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Physics
Beyond the Standard Models
Implications of Nishida's mass/CKM observation
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[QUOTE="ohwilleke, post: 6052925, member: 19562"] A few more relevant observations about the CKM matrix that suggest that it and not the mass matrix is primary, because generational differences seem to be primary. The [URL='http://en.wikipedia.org/wiki/Cabibbo%E2%80%93Kobayashi%E2%80%93Maskawa_matrix#Wolfenstein_parameters']Wolfenstein parameterization[/URL] of the CKM matrix (articulated first in L. Wolfenstein, "Parametrization of the Kobayashi-Maskawa Matrix", 51 (21) Physical Review Letters 1945 (1983)) emphasizes the extent to which the probability of a quark flavor change when it emits a W boson depends upon a change in quark family. * In the Wolfenstein parameterization, "lambda" is roughly 0.02257 (and is another way of stating the Cabibbo angle), "A" is roughly 0.814, and the "p-in" CP violating term is about 0.135 minus 0.349i. * A transition from the first generation to the second generation (or visa versa) happens with a probability of lambda squared (about 5.07%-5.08%). * A transition from the second generation to the third generation (or visa verse) happens with a probability of about A squared times lambda to the fourth power (about 0.16%-0.17%). * A transition from the first generation to the third generation (or visa versa) happens with a probability roughly equal to the probability of a transition from the first generation to the second generation, multiplied by the probability of a transition from the second generation to the third generation, times an adjustment in the form of a complex number an absolute value of a magnitude on the O(1) that includes a CP violating phase. In all, a first to third generation (or visa versa) quark family transition happens with a probability of about 0.0012% to 0.0075%. * The probability of a second to third generation transition is consistent with two-thirds (between 62.7% and 69.7% with a best fit value of 66.3%) of the square of the probability of a first to second generation transition. It isn't impossible that this is really a formula constant in the theory derived with algebra from a deeper theory, rather than a physically measured constant "A". * The probability that a quark will remain in the same quark generation is equal to one minus the probability that it will change generations (about 94.9202% in the first generation, about 94.7585 in the second generation, and about 99.8293% in the third generation). The Wolfenstein parameterization emphasizes that the slight percentage differences between the probability of CKM matrix entry Vcb and Vts, between Vcd and Vus, flows mostly from compensating from other entries in that row, such as the considerably more significant (roughly 6-1) differences between the tiny Vtd and Vub. There are, in fact, more entries in the CKM matrix with the two CP violating parameters than are shown in a simplified version of the Wolfenstein parameterization, in the Standard Model CKM matrix, but those effects are tiny on a percentage basis relative to the magnitude of the other, much larger CKM matrix entries. Of course, the decay of a quark at rest is mass-energy conservation barred from becoming a heavier quark. It can only decay to the lighter quark (something that is possible for all types of quarks except up quarks). Only quarks with sufficient momentum can transition to higher mass quarks. The point that the Wolfenstein parameterization underscores is that the CKM matrix derives largely from crossing one of two (or both) of the fundamental fermion families, not just from the particular quarks involved in the transition. I also wonder if the CP violating parameter of the CKM matrix really has the same source as the other parameters of the CKM matrix, or if the CKM matrix just ends up conflating the two when the actually have sources in separate mechanisms in a deeper theory, because the observational evidence doesn't provide an easy way to disentangle the two effects. [/QUOTE]
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Implications of Nishida's mass/CKM observation
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