It is good to back after my unexpected sabbatical of 2 years and 4 months in South America. During that time the BEH scalar boson (called \(H\)) was discovered on July 4th, 2012 at the LHC by both the CMS and ATLAS groups. The subsequent experimental study of the production and decay of \(H\) provides particle phenomenology with the first really new data for decades. Physicists who are less than 50 years old cannot remember the excitement in particle phenomenology of the 1970s. In the 1980s, 1990s and 2000s which included the important discoveries of the \(W^\pm\) and \(Z^0\), and the top quark the interplay between theory and experiment was nevertheless less exciting than the 1970s. Now the study of \(H\) again is.
In this paper, two assumptions are made:
- The masses of the fermions arise entirely from their Yukawa couplings.
- The mass of \(W^\pm\) arises entirely from the BEH mechanism. Both of these assumptions are implicit in the standard model so, if violated, there is already new physics to understand.
With these two assumptions we (my coauthor is Tom Kephart) derive a sum rule which must be satisfied by the Yukawa coupling constants. It states that the sum of the squares of the standard model Yukawa couplings divided by their measured values must equal one. This sum rule has several immediate consequences.
The partial decay rates for the decays \(H\to b+b\) and \(H \to \tau + \tau\) (one of the decay products has a bar over it) cannot be less than the corresponding rate in the standard model. The reason is simple to explain. If the Yukawa coupling were smaller, the corresponding vacuum value must be bigger but that gives too large a \(W\)-mass by the BEH mechanism and hence is disallowed because the W mass is known to an accuracy better than 0.01%.
In beyond the standard model (BSM) theories with two distinct scalar doublets coupling respectively to the top, and to the bottom and tau, such as the MSSM, the sum rule constrains \(\tan\beta\) certainly to be less than one, quite different from what is often assumed in fits. Although the MSSM was already on life support before this work, I would dare to say that the plug is now pulled half-way out of the socket. BSM theories like Peccei-Quinn and the 2HDMs are likewise constrained by the sum rule.
There are BSM models where three distinct scalar doublets couple to the top, bottom and tau. These include theories with global flavor symmetries, including several of my group's old models. Here the sum rule is even more exacting and almost no model of this type can survive at 3 sigma.
Regarding the MSSM, the supersymmetry community is very clever and no doubt a generalization of MSSM will be constructed which can satisfy the new sum rule even with the higher accuracy data expected from the LHC. But it will be challenging.
More generally, the sum rule means that constructing any viable theory beyond the standard model becomes more difficult and that is obviously a good thing.
So that's my guest blog, Lubos.
With my best regards as always,