The Z-Boson Mass and its Formula as Multiple Proofs in One Bowl of Yummy Pudding

By: Sean Sheeter
Submitted: 2008-08-04 13:23:42
Print this article | Tell a friend | For publisher |

Rating:

 

Though its origin is disputed, the phrase “the proof of the pudding is in the eating” is popularly attributed to Cervantes 1615 comic novel Don Quixote. And while one can talk about a pudding’s ingredients all they want, the saying’s meaning stays intact when shortened to “the proof is in the pudding” - because that is where you will ultimately find it; if you bother to taste it – as it’s the results that count.

Which is unlike a mathematical proof obtained by logic alone since one’s pallet will sometimes disagree with what one thinks is a delicious recipe. In this sense, the implied dichotomy is akin to Kepler’s contribution to elliptic geometry, which per se is independent of experience in the sense that elliptic theorems can be constructed and proven without appeals to any physical phenomena. But in practice Kepler refined Copernicus’s resurrected heliocentric heresy of planetary orbits in a manner that just as clearly is non-abstractly physical and empirically testable. Which ultimately is a key characteristic of the scientific method or ‘revolution,’ soon further cemented by Newton and Galileo’s discoveries expressing physical laws by experimental confirmation of their mathematical formulation.

This report accordingly pares the phrase down to a “Pudding Proof” that employs multiple means of what a mathematical formula represents, not only being theoretically correct in all senses, but confirmed to be correct by a clear correspondence with the most precisely measured empirical value in high-energy particle physics, specifically the neutral weak or Z-boson mass. For the Z’s present measured mass value of 91187.6 +/-2.1 MeV (million electron Volts) is what truly represents the operative meaning of this term. But the ultimate result as ‘physical proof’ is he following equation for an invariant mass of Z = 91187.633 MeV = 9y1/8 + m(s) - m(b), though one doesn’t really need to know the mass m of the strange and bottom quarks, or the 'Higgs vacuum minima' y1.

So how we obtained these other, presently “unknown,” values isn’t at issue either, though obviously it was not achieved by empirical measure nor is related to this equation. Which isn’t meant to squelch natural curiosity of course, as anyone interested in the history of these discoveries is directed to a preceding article describing the dimensionless scaling system of physics that generates the gamete of such fundamental physical constants (see resource box). In any case, these empirically ‘unknown masses’ contribute to this equation to give the above Z-mass that corresponds precisely with its measured mass average. So the phrase ‘pudding proof’ here basically, and more importantly empirically, implies that these three ill-measured and non-given 'fundamental masses' are just as precisely determined and confirmed as 'proven' mass values as the Z itself!

And though this empirical pudding proof iss unprecedented with regard to the implication of the validity the precision of a parameter such as a strange or bottom quark mass (that can’t be directly measured anyway), it certainly remains an outstanding example of the validity of empirical measure as the bedrock of scientific method. For the ultimate strength of the dimensionless numerical scaling system that sets it apart from all other modern theoretical ‘models’ is evident from the raft of provable predictions it makes – and largely are presently accessible in well-tested standard contexts (such as the Z) that require no greater experimentally contrived studies to ‘test’ whether some “theoretical interpretation” is ‘correct.’

Yet in a related regard, the equation for the Z-mass further represents multiple theoretical proofs that strengthen the outstanding empirical correspondence with the pudding of its measured mass. The first matter in this regard straddles both spheres in that the predominant observed or theoretical decay products of a weak neutral boson are admixtures of bottom with strange and/or down quarks in heavy mesons, and practically is the only known particle that can directly decay to a strange Bs-meson. Which according to our equation consists of a –e/3-charged b-quark with a +e/3-charged strange antiquark – which thus assures the charge neutrality of a Bs-meson.

Then over and above these confirmed theoretical considerations with respect to the equation’s quarks, there looms the fundamental observations of Peter Higgs concerning the origin of mass in general, and specifically with respect to electroweak symmetry breaking by which the weak Z and W gauge bosons acquire a mass from some mechanism while leaving photons massless. The above equation employs the appropriate Higgs field mechanism best called the vacuum minima y1, which again is generically associated with the ‘3rd generation’ bottom of the -1e/3 ‘down quark family,’ in the same sense that the heavier ‘Higgs vacuum doublet’ u2 represents a neutral pair of tops of the +2e/3 ‘up quark family.’
(Incidentally cognoscenti, they saw evidence of the ‘light Higgs boson’ before CERN replaced the lepton collider with the Large Hadron over five years ago, which thankfully will generate the far more fundamental Heavy Higgs scalar – when that pudding is ready to take out of their oven. [Though it would be a rather big deal for the researchers, it’s just the basic, strongest set parameter in a real system of numeric Planck-scaling. Which is to say that knowing its mass is no big whoop, so I’d say the Nobel should go to the machine itself – i.e. for lord knows it should be a much bigger deal for everyone when they witness baryogenesis {creation of nuclear matter over antimatter}!]

Actually the above equation is one of two expressions for the Z-mass; as the other naturally involves a similar relation to the charged W-boson mass. The W itself is a predominant decay product from the heavier Higgs doublet, where convention has the +2e/3 top imparting its +charge to the W in mediating a transformation to a –1e/3 bottom. So once again the Higgs fields impart their mass to quarks and gauge bosons, where each theoretical argument reinforces others (there being further supporting pudding proofs that involve equations for neutral and charged pairs of B-mesons that reinforce the basic equation for Z-mass, for example.) And each theoretical nuance is of course supported by the latest measures of even subtler masses. But the mathematical form of these equations give insights into theoretical and predictive empirical realms that are unavailable in any other standard theoretical scheme. Example: I’ll give a hundred dollars (I’d make it more but care too much to be going broke) to anyone who can find a reference containing the above equation for the Z-mass.

Having established that theoretically it’s a perfectly good equation, there should be some possibility it’s not unique. But I highly doubt it would ever have been published, especially without any knowledge of these other parameters; that I can safely assume are within my copyrights if just because of the strength of this Pudding Proof demands it. Which brings us back to the basic meaning of this old saying – the results are in the tasting and eating of the pudding. And the bottom line test of this principle after the above equation has been posted for six years on this web of a so-called information highway is this – I’ve yet to find an individual who is capable of appreciating a pudding full of yummy plums and proofs, let alone anyone who wants to buy a small bowl eat any for a fuller taste of all the results for themselves.