## Friday, July 23, 2010

### M Theory Lesson 342

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.

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

$(u,c,t): \mu =22600, x =1.760, \theta = 0.074$
$(d,s,b): \mu =570, x = 1.714, \theta = 0.167$

2. So for

$(u,c,t): 22600, 1.76, 2/27$
$(d,s,b): 570, 1.76, 4/27$

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.

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