Mechanisms of Proton-Proton Inelastic Cross-Section Growth in Multi-Peripheral Model within the Framework of Perturbation Theory. Part 1

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

ABSTRACT

We demonstrate a possibility of computation of inelastic scattering cross-section in a multi-peripheral model by application of the Laplace method to multidimensional integral over the domain of physical process. Founded the constrained maximum point of scattering cross-section integral under condition of the energy-momentum conservation. The integrand is substituted for an expression of Gaussian type in the neighborhood of this point. It made possible to compute this integral numerically. The paper has two parts. The hunting procedure of the constrained maximum point is considered and the properties of this maximum point are discussed in the given part of the paper. It is shown that virtuality of all internal lines of the “comb” diagram reduced at the constrained maximum point with energy growth. In the second part of the paper we give some the arguments in favor of consideration of the mechanism of virtuality reduction as the mechanism of the total hadron scattering cross-section growth, which is not taken into account within the framework of Regge theory.

We demonstrate a possibility of computation of inelastic scattering cross-section in a multi-peripheral model by application of the Laplace method to multidimensional integral over the domain of physical process. Founded the constrained maximum point of scattering cross-section integral under condition of the energy-momentum conservation. The integrand is substituted for an expression of Gaussian type in the neighborhood of this point. It made possible to compute this integral numerically. The paper has two parts. The hunting procedure of the constrained maximum point is considered and the properties of this maximum point are discussed in the given part of the paper. It is shown that virtuality of all internal lines of the “comb” diagram reduced at the constrained maximum point with energy growth. In the second part of the paper we give some the arguments in favor of consideration of the mechanism of virtuality reduction as the mechanism of the total hadron scattering cross-section growth, which is not taken into account within the framework of Regge theory.

KEYWORDS

Inelastic Scattering Cross-Section, Total Scattering Cross-Section, Laplace Method, Virtuality, Multi-Peripheral Model, Regge Theory

Inelastic Scattering Cross-Section, Total Scattering Cross-Section, Laplace Method, Virtuality, Multi-Peripheral Model, Regge Theory

Cite this paper

nullI. 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 1,"*Journal of Modern Physics*, Vol. 2 No. 12, 2011, pp. 1480-1506. doi: 10.4236/jmp.2011.212182.

nullI. 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 1,"

References

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[1] D. Amati, A. Stanghellini and S. Fubini, “Theory of High- Energy Scattering and Multiple Production,” Il Nuovo Cimento, Vol. 26, No. 5, 1962, pp. 896-954. doi:10.1007/BF02781901

[2] E. Byckling and Keijo Kajantie. “Particle Kinematics,” Wiley, London, 1973.

[3] P. D. B. Collins, “An Introduction to Regge Theory and High Energy Physics,” Cambridge University Press, Cam- bridge, 1977. doi:10.1017/CBO9780511897603

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

[5] Y. P. Nikitin and I. L. Rozental, “Theory of Multiparticle Production Processes,” Studies in High Energy Physics, (Harwood, Chur, 1988) transl. from the Russian.

[6] E. M. Levin and M. G. Ryskin, “Multiplicity Distribution in the Multiperipheral Model,” Yadernaya Fizika, Vol. 19, 1974, pp. 669-681.

[7] E. M. Levin and M. G. Ryskin, “The Increase in the Total Cross Sections for Hadronic Interactions with Increasing Energy,” Physics-Uspekh Vol. 32, pp. 479- 499.

[8] K. A. Ter-Martirosyan. “Results of Regge Scheme Development and Experiment,” MIPHI, Moscow, 1975.

[9] 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.

[10] L. N. Lipatov, “Bjorken and Regge Asymptotics of Scat- tering Amplitudes in QCD and in Supersymmetric Gauge Models,” Physics-Uspekhi, Vol. 178, No. 6, 2008, pp. 663-668.

[11] N. G. De Bruijn, “Asymptotic Methods in Analysis,” North-Holland, Amsterdam, 1958.

[12] B. Maxfield, “Essential Mathcad for Engineering, Science and Math,” Academic Press, Boston, 2009.

[13] Mathcad Official Website, http://www.ptc.com/appserver/mkt/products/home.jsp?k=3901

[14] L. N. Lipatov, “Integrability Properties of High Energy Dynamics in Multi-Color QCD,” Physics-Uspekhi, Vol. 174, Vol. 47, No. 4, 2004, pp. 337-352.

[15] M. Baker and K. A. Ter-Martirosyan, “Gribov’s Reggeon Calculus: Its Physical Basis and Implications,” Physics Reports, Vol. 28, No. 1, 1976, pp. 1-143. doi:10.1016/0370-1573(76)90002-8

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