Sunday, 6 September 2015

particle physics - 115 GeV, 170 GeV, and the noncommutative standard model



Several years ago, noncommutative geometry was used to describe the standard model, somehow yielding a prediction of 170 GeV for the mass of the Higgs boson, a prediction which was falsified a few years later.


Meanwhile, for a long time there have been indications of a Higgs boson at 115 GeV. As it happens, 115 GeV and 170 GeV form somewhat natural theoretical bounds on the mass of the Higgs: above 170 GeV, the theory would develop a Landau pole, and below 115 GeV, the electroweak vacuum would become unstable.


So I'm wondering whether the mechanism or the logic behind the original prediction can be reversed, so as to drive the Higgs mass to the lower bound, rather than to the upper bound, in an altered version of the noncommutative standard model.


EDIT: I am nowhere near decoding how the prediction of 170 GeV was made, but simple algebra shows that it is amazingly easy to get very close to 115 GeV instead, by adjusting some of the penultimate quantities appearing in the calculation.


A comment at Resonaances points out that $\sqrt{2} m_W$ is close to 115 GeV (it's a little over 113 GeV). In equation 5.15 of hep-th/0610241, we see this formula:


$$m_H = \sqrt{2\lambda}\frac{2M}{g} $$


On page 36 (section 4.1), we read that $M = m_W$ and $g = \sqrt{4\pi\alpha}$. So for $m_H$ to be approximately 115 GeV, we need $\lambda = \pi\alpha$.


In equation 5.10, we have that lambda-tilde is approximately $4/3 \pi\alpha_3$, and in remark 5.1 we read that "the factor of 4/3 in (5.10) should be corrected to 1". So we have $\tilde\lambda = \pi\alpha_3$. Almost what we need - it's just a different lambda and a different alpha! :-)


And I'll point out again that 115 GeV is a special value theoretically: it's in a narrow range of values for m_H for which, given the measured value of m_top, the vacuum of the minimal standard model is metastable (see figure 13, arxiv:0704.2232). So I can't believe any of this is coincidence.




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