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Re: [Phys-l] QGP Not According to Theory?




Follow up.

The reason nature choose three color degrees of freedom isn't really known.
Perhaps N_c =3 is the low energy manifestation of QCD. Higher fractional
statistics exist in the FQHE. Some support for this unorthodox idea comes some
work by Feynman who is his parton model observed that a high energy hadron could
be regarded not as composite particle composed of three quarks but as a
collection of partons approaching infinity. ( RP. Feynman The behavior of Hadron
Collisions at Extreme energies, in High energy collisions, Proceedings of
the Third International conference, Stony Brook, New York edited by C. N. Yang
et al Pages 237-249. )

I wrote the below post several years ago which perhaps might be on interest.




Skyrme Topological Model And Mesons
It is commonly believed that the observed decay rate of neutral pions stand
as proof that M_c, the number of colors in QCD theory equals three. However,
this assumption is based on the mistaken notion that electric charge values
are independent of the color degrees of freedom. In fact the Standard Model
seems to support that the electric charge structure is directly tied to color
multiplicity, and that this structure is the result of a phase transition at
the EW scale.
Of course we do know (by means other than pion decay) that M_c does in fact
equal three. However, a proposal by Skyrme based on the idea that baryon
current can be constructed from pion fields provides a topological model for
quarks. Pions of course do not carry baryon charge but in Skymre's formulation
Baryons are viewed as what are called multiple pole solitons. (which have
come to be called Skymions). This theory goes under the name of the Skyrme
Topological Model.
In STM, baryon number is a topological charge equal to the "winding number "
of the fermion soliton. The fact that we observe that M_c =3 in our universe
today may be just the low energy configuration of SM topology. In the Skyrme
Topological model baryons retain their topological characteristics up to the
QCD phase transition energy of roughly 200 Mev. Little is known concerning
the physics of Baryons above this temperature, though ongoing experiments at
Brookhaven and elsewhere may hopefully remedy this situation.
To see the relationship of electric charge to multiplicity we need to look
at the decay rate equation for the neutral pion.

capGAMMA ( pion to 2Xgamma)=
(M_c^2)*((q_u^2-q_d^2)^2)*alpha^2*M_pi0^3/(64*pi^3*F_pi)

Where q_u & q_d are the up and down quark electric charge, alpha is the
fine structure constant, M_pi0 is the neutral pion mass and F_pi is the pion
decay constant.
Note that when tr[Q]=0 (Q being the SU(2) diagonal electric charge matrix)
capGAMMA =0. (Interestingly, this highly symmetric charge structure which
occurs at the limit of 1/M_c=0, correlates to an S duel magnetic charge equal
to hbar*C.) When it is recognized that the electric charge structure is a
function of M_c then we can see that

(M_c^2)*((q_u^2-q_d^2)^2)=constant= 1

We then easily see that

q_u=(1/2)*(1+1/M_c) and q_d=(1/2)*(-1+1/M_c)

Very significantly the values of q_u and q_d avoid ALL the various SM
anomalies as long as M_c is any odd valued integer.
Based on this we have no reason to assume that every pion we observe are
combinations of quarks and anti quarks with three color degrees of freedom. A
pion could just as well be composed of multiplicity 5 or multiplicity 7 and we
would have no way of to determine this based on the pion decay rate. Is it
possibly that pions (and other pseudoscalers and vector mesons) produced near
the QCD transition energy may really be composed of higher multiplicity
quarks? Of course if there is no observational consequence of this then this
question has no meaning. Nevertheless, if the Skyrme Topological Model is a correct
description of color dynamics this conclusion seems at least reasonable.
Therefore some thought is needed to determine if there are observational
consequences of this possibility. (One possibility would be that higher
multiplicity mesons would not be strongly coupled to baryons though whether this can be
observed is questionable.)
In the Skyrme Topological Model the diagonal SU(3)_flavor electric charge
matrix is given by

Q=(1/2)*Lambda_3+(1/(2*sqrt3))*Lambda_8

Where Lambda_3 and Lambda_8 are SU(3)_c diagonal generators. Interestingly
this gives us

Q= U+V

Where U and V are 3X3 diagonal matrixes whose values are the u and v charges
of the Fitzpatrick fermion electric charge model. Here again we see the
intimate connection between color multiplicity and electric charge structure.
All of this in no way suggest that protons and neutrons, etc., are not
composed of color multiplicity three particles. Other experimental evidence makes
this certain. However, I do believe that the Skyrme Topological Model forces
us to consider the possibility of higher multiplicity pseudoscalers mesons
and composite vector mesons at energies near the QCD transition temperature.

Bob Zannelli