Wednesday, May 22, 2013

t, H, W, Z again

(A continuation of "t, H, W, Z".)

A recent paper informs us that 

(mH)2 + (mW)2 + (mZ)2 + Σquarks(mq)2 + Σleptons(ml)2 = (HiggsVEV)2

... almost identical to the formula

(mH)2 + (mW)2 + (mZ)2 + (Σquarksmq)2 + (Σleptonsml)2 = (HiggsVEV)2

which appeared as part of the very first exercise of physics numerology examined by this blog (in July 2011), due to A. Garcés Doz. (I cannot find the formula in any of his papers at - search for "author=doz" for a full listing - but perhaps it's there too.)

The similarity may be attributed to the fact that the top mass, mt, is so much greater than all the other fermions, that it hardly matters whether you add the masses and square them, or square the masses and then add them. Just the following formula still works quite well:

(mH)2 + (mW)2 + (mZ)2 + (mt)2 = (HiggsVEV)2

Curiously, when Garcés Doz posted his formula two years ago, he was using mH = 119 GeV, a value which must have come from someone's supersymmetric model; but the value of the Higgs VEV is then off by a few GeV. It actually works much better using mH = 125 GeV, the measured value; so he could have actually predicted the Higgs mass using this formula.

(Caution: I have been a little careless in checking these facts and calculations; will check them more closely, later.)

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