THE "W" INTERMEDIATE VECTOR BOSON AND THE
WEAK FORCE MECHANISM
(revised Dec., 2012)
JOHN A. GOWAN
This paper has been translated into French (click here)
page (page 1)
home page (page 2)
(Readers unfamiliar with the particles in the reactions below should consult "The Particle Table". This paper is more technically oriented than most on my website, and may be of lesser interest to the general reader, in which case see the "guide" paper linked below. See also: "The Weak Force "Identity" Charge".)
(I recommend the reader consult the "preface" or "guide" to this paper, which may be found at "About the Papers: An Introduction"- Section IV).
Table of Contents:
Elementary particles created today must be the same in every respect as those created eons ago during the "Big Bang". The conservation requirement of elementary particle invariance constrains the mechanism of weak force particle creation and transformation. Weak force transformations recreate primordial symmetric energy states of the "Big Bang" force-unification eras (in the case of the "W", the electroweak force unification era) to accomplish the invariant creation and transformation of single elementary particles.
The "W" Intermediate Vector Boson (IVB) is the "black box" as well as the "workhorse" of the weak force. The W mediates transformations of "identity" charge (also known as "number" or "flavor" charge) among the quarks and leptons, especially their creation and destruction as "singlets", that is, when they are not paired with antimatter partners. The transformation, creation, and destruction of single elementary particles is the exclusive province of, and the rationale for, the weak force.
The W is very massive - about 80 times heavier than a proton. Because the large mass-energy of the W must be borrowed within the Heisenberg time limit for virtual particles, decays mediated by the W are both very short range and very slow - particles have to wait a (relatively) long time for such a large amount of energy to become available as a quantum fluctuation within the temporal bounds of the Heisenberg "virtual reality interval". However, the decays of the weak force are slow only in relation to other nuclear processes. Typically, the lifetimes of particles undergoing weak reactions is around 10(-10) seconds (one 10 billionth of a second, or a tenth of a nanosecond), but this may nevertheless be ten billion times (or more) longer than typical strong force nuclear reactions. Because the W mediates so many different kinds of reactions, involving the decays of baryons, mesons, and leptons, with the production of so many different products, including photons, neutrinos, leptons, quarks, mesons, and baryons, one has to wonder what sort of transformation mechanism is operating inside the "black box" that is the "W" IVB of the "Standard Model".
In this paper I propose a very simple mechanism to explain the manifold transformations and products of the "W" IVB. I begin by making an assumption about the nature of the W itself, a speculation concerning the origin of its great mass. This mass cannot be derived from quarks, the source of mass in ordinary nuclear particles. I suggest that the W and the other weak force "Intermediate Vector Bosons" (IVBs) (the "Z" and the hypothetical "X") are "metric" particles, composed simply of a very dense spacetime metric, similar to the spacetime of the very early, energy-dense Universe in the first micro-moments of the Big Bang - similar, in fact, to the energy density of the primordial environment in which these transformations first occurred - the "electroweak" force unification era. The huge mass of the IVBs is due to the binding energy needed to compress, perhaps convolute, and maintain the metric of spacetime in these particular dense and heavy forms. In fact, the "W" IVB mass recreates the energy density of the primordial, symmetric, electroweak force-unification energy state. This is the essential secret of the W's ability to cause elementary particle transformations, for within this symmetric energy state of the unified electroweak force, lepton-lepton and quark-quark transformations are simply the normal course of events - as "species" level lepton or quark identities are incorporated into "genus" level collective identities (all leptons become equivalent, all quarks become equivalent).
The actual transformation mechanism is envisioned as follows: an IVB "metric particle", mediator, or catalyst functions by engulfing a particle ripe for transformation (referred to below as the "parent" particle), and combining it with one or more suitable particle-antiparticle pairs, these latter drawn from the infinitely varied resources of the Dirac/Heisenberg virtual particle "sea", the quantum fluctuations of the vacuum. (The vacuum will be polarized by the presence of the "parent" particle, facilitating the production of suitable particle-antiparticle pairs.) The W works its transformations simply by virtue of its dense (and perhaps convoluted) metric. The dense metric brings particles so close together they can react with each other quickly and in ways which are impossible when they are separated by ordinary distances. In particular, particles can exchange charges, spin, momentum, and energy without violating (or even threatening) the conservation laws, due to their intimate proximity (perhaps essentially "touching") within the embrace of the IVB's dense metric. The massive IVBs provide a "conservation containment" or "safe house" in which charge and energy can be transferred at very close range between "real" and virtual particles. The W acts simply as a "metric catalyst" while the virtual quantum "sea" provides the diversity of reactants.
