Abstract
The paper presents short historical reviews of the processes of lepton pairs production in peripheral interaction of leptons and ions at high energies. The orders of magnitude of the QED and QCD cross sections with the production of two and three jets are given. The technique of the analysis is described in detail based on the parameterization of Sudakov 4-momentum tasks and writing the amplitude in an explicit gaugeinvariant form.
Based on this formalism the differential cross sections of QCD processes \(gp \to (ggg)p;qp \to (q\bar QQ)p;gp \to (gQ\bar Q)P\) were obtained, including the distribution on transverse momentum component of jets fragments. It was shown that the role of the contribution of “non-Abelian” nature may become dominant in a particular kinematics of the final particles. The kinematics, in which the initial particle changes the direction of movement to the opposite one, was considered in the case of heavy quark-antiquark pair production.
In the appendices, the details of the calculations and the explicit form of the differential cross sections are given. Some extended comments on the frequently used cross sections of the pair production in the case of two-photon scattering are presented. In particular, the degree of the longitudinal polarization of the positron, the interaction polarized initial electron, was calculated. The method of calculating the cross sections of the 2 → 2 processes in QCD, based on the isolation of irreducible color structures and the method CALCUL of spiral amplitudes, was discussed in detail.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
V. G. Gorshkov, “Electrodynamic processes in colliding beams of high-energy particles,” Sov. Phys. Usp. 16, 322–338 (1973).
A. I. Akhiezer and V. B. Berestetskii, Quantum Electrodynamics (Nauka, M., 1981).
V. B. Berestetskii, E. M. Lifshits, and L. P. Pitaevskii, Quantum Electrodynamics (Nauka, M., 1980).
V. N. Baier, V. Katkov, and V. S. Fadin, Emission of Relativistic Electrons (Atomizdat, M., 1973).
N. N. Bogoljubov and D. V. Shirkov, Introduction to the Theory of Quantum Fields (Nauka, M., 1973).
C. Itzykson and J.-B. Zuber, Quantum Field Theory (New York, 1980).
C. Weizsäcker, “Radiation emitted in collisions of very fast electrons,” Zs. f. Phys. 88, 612 (1934); E. Williams, “Nature of the high-energy particles of penetrating radiation and status of ionization and radiation formulae,” Phys. Rev. 45, 729 (1934).
L. Landau and E. Lifshitz, “On the production of electrons and positrons by a collision of two particles,” Phys. Zeitschrift der Sowietunion. 6, 244 (1934).
G. Racah, “On pair production through charged particle collisions,” Nuovo Cimento. 14, 93 (1937).
V. N. Baier and V. S. Fadin, “Quasireal photon approximation for describing electroproduction processes,” Zh. Eksp. Teor. Fiz. 63, 761 (1972); Sov. Phys. JETP. 36, 399 (1973).
E. A. Kuraev and L. N. Lipatov, “Creation of electron and muon pairs in colliding e − e − and e + e − beams,” Yad. Fiz. 16, 1060 (1972).
S. Brodsky, T. Kinoshita, and H. Terazawa, “Two photon mechanism of particle production by high-energy colliding beams,” Phys. Rev. D 4, 1532 (1971); “Dominant colliding beam cross-sections at high-energies,” Phys. Rev. Lett. 25, 972 (1970).
V. N. Baier, et al., “Inelastic processes in quantum electrodynamics at high-energies,” Phys. Rep. 78, 293 (1981).
V. Budnev, et al., “The two photon particle production mechanism. Physical problems. Applications. Equivalent photon approximation,” Phys. Rep. C 15, 181 (1975).
J. Motz, H. Olsen, and H. Koch, “Pair production by photons,” Rev. Mod. Phys. 41, 581 (1969).
E. A. Kuraev and L. N. Lipatov, “Bremsstrahlung mechanism of e + e − and mu+mu − pair production in electron colliding beams,” Yad. Fiz. 20, 112 (1974).
E. A. Kuraev, L. N. Lipatov, and M. I. Strikman, “Identity of electrons in the final state in pair production in colliding e + e − beams,” Yad. Fiz. 18, 1270 (1973).
V. Sudakov, “Vertex parts at very high-energies in quantum electrodynamics,” Zh. Eksp. Teor. Phys. 30, 87 (1956); A. Arbuzov, et al., “Peripherical processes in QED at high energies,” Phys. Part. Nucl. 41, 593 (2010).
V. I. Borodulin, R. N. Rogalev, and S. R. Slabospitsky, “CORE: COmpendium of RElations: Version 2.1,” hep-ph/9507456.
F. A. Berends, et al., “Multiple bremsstrahlung in gauge theories at high-energies. 2. Single bremsstrahlung,” Nucl. Phys. B 206, 61 (1982).
E. A. Kuraev, et al., “Double bremsstrahlung in the same direction in e + e − colliding beams,” Yad. Fyz. 19, 331 (1974).
J. J. Marian and Yu. V. Kovchegov, “Inclusive two-gluon and valence quark-gluon production in DIS and pA,” Phys. Rev. D 70, 114017 (2004); [Erratum-ibid. D 71, 079901 (2005)].
H. Fujii and K. Watanabe, “Heavy quark pair production in high energy pA collisions: Open heavy flavors,” Nucl. Phys. A 920, 78 (2013); arXiv: 1308.1258 [hep-ph].
K. Mork and H. Olsen, “Radiative corrections. 1. High-energy bremsstrahlung and pair production,” Phys. Rev. 140, B1661 (1965).
F. Mandl and T. H. R. Skyrme, “The theory of the double Compton effect,” Proc. Roy. Soc. 215, 497 (1952).
I. B. Khriplovich, Private communication, 1976.
E. A. Kuraev, S. Bakmaev, E. S. Kokoulina, “Azimuthal correlation of gluon jets created in proton-antiproton annihilation,” Nucl. Phys. B 851, 551 (2011).
D. Benaksas and R. Morrison, “Electron triplets and pairs observed in a streamer chamber,” Phys. Rev. 160, 1245 (1967).
J. Beringer, et al., “Particle data group,” Phys. Rev. D 86, 010001 (2012).
N. Kidonakis and J. Owens, “Effects of higher order threshold corrections in high E(T) jet production,” Phys. Rev. D 63, 054019 (2001).
A. Macfarlane, A. Sudbery, and P. Weisz, “On Gell-Mann’s lambda-matrices, d- and f-tensors, octets, and parametrizations of SU(3),” Comm. Math. Phys. 11, 77 (1968).
Author information
Authors and Affiliations
Corresponding author
Additional information
The article is published in the original.
Rights and permissions
About this article
Cite this article
Ahmadov, A.I., Kuraev, E.A. Jets production in peripheral interactions of high energy leptons, quarks, photons, and gluons with the proton. Phys. Part. Nuclei 45, 1033–1059 (2014). https://doi.org/10.1134/S1063779614060021
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1063779614060021