Abstract
In this paper we address two problems in pomeron calculus in zero transverse dimensions: the summation of the pomeron loops and the calculation of the processes of multiparticle generation. We introduce a new generating functional for these processes and obtain the evolution equation for it. We argue that in the kinematic range given by \(1 \ll\ln(1/\alpha_{\text{S}}<Superscript>2</Superscript>) \ll\alpha_{\text{S}} Y \ll\frac{1}{\alpha_{\text{S}}}\), we can reduce the pomeron calculus to the exchange of non-interacting pomerons with the renormalized amplitude of their interaction with the target. Therefore, the summation of the pomeron loops can be performed using the Mueller–Patel–Salam–Iancu approximation.
References
D. Amati, L. Caneschi, R. Jengo, Nucl. Phys. B 101, 397 (1975)
V. Alessandrini, D. Amati, R. Jengo, Nucl. Phys. B 108, 425 (1976)
R. Jengo, Nucl. Phys. B 108, 447 (1976)
D. Amati, M. Le Bellac, G. Marchesini, M. Ciafaloni, Nucl. Phys. B 112, 107 (1976)
D. Amati, G. Marchesini, M. Ciafaloni, G. Parisi, Nucl. Phys. B 114, 483 (1976)
M. Ciafaloni, M. Le Bellac, G.C. Rossi, Nucl. Phys. B 130, 388 (1977)
E. Levin, Nucl. Phys. A 763, 140 (2005) [hep-ph/0502243]
K.G. Boreskov, A.B. Kaidalov, V.A. Khoze, A.D. Martin, M.G. Ryskin, Eur. Phys. J. C 44, 523 (2005) [hep-ph/0506211]
A.I. Shoshi, B.W. Xiao, Phys. Rev. D 73, 094014 (2006) [hep-ph/0512206]
M. Kozlov, E. Levin, Nucl. Phys. A 779, 142 (2006) [hep-ph/0604039]
A.I. Shoshi, B.W. Xiao, hep-ph/0605282
J.P. Blaizot, E. Iancu, D.N. Triantafyllopoulos, hep-ph/0606253
S. Bondarenko, L. Motyka, A.H. Mueller, A.I. Shoshi, B.W. Xiao, hep-ph/0609213
M. Kozlov, V. Khachatryan, E. Levin, J. Miller, hep-ph/0610084
L.V. Gribov, E.M. Levin, M.G. Ryskin, Phys. Rep. 100, 1 (1983)
A.H. Mueller, J. Qiu, Nucl. Phys. B 268, 427 (1986)
L. McLerran, R. Venugopalan, Phys. Rev. D 49, 2233 (1994)
L. McLerran, R. Venugopalan, Phys. Rev. D 50, 2225 (1994)
L. McLerran, R. Venugopalan, Phys. Rev. D 53, 458 (1996)
L. McLerran, R. Venugopalan, Phys. Rev. D 59, 09400 (1999)
I. Balitsky, hep-ph/9509348
I. Balitsky, Phys. Rev. D 60, 014020 (1999) [hep-ph/9812311]
Y.V. Kovchegov, Phys. Rev. D 60, 034008 (1999) [hep-ph/9901281]
J. Jalilian-Marian, A. Kovner, A. Leonidov, H. Weigert, Phys. Rev. D 59, 014014 (1999) [hep-ph/9706377]
J. Jalilian-Marian, A. Kovner, A. Leonidov, H. Weigert, Nucl. Phys. B 504, 415 (1997) [hep-ph/9701284]