The basic role of the IVBs is therefore to form a bridge between real particles and the virtual particle "sea" of the vacuum; the IVBs thus make available all the electric, number, color, and flavor charges (and spin) of the virtual particle "sea", so that "real" (temporal) particles can use them to accomplish transformations and decays, and to materialize and dematerialize as conservation requires. It is the ability of the IVBs to contact and materialize the virtual particle "sea" that is their distinguishing characteristic and that requires their unique mass and structure. Because the real and virtual particles of today were once all part of the same primordial high energy particle "sea", it appears that the IVBs are simply reconnecting the manifest and unmanifest parts of the original "sea" by reconstituting the dense metric in which both were born.
The "safe house" or "conservation containment" interpretation of the "W" IVB function is a purely mechanistic perspective. It is complemented by what is perhaps a more theoretically satisfying interpretation in terms of force- unification energy levels and symmetry states. In this regard, the IVB mass may be seen as a reconstruction of the original force-unification symmetry state (the "electroweak" force-unification energy level), at which the transformations in question originally took place (during the "Big Bang") - simply as the normal course of events, typical of a specific force-unification regime (see the table at the end of this paper).
Even the surprisingly large mass of the top quark (about 170 GEV) is not a problem for the transformation mechanism proposed here. The "W" IVB does not create the "parent" particle in any reaction. The parent particle is always provided by the environment; only the mass of the reactive particle-antiparticle pair must be provided by the IVB. In the decay of the top quark, the mediating virtual pair is (at most) a bottom-antibottom meson; since the bottom quark mass is only about 4 GEV, this meson is readily produced by the 80 GEV "W".
Weak Force Creation of "Singlets"
To the extent that charge and mass invariance is a critical issue for charge, symmetry, and energy conservation, so also must be the mechanism of elementary charge-carrier transformations (transformations of quarks and leptons). The role of the weak force and the massive IVBs is to ensure that charge invariance, charge conservation, and energy conservation are all scrupulously observed in any transformation of elementary particle charge, mass, and/or spin. Conservation demands that elementary particles created today or tomorrow be exactly the same in all respects as those created yesterday or in the "Big Bang". This is the conservation challenge posed to the weak force in the creation of "singlets" (elementary particles of matter not paired with antimatter partners), and is the reason for the great mass and unusual features of the IVBs (and the scalar Higgs boson). (CERN announced discovery of the 126 GEV Higgs boson on 4 July, 2012. See: Science 13 July, 2012 page 141; see also: Scientific American Oct., 2012 pages 68-73.)
The most significant feature of the massive IVBs is that they recreate the original conditions of the energy-dense primordial metric in which particles were first created and transformed during the early micro-moments of the "Big Bang". This recapitulation of a specific symmetry state or force unification regime (the "electroweak" force unification era, in the case of the "W" IVB) ensures that the original and invariant values of charge, mass, spin, and energy are handed on to a new generation of elementary particles. The IVB mass not only provides a "conservation containment" where charge and energy transfers can take place safely, it simultaneously ensures that the appropriate alternative charge carriers (leptons, mesons, neutrinos) are present to accomplish the required transformations. The role of the Higgs boson in this process is to gauge or scale the IVBs to the proper energy level or mass so that they become part of a specific force-unification regime where the transformations they perform are: 1) a natural characteristic of the symmetry state; 2) invariant in their output. The IVBs are necessary to actually perform the transformations; the Higgs is necessary to select the proper IVB "family" (there are probably three), and to ensure the invariance of their product. Transformations of "species" identity within a given "genus" are accomplished readily, since all species are equivalent. It is because the Higgs and IVBs recreate this "generic" level of particle symmetry and force unity that the weak force transformations can be so readily accomplished.
