Alternatively, since the current quark mass estimates rely heavily on traditional methods in QCD, we could just ignore the quoted error bars. Doing so, we might seek Koide phases $\theta_{u}$ and $\theta_{d}$, for the quark triplets $(u,c,t)$ and $(d,s,b)$, such that

$\frac{2}{9} = \frac{6}{27} = \theta_{u} + \theta_{d}$

where $2/9$ is the well known Koide phase. This works nicely with

$\theta_{u} = \frac{2}{27}$

$\theta_{d} = \frac{4}{27}$

although one of the $(d,s,b)$ triplet must fall outside current error estimates. Now both triplets use a parameter $x = 1.76$, and this coincidence leads us to suspect that the strange quark is a little lighter than is currently believed.

8 years ago

Actually, according to the enormous errors on the PDG page, all these values are OK, but the best fit seems to be

ReplyDelete$(u,c,t): \mu =22600, x =1.760, \theta = 0.074$

$(d,s,b): \mu =570, x = 1.714, \theta = 0.167$

So for

ReplyDelete$(u,c,t): 22600, 1.76, 2/27$

$(d,s,b): 570, 1.76, 4/27$

we get the six masses (in MeV$/c^{2}$)

$(u,c,t): 2.1, 1250, 171556$

$(d,s,b): 5.2, 72, 4282$

which all lie in the allowed PDG ranges, although the strange quark mass is at the lower end of its range.

... unfortunately this makes the ratio $m_s / m_d$ too small ... but other fits are possible.

ReplyDelete