Mechanisms of Proton-Proton Inelastic Cross-Section Growth in Multi-Peripheral Model within the Framework of Perturbation Theory. Part 3

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

Affiliation(s)

Department of Theoretical and Experimental Nuclear Physics, Odessa National Polytechnic University, Odessa, Ukraine.

Department of Experimental Particle Physics, Jo?ef Stefan Institute, Ljubljana, Slovenia.

Department of Theoretical and Experimental Nuclear Physics, Odessa National Polytechnic University.

Department of Mathematics, Bielefeld University, Bielefeld, Germany.

Department of Theoretical and Experimental Nuclear Physics, Odessa National Polytechnic University, Odessa, Ukraine.

Department of Experimental Particle Physics, Jo?ef Stefan Institute, Ljubljana, Slovenia.

Department of Theoretical and Experimental Nuclear Physics, Odessa National Polytechnic University.

Department of Mathematics, Bielefeld University, Bielefeld, Germany.

ABSTRACT

We develop a new method for taking into account the interference contributions to proton-proton inelastic cross-section within the framework of the simplest multi-peripheral model based on the self-interacting scalar φ3 field theory, using Laplace’s method for calculation of each interference contribution. We do not know any works that adopted the inter- ference contributions for inelastic processes. This is due to the generally adopted assumption that the main contribution to the integrals expressing the cross section makes multi-Regge domains with its characteristic strong ordering of secon- dary particles by rapidity. However, in this work, we find what kind of space domains makes a major contribution to the integral and these space domains are not multi-Regge. We demonstrated that because these interference contributions are significant, so they cannot be limited by a small part of them. With the help of the approximate replacement the sum of a huge number of these contributions by the integral were calculated partial cross sections for such numbers of secondary particles for which direct calculation would be impossible. The offered model qualitative agrees with experimental dependence of total scattering cross-section on energy with a characteristic minimum in the range ≈ 10 GeV. However, quantitative agreement was not achieved; we assume that due to the fact that we have examined the simplest diagrams of theory.

We develop a new method for taking into account the interference contributions to proton-proton inelastic cross-section within the framework of the simplest multi-peripheral model based on the self-interacting scalar φ3 field theory, using Laplace’s method for calculation of each interference contribution. We do not know any works that adopted the inter- ference contributions for inelastic processes. This is due to the generally adopted assumption that the main contribution to the integrals expressing the cross section makes multi-Regge domains with its characteristic strong ordering of secon- dary particles by rapidity. However, in this work, we find what kind of space domains makes a major contribution to the integral and these space domains are not multi-Regge. We demonstrated that because these interference contributions are significant, so they cannot be limited by a small part of them. With the help of the approximate replacement the sum of a huge number of these contributions by the integral were calculated partial cross sections for such numbers of secondary particles for which direct calculation would be impossible. The offered model qualitative agrees with experimental dependence of total scattering cross-section on energy with a characteristic minimum in the range ≈ 10 GeV. However, quantitative agreement was not achieved; we assume that due to the fact that we have examined the simplest diagrams of theory.

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 3,"*Journal of Modern Physics*, Vol. 3 No. 2, 2012, pp. 129-144. doi: 10.4236/jmp.2012.32018.

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 3,"

References

[1] I. Sharf, A. Tykhonov, G. Sokhrannyi, M. Deliyergiyev, N. Podolyan and V. Rusov, “Mechanisms of Proton-Pro- ton Inelastic Cross-Section Growth in Multi-Peripheral Mo- del within the Framework of Perturbation Theory. Part 1,” Journal of Modern Physics, Vol. 2, No. 12, 2011, pp. 1480-1506. arXiv:0605110[hep-ph].

[2] I. Sharf, A. Tykhonov, G. Sokhrannyi, M. Deliyergiyev, N. Podolyan and V. Rusov, “Mechanisms of Proton-Pro- ton Inelastic Cross-Section Growth in Multi-Peripheral Mo- del within the Framework of Perturbation Theory. Part 2,” Journal of Modern Physics, Vol. 3, No. 1, 2012, pp. 16-27. arXiv:0605110[hep-ph].

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

[4] J. Bartels, L. N. Lipatov and A. Sabio Vera, “BFKL Pomeron, Reggeized Gluons, and Bern-Dixon-Smirnov Amplitudes,” Physical Review D, Vol. 80, No. 4, 2009, Article No. 045002.

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

[6] G. S. Danilov and L. N. Lipatov, “BFKL Pomeron in String Models,” Nuclear Physics B, Vol. 754, No. 1-2, 2006, pp. 187-232.

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

[8] ATLAS Collaboration. “Measurement of the Inelastic Proton-Proton Cross-Section at sqrt{s} = 7 TeV with the ATLAS Detector,” Nature Communications, Vol. 2, 2011, Article No. 463.

[1] I. Sharf, A. Tykhonov, G. Sokhrannyi, M. Deliyergiyev, N. Podolyan and V. Rusov, “Mechanisms of Proton-Pro- ton Inelastic Cross-Section Growth in Multi-Peripheral Mo- del within the Framework of Perturbation Theory. Part 1,” Journal of Modern Physics, Vol. 2, No. 12, 2011, pp. 1480-1506. arXiv:0605110[hep-ph].

[2] I. Sharf, A. Tykhonov, G. Sokhrannyi, M. Deliyergiyev, N. Podolyan and V. Rusov, “Mechanisms of Proton-Pro- ton Inelastic Cross-Section Growth in Multi-Peripheral Mo- del within the Framework of Perturbation Theory. Part 2,” Journal of Modern Physics, Vol. 3, No. 1, 2012, pp. 16-27. arXiv:0605110[hep-ph].

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

[4] J. Bartels, L. N. Lipatov and A. Sabio Vera, “BFKL Pomeron, Reggeized Gluons, and Bern-Dixon-Smirnov Amplitudes,” Physical Review D, Vol. 80, No. 4, 2009, Article No. 045002.

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

[6] G. S. Danilov and L. N. Lipatov, “BFKL Pomeron in String Models,” Nuclear Physics B, Vol. 754, No. 1-2, 2006, pp. 187-232.

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

[8] ATLAS Collaboration. “Measurement of the Inelastic Proton-Proton Cross-Section at sqrt{s} = 7 TeV with the ATLAS Detector,” Nature Communications, Vol. 2, 2011, Article No. 463.