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.

]]>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).

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