Monday, March 13, 2023

Could g=1-gluons relate to the intrinsic strangeness and charm of the proton?

The TGD predicts that ordinary gauge bosons and Higgs are accompanied by SU(3)g octet, where g refers to the genus of partonic 2-surface to which fundamental fermions are associated. 3 fermion families with g=0,1,2 are conformally special and can be seen in a combinatorial sense triplet representations of SU(3)g. Gauge bosons and Higgs as fermion pairs naturally correspond to SU(3)g singlet (ordinary gauge bosons) and octet, whose presence implies violation of fermion universality.

Strange and charmed quarks s and c are produced in high energy collisions of protons. The effective presence of s and c in the initial states can be understood in terms of radiative corrections, which affect the scale dependent parton distribution functions (PDFs) of proton, which depend on the scale of momentum exchange Q2. PDFs are determined by the renormalization group evolution equations, which are differential equations with respect to Q2. Q2≠ 0 is associated with interacting proton and means that the light u and d quarks are excited to strange and charmed states. The initial values of PDFs at Q2=0 correspond to non-interacting proton.

A long standing question has been whether proton has also intrinsic strangeness and charm, which should be distinguished from the radiatively generated energy scale dependent intrinsic charm and strangeness. The intrinsic strangeness and charm cannot be calculated perturbatively and would appear in the initial values of PDFs at the limit Q2=0

Quite recently an article with the title "Evidence for intrinsic charm quarks in the proton" \cite{bpnu/intcharm} appeared in Nature (this). Could the intrinsic charm be seen as an evidence for the presence of light g-gluons in the octet representation of SU(3)g?

Could the presence of light g-gluons make possible intrinsic valence charm and strangeness so that the proton could be a superposition of states in which parton sea contains g-gluons and and valence quarks can be strange or charmed? These states would however be superpositions of states with same SU(3)g quantum numbers?

Is this energetically possible?

  1. This is impossible in the simplest model of baryon involving only on-mass-shell constituent quarks, which in the TGD framework would correspond to current quark plus color magnetic flux tube.
  2. However, current quarks contribute only a small fraction to the proton total mass. In the TGD framework, the remaining mass could be assigned to the color magnetic body (MB) of proton and sea partons. One could therefore consider a superposition of states for which color MBs could have varying masses. This would allow strange valence quark with a reduced mass of the color MB. This component in the proton wave function would involve sea g-gluon(s) at a color magnetic flux tubes assignable to the sea.
  3. The mass of proton is smaller than that of charmed quark so that the charmed quark is off-mass shell. What does off-mass-shell property mean in the TGD framework?

    Galois confinement generalizes the color confinement to a universal mechanism for the formation of bound states. Galois confinement states that the observed particles consist of building blocks with momenta, whose components are algebraic integers, which can be complex. Momentum components can also have negative real parts so that they would be tachyonic. The interpretation as number theoretically quantized counterparts of off-mass-shell momenta is natural. Since mass squared correspond to conformal weight, Galois confinement involves also conformal confinement stating the total conformal weights are ordinary integers.

    In this picture, virtual quarks would correspond to on-mass-shell states in a number teoretical sense. Mass squared would be an algebraic number determined as a root of a polynomial P with integer coefficients smaller than the degree of P. Color confinement implies that it is strictly speaking not possible to talk about on-mass-shell quarks.

    For the physical states both mass squared and momentum components are ordinary integers in a scale determined by the p-adic length scale assigned to the particle: this scale is also determined by the polynomial P allowing however several ramified primes defining the p-adic primes. Mass squared obeys a stringy mass formula.

  4. If the off-mass-shell g=1-gluon is massive enough, its decay would reduce the mass of the sea and the total energy would be conserved. λ-n mass difference, pion mass, and ΛQCD, which are all of order 100 MeV, give a rough idea about the mass scale of g=1 gluons. This would support the d\rightarrow s option which however increases the contribution of the valence quarks. Therefore the proposed idea does not look attractive.
See the article What it means if a Higgs-like particle decaying to eμ pairs exists? or the chapter with the same title.

For a summary of earlier postings see Latest progress in TGD.

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