TOTAL CROSS SECTION FOR PHOTON-PHOTON INTERACTIONS

Regge model has been used to calculate photon – photon total cross section. The couplings of the exchanged soft pomeron, hard pomeron and Reggeons with photons have been calculated. It has been assumed that soft and hard pomerons couple to photons in away similar to that of the pseudo scalar mesons. A comparison with data on photon-photon total cross section shows a good agreement .


INTRODUCTION
It is well known that the hadronic total cross sections increase with energy above 10 GeV .At lower energies these cross sections decrease with energy.
The behavior in this region is different from one process to the other.Thus at high energies it is possible to compare models, which describe the proton proton, protonantiproton, photon -proton and photon -photon total cross sections.
Models that used to describe the photonphoton total cross section can be classified into two main groups   1 .The first group involves models, which depend on Regge theory.Photons and hadrons exchange Reggeons and pomerons.Reggeons describe the initial decrease of the cross section with energy while pomerons describe the subsequent rise with increasing energy.This group also involves the factorization models where a simple constant allows us to move from one process to the other and the scaling models where the various hadronic processes are related through the dimension counting rule.
The second group involves the QCD models.These models ascribe the rise of the total cross section to partonparton scattering.Some of these models used as well higher order QCD effects, soft gluon summation and the transverse momentum distribution of partons.
According to Regge model the total cross section is given by     This term was attributed to hard pomeron exchange.
The general form of Regge equation should be written as The powers were taken as

2-Photon-Photon Total Cross Section
The amplitude of elastic photon-photon scattering is given in fig. 1.The dotted line represents the Reggeons and pomerons which couple to photons through the quark loop.In general the Regge amplitude   Then the total cross-section is given by

2-1 Soft Pomeron -Photon Coupling
We notice that the pomeron-two photons vertex in fig . 1 We notice that (12) gives the transfer momentum dependence of the form factor.Since we are interested in the region where 0  t then equation ( 12) gives  13) in (7) we get the following equation for the soft pomeron-photons coupling This is similar to the    0 coupling constant in the mass less limit but the summation is now carried over all types of the quarks.Suppose that  is a dimensional quantity with q m g 


. If  were the average coupling of the pomeron to the quarks then q q q m g e  2 would equal to c  with c is around 1.2.
Assuming that  is the coupling of the pomeron to up or down quark then the quantity q q q m g e  2 can be expanded in terms of  so  c m g e q q q   2 with c is the sum of the coefficients of  in the expansion.
With c is around one.The value of  can be calculated from the proton-proton total cross sections in the pomeron region.Using (6) then


The contribution from the soft pomeron can be given as For c =1.25 we get nb s

2-2 Hard Pomeron -Photons Coupling
It has been found   5 that hard pomeron is a flavour blind.It couples equally to all types of the quarks then (14) can be written in the form Where n is the number of the quarks involved in the process and H  is the hard pomeron-quark coupling.
The value of H  can be calculated from the proton- proton total cross section in the hard pomeron region as well.Therefore, the contribution from the hard pomeron to the cross section can be written as:

2-3 Reggeons-Photons Coupling
Reggeons that could couple with two photons are particles with even charge conjugation.We consider here the leading Reggeons   Then the contribution from Reggeons to the photonphoton total cross section is given as Finally the contribution from the quark box   13 diagram should be added to the photon-photon total cross section.

3-DISCUSSION
The predictions from our model (curve 2) compared with data  

.
These powers were assumed to have the same values for all hadronic processes.The coefficients in (1) obey the following factorization khalid_hamad2002@yahoo.com

7 data
indicated that a third term should be added to(1).
photons interactions.This can be done simply by calculating the couplings of the photons with the exchanged Reggeons and pomerons.The effect of the photon mass was discussed in ref   5 although more the upper vertex and to d and b at the lower vertex.The factorization property of the coupling is included.The form of ) (t  is taken as: of the trajectory at t=0.The constant 1 c is nearly one for soft pomeron, fig .1 is similar to the

P
-ISSN 1991-8941 E-ISSN 2706-6703 Journal of University of Anbar for Pure Science (JUAPS) spin states.The coupling constant is given by  

4 , 3 Furthermore
and some theoretical models are given in fig.2.The contribution from the soft pomeron alone (curve 1) is appeared in the figure.We notice that the hard pomeron becomes effective above GeV w 50  .The model of Schuler and Sjostrand is shown.According to this model the photon has VMD component, anomalous and QCD contributions.The model of Engel and Rafnt is also shown.More details on these models are given in ref.   1 .The predictions from our model agree nicely with the data.the above coefficients are given in mb .The quark box diagram should be added to (26) and (27).Compare the figures in these two equations we find that our calculated figures in (27) are nearly equal to the corresponding figures obtained from data fit in (26).Since the factorization is a characteristic of Regge poles then this result is clearly consistent with our calculations which treated the soft and hard pomerons as simple poles.