There is a crucial difference between the electromagnetic (or strong force) creation of particles via particle-antiparticle formation, and the weak force creation of "singlets", or the transformation of existing particles to other elementary forms. In the case of electromagnetic "pair creation", there can be no question as to the suitability of either partner for a subsequent annihilation reaction, conserving symmetry (since they are referenced against each other, and gauged or scaled by universal physical and metric constants such as c, e, and h). However, in the weak force creation of "singlets", or the transformation of an existing elementary particle to another elementary form, "alternative charge carriers" must be used to balance charges, since using actual antiparticles for this purpose would only produce annihilation reactions. But how is the weak force to guarantee that the alternative charge carrier - which may be a meson, a neutrino, or a massive lepton - will have the correct charge in kind and magnitude to balance and conserve symmetry in some future reaction with an unknown partner which is not its antiparticle? Furthermore, quark charges are both partial and hidden (because they are "confined"), and number charges of the massive leptons and baryons are also hidden (because they are "implicit" to moot the parity conservation issue). Neither color nor number charge has a long-range projection (such as the magnetic field of electric charge) to indicate to a potential reaction partner its relative energy state.
Energy conservation combined with charge and symmetry conservation, hidden charges, and alternative charge carriers, all pose a unique challenge to the weak force transformation and/or creation of elementary, "singlet" particles. And this is to say nothing about such problems as relative motion, entropy, the passage of time, or the expansion of the Universe - all factors which could possibly affect the invariance of the physical parameters of elementary particles produced or transformed by the weak force in any time or place after their original creation in the "Big Bang". This would not be a problem if elementary particles were produced just once during the "Big Bang" and never again. However, elementary particles are still produced today (leptons, neutrinos, mesons, quarks), and they must be indistinguishable from the originals created almost 14 billion years ago.
All such conservation problems are solved or circumvented by a return to the original "Big Bang" conditions in which these particles and transformations were first created, much as we return and refer to the Bureau of Standards when we need to re-calibrate our instruments. The necessity for charge and mass invariance, in the service of symmetry and energy conservation, therefore offers a plausible explanation for the otherwise enigmatic large mass of the weak force IVBs. The IVB mass serves to recreate the original environmental conditions - metric and energetic, particle and charge - in which the reactions they now mediate took place, ensuring charge and mass invariance, and symmetry and energy conservation, regardless of the type of elementary particle, alternative charge carrier, or transformation involved. There is little practical difference between the theoretical "original metric" and the mechanical "safe house" explanations for the huge IVB mass; one effect can hardly be distinguished from the other, and both may be necessary to adequately explain the transformation process. Finally, we note that the mass of a particle is not affected by the entropic expansion of the Cosmos, and can be readily quantized - hence the massive weak force mechanism (Higgs, IVBs) is a natural choice to maintain invariant the conserved parameters of the elementary particles over the lifetime of the Universe. (See also: The Higgs Boson and the Weak Force IVBs.)
As to why the Z is heavier than the W, I suggest it is because the W, within the symmetric energy state the IVBs create, has only to accommodate the quarks and massive leptons (since only they bear electric charges), but the Z has to account for the neutrinos in addition. Since Z-neutral elastic scattering can occur with all quarks and leptons, the set of particles "under the Z's wing", as it were, is larger than the W's, hence requiring more energy to conjure from the vacuum. There are simply more possibilities for neutral interactions than for charged interactions, and therefore the primordial electroweak unified-force symmetric energy state recreated by the Z is larger and more inclusive (in terms of membership) than that created by the W. Furthermore, since the role of the massive IVBs is expressly to ensure the exact replication of single elementary particles, we may suspect that the neutrino which emerges from a seemingly humble Z-neutral scattering event is not the same "individual" that entered the interaction, even though both are of the same "flavor". This points up the fact that Nature is at considerable pains to protect the integrity and value of the "identity" charge of the neutrinos, requiring a full-on 91 Gev Z-neutral interaction even for an apparently simple scattering event.
It is the role of the weak force to produce single elementary
particles, but with a stringent qualification: every elementary
particle ever produced from the beginning of the universe (and
onward into its future) must be exactly the same as its fellows
within type (all electrons must be identical, and likewise the
muon and tau). We have seen that the neutrino has a role to play
in this process, allowing the creation of a single electron (for
example) in the absence of a positron (anti-electron), and in
effect certifying that any newly created electron is the genuine
article in all respects. But the actual mechanism of manufacture
involves the hugely massive IVBs (81 proton masses) even for the
tiny electron, which weighs about 1/2000 of a proton. Why is this
huge "overkill" of energy during the creation process necessary?
