Remembering mother on International Working Women's Day

My late mother, Saraswathi, was a little over 21 when she was married and went with her newly married husband to Shillong where father was working in the Accountant General's Office, I guess of undivided Assam. She worked there shortly in Lady Keane College, teaching Chemistry. She has asked me couple of times to take me back there, but it was never to happen. In a few years, she had lived in Trivandrum and then in Delhi and Hyderabad, by which time she had two children, and then in Ahmedabad. By the time we were little older, she went back to to Osmania University, first getting a degree in Journalism, and then eventually settled down to a career in education, earning a Bachelors and Masters in Education first from Osmania and then a Masters from SUNY Buffalo working on a short thesis with the renowned Philip Altbach, and then her Ph. D. from Osmania under the supervision of Prof. Ramachandra Reddy of a different department. Her thesis work was published as a book and now I have two copies. In the meantime, she started to work in Neelam Sanjeeva Reddy College of the Vivek Vardhini Society in Putli Bowli and spent a couple of decades there as a teacher, in toto and retired in 1996. A very practical person, who taught her subject of educational philosophy and science methodology with a rare passion, she trained a generation of students many who went back to the hinterland as teachers. Her infectious enthusiasm for science rubbed off on everyone and love for kids. Her other major love was for the language of Telugu from which she translated several stories and the like. Although in essence she stood for the rights of, and emancipation of women, I rarely heard her talking about it. I guess actions are louder than words and to us those stay etched in our minds. Also a tireless fighter against discrimination and caste system, she could speak her mind fearlessly. Even though it is over 13 months since her altogether early departure, I thought it fit to think about her on the day after the International Working Women's Day.

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.