# Why are WW gg ττ branching ratios so similar for a 115 GeV SM Higgs?

In a previous question on Higgs branching ratios, I find this image

(originally from page 15 here).

I am VERY intrigued by the fact that decays to WW, gg, and ττ are almost equally probable, for a standard model Higgs with a mass in the vicinity of 115 GeV. I've noted previously that this is a special value: it lies in a narrow range of values for which the SM vacuum is metastable. Is there a connection?

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Question downvoted, I don't know why. Is that someone's way of saying they think this is just a coincidence? Or that I posted too many questions at once? –  Mitchell Porter Jun 20 '11 at 7:42
I have no idea who down-voted you but this is an intriguing question. +1 –  Marek Jun 20 '11 at 9:12
at 115 they're not really close together, e.g. the BRs for gg, tautau and ZZ at around 135 are closer. the point you're referring to is more at 117-8. The tautau and gluon-gluon BRs are in general very close so whatever BR crosses this line to become dominant (WW,ZZ) would produce just an "intruguing" point, and they do (both WW and ZZ). I wouldn't really see any mystery in there. –  luksen Jun 20 '11 at 13:41
Just given the number of crossings present in the figure one must consider "coincidence" as a candidate. But then, I'm a wrench turning monkey of a physicist. –  dmckee Jun 22 '11 at 2:01
I think that you can separate the first part of your question in two different ones: why should the decays of higgs to gluons and tau be similar in all the range, and why so near of the W for this particular range. –  arivero Aug 29 '11 at 10:11
In this graph, you have clearly found the triangle composed of three curves which is the smallest one. The triangle made of $gg$, $ZZ$, $\tau\tau$ near $m_H=130$ GeV is comparably small but larger.
In the MSSM, one modifies the spectrum so that the intersection of three lines, depicting the gauge couplings for $U(1)$, $SU(2)$, and $SU(3)$, is exact within the error margins. It also has a good reason: the groups become subgroups of a larger unified group such as $SU(5)$ which only has one coupling so the smaller groups' couplings have to agree at the GUT scale. In your case, no such improvement is known. At any rate, your lucky hunch is a coincidence, the triangle is not "anomalously small". Its size is not far from what you expect from the smallest triangle in a similarly large chaotic graph with intersecting curves.