It is because the only way to circumvent the enervating effects of
the entropy of a constantly expanding and cooling universe upon
the manufacture of identical elementary particles over eons of
time is to return to the original primordial energy density and
creative phase of the Big Bang in which these particles were first
formed - every elementary particle forged in the original mold, as
it were. Every weak force transformation involving an IVB is
therefore a recreation of a particular energy density of the Big
Bang, but in miniature. Only by such extreme measures is the exact
similarity of every electron (past, present, and future)
guaranteed, and only these are given the neutrinos'
"certificate of authenticity".
The energy-density recreated by the "W" IVBs is that of the electroweak unification energy density, and all of the leptons and mesons of the "Standard Model" (the alternative charge carriers) can be faithfully reproduced at this energy level. Hence we see the the "alternative charge carriers" (leptons and mesons) occupy a special place both in the functional hierarchy of the cosmos, where they function as catalysts facilitating the creation, destruction, and transformation of single elementary particles, and in the hierarchy of cosmic force-unification energy levels (the electroweak force-unification energy level of the "W" and "Z" IVBs). Baryons cannot be created or destroyed at this energy level, but their quark content can be transformed (via mesons). Creating/destroying the baryons themselves requires the next higher energy level of the "Grand Unified Theory" and the supermassive "X" IVB (unifying the electroweak and strong forces and allowing lepton-quark transformations). The force-unification levels themselves demarcate specific energy-densities at which elementary particles of various kinds can be created or destroyed: 1) leptons/mesons at the electroweak (EW) energy level; 2) baryons/hyperons at the "Grand Unified Theory" (GUT) energy level; 3)leptoquarks at the "Theory of Everything" (TOE) energy level.
One can think of the IVBs as "wormholes" to a younger, hotter universe, connecting our ground-state cold electromagnetic universe with the universe as it existed a few micro-seconds after the "Big Bang". What comes through the "IVB wormhole" is a single elementary particle, newly minted in the original forge and mold of the electroweak era from long ago, and hence identical to every elementary particle (of its type) ever created, or that ever will be created. The "wormhole" connection effectively circumvents the enervating entropy of eons of cosmic expansion that would otherwise make the exact replication of single elementary particles impossible. After a little reflection it becomes obvious that this is the only method which can possibly work reliably. It is this "wormhole" connection between our ground state electromagnetic and the primordial electroweak universe that frees the alternative charge carriers (leptons and mesons), held in the electroweak symmetric energy state, to do (in our ground-state universe) their necessary work of transformation, creation, and destruction of single quarks and leptons that allows atomic matter to exist, the Sun to shine, and the information-rich Periodic Table of the Elements to be built. The universe remains a single connected unit - not only in space, but in time and historic spacetime - a connectivity that is essential to its proper functioning and conservation.
Weak Force Reactions
Below I list all the major examples of the weak force reactions as recorded in the "Stable Particle Table" of the 65th CRC Handbook of Chemistry and Physics. A typical way of writing a weak reaction might be as follows, illustrating the weak decay of a negative pion (ud-), producing a negative muon (u-) and an antimuon neutrino (vu) (antiparticles underlined):
ud-(W-) ---> vu + u-
I could write this reaction as:
ud-( )W- ---> vu + u-
suggesting there are virtual reactants in the empty parenthesis which actually make the reaction happen. For example:
ud-(u+ x u-)W- ---> vu + u-
Here I show the "W" IVB joining a muon-antimuon particle pair (u+ x u-) drawn from the virtual vacuum "sea", with the negative pion (ud-) to produce the actual reaction and its products. In this example the electric charges of the antimuon and pion cancel each other, releasing the antimuon's neutrino. The original electric charge of the pion is conserved in the reaction's product by the muon; the pion's u and d quarks undergo a matter-antimatter annihilation, possible because their electric charge, momentum, and rest energy can be transferred to the product particles by their close proximity within the metric containment of the "W" (individual quark flavors are not strictly conserved).
