Friday, March 18, 2011

New Quark Masses

Recall that we could calculate the top quark triplet of rest masses using a Koide phase parameter of $2/9 - 2/27$. The resulting rest masses are

$173490$, $2.04$, $1263$ MeV

in rough agreement with observation. Naively taking the same quark scale parameter, with a phase of $2/9 + 2/27$, we calculate a triplet of mirror quark masses, in analogy with the complementation of secondary phases for the neutrino and mirror neutrino masses. We obtain the new Koide mass triplet

$214255$, $611.5$, $235.3$ MeV

for a top quark $\Delta M$ of $- 41$ GeV, which is of the same sign but somewhat larger than the recent CDF results (which give $\Delta M$ around $- 3.3$ GeV). The triplet is very sensitive to phase choices, so we should investigate these parameters further. However, one does not expect the quarks to be mirrored in the same way that neutrinos or neutrons are, since they are charged. Rather, we should consider a neutral component of the quarks in determining mass differences. The missing factor of $10$ in this first estimate for $\Delta M$ might then be roughly attributed to the tripling (where $3$ is around $\sqrt{10}$) of strand number, from the one neutral strand of a top quark braid to three strands of the full braid.

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