## A Problem with the Photon-Nucleon Interaction

The cross section of a hard photon scattered on a proton is similar to that of a neutron [1]. Furthermore, the electric charge of the nucleon quark constituents is too small to explain the strength of this interaction. Thus, an alternative explanation is called for.

Nearly 60 years ago, VMD was proposed as a possible explanation. However, as discussed further on, VMD (and its variants GVMD [2] and VDM) suffers major faults preventing it from becoming a valid explanation. The VMD concept experimental failure is pointed out in the literature, and by the Nobel Laureate J. I. Friedman in his 1991 Nobel Lecture [3] who mentioned that ”these calculations of the generalized vector-dominance model failed in general to describe the data over the full kinematic range.” The review article [4] states that ”no direct translation between the Standard Model and VMD has yet been made”. Consequently, the cross section of a hard photon scattered on a proton phenomenon is still unexplained more than 60 years after its discovery.

### Fundamental problems with the Vector Meson Dominance and its variants

In the heart of VMD lies the idea that the wave function of an energetic photon takes the form (see [1], p. 271)

where denotes the wave function of a physical photon , denotes the pure electromagnetic component of a physical photon and denotes its hypothetical hadronic component. are appropriate numerical coefficients. Expression (1) is inconsistent with Wigner’s analysis of the unitary representations of the inhomogeneous Lorentz group (see [5, 6, 7]). This analysis proves that a massive quantum particle has a well-defined mass and spin, whereas a massless particle has two components of helicity. It means that the first term of (1) has only two values of the z-component of its spin, whereas the second term of (1) has three values of the z-component of its spin. This is a contradiction because a free quantum particle has a well-defined spin (see [5, 6, 7]).

The following simple experiment provides an illustration of the validity of the above mentioned Wigner’s work. It demonstrates that VMD is inconsistent with special relativity. Let us examine two optical beams that are emitted from source , respectively (see fig. 1). are at points , respectively, and the figure is embedded in the plane. The beams intersect at point O and each of them continues in its original direction. Namely, in the case of optical photons, no photon-photon scattering event takes place. Now let us examine this system from an inertial frame that moves nearly at the speed of light in the negative direction of the y-axis. If VMD is correct, than the energetic photons of the beams that are seen in contain hadrons, and scattering events should take place. It means that one and the same process yields contradictory observations. This contradiction proves that VMD is inconsistent with special relativity.

Figure 1: Two beams of optical photons intersect at point **O**. (See text.)

### The invalidity of VMD in contemporary physics

The following statements summarize the invalidity of VMD and of its associates. The Particle Data Group is the institute that is authorized to summarize and evaluate experimental work in the field of elementary particles. It turns out that in the photon item of its annual 2018 report, this institute says nothing on any property of the photon that pertains to the hadronic structure of the photon [8]. In fact, this annual report indicates two other experimental measurements of the photon, that fit very accurately two theoretical elements of electrodynamics: the photon has no self-mass and it carries no electric charge. This evidence means that even though the VMD concept was published more than 50 years ago, it remained on the margins of physics.

People who write textbooks and people who are in charge of evaluating results of experimental physics ignore VMD.

**Research topic #1:** Provide a theoretical explanation to the strength of the photon-nucleon interaction.

**Research topic #2:** Provide a theoretical explanation to the similarity between photon-proton interaction and photon-neutron interaction.

#### References

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

[2] J. J. Sakurai and D. Schildknecht, Phys. Lett., 40B, 121 (1972).

[3] J. I. Friedman, Rev. Mod. Phys., 63, 615 (1991).

[4] H. B. O’Connell, B. C. Pearce, A. W. Thomas and A. G. Williams, Prog. Part. Nucl. Phys., 39, 201 (1997).

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

[6] S. S. Schweber, An Introduction to Relativistic Quantum Field Theory (Harper & Row, New York, 1964). pp. 44-53.

[7] S.Weinberg, The Quantum Theory of Fields, Vol. I (Cambridge University Press, Cambridge, 1995). pp. 58-74.

[8] http://pdg.lbl.gov/2018/listings/rpp2018-list-photon.pdf