All the reactions and their products listed below (essentially all the common weak force decays) can be produced by placing a suitably chosen particle-antiparticle pair (sometimes two) in the brackets between the reacting particle and the "W". Since adding a particle-antiparticle pair (or two) to a reaction is like adding zero to a mathematics equation, it is no surprise that it works in every case. Still, I do not think this result is trivial. At least it gives us a plausible, specific mechanism and reaction pathway rather than the "black box" as the "W" appears to us now. In addition, notice that in the baryon decays a specific meson is always necessary to both annihilate and supply a specific quark flavor in the baryon being transformed. The antiparticle of this specific meson always appears among the product particles, suggesting that the proposed mechanism is in fact the actual pathway. From this observation we deduce the two-stage "beta" decay of the neutron, which helps explain the enormous lifetime of this particle. While this observation always applies to baryons, it only sometimes applies to the decay pathways of the mesons themselves, as in mesons we are dealing with particle-antiparticle pairs which can eventually annihilate each other regardless of differences in their quark's flavors.
Because mesons are the only alternative charge carriers which can carry the partial charges of quarks, mesons are instrumental to both weak and strong force transformations of baryons and quark flavors. In the strong force, mesons serve as the "Yukawa" field of exchange particles binding protons and neutrons ("nucleons") into compound atomic nuclei. This long-recognized (since 1934) strong force meson role lends credence to the weak force meson role hypothesized in this paper. (See: "The Strong Force: Two Expressions".)
In reading the reactions below, notice that typically the first member of the particle-antiparticle pair reacts with the "parent" particle outside the brackets, while the second member of the pair usually goes straight to the product unaffected. A few reactions have three or four components and apparently two steps, but none are particularly complicated. The energy released in the transformation of the "parent" particle to a lower mass product (E = mcc) is used to manifest virtual particles, and appears in the reaction products as rest mass, momentum, and/or free energy (photons).
In quantum mechanics, unless a process is expressly forbidden by some physical conservation law, it is presumed to occur. Hence, unless the participation of virtual particle-antiparticle pairs in particle decays is for some reason forbidden, the reactions as written below, at least for the most part, should occur in nature. The only question would be the percentage of the total pathway they represent, in cases (if any) where simpler, alternative, or multiple decay pathways exist.
I presume in these reactions that quarks annihilate only with antiquarks, and leptons annihilate only with antileptons. Thus, in the case of tau decay producing a negative pion (as in reaction 2c below), the tau's and positive pion's electric charges cancel, allowing the quarks of the positive pion to self-annihilate, simultaneously releasing the tau neutrino. The considerable mass difference between the "parent" tau and the product pion supplies the energy to materialize the remaining negative pion of the virtual pair.
(u = muon, t = tau, v = neutrino, y
(antiparticles underlined; lifetimes in seconds (with exponents in brackets); mass in MeV)
(all reaction products, percentages, lifetimes, and masses are as reported in the 65th CRC Handbook, Stable Particle Table pages F214 - 220)
1) muon: u-, u+; mass 105.7, lifetime 2.2x10(-6) = 0.0000022 sec.
In a) and b), muons and positrons (e+) annihilate, canceling electric charge, and releasing both their neutrinos. The mass energy of the muon materializes the electron as the remaining member of the virtual positron x electron pairs, conserving electric charge. The charge of the W is always the same as the "orphaned" or product member of the particle-antiparticle pair.
Principle decay products:
a) muon neutrino, positron neutrino, electron (98.6%):
u-[ e+ x e- ]W- ---> vu + ve + e-
b) muon neutrino, positron neutrino, electron, photon (1.4%):
u-[ e+ x e- ]W- ---> vu + ve + e- + y
2) tau: t-, t+; mass 1784.2, lifetime 4.6x10(-13)
In a) and b), tau annihilates with antimuon or positron, releasing neutrinos. The mass energy of the tau materializes the muon or electron from the virtual particle x antiparticle pairs, conserving electric charge.
Principle decay products:
a) tau neutrino, muon antineutrino, muon (18.5%):
t-[ u+ x u- ]W- ---> vt + vu + u-
b) tau neutrino, positron neutrino, electron (16.2%):
t-[ e+ x e- ]W- ---> vt + ve + e-
In c) and d), tau and positive pion cancel electric charges, releasing the tau neutrino and allowing the positive pion(s) to self-annihilate. The mass energy of the tau materializes the remaining negative pion(s) from the virtual particle x antiparticle pairs, conserving electric charge.
c) hadron-, neutrino, (37%) similar to:
t-[ ud+ x ud- ]W- ---> vt + ud-
d) 3 hadrons+-, neutrino, (28.4%) similar to:
t-[ (ud+ x ud- )( ud+ x ud-) ]W- ---> vt + ud- + (ud+ x ud-)
(Quark flavors and electric charges: u, c, t = +2/3; d, s, b = -1/3; charges reversed in antiparticles)
3) pion: ud+, ud-; mass 139.6, lifetime 2.6x10(-8)
In a) and b), pion/muon cancel electric charge, releasing the muon's neutrino and allowing the pion to self-annihilate. The energy of annihilation materializes the remaining muon from the virtual particle x antiparticle pair as a product, conserving electric charge.
