The Hard Photon-Nucleon Scattering Process is Another Standard Model Failure

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The data prove that the interaction of an energetic photon with a proton is (nearly) the same as its interaction with a neutron (see [1] or [2], section 10.10). It is now recognized that the photon's electromagnetic interaction cannot explain the data. The Vector Meson Dominance (VMD) idea was proposed at about 1960 in order to explain this effect. It argues that the physical photon is a combination of a pure electromagnetic photon and a vector meson. More general ideas are called generalized vector-dominance models. The expression "hadronic structure of the photon" is another version of this idea. A search by Google proves that the string of words "hadronic structure of the photon" is found on the web more than 5000 times. Here the acronym VMD refers to the idea that a real photon takes the following form

Φ = a0Φ0 + ahΦh, (1)
where Φ denotes a real photon, Φ0 is the pure electromagnetic component of the photon and Φh is the hadronic structure of the photon. a0 and ah are appropriately normalized coefficients whose relative value depends on the photon's energy. Here the hadronic contribution for low-energy photons is insignificant and high energy photons comprise an experimentally detectable hadronic component (see [1], p. 271 or [2], pp. 318, 319).

Referring to VMD, one should remember Wigner's work: "On Unitary Representations of the Inhomogeneous Lorentz Group" [3]. (Hereafter this article is called Wigner's work.) The significance of Wigner's work is described by the following words: "It is difficult to overestimate the importance of this paper, which will certainly stand as one of the great intellectual achievements of our century" (see [4], p. 149). A discussion of Wigner's work can be found in [5], pp. 57-74 and in [6], pp. 44-53. A physically important outcome of Wigner's work says that a quantum particle belongs to one of the following categories: particles whose rest mass is greater than zero and massless particles. Massive particles are characterized by the value of their mass and of their spin. Massless particles are characterized by their helicity. Evidently, this Wigner's work is a mathematical analysis of the inhomogeneous Lorentz group. Hence, its results are inherent properties of special relativity.

It turns out that the VMD idea (1) argues that a physically real photon is a sum of two states - an electromagnetic massless photon and a massive hadron. This idea is clearly inconsistent with the above mentioned results of Wigner's work. Conclusion: VMD is physically unacceptable because it violates special relativity.

An examination of Wigner's work shows that it uses general mathematical arguments. The correctness of its results means that one may find specific physical examples that illustrate the inconsistency between VMD and special relativity. For reading some discussions of this matter click here .

The photon is a very important elementary particle and the proton and the neutron are the most well-known hadronic states. There is no doubt that physical properties of hard photon-nucleon interaction deserve a serious discussion in particle physics textbooks. The present status of hard photon-nucleon interaction is as follows:

The subject index part of quite a few particle physics textbooks indicates that the phenomenon of hard photon-nucleon interaction is not discussed in these textbooks. The same is true for the VMD idea. It means that the present physical community adopts an Ostrich policy and simply ignores this Standard Model serious failure.

It can be concluded that the Standard Model provides no explanation for the hard photon-nucleon scattering data.


[1] T. H. Bauer, R. D. Spital, D. R. Yennie and F. M. Pipkin, Rev. Mod. Phys. 50, 261 (1978).

[2] E. M. Henley and A. Garcia, Subatomic Physics (3rd edition) (World Scientific Publishing, Singapore, 2007).

[3] E. Wigner, Ann. Math., 40, 149 (1939).

[4] S. Sternberg, Group Theory and Physics (Cambridge University Press, Cambridge, 1994).

[5] S. Weinberg, The Quantum Theory of Fields, Vol. I, (Cambridge University Press, Cambridge, 1995).

[6] S. S. Schweber, An Introduction to Relativistic Quantum Field Theory (Harper \& Row, New York, 1962).