Next: Conclusion. Up: Chiral Invariant Phase Space Previous: Chiral invariant phase-space decay   Contents

Neutrino-nuclear interactions

The simulation of DIS reactions includes reactions with high . The first approximation of the -dependent photonuclear cross-sections at high was made in [11], where the modified photonuclear cross sections of virtual photons [34] were used. The structure functions of protons and deuterons have been approximated in CHIPS by the sum of non-perturbative multiperipheral and non-perturbative direct interactions of virtual photons with hadronic partons:

 (23.59)

where , , , , , , , , , , , , , , , , , , . The parton distributions are normalized to the unit total momentum fraction.

The photonuclear cross sections are calculated by the eikonal formula:

 (23.60)

An example of the approximation is shown in Fig. 23.20. One can see that the hadronic resonances are melted'' in nuclear matter and the multi-peripheral part of the cross section (high energy) is shadowed.

The differential cross section of the reaction was approximated as

 (23.61)

where , , . As in Eq.23.59, hence , , with and . The approximation is compared with data in Fig.23.21 for deuterium [35] and in Fig.23.22 for iron [36,37]. It must be emphasized that the CHIPS parton distributions are the same as for electromagnetic reactions.

For the amplitudes one can not apply the optical theorem, To calculate the total cross sections, it is therefore necessary to integrate the differential cross sections first over and then over . For the reactions the differential cross section can be integrated with good accuracy even for low energies because it does not have the factor of the boson propagator. The quasi-elastic part of the total cross-section can be calculated for . The total cross-sections are shown in Fig.23.23(a,b). The dashed curve corresponds to the GRV [38] approximation of parton distributions and the dash-dotted curves correspond to the KMRS [39] approximation. Neither approximation fits low energies, because the perturbative calculations give parton distributions only for . In [40] an attempt was made to freeze the DIS parton distributions at and to use them at low . The part of DIS was replaced by the quasi-elastic and one pion production contributions, calculated on the basis of the low energy models. The results of [40] are shown by the dotted lines. The nonperturbative CHIPS approximation (solid curves) fits both total and quasi-elastic cross sections even at low energies.

The quasi-elastic cross sections are shown in Fig.23.23(c,d). The CHIPS approximation (solid line) is compared with calculations made in [40] (the dotted line) and the best fit of the theory was made in [41] (the dashed lines). One can see that CHIPS gives reasonable agreement.

The spectra for each energy are known as an intermediate result of the calculation of total or quasi-elastic cross sections. For the quasi-elastic interactions () one can use and simulate a binary reaction. In the final state the recoil nucleon has some probability of interacting with the nucleus. If the value is randomized and therefore the dependent coefficients (the number of partons in non-perturbative phase space , the Pomeron intercept , the fraction of the direct interactions, etc.) can be calculated. Then for fixed energy and the neutrino interaction with quark-partons (directly or through the Pomeron ladder) can be randomized and the secondary parton distribution can be calculated. In vacuum or in nuclear matter the secondary partons are creating quasmons [2,3] which decay to secondary hadrons.

Next: Conclusion. Up: Chiral Invariant Phase Space Previous: Chiral invariant phase-space decay   Contents