Principle decay products:
a) muon neutrino, antimuon (100%):
ud+[ u- x u+ ]W+ ---> vu + u+
b) muon antineutrino, muon (100%):
ud-[ u+ x u- ]W- ---> vu + u-
4) Kaon: us+, us-; mass 493.7, lifetime 1.2x10(-8)
In a), b), and c), kaons and leptons cancel electric charges, releasing lepton neutrinos and allowing kaons to self-annihilate. The energy of annihilation materializes all remaining leptons and pions from the virtual particle x antiparticle pairs, conserving electric charge.
Principle decay products:
a) antimuon neutrino, muon (63.5%)
us-[ u+ x u- ]W- ---> vu + u-
b) antimuon neutrino, muon, neutral pion (3.2%):
us-[ (u+ x u-) x uu ]W- ---> vu + u- + uu
c) positron neutrino, electron, neutral pion (4.8%):
us-[ (e+ x e-) x uu ]W- ---> ve + e- + uu
In d), e), and f), kaons and pions annihilate each other. The energy of annihilation materializes all remaining virtual pions and particle x antiparticle pairs, conserving electric charge.
d) neutral pion, positive pion (21.2%):
us+[ (ud- x ud+) x uu ]W+ ---> uu + ud+
e) 2 positive pions, 1 negative pion (5.6%):
us+[ (ud- x ud+) x (ud- x ud+) ]W+ ---> ud+ + (ud- x ud+)
f) 1 positive pion, 2 neutral pions (1.7%):
us+[ (ud- x ud+) x (uu x uu) ]W+ ---> ud+ + (uu x uu)
5) neutral kaons: ds, sd; mass 497.7, lifetime "Short": 0.9x10(-10)
"Short" (referring to lifetime) neutral kaons annihilate with neutral pions, materializing charged or neutral pions from the virtual particle x antiparticle pairs, needed for absorbing and distributing momentum.
Principle decay modes ds or ds ("Short"):
a) positive pion, negative pion (68.6%):
ds or ds[ dd x (ud- x ud+) ]W ---> (ud- x ud+)
b) 2 neutral pions (31.4%):
ds or ds[ dd x (dd x dd) ]W ---> (dd x dd)
6) Lifetime "Long": 5x10(-8); ("Long" is a superposition of ds and ds)
In a) and b),"long" (referring to lifetime) neutral kaons self-annihilate, materializing charged and neutral pions from the virtual particle x antiparticle pairs, necessary for absorbing and distributing momentum. The "long" reaction pathway is more complex than the "short" reaction pathway; apparently the superposition ds/ds self-annihilates (why wouldn't it?) rather than reacting with the virtual pions; this evidently takes longer and requires more particles in the product to conserve momentum. Hence although the virtual particle x antiparticle complex is identical in both the "short" and "long" decay sequences, the products are different because the "short" annihilates one member of its virtual complex, whereas the "long" does not. In the decays of neutral particles, the problem is not so much charge conservation as momentum conservation.
Principle decay modes ds/ds ("Long"):
a) 3 neutral pions (21.5%):
ds/ds[ dd x (dd x dd) ]W ---> dd + (dd + dd)
b) 2 charged, 1 neutral pion (12.4%):
ds/ds[ dd x (ud+ x ud-) ]W ---> dd + (ud+ x ud-)
In c) and d), "long" neutral kaons self-annihilate, materializing leptons and charged pions from the virtual particle x antiparticle pairs. The W complex includes both pion and lepton virtual particle-antiparticle pairs; the positive leptons react with a negative pion as seen previously in meson decay 3b. All products help absorb and distribute momentum.
c) charged pion, antimuon neutrino, muon (27.1%):
ds/ds[ (ud+ x ud-)(u+ x u-) ]W- ---> ud+ + vu + u-
d) charged pion, positron neutrino, electron (38.7%):
ds/ds[ (ud+ x ud-)(e+ x e-) ]W- ---> ud+ + ve + e-
Mesons "come into their own" in baryon decays, where we discover their great utility as suppliers of quark flavors and colors to facilitate baryon transformations (a role they also perform in the "Yukawa" strong force of compound atomic nuclei and the creation of "nucleons"). Mesons function as alternative carriers of color charge and quark flavor, just as leptons (electrons and neutrinos) function as alternative carriers of electric charge and lepton number ("identity") charge, functions which allow baryons to transform, conserve, neutralize, and cancel their charges without suffering annihilation by antibaryons.
