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As far as I know, the total cross-sections of the following hadron interactions are well described by a single Reggeon trajectory and a single Pomeron (soft Pomeron) trajectory. It seems to work for most tested hadrons!, but why?

  1. $K^-p:(11.93s^{0.0808}+25.33s^{-0.4525})mb$
  2. $K^+p:(11.93s^{0.0808}+7.58s^{-0.4525})mb$
  3. $\bar pn:(21.70s^{0.0808}+92.71s^{-0.4525})mb$
  4. $pn:(21.70s^{0.0808}+92.71s^{-0.4525})mb$
  5. $p\bar p:(21.70s^{0.0808}+98.39s^{-0.4524})mb$
  6. $pp:(21.70s^{0.0808}+56.08.39s^{-0.4524})mb$
  7. $\pi^-p:(11.63s^{0.0808}+36.02s^{-0.4525})mb$
  8. $\pi^+p:(11.63s^{0.0808}+7.58s^{-0.4525})mb$
  9. $\gamma p:(0.0677s^{0.0808}+0.129s^{-0.4525})mb$

$s$ is a Madelstam variable, the COM energy.

The last expression is hard for me to understand: in the $1$ to $20 GeV$ range the photon and the proton seem to exchange a Reggeon trajectory and a Pomeron trajectory, although I would tend to think that it should be some kind of Compton scattering. I just don't get it, the only charge a photon sees is the EM charge!! Could anyone, please, offer a reasonable explanation?

Why are these results so unexpectedly accurate? Specially if you add multiple Pomerons and the Odderon. No other phenomenological model is able to match its accuracy.

Do we have to go back to the 60's to explain hadron interactions?

These plots can be see in slides number 35 and 36 of the following presentation (from a physicist working at the "KEK Theory Center"):

https://indico2.riken.jp/event/2729/attachments/7480/8729/PomeronRIKEN.pdf

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Regge theory provides a good description of soft interactions - elastic scattering through small angles, and similar gentle processes. (The link to the total cross section comes from the optical theorem.)

Today we would say that such elastic scattering comes from exchange of 2 gluons (not 1 gluon, as there is no colour exchange). For hard interactions one can calculate the Feynman diagram, this goes over into the Regge description at lower energies/momenta as $\alpha_s$ becomes large.

The photon joins the list as it behaves like a $\rho$ meson at short distances/large $q^2$. It gets there through a $q \overline q$ loop.

But Regge theory can't describe hard scattering. You do need quarks and gluons and other post 60's concepts for that.

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  • $\begingroup$ As far as I know, a two gluon exchange would not be enough to describe hadron elastic scattering. At present, a meson Regge trajectory, several Pomerons (collectively called Froissaron) and an Odderon are needed to correctly fit the experimental data of $pp$ and $p\bar p$ total and elastic cross-sections (up to 14 TeV). A photon behaving like a $\rho$ meson is something that I don't understand. $\endgroup$ – Carlos L. Janer Sep 4 '18 at 16:54

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