J. Jalilian-Marian, A. Kovner, H. Weigert, Phys. Rev. D 59, 014015 (1999) [hep-ph/9709432]
A. Kovner, J.G. Milhano, H. Weigert, Phys. Rev. D 62, 114005 (2000) [hep-ph/0004014]
E. Iancu, A. Leonidov, L.D. McLerran, Phys. Lett. B 510, 133 (2001)
E. Iancu, A. Leonidov, L.D. McLerran, hep-ph/0102009
E. Iancu, A. Leonidov, L.D. McLerran, Nucl. Phys. A 692, 583 (2001) [hep-ph/0011241]
E. Ferreiro, E. Iancu, A. Leonidov, L. McLerran, Nucl. Phys. A 703, 489 (2002) [hep-ph/0109115]
H. Weigert, Nucl. Phys. A 703, 823 (2002) [hep-ph/0004044]
E. Levin, K. Tuchin, Nucl. Phys. A 693, 787 (2001) [hep-ph/0101275]
E. Levin, K. Tuchin, Nucl. Phys. A 691, 779 (2001) [hep-ph/0012167]
E. Levin, K. Tuchin, Nucl. Phys. B 573, 833 (2000) [hep-ph/9908317]
E. Iancu, K. Itakura, L. McLerran, Nucl. Phys. A 708, 327 (2002) [hep-ph/0203137]
N. Armesto, M.A. Braun, Eur. Phys. J. C 20, 517 (2001) [hep-ph/0104038]
M. Lublinsky, Eur. Phys. J. C 21, 513 (2001) [hep-ph/0106112]
E. Levin, M. Lublinsky, Nucl. Phys. A 712, 95 (2002) [hep-ph/0207374]
E. Levin, M. Lublinsky, Eur. Phys. J. C 22, 647 (2002) [hep-ph/0108239]
M. Lublinsky, E. Gotsman, E. Levin, U. Maor, Nucl. Phys. A 696, 851 (2001) [hep-ph/0102321]
M. Lublinsky, E. Gotsman, E. Levin, U. Maor, Eur. Phys. J. C 27, 411 (2003) [hep-ph/0209074]
K. Golec-Biernat, L. Motyka, A. Stasto, Phys. Rev. D 65, 074037 (2002) [hep-ph/0110325]
E. Iancu, K. Itakura, S. Munier, Phys. Lett. B 590, 199 (2004) [hep-ph/0310338]
K. Rummukainen, H. Weigert, Nucl. Phys. A 739, 183 (2004) [hep-ph/0309306]
K. Golec-Biernat, A.M. Stasto, Nucl. Phys. B 668, 345 (2003) [hep-ph/0306279]
E. Gotsman, M. Kozlov, E. Levin, U. Maor, E. Naftali, Nucl. Phys. A 742, 55 (2004) [hep-ph/0401021]
K. Kutak, A.M. Stasto, Eur. Phys. J. C 41, 343 (2005) [hep-ph/0408117]
G. Chachamis, M. Lublinsky, A. Sabio Vera, Nucl. Phys. A 748, 649 (2005) [hep-ph/0408333]
J.L. Albacete, N. Armesto, J.G. Milhano, C.A. Salgado, U.A. Wiedemann, Phys. Rev. D 71, 014003 (2005) [hep-ph/0408216]
E. Gotsman, E. Levin, U. Maor, E. Naftali, Nucl. Phys. A 750, 391 (2005) [hep-ph/0411242]
A.H. Mueller, A.I. Shoshi, S.M.H. Wong, Nucl. Phys. B 715, 440 (2005) [hep-ph/0501088]
E. Levin, M. Lublinsky, Nucl. Phys. A 763, 172 (2005) [hep-ph/0501173]
E. Iancu, D.N. Triantafyllopoulos, Nucl. Phys. A 756, 419 (2005) [hep-ph/0411405]
E. Iancu, D.N. Triantafyllopoulos, Phys. Lett. B 610, 253 (2005) [hep-ph/0501193]
A. Kovner, M. Lublinsky, Phys. Rev. D 71, 085004 (2005) [hep-ph/0501198]
