Mechanisms of Proton-Proton Inelastic Cross-Section Growth in Multi-Peripheral Model within the Framework of Perturbation Theory. Part 2

Author(s)
Igor Sharf,
Andrii Tykhonov,
Grygorii Sokhrannyi,
Maksym Deliyergiyev,
Natalia Podolyan,
Vitaliy Rusov

ABSTRACT

We demonstrate a new technique for calculating proton-proton inelastic cross-section, which allows one by application of the Laplace' method replace the integrand in the integral for the scattering amplitude in the vicinity of the maximum point by expression of Gaussian type. This, in turn, allows us to overcome the computational difficulties for the calculation of the integrals expressing the cross section to sufficiently large numbers of particles. We have managed to overcome these problems in calculating the proton-proton inelastic cross-section for production (n ≤ 8) number of secondary particles in within the framework of φ^{3} model. As the result the obtained dependence of inelastic cross-section and total scattering cross-section on the energy √s are qualitative agrees with the experimental data. Such description of total cross-section behavior differs considerably from existing now description, where reggeons exchange with the intercept greater than unity is considered.

We demonstrate a new technique for calculating proton-proton inelastic cross-section, which allows one by application of the Laplace' method replace the integrand in the integral for the scattering amplitude in the vicinity of the maximum point by expression of Gaussian type. This, in turn, allows us to overcome the computational difficulties for the calculation of the integrals expressing the cross section to sufficiently large numbers of particles. We have managed to overcome these problems in calculating the proton-proton inelastic cross-section for production (n ≤ 8) number of secondary particles in within the framework of φ

Cite this paper

I. Sharf, A. Tykhonov, G. Sokhrannyi, M. Deliyergiyev, N. Podolyan and V. Rusov, "Mechanisms of Proton-Proton Inelastic Cross-Section Growth in Multi-Peripheral Model within the Framework of Perturbation Theory. Part 2,"*Journal of Modern Physics*, Vol. 3 No. 1, 2012, pp. 16-27. doi: 10.4236/jmp.2012.31003.

I. Sharf, A. Tykhonov, G. Sokhrannyi, M. Deliyergiyev, N. Podolyan and V. Rusov, "Mechanisms of Proton-Proton Inelastic Cross-Section Growth in Multi-Peripheral Model within the Framework of Perturbation Theory. Part 2,"

References

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[12] A. Donnachie and P. V. Landsho, “Total Cross Sections,” Physics Letters B, Vol. 296, No. 1-2, 1992, pp. 227-232. doi:10.1016/0370-2693(92)90832-O

[13] A. B. Kaidalov, “Pomeranchuk Singularity and High- Energy Hadronic Interactions,” Uspekhi Fizicheskikh Nauk, Vol. 173, No. 11, 2003, pp. 1153-1170. doi:10.3367/UFNr.0173.200311a.1153

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[15] E. Byckling and K. Kajantie, “Particle Kinematics,” Wiley, London, 1973.

[1] I. Sharf, G. Sokhrannyi, A. Tykhonov, K. Yatkin, N. Po-dolyan, M. Deliyergiyev and V. Rusov, “Mechanisms of Proton-Proton Inelastic Cross-Section Growth in Multi-Peripheral Model within the Framework of Perturbation Theory. Part 1,” Journal of Modern Physics, Vol. 2, No. 12, 2011, pp. 1480-1506.

[2] D. Amati, A. Stanghellini and S. Fubini, “Theory of High-Energy Scattering and Multiple Production,” Il Nuovo Cimento (1955-1965), Vol. 26, No. 5, 1962, pp. 896-954.

[3] I. G. Halliday, “Self-Consistent Regge Singularities,” Il Nuovo Cimento A (1965-1970), Vol. 60, No. 2, 1969, pp. 177-184.

[4] E. A. Kuraev, L. N. Lipatov and V. S. Fadin, “Multi Reggeon Processes in the Yang-Mills Theory,” Soviet Physics—JETP, Vol. 44, 1976, pp. 443-450.

[5] P. D. B. Collins, “An Introduction to Regge Theory and High Energy Physics,” Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge, 1977. doi:10.1017/CBO9780511897603

[6] L. N. Lipatov, “Integrability Properties of High Energy Dynamics in Multi-Color QCD,” Uspekhi Fizicheskikh Nauk, Vol. 174, No. 4, 2004, pp. 337-352. doi:10.3367/UFNr.0174.200404a.0337

[7] L. N. Lipatov, “Bjorken and Regge Asymptotics of Scattering Amplitudes in QCD and in Supersymmetric Gauge Models,” Uspekhi Fizicheskikh Nauk, Vol. 178, No. 6, 2008, pp. 663-668.

[8] M. G. Kozlov, A. V. Reznichenko and V. S. Fadin, “Quantum Chromodynamics at High Energies,” Vestnik NSU, Vol. 2, No. 4, 2007, pp. 3-31.

[9] N. G. De Bruijn, “Asymptotic Methods in Analysis,” 1st Edition, Bibl. Matematica, Amsterdam, 1958.

[10] K. Nakamura and Particle Data Group, “Review of Particle Physics,” Journal of Physics G: Nuclear and Particle Physics, Vol. 37, No. 7A, 2010, p. 075021. doi:10.1088/0954-3899/37/7A/075021

[11] G. Aad et al., “Measurement of the Inelastic Proton-Proton Cross-Section at = 7 TeV with the ATLAS Detector,” Nature Communication, Vol. 2, 2011, p. 463. doi:10.1038/ncomms 1472

[12] A. Donnachie and P. V. Landsho, “Total Cross Sections,” Physics Letters B, Vol. 296, No. 1-2, 1992, pp. 227-232. doi:10.1016/0370-2693(92)90832-O

[13] A. B. Kaidalov, “Pomeranchuk Singularity and High- Energy Hadronic Interactions,” Uspekhi Fizicheskikh Nauk, Vol. 173, No. 11, 2003, pp. 1153-1170. doi:10.3367/UFNr.0173.200311a.1153

[14] Y. Nikitin and I. Rozental, “Theory of Multiparticle Production Processes,” Harwood Academic Publishers, New York, 1988.

[15] E. Byckling and K. Kajantie, “Particle Kinematics,” Wiley, London, 1973.