Some people bite their nails when they are nervous or stressed. I analyze data. And, with a trial last week two hours from home and another big court deadline breathing down my neck, my spare moments have been spent on data analysis instead of blogging.
Lately, I've been looking at the available data points on hadron masses, which I have on a spreadsheet on my computer (that I fear may die in the near future), on the backs of envelopes, and in scribbled notes that are impossible for anyone but me to read on yellow pads. The spreadsheet contains a regression model that summarizes the data with a small number of variables to an accuracy of about 99%. Some of the process is mnemonic. There is no better way to learn the nuances of a bunch of numbers than to play around with them.
Maybe some day, I'll blog about the topic. But, right now, I don't have the time for a quality post and I am more inclined to simply parse and deconstruct the data set in stolen minutes here and there.
2 comments:
Extrapolating from the Wolfenstein parameterization, the probability of a transition from a third to a fourth generation would be something less than A^2 times Lambda^4=5.8*10^10^5, the probability of a second to fourth generation transition would be something less than 9.3*10^8, and the probability of a first to fourth generation transition would be something less than 5*10^9.
This would be the percentage of sufficiently energetic quarks of each type (i.e. several hundred GeV to several GeV) would create a fourth generation quark upon emitting a W boson.
These probabilities are, in general, less than the margin of error in the respective measurements and in the case of third generation quarks, a very low number when compared to the total number of t and b quarks created.
The number of third generation (or any generation) events is much lower when only t and b quark events where the kinetic energy in insufficient to make the creation of a b' or t' of sufficient mass possible. Certainly, one would expect a b' mass of at least 2.5+ times the mass of the t quark (432.68 GeV) and a t' at least 2.5+ times that (1,081.7 GeV), since that is about the smallest ratio of successive Standard Model fundamental particles.
The expected b' and t' masses would be more if one assumed b'-t-b (3.556 TeV) and a t'-b'-t (83.583 TeV) involved Koide triple relationships.
No collider has ever generated an 83.583+ TeV interaction, so none of those have probably ever been created even if they existed. The number of collisions in colliders that would energetic enough to have created 3.556 TeV interactions is very small (although a 100 TeV collider would create many such interactions).
Given that the top quark does not hadronize, presumably, the fourth generation t' and b' would not hadronize either and would have very large widths with half lives of much less than (or equal to) 5*10^-25 seconds since the W boson width might create a upper bound on weak force transitions, and would with more than a 99.5% chance at each step have a t'=>b'=>t decay chain.
The b'=>t chain would look just like a single t decay but with an additional highly energetic W+ jet, a hard to miss profile that hasn't been seen but could have been confused perhaps for a collision that produced multiple top quarks.
The t'=>b'=>t decay chain would look just like a t decay but with a highly energetic W- jet (that might often create a b'-b' bar pair) and a highly energetic W+ jet, another hard to miss profile.
Of course, none of these considerations that would make b' and t' beyond reliable detection even at LHC energies, would explain why the sum of the square of all other Standard Model particle masses equals the square of the Higgs vacuum expectation value, while these particles would greatly exceed that amount. This is one factor among many that argues that there really isn't a fourth generation of fermions out there to find.
Perhaps it would only be possible to create a b' or t' in the presence of a Higgs field with a sufficiently high energy (slightly more than the b' or t' mass respectively), or if these quarks interacted with a different Higgs field (a possibility with, for example, a SUSY stop or sbottom, but not in an SM4 model).
The best argument for a fourth generation model would be indications of a fourth generation neutrino which, if heavier than 45 GeV might not have been detected by precision electroweak interaction - but the best indications there are for 1 eV or 2 keV scale sterile neutrino, not a superheavy relative to the other three fertile neutrino, or the lack of detection of a fourth generation electron which would be expected to be 43.625 TeV based on a Koide triple relationship, and 4.44 TeV based upon a minimum 2.5x mass relationship.
The LHC exclusion of a b' and t' are less than 400 GeV, and the exclusion of a fourth generation electron are only a bit more than 100 GeV, and only about 45 GeV for fourth generation neutrinos. Astrophysical data, however, have been argued to prohibit the existence of neutrinos from 26 GeV to 4700 GeV, which since it overlaps with the electroweak collider exclusions would exclude all fertile neutrinos up to 4.7 TeV, which seems absurd given that all three known fertile neutrino masses eigenstates are less than 0.1 eV by any reasonable measure (both from cosmology which puts the sum of the three states at less than 0.28 eV and closer to 0.06 eV with a best fit, and delta mass from neutrion oscillations which are in the single and double digit meV). Also it seems very odd for a fourth fertile neutrino to has a mass in excess of 45 GeV if the other three have almost degenerate masses.
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