Yukawa Unification -- 30th Anniversary of the Discovery

Going down memory lane, my mind went back 30 years to my last year at the University of Delaware. At this time I was busy with a small project suggested by my thesis advisor Qaisar Shafi , which was to look at the possibility of seeing what happens to the Yukawa couplings of the top-quark, b-quark and tau-lepton in a supersymmetric extension of the standard model.

Recall that the top-quark had not yet been discovered at that time. I had a set of renormalization group equations for these, but the model also had an unknown parameter called tan(beta), the ratio of the vacuum expectation values of the u- and down-type Higgs fields that are present in such supersymmetric models.

Using a bit of numerical analysis that I had learnt during my hoary B. Tech days in IIT Madras, I wrote a program (these days we don't call them programs but codes) which I could in Fortran and also because I had a terminal on my desk, having spirited away from from my advisor's office since he was not using it. I used a 4th order Runge-Kutta integrator and then I had complicated do-loops in fortran with the coupling constants input into the program, and a search for these Yukawa couplings.

I remember that the program would keep exiting and then entering the loop again and again, and one day, late in the evening, it found a solution. It pinned down the tan(beta) to a ratio of the masses of the top- and b-quarks at the low-scale, and then the program also evolved the couplings to the unification scale (of the coupling constants) and lo and behold the Yukawa couplings also got unified! The mass of the tau-lepton was an input, and the b-quark mass was taken within its experimental range, and out popped a value for the top-quark mass which was much larger than the experimental limit.

I soon afterwards showed these results to my advisor. I remember that he was planning to set off to a conference in Boston. Anyway, it was also a tough period because I had accumulated over 50 regrets and the thought of being unemployed loomed large on the horizon. When my advisor returned from Boston towards the end of March (I just googled and found that the conference was held at North-Eastern University and proceedings were published by World Scientific edited by Pran Nath and Stephen Reucroft), he told me that he showed these plots to Richard Arnowitt. Arnowitt told him he had not seen anything like this before and that we should write it up.

We did, along with George Lazarides write it up and it was all of 3 pages long and we submitted to Physical Review as a `Brief Report'. This section is now extinct. I saw that the received date on the paper is April 22, 1991. And the rest is history.

Over 300 citations later it stands as an important piece of evidence in support of supersymmetric unification.