## Tuesday, March 21, 2006

### Peter Woit recommends supersymmetry

Top quark is the heaviest elementary fermion, the king of quarks. Its mass used to be thought to be 178 GeV. It was lowered to 175 GeV and now to 172.5 GeV, with error margin around 2 GeV. When you divide this number by 247 GeV, the vacuum expectation value of the Higgs boson, you obtain the tree-level top Yukawa coupling which happens to be close to "1/sqrt(2)".

I hope that many readers will be excited about this fact and will incorporate this fact into their guitar theories. :-) Regardless of this nice value, the top quark mass is, in principle, the easiest fermionic mass to calculate from a full model.

As you know very well, particular string models predict the exact masses of all particles. The most popular models in the early 1990s were the heterotic models, so what is their prediction? In fact, it is a rather well-defined question because the top quark mass value is more or less a general feature of these models. The top quark mass predicted by the "free fermionic" heterotic string Standard Models was first "almost" properly calculated by Alon Faraggi in 1991 and he obtained a mass in the range
• 175 - 180 GeV.
See this page for a scanned version of his Physics Letters B paper from 1992 where this prediction was made. More than three years later, in 1995, the top quark was eventually discovered at the Tevatron and the mass was between 175 - 180 GeV. Faraggi's string-theoretical prediction was experimentally confirmed. At roughly the same time, Faraggi included some loop corrections which made the agreement worse because the physical mass he obtained was 192 - 200 GeV.

At any rate, this story is an example that string theory can predict properties of particle physics and it can even give us the right predictions.

The experimentalists who work on top physics - and the theorists who work with them - explain the importance of their work in their talks, much like everyone else. See, for example, this talk by Timothy Tait who is a theorist. It is one of these nice talks that you can often hear and that follow a certain standard scheme. It reviews the theoretical side of the experimental methods, the current theories - the Standard Model - and then they study physics beyond the Standard Model. The pages 10,11,12,13,14,17,19 - more than one third of the talk - are dedicated to supersymmetry, the "best studied and best motivated solution to the hierarchy problem" as (not only) Tait calls it. Tait explains that the Higgs mass in the minimal supersymmetric Standard Model depends primarily on the top and stop masses which is what makes a continuing research of the top quark important.

The funny thing is that Peter Woit has not checked the talk carefully and actually recommended this talk as an explanation why the top quark is important! :-) That's very unusual because all of you know very well that the only physics articles that Peter Woit normally links with positive (or without negative) remarks are scientifically worthless rants whose only "virtue" is that they are critical about string theory and the whole modern high-energy physics for that matter, which makes them the ideal material to please the crackpots who constitute the core of Peter Woit's readership: Quantoken, Nigel Cook, Tony Smith, Danny Ross Lunsford (who stopped posting, thanks God, because he could not survive that WMAP seems to confirm inflation), Alejandro Rivero, MathPhys, stan, secret milkshake, and a whole army of others.

Which scientifically worthless texts promoted by "Not Even Wrong" am I talking about? Well, the new article on Peter's blog that immediately follows the announcement of the corrected top quark mass - a text about some new poetry about political incorrectness of geometry by Bert Schroer - may be used as an example.

As you can see, Peter Woit does not really read any of these talks, not even the superficial talks for the non-experts, which allowed him to publish a whole blog article about the fact that the research of the top quark is important because it is important for the fate of the minimal supersymmetric Standard Model. Some readers are asking him: So why is the mass of the top quark so important? And of course he won't be brave enough to give them the answer, even after he learns it from this blog.

If you don't care about the details of the Yukawa coupling, the content of the text above can be replaced by GoogleFights. ;-)

1. Lubos:
Proximity of 1% or so is just a coincidence that happens TOO often and that's the basis of most numerology theories. You and I both reject numerology as crackpot theory. I try to make it very clear that GUITAR theory has no basis in numerology, every derivation of my formula has a logical sounding physics reason behind it, I am not not ready to reveal these details yet. But when you get a precision of up to 9 digits matching experimental value, it can NOT possibly be a numerological coincidence. That much is clear.

Likewise, if string theory makes a "prediction", and the prediction is only good to 1%, it is not very credible or convincing. At best it's a nice coincidence, at worst it's just numerology. A prediction needs to be at least one part in a million in discrepancy, or even better, to be convincingly proven. Newtonian Mechanics can go many digits before any relativity effect is detected, but it is still obsolete now.

Not to meantion now there are no less than a dozen different ways of obtaining the correct Hawking Entropy of a blackhole, LQG and SST notwithstanding.

QUANTOKEN

2. The Review of Particle Properties published in June 1992 was giving as electroweak estimate for the mass of top

150 GeV +23 -26

plus an additional \pm 16 GeV uncertainty due to the mass of the Higgs. Particularly for M_Higgs=250 GeV a upper bound m_t<178 (resp 186) was quoted at 90% (resp 85%) confidence level. As far as I understand, these limits are based on searches and electroweak fitting only, independently of SUSY considerations or other kind of modelling.

http://prola.aps.org/pagegif/PRD/v45/i11/pS1_1/pS388

Incidendentally, the author of the review for PDG has also a contemporaty review on SUSY predictions, http://es.arxiv.org/abs/hep-ph/9306205

3. Abiut this casual which happens to be close to "1/sqrt(2)"., it is perhaps interesting to remark that "close" should be changed to "exact" for a top mass value of 174.1042 (\pm 0.00075 at the current level of precision of Fermi constant)

Some people prefer the normalisation where this value is not 1/sqrt(2) but just unity,