Y. Hatta, E. Iancu, L. McLerran, A. Stasto, D.N. Triantafyllopoulos, Nucl. Phys. A 764, 423 (2006) [hep-ph/0504182]
E.A. Kuraev, L.N. Lipatov, F.S. Fadin, Sov. Phys. JETP 45, 199 (1977)
Y.Y. Balitsky, L.N. Lipatov, Sov. J. Nucl. Phys. 28, 22 (1978)
J. Bartels, M. Braun, G.P. Vacca, Eur. Phys. J. C 40, 419 (2005) [hep-ph/0412218]
J. Bartels, C. Ewerz, JHEP 9909, 026 (1999) [hep-ph/9908454]
J. Bartels, M. Wusthoff, Z. Phys. C 66, 157 (1995)
A.H. Mueller, B. Patel, Nucl. Phys. B 425, 471 (1994) [hep-ph/9403256]
J. Bartels, Z. Phys. C 60, 471 (1993)
M.A. Braun, Phys. Lett. B 632, 297 (2006) [hep-ph/0512057]
M.A. Braun, hep-ph/0504002
M.A. Braun, Eur. Phys. J. C 16, 337 (2000) [hep-ph/0001268]
M.A. Braun, Phys. Lett. B 483, 115 (2000) [hep-ph/0003004]
M.A. Braun, Eur. Phys. J. C 33, 113 (2004) [hep-ph/0309293]
M.A. Braun, Eur. Phys. J. C 6, 321 (1999) [hep-ph/9706373]
M.A. Braun, G.P. Vacca, Eur. Phys. J. C 6, 147 (1999) [hep-ph/9711486]
E. Iancu, A.H. Mueller, S. Munier, Phys. Lett. B 606, 342 (2005) [hep-ph/0410018]
E. Brunet, B. Derrida, A.H. Mueller, S. Munier, cond-mat/0603160
E. Brunet, B. Derrida, A.H. Mueller, S. Munier, Phys. Rev. E 73, 056126 (2006) [cond-mat/0512021]
R. Enberg, K. Golec-Biernat, S. Munier, Phys. Rev. D 72, 074021 (2005) [hep-ph/0505101]
S. Munier, hep-ph/0608036
M. Kozlov, E. Levin, A. Prygarin, hep-ph/0606260
P. Grassberger, K. Sundermeyer, Phys. Lett. B 77, 220 (1978)
K.G. Boreskov, hep-ph/0112325 and references therein
A.H. Mueller, Nucl. Phys. B 415, 373 (1994)
A.H. Mueller, Nucl. Phys. B 437, 107 (1995)
M. Ciafaloni, G. Marchesini, Nucl. Phys. B 105, 113 (1976)
V.A. Abramovsky, V.N. Gribov, O.V. Kancheli, Yad. Fiz. 18, 595 (1973) [Sov. J. Nucl. Phys. 18, 308 (1974)]
M. Kozlov, E. Levin, V. Khachatryan, J. Miller, Nucl. Phys. A 791, 382 (2007) [hep-ph/0610084]
A.H. Mueller, B. Patel, Nucl. Phys. B 425, 471 (1994)
A.H. Mueller, G.P. Salam, Nucl. Phys. B 475, 293 (1996) [hep-ph/9605302]
G.P. Salam, Nucl. Phys. B 461, 512 (1996)
E. Iancu, A.H. Mueller, Nucl. Phys. A 730, 460 (2004) [hep-ph/0308315], [hep-ph/0309276]
Y.V. Kovchegov, E. Levin, Nucl. Phys. B 577, 221 (2000) [hep-ph/9911523]
E. Levin, M. Lublinsky, Nucl. Phys. A 730, 191 (2004) [hep-ph/0308279]
E. Levin, M. Lublinsky, Phys. Lett. B 607, 131 (2005) [hep-ph/0411121]
E. Levin, M. Lublinsky, Phys. Lett. B 521, 233 (2001) [hep-ph/0108265]
E. Levin, M. Lublinsky, Eur. Phys. J. C 22, 647 (2002) [hep-ph/0108239]
S. Bondarenko, E. Gotsman, E. Levin, U. Maor, