Abstract
We calculate the classical single-gluon production amplitude in nucleus-nucleus collisions including the first saturation correction in one of the nuclei (the projectile) while keeping multiple-rescattering (saturation) corrections to all orders in the other nucleus (the target). In our approximation only two nucleons interact in the projectile nucleus: the single-gluon production amplitude we calculate is order-g 3 and is leading-order in the atomic number of the projectile, while resumming all order-one saturation corrections in the target nucleus. Our result is the first step towards obtaining an analytic expression for the first projectile saturation correction to the gluon production cross section in nucleus-nucleus collisions.
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L.V. Gribov, E.M. Levin and M.G. Ryskin, Semihard processes in QCD, Phys. Rept. 100 (1983) 1 [INSPIRE].
E. Iancu and R. Venugopalan, The color glass condensate and high-energy scattering in QCD, hep-ph/0303204 [INSPIRE].
J. Jalilian-Marian and Y.V. Kovchegov, Saturation physics and deuteron-gold collisions at RHIC, Prog. Part. Nucl. Phys. 56 (2006) 104 [hep-ph/0505052] [INSPIRE].
H. Weigert, Evolution at small x bj : the color glass condensate, Prog. Part. Nucl. Phys. 55 (2005) 461 [hep-ph/0501087] [INSPIRE].
F. Gelis, E. Iancu, J. Jalilian-Marian and R. Venugopalan, The color glass condensate, Ann. Rev. Nucl. Part. Sci. 60 (2010) 463 [arXiv:1002.0333] [INSPIRE].
J.L. Albacete and C. Marquet, Gluon saturation and initial conditions for relativistic heavy ion collisions, Prog. Part. Nucl. Phys. 76 (2014) 1 [arXiv:1401.4866] [INSPIRE].
I. Balitsky, High-energy QCD and Wilson lines, hep-ph/0101042 [INSPIRE].
Y.V. Kovchegov and E. Levin, Quantum chromodynamics at high energy, Cambridge University Press, Cambridge U.K. (2012).
A. Kovner, L.D. McLerran and H. Weigert, Gluon production at high transverse momentum in the McLerran-Venugopalan model of nuclear structure functions, Phys. Rev. D 52 (1995) 3809 [hep-ph/9505320] [INSPIRE].
A. Kovner, L.D. McLerran and H. Weigert, Gluon production from non-Abelian Weizsacker-Williams fields in nucleus-nucleus collisions, Phys. Rev. D 52 (1995) 6231 [hep-ph/9502289] [INSPIRE].
Y.V. Kovchegov, Non-Abelian Weizsacker-Williams field and a two-dimensional effective color charge density for a very large nucleus, Phys. Rev. D 54 (1996) 5463 [hep-ph/9605446] [INSPIRE].
Y.V. Kovchegov and D.H. Rischke, Classical gluon radiation in ultrarelativistic nucleus-nucleus collisions, Phys. Rev. C 56 (1997) 1084 [hep-ph/9704201] [INSPIRE].
J. Jalilian-Marian, A. Kovner, L.D. McLerran and H. Weigert, The intrinsic glue distribution at very small x, Phys. Rev. D 55 (1997) 5414 [hep-ph/9606337] [INSPIRE].
L.D. McLerran and R. Venugopalan, Green’s functions in the color field of a large nucleus, Phys. Rev. D 50 (1994) 2225 [hep-ph/9402335] [INSPIRE].
L.D. McLerran and R. Venugopalan, Gluon distribution functions for very large nuclei at small transverse momentum, Phys. Rev. D 49 (1994) 33512 [hep-ph/9311205] [INSPIRE].
L.D. McLerran and R. Venugopalan, Computing quark and gluon distribution functions for very large nuclei, Phys. Rev. D 49 (1994) 2233 [hep-ph/9309289] [INSPIRE].
Y.V. Kovchegov, Quantum structure of the non-Abelian Weizsacker-Williams field for a very large nucleus, Phys. Rev. D 55 (1997) 5445 [hep-ph/9701229] [INSPIRE].
A. Krasnitz and R. Venugopalan, Nonperturbative computation of gluon minijet production in nuclear collisions at very high-energies, Nucl. Phys. B 557 (1999) 237 [hep-ph/9809433] [INSPIRE].
A. Krasnitz and R. Venugopalan, The initial energy density of gluons produced in very high-energy nuclear collisions, Phys. Rev. Lett. 84 (2000) 4309 [hep-ph/9909203] [INSPIRE].
A. Krasnitz, Y. Nara and R. Venugopalan, Gluon production in the color glass condensate model of collisions of ultrarelativistic finite nuclei, Nucl. Phys. A 717 (2003) 268 [hep-ph/0209269] [INSPIRE].
A. Krasnitz, Y. Nara and R. Venugopalan, Classical gluodynamics of high-energy nuclear collisions: an erratum and an update, Nucl. Phys. A 727 (2003) 427 [hep-ph/0305112] [INSPIRE].
A. Krasnitz, Y. Nara and R. Venugopalan, Probing a color glass condensate in high energy heavy ion collisions, Braz. J. Phys. 33 (2003) 223 [INSPIRE].
T. Lappi, Production of gluons in the classical field model for heavy ion collisions, Phys. Rev. C 67 (2003) 054903 [hep-ph/0303076] [INSPIRE].
J.-P. Blaizot, T. Lappi and Y. Mehtar-Tani, On the gluon spectrum in the glasma, Nucl. Phys. A 846 (2010) 63 [arXiv:1005.0955] [INSPIRE].
E.A. Kuraev, L.N. Lipatov and V.S. Fadin, The Pomeranchuk singularity in non-Abelian gauge theories, Sov. Phys. JETP 45 (1977) 199 [Zh. Eksp. Teor. Fiz. 72 (1977) 377] [INSPIRE].
I.I. Balitsky and L.N. Lipatov, The Pomeranchuk singularity in quantum chromodynamics, Sov. J. Nucl. Phys. 28 (1978) 822 [Yad. Fiz. 28 (1978) 1597] [INSPIRE].
I. Balitsky, Operator expansion for high-energy scattering, Nucl. Phys. B 463 (1996) 99 [hep-ph/9509348] [INSPIRE].
I. Balitsky, Factorization and high-energy effective action, Phys. Rev. D 60 (1999) 014020 [hep-ph/9812311] [INSPIRE].
Y.V. Kovchegov, Small-x F 2 structure function of a nucleus including multiple Pomeron exchanges, Phys. Rev. D 60 (1999) 034008 [hep-ph/9901281] [INSPIRE].
Y.V. Kovchegov, Unitarization of the BFKL Pomeron on a nucleus, Phys. Rev. D 61 (2000) 074018 [hep-ph/9905214] [INSPIRE].
J. Jalilian-Marian, A. Kovner and H. Weigert, The Wilson renormalization group for low x physics: gluon evolution at finite parton density, Phys. Rev. D 59 (1998) 014015 [hep-ph/9709432] [INSPIRE].
J. Jalilian-Marian, A. Kovner, A. Leonidov and H. Weigert, The Wilson renormalization group for low x physics: towards the high density regime, Phys. Rev. D 59 (1998) 014014 [hep-ph/9706377] [INSPIRE].
E. Iancu, A. Leonidov and L.D. McLerran, The renormalization group equation for the color glass condensate, Phys. Lett. B 510 (2001) 133 [hep-ph/0102009] [INSPIRE].
E. Iancu, A. Leonidov and L.D. McLerran, Nonlinear gluon evolution in the color glass condensate. 1, Nucl. Phys. A 692 (2001) 583 [hep-ph/0011241] [INSPIRE].
E. Gardi, J. Kuokkanen, K. Rummukainen and H. Weigert, Running coupling and power corrections in nonlinear evolution at the high-energy limit, Nucl. Phys. A 784 (2007) 282 [hep-ph/0609087] [INSPIRE].
I. Balitsky, Quark contribution to the small-x evolution of color dipole, Phys. Rev. D 75 (2007) 014001 [hep-ph/0609105] [INSPIRE].
Y.V. Kovchegov and H. Weigert, Triumvirate of running couplings in small-x evolution, Nucl. Phys. A 784 (2007) 188 [hep-ph/0609090] [INSPIRE].
J.L. Albacete and Y.V. Kovchegov, Solving high energy evolution equation including running coupling corrections, Phys. Rev. D 75 (2007) 125021 [arXiv:0704.0612] [INSPIRE].
W.A. Horowitz and Y.V. Kovchegov, Running coupling corrections to high energy inclusive gluon production, Nucl. Phys. A 849 (2011) 72 [arXiv:1009.0545] [INSPIRE].
V.S. Fadin, E.A. Kuraev and L.N. Lipatov, On the Pomeranchuk singularity in asymptotically free theories, Phys. Lett. B 60 (1975) 50 [INSPIRE].
Y.V. Kovchegov and A.H. Mueller, Gluon production in current nucleus and nucleon-nucleus collisions in a quasiclassical approximation, Nucl. Phys. B 529 (1998) 451 [hep-ph/9802440] [INSPIRE].
B.Z. Kopeliovich, A.V. Tarasov and A. Schafer, Bremsstrahlung of a quark propagating through a nucleus, Phys. Rev. C 59 (1999) 1609 [hep-ph/9808378] [INSPIRE].
A. Dumitru and L.D. McLerran, How protons shatter colored glass, Nucl. Phys. A 700 (2002) 492 [hep-ph/0105268] [INSPIRE].
Y.V. Kovchegov, Classical initial conditions for ultrarelativistic heavy ion collisions, Nucl. Phys. A 692 (2001) 557 [hep-ph/0011252] [INSPIRE].
J.-P. Blaizot and Y. Mehtar-Tani, The classical field created in early stages of high energy nucleus-nucleus collisions, Nucl. Phys. A 818 (2009) 97 [arXiv:0806.1422] [INSPIRE].
D. Kharzeev and E. Levin, Manifestations of high density QCD in the first RHIC data, Phys. Lett. B 523 (2001) 79 [nucl-th/0108006] [INSPIRE].
D. Kharzeev and M. Nardi, Hadron production in nuclear collisions at RHIC and high density QCD, Phys. Lett. B 507 (2001) 121 [nucl-th/0012025] [INSPIRE].
J.L. ALbacete and A. Dumitru, A model for gluon production in heavy-ion collisions at the LHC with rcBK unintegrated gluon densities, arXiv:1011.5161 [INSPIRE].
Y.V. Kovchegov and K. Tuchin, Inclusive gluon production in DIS at high parton density, Phys. Rev. D 65 (2002) 074026 [hep-ph/0111362] [INSPIRE].
D. Kharzeev, Y.V. Kovchegov and K. Tuchin, Cronin effect and high p T suppression in pA collisions, Phys. Rev. D 68 (2003) 094013 [hep-ph/0307037] [INSPIRE].
A.H. Mueller, Small x behavior and parton saturation: a QCD model, Nucl. Phys. B 335 (1990) 115 [INSPIRE].
I. Balitsky, Scattering of shock waves in QCD, Phys. Rev. D 70 (2004) 114030 [hep-ph/0409314] [INSPIRE].
A.V. Belitsky, X. Ji and F. Yuan, Final state interactions and gauge invariant parton distributions, Nucl. Phys. B 656 (2003) 165 [hep-ph/0208038] [INSPIRE].
T. Liou, Color-neutral heavy particle production in nucleus-nucleus collisions in the quasi-classical approximation, Nucl. Phys. A 897 (2013) 122 [arXiv:1206.6123] [INSPIRE].
T. Liou, A.H. Mueller and B. Wu, Radiative p ⊥ -broadening of high-energy quarks and gluons in QCD matter, Nucl. Phys. A 916 (2013) 102 [arXiv:1304.7677] [INSPIRE].
G.P. Lepage and S.J. Brodsky, Exclusive processes in perturbative quantum chromodynamics, Phys. Rev. D 22 (1980) 2157 [INSPIRE].
L.V. Keldysh, Diagram technique for nonequilibrium processes, Zh. Eksp. Teor. Fiz. 47 (1964) 1515 [Sov. Phys. JETP 20 (1965) 1018] [INSPIRE].
J.S. Schwinger, Brownian motion of a quantum oscillator, J. Math. Phys. 2 (1961) 407 [INSPIRE].
F. Gelis, T. Lappi and R. Venugopalan, High energy factorization in nucleus-nucleus collisions, Phys. Rev. D 78 (2008) 054019 [arXiv:0804.2630] [INSPIRE].
A.H. Mueller and S. Munier, p T -broadening and production processes versus dipole/quadrupole amplitudes at next-to-leading order, Nucl. Phys. A 893 (2012) 43 [arXiv:1206.1333] [INSPIRE].
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Chirilli, G.A., Kovchegov, Y.V. & Wertepny, D.E. Classical gluon production amplitude for nucleus-nucleus collisions: First saturation correction in the projectile. J. High Energ. Phys. 2015, 15 (2015). https://doi.org/10.1007/JHEP03(2015)015
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DOI: https://doi.org/10.1007/JHEP03(2015)015