Robert Garisto is an Editor of Physical Review Letters, the flagship journal of American Physical Society and the one with the highest impact factor in physics. I follow him on twitter (@RobertGaristo) and he points out interesting papers that appear in the journal he works in. This time I read the following

and turned immediately my attention to the linked paper: This one (if you have not a subscription you can find it at arxiv) by Tom Steele and Zhi-Wei Wang showing, with the technique of Padè approximants and an average method how to compute the exact mass of Higgs particle from Coleman-Weinberg mechanism arriving to estimate the ninth order contribution. This is so beacuse they need a stronger coupling with respect to the original Higgs mechanism. They reach an upper bound of 141 GeV for the mass and 0.352 for the self-coupling while they get the mass of 124 GeV for a self-coupling of 0.23. This shows unequivocally that the quadratic term, the one generating the hierarchy problem, is absolutely not needed and the Standard Model, in its conformal formulation, is able to predict the mass of the Higgs particle. Besides, the production rates are identical to the original model but differ for the production of Higgs pairs and this is where one could tell which way nature has chosen. This implies that, at the moment, one has no way to be sure this is the right solution but we have to wait till 2015 after LHC upgrade. So, once again, the precise measurements of these decay rates are essential to tell if we are coping with the original Higgs mechanism or something different or if we need two more years to answer this question. In any case, it is possible that Nobel committee has to wait yet before to take a decision. However, in the sixties that formulation was the only possible and any other solution would have been impossible to discover for the lack of knowledge. They did a great job even if we will prove a different mechanism at work as they provided credibility to the Standard Model and people could trust it.

Finally, I would like to note how the value of the coupling is consistent with my recent estimation where I get 0.36 for the self-interaction. I get different production rates and I would be just curious to see how pictures from ATLAS and CMS would change comparing differently from the Standard Model in order to claim no other Higgs-like particle is seen.

What we can conclude is that the conformal Standard Model is in even more better shape than before and just a single Higgs particle would be needed. An astonishing result.

Steele, T., & Wang, Z. (2013). Is Radiative Electroweak Symmetry Breaking Consistent with a 125 GeV Higgs Mass? Physical Review Letters, 110 (15) DOI: 10.1103/PhysRevLett.110.151601

Marco Frasca (2013). Revisiting the Higgs sector of the Standard Model arXiv arXiv: 1303.3158v1

For comparison purposes (a point which the referenced article should really have made more prominently in the body text IMHO), in the conventional SM, for “a Higgs mass of 125 GeV the value of the Higgs self-interaction would be lambda(MH) ≈ 0.13 at the scale of the Higgs mass.” http://arxiv.org/pdf/1205.2892.pdf

Thus, the radiative EWSB implies a Higgs self-coupling 77% greater than the conventional SM EWSB mechanism, and your recent estimation is 177% greater than the conventional SM EWSB mechanism Higgs self-coupling.

To distinguish between the 0.13 and 0.23 value at 3 sigma you need a precision of +/- 25% in your self-coupling measurement and to do so at 5 sigma you need a precision of +/- 15% in your self-coupling measurement.

Apparently the precision of the self-coupling measurement so far at LHC, it is not very great, according to a January 15, 2013 paper: “We show that the trilinear self-coupling can be constrained to be positive with a 600/fb LHC dataset at 95% confidence. Moreover, we demonstrate that we expect to obtain a +30% and -20% uncertainty on the self-coupling at 3000/fb without statistical fitting of differential distributions.” Specifically, it states, “if we assume or believe that the `true’ value of the triple Higgs coupling is true = 1, then . . . We can conclude that the expected experimental result should lie within lambda (0:62; 1:52) with 68% confidence (1 sigma), and lambda (0:31; 3:08) at 95% (2 sigma) confidence. We expect to exclude any values outside this range after 600 fb^-1, given the value true = 1.”

http://arxiv.org/abs/1301.3492

Thus 0.23 value and proposed value are both in excess of the one sigma confidence interval, but are within the two sigma confidence interval of current data. The 0.13 v. 0.23 Higgs self-coupling value distinction looks like it won’t get to be much more than a 2.6 sigma preference even after much more data collection at the LHC, although it should ultimately be possible to distinguish your estimate from the SM estimate at the 5.9 sigma level before the LHC is done and a the 2 sigma level much sooner. Realistically, if a non-SM hypothesis is excluded by even 2 sigma it is going to have a very hard time beinng accepted (unless it is a SUSY model).

Dear ohwilleke,

Thanks for this helpful comment. The second paper you cite is really useful and gives a clear understanding on the way the self-coupling of the Higgs field could be measured. Their estimations, even if rather rough ones, are somewhat aligned on the estimations of a larger coupling than expected. Of course, it is too early to draw some conclusion and we have to wait the restart of LHC when, at higher energies, some processes with double Higgs production will be accessible. The only thing I would like to add to your comment is that, after resummation, my approach and the one of Steele and Wang should agree with my exact solutions. This computation is impossible yet and they do some (sound let me say) magic to get a proper estimation at ninth order. But a strong coupling for the Higgs field implies immediately SUSY. This conclusion is inescapable already at classical level.