- may result from a simple formula valid at energies below a fundamental mass scale $M$, not yet tested by present accelerators but of the order of a trillion electron-volts, and thus accessible at the Large Hadron Collider (the highest energy proton collisions provided by the LHC will equal a dozen trillion electron-volts).

Masses of fermions in the Standard Model Lagrangian -the function which enshrines the dynamics of a physical system- depend by so-called Yukawa couplings. In Giudice’s and Lebedev’s scheme these couplings are simple formulas, powers of the Higgs boson’s vacuum expectation value divided by a suitable mass, $/M$. This is an effective theory -one that is only valid below a certain energy, pretty much like newtonian mechanics which is valid for speeds much smaller than that of light. and indeed the formulation is not based on first principles. However, it has the merit of providing a reason for the expected pattern of masses and the weak interaction phenomenology, which depend on some further sets of unexplained numbers (describing the flavor matrix) in the Standard Model.

The nice thing is that we get very clear and testable predictions. The introduction of a reachable mass scale connected to the weak flavor matrix has direct consequences on the existence of processes whereby quarks change flavor without changing electric charge: flavor-changing neutral currents, known as FCNC for insiders. But, hear this: the most interesting, intriguing consequence is that these effective couplings modify the way the Higgs boson couples to fermions, resulting in a completely different pattern of fermion-fermion decays of the Higgs. The Higgs in this model decays more often to fermion pairs than it does in the Standard Model, and it is also produced in top quark decays, such as $t \to Hc$!

The only Yukawa coupling which is unaffected by the scheme described is the one of the top quark, which is equal to one to very good approximation (even a suspiciously good one, as Alejandro Rivero, Chris Quigg, and others have noticed in the past) in the Standard Model: therefore, the branching fraction of Higgs bosons to top quark pairs is unaffected. So are the branching fractions of $H \to WW$ and $H \to ZZ$. However, the boosts in the lighter fermion couplings mean a lot in some cases: the Higgs may decay 25 times more frequently to muon pairs, making itself observable at low mass (with enough statistics) despite the depletion in $H \to \gamma \gamma$ final states !

Below is a picture worth a thousand words: it shows how the complex and fascinating phenomenology of Higgs decay varies as a function of its mass (on the x axis) in the Standard Model (hatched lines) and in Giudice and Lebedev model (full lines). As you see, the gamma-gamma final state is reduced by almost an order of magnitude (since it does not receive any boost, it has to shrink to give extra space to the fermion decays), and the $b \bar b$ one remains dominant up to 150 GeV: in this picture, the LHC may need to resort to dimuon final states to see a light Higgs boson!!

I must give it to Giudice and Lebedev: an extremely interesting, fresh new idea, with clear and easily testable predictions. Way to go, in times when the theoretical panorama is dominated by strings, supersymmetry, and large extra dimensions – all things that either give no predictions or have so many degrees of freedom they can accommodate almost anything new we see…

1. Tripitaka - May 28, 2008

Cool!
Since you didn’t mention anything, I assume that there are no potential consequences arising from this theory in relation to work being done at Tevatron, is that right?

2. dorigo - May 28, 2008

Well, I did not take the existing Tevatron limits in consideration,
but if you do, you get better limits at low mass (due to the higher BR of H->bb) and worse limits at intermediate to high mass (due to the worse BR of H->WW).
Looking at the latest Tevatron limit plot and the graph above for BR boosts, and keeping in mind that a double BR becomes a halved limit and vice-versa, I would say that little would change if you were to marry the model by Giudice and Lebedev: you’d get a limit curve which peaks at 120 GeV more or less at the same value as before (6xSM, say), then a steeper descent to 1.5xSM at 140 GeV, and a flattening out to the same value up to 175 GeV (instead then the dipping to 1.1xSM of the existing plot).

I believe it is not worth playing the game though. Rather, it is useful to keep in mind that a $H \to \mu \mu$ search might be interesting to do as soon as we collect >1/fb of data.

Cheers,
T.

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