This page summarizes discussions held between Eliyahu Comay and physicists after this web site was published. The Questions & Answers are edited in order to make it more readable. We do not publish names of physicists who asked the questions, and we encourage you to ask or comment about this web site contents. Do it simply by emailing to Eliyahu or Ofer.

Gell-Mann—Okubo mass formulae
Lattice QCD predictions
VMD dicussion

Gell-Mann—Okubo mass formulae
Q. Can you reproduce or surpass the Gell-Mann—Okubo mass formulae both for baryons and mesons?
A. The phenomenological Gell-Mann—Okubo formulas are based on the SU(3) approximation to the u,d,s quarks. They have been suggested before the QCD formulation and are independent of it.
Q. I agree that the Gell-Mann–Okubo relations are “kinematical” and not “dynamical”, i.e., using only the flavor global symmetries and not the QCD local gauge theory. As such, they indeed seem not to decide between QCD and the competing theory.

Lattice QCD predictions
Q. Can you get mass predictions as good as (or better than) lattice QCD ones?
A.Obviously, the problem of doing a concrete dynamical calculation is very far from being a simple task. For practical reasons, an undertaking this kind of assignment depends on the amount of man power ready to work on the New Theory. At present it is recognized that many qualitative arguments (like the existence or nonexistence of phenomena or larger or smaller value of measured quantities) can provide good evidence for supporting or rejecting theories.
Q.The agreement between lattice QCD and experiment now is in the order of a few percent, and within the uncertainties (computational and experimental), for several hadron masses, when only one parameter is free (Lambda_QCD). This I take as very compelling. A radically new theory would need to claim that this is an amazing coincidence.
A. Nevertheless, relying on the Regular Charge-Monopole Theory, a phenomenological approach has been used for predicting the yet unmeasured charge radius of the Sigma+ baryon [1]. This prediction differs from the corresponding QCD values [2]. Let us wait and see what will experimental people say.
[1] E. Comay, Prog. In Phys. 4, 13 (2010). http://www.tau.ac.il/~elicomay/Predict.pdf
[2] Wang P., Leinweber D. B., Thomas A.W. and Young R. D. Chiral extrapolation of octet-baryon charge radii. Phys. Rev. D, 2009, v. 79, 094001-1–094001-12.

VMD discussion
Q. Let us discuss VMD’s covariance (I emphasize again: VMD is not a part of the standard model). You are tricked again here by your usage of quantum mechanical thinking. No serious physicist would claim ever that a real photon is a linear combination of real particles, one of which is a vector meson. What one is thinking here is that a single particle state in a quantum field can be thought, in very short periods of time, as a combination of virtual states of any set of particles with which the photon can interact. It is not right to say that a photon “has an hadron component” which depends on energy, but if the photon is probed by some hadron that hadron will “see” the virtual hadrons in the photon. This is a description in the frame of reference where the hadron is at rest. If you change the frame to render the photon as “soft”, then you will be boosting the hadron. You can see an application of this for UHE cosmic rays: they cannot come from too far away because high energy protons would see photons from the microwave background as hard photons in its rest reference frame, thus occurring photopion production.

A. In your last remark you state:” No serious physicist would claim ever that a real photon is a linear combination of real particles, one of which is a vector meson.” Well, on page 271 of [1], the state of a physical photon is defined as follows

|Gamma> = c_0 |Gamma_b> + c_h |h> (2.1)

where c_i are normalization coefficients, |Gamma_b> is the pure electromagnetic (“bare”) component of the photon and |h> is its hadronic component, which is made of a chargeless meson, like the rho_0, omega and phi. (Here I use different symbols for the numerical coefficients of (2.1).)

Eq. (2.1) exactly agrees with (10.104) which can be seen on p. 298 of [2]. These quotations from the literature prove that the above mentioned citation from your last remark does not hold water.

Another statement made in your last remark supposedly relies on work from the 60′s says about VMD: “The theory has a math formulation, of course, which is explicitly covariant.” Well, note please that [1,2] have been written in a later period. The Authors of [1] and [2] use a contradictory terminology. Indeed, just below (2.1) of [1] it is claimed that: “all states in Eq. (2.1) have the same 3-momentum k.” This is certainly a violation of covariance, because, in order to represent a meson, the 0-component of the photon’s 4-momentum is altered, whereas covariance must conserve the invariant E^2 – k^2. An analogous violation of covariance can be found on p. 299 of [2] which says: “the ratio of c_h/c_0 increases with increasing energy.”

I stop here and ask you two questions:

1. Why the Authors of [1,2] ignore the “explicitly covariant” attribute that you ascribe to VMD of the 60s?
2. Can you show me an explicit reference from the 60s, proving covariance of VMD?

[1] T. H. Bauer, R. D. Spital, D. R. Yennie and F. M. Pipkin, Rev. Mod. Phys., 50, 261 (1978).
[2] H. Frauenfelder and E. M. Henley, Subatomic Physics (Prentice Hall, Englewood Cliffs, 1991).

Q. You will not find a paper showing VMD covariance, because there is no need for such explicitations. If there was, refereees would have asked Sakurai et al to provide them.

A. Wigner’s analysis of the irreducible representations of the Poincare group applies to systems that are stable for appropriately long period of time. A real photon certainly belongs to this category. Now, VMD writes the state of a real photon as a linear combination of a pure electromagnetic photon and a vector meson:

|Gamma> = c_0 |Gamma_b> + c_h |h> (1)

Here the sum of the absolute value of the coefficients is unity and each of them does not vanish. I call (1) a supperposition of two different states, each of which has a probability greater than zero. On the other hand, you argue that the second term of (1) is virtual. I think that you just try to evade a problem by playing with words. Moreover, (1) is a mixture of a massless state (characterized by helicity) and a massive state (characterized by spin). I rely on Wigner’s work and conclude that VMD is a clear violation of Special Relativity.


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