Friday, December 9, 2016

Reverse Engineering The Quark Masses And CKM Matrix

Another interesting effort has been made to try to figure out the logic of the quark masses and CKM matrix values in the Standard Model of Particle Physics which is notorious for having a large number of physical constants that have to be experimentally measured because their basis is not specified. The abstract states:

The minimal structure of quark mass matrices is addressed from a general perspective within the Standard Model (SM) framework. It is argued that within the flavor basis of diagonal up-type quark sector, the minimal phase as well as texture structure for these mass matrices follow naturally from the observed strong mass hierarchy among the quark masses and mixing angles. The minimal phase structure appears as a consequence of the translation of the CKM phase on the down-type quark matrix while the minimal texture structure follows from the Gatto-Sartori-Tonin relation for s12=md/ms. The corresponding matrix elements are uniquely expressible in terms of six physical observables namely, msmbmd (or s12),s13s23 and δ13 and relations like |Vcd|=|Vus||Vtb||Vcs|=|Vud||Vtb||Vts|=|Vud||Vcb|s12(md/ms)1/2 are naturally predicted offering a promising phenomenological mechanism for reverse engineering the mass matrices using the physical observables.
Rohit Verma, "Minimal Quark Mass Matrices from Physical Observables" (December 8, 2016).

More about the GST relation from the link in the body text quoted above:
The pioneering work of Gatto, Sartori, and Tonin showed a relation satisfying, with good accuracy, the experimental value of the Cabibbo angle [1] tan2 θC ≈ md ms . (1) At present, a more complete relation with greater accuracy includes the contribution coming from the up-quark sector and a small correction through the denominator [2, 3] tan2 θC ≈ mˆ d + ˆmu (1 + ˆmd)(1 + ˆmu) , (2) with mˆ d = md/ms and mˆ u = mu/mc. From now on, we will refer to it, in its generic form which only encompasses a single fermion species, tan2 θij = mi/mj , as the Gatto-Sartori-Tonin (GST) relation, for a review on this topic please refer to [4].
It has been already recognized by different authors that not only the observed hierarchy in the quark masses [3–13] mt(MZ) ≫ mc(MZ) ≫ mu(MZ), (3) mb(MZ) ≫ ms(MZ) ≫ md(MZ), (4) can give access to desired GST relations, but also the charged leptons hierarchy plus the possible milder one in the neutrino masses [3, 13–15] mτ (MZ) ≫ mµ(MZ) ≫ me(MZ), (5) m2 ν3 (MZ) ≫ m2 ν2 (MZ) ≫ m2 ν1 (MZ). (6) However, only until recently, a procedure to build a mixing parametrization in terms of only the four independent mass ratios of the corresponding fermion sector was fully achieved [3]. This new parametrization makes one to wonder about the possible physical meaning of the GST relation and the necessary conditions to find it in an exact way. . . .
[T]he GST relation originates . . . by uncoupling and demanding resonance (same frequencies) to the two coupled quantum harmonic oscillators with different masses.
The references for that paper which are interesting and unusually for a physics paper contain the titles of the articles cited are:

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