7) neutron: udd (neutral); mass 939.6, lifetime 9.25x10(2)
Neutron decay is very slow (half-life about 15 minutes), both because there is such a small bound energy difference between reactants and products, and because the reaction pathway is complex. The d quark of the virtual positive pion annihilates with the d quark in the neutron, replacing it with an up quark, creating the proton. Meanwhile, in a secondary reaction, the remaining negative pion and a positron from a second (leptonic) virtual pair undergo a typical charged pion decay, canceling each other's electric charge and releasing the positron's neutrino. The d and u quarks of the negative pion simply annihilate each other. The mass difference between the neutron and proton produces just enough energy to materialize the electron and positron neutrino, balancing the proton's electric charge, and the reaction's overall lepton "number" ("identity") charge.
Principle decay products ("beta" decay):
a) proton plus positron neutrino plus electron (100%):
udd[ (du+ x du-)(e+ x e-) ]W- ---> udu+ + ve + e-
8) lambda: dus (neutral); mass 1115.6, lifetime 2.6x10(-10)
A d quark of the virtual positive meson annihilates with the s quark of the lambda, and replaces it with an up quark in reaction a), creating a proton, and a d quark in reaction b), creating a neutron. The annihilation energy materializes the remaining virtual pion in both cases, conserving charge and/or momentum. This reaction is faster than reaction 1) because there is far more available energy from the decay of the heavy s quark, and the reaction pathway is simpler.
Principle decay products:
a) proton plus negative pion (64.2%):
dus[ du+ x du- ]W- ---> duu+ + du-
b) neutron plus neutral pion (35.8%):
dus[ dd x dd ]W ---> dud x dd
9) Sigma: uus+; mass 1189.4, lifetime 0.8x10(-10)
In a), a d quark in the virtual pion annihilates with the s quark of the sigma, replacing it with a d quark to create a proton and simultaneously materializing the remaining neutral pion. In b), both the negative and neutral pion react with sigma s and u quarks, replacing them with d quarks (first the intermediate lambda uds is formed, which then reacts with the neutral pion dd to produce the neutron udd). The remaining positive pion is materialized to balance electric charge. In both a) and b) the mass energy difference between the s and d quarks fuels the reaction.
Principle decay products:
a) proton + neutral pion (51.6%):
uus+[ dd x dd ]W+ ---> uud+ + dd
b) neutron + positive pion (48.4%):
uus+[ dd x (ud- x ud+) ]W+ ---> udd + ud+
10) Sigma: dds-; mass 1197, lifetime 1.5x10(-10)
The d quark of the positive pion annihilates the s quark in the sigma and replaces it with an up quark, forming a neutron and materializing the remaining negative pion, conserving electric charge.
Principle decay products:
a) neutron + negative pion (100%):
dds-[ ud+ x ud- ]W- ---> ddu + ud-
11) Xi: uss (neutral); mass 1315, lifetime 2.9x10(-10)
A d quark from a neutral pion annihilates with the s quark in the xi, replacing it with a d quark; the annihilation energy materializes the remaining neutral pion of the virtual pair.
Principle decay products:
a) lambda plus neutral pion (100%):
uss[ dd x dd ]W ---> usd + dd
12) Xi: dss-; mass 1321.3, lifetime 1.6x10(-10)
A d quark from a positive pion annihilates with the s quark in the xi, replacing it with an up quark; the annihilation energy materializes the remaining negative pion of the virtual pair, conserving electric charge.
Principle decay products:
a) lambda plus negative pion (100%):
dss-[ ud+ x ud- ]W- ---> dsu + ud-
13) Omega: sss-; mass 1672.5, lifetime 0.8x10(-10)
In a), s and d quarks in the positive and neutral pions of the virtual complex annihilate with two s quarks in the omega, replacing them with u and d quarks; annihilation energy materializes the remaining negative pion, conserving electric charge. (This reaction pathway is similar to 9b, which also changes two quarks.) The intermediate product is the xi sus, which reacts with the neutral pion dd to form the lambda sud.
In b), a d quark in the positive pion of the virtual pair annihilates with the s quark in the omega, replacing it with an up quark; annihilation energy materializes the remaining negative pion, conserving electric charge.
In c), a d quark in one of the neutral virtual pions annihilates with the s quark in the omega, replacing it with a d quark and materializing the remaining neutral pion.
Note how naturally the virtual particle-antiparticle pair mechanism advocated here produces all the exotic products in the three decays of the omega listed below. Recall these are the experimentally observed products as listed in the CRC Handbook. This is strong evidence that the proposed mechanism is the actual pathway used by the W.
Reaction a) is favored overall in spite of its more complex pathway because two of the heavy s quarks can decay simultaneously (or sequentially), releasing more free energy to drive the reaction. Reaction b) is favored over c) because, as is evident from several other comparable decays (see 4 e, f; 5a, b; and 8 a, b) it is more difficult to assemble neutral particle pairs than charged particle pairs - all other things being equal.
Principle decay products:
a) lambda plus negative kaon (68.6%):
sss-[ dd x (su+ x su-) ]W- ---> sud + su-
b) xi (neutral) plus negative pion (23.4%):
sss-[ ud+ x ud- ]W- ---> ssu + ud-
c) Xi- plus neutral pion (8%):
sss-[ dd x dd ]W- ---> ssd- + dd
Postscript to the Weak Force Mechanism Paper
The particle-antiparticle charge-carrying mechanism that works so well to illustrate the weak force decay pathways of leptons, mesons, and baryons (revealing as well the generic utility of mesons in hadron transformations), may also have some explanatory power for other types of transformations (especially electromagnetic transformations) - as we might expect of such a fundamental process, and in consideration of the electroweak unification.
I will consider only one example of such an electromagnetic transformation: when protons (uud)+ are bombarded with negative pions (ud)-, a negative sigma (dds)- and a positive kaon (us)+ are readily produced, but the "reciprocal" product of a positive sigma (uus)+ and a negative kaon (us)- never occurs. Why this should be true may be seen in terms of the particle-antiparticle charge carrier mechanism (operating this time without the mediation of the weak force IVBs). An external source (the laboratory accelerator) supplies as much energy as is needed to achieve the reaction threshold. (No single elementary particles (leptons) are created or destroyed in these reactions, which would require the mediation of the weak force IVBs.)
Of the two products here considered (sigma- vs sigma+), there is a straightforward and simple electromagnetic reaction pathway only to the sigma-:
a) ud- + uud+(us- x us+) -----> dsd- + us+
In reaction a) the energy of collision between the negative pion and proton creates a kaon x antikaon particle pair; the negative member of this pair reacts with the proton, annihilating a "u" quark in the proton with its anti "u" quark, and replacing it with a "s" quark. The colliding negative pion similarly reacts with the proton, annihilating an "u" quark and replacing it with a "d" quark. These two (probably simultaneous) reactions produce the negative sigma and materialize the positive kaon of the particle-antiparticle pair, conserving electric charge.
Nothing is involved in this reaction beyond matter-antimatter annihilations of one quark flavor by its corresponding antiflavor, and the substitution of one quark for another from both the negative pion and the negative kaon. However, when we try to reach the sigma+ by an analogous pathway, we can do so only with difficulty. The "reciprocal" reaction we are trying to create is:
b) ud- + uud+ -----> uus+ + us-
Reaction b), however, achieves the desired product only via an improbable two-step pathway:
b1) ud- + uud+(ds x ds) -----> dus + ds (possible)
b2) dus(us+ x us-) -----> uus+ + us- (highly unlikely)
In the second step, the "s" quark of the antikaon would
have to annihilate with the "d" quark of the baryon, rather than
with the baryon's "s" quark, which it would much prefer (creating
a proton). Clearly, this improbable two-step reaction cannot
compete with the single step, straightforward reaction in a).
Hence the particle-antiparticle charge-carrying mechanism does
seem to have some explanatory power (beyond the weak force
mechanism) regarding the pathways of transformation among
elementary particles, both with regard to what does happen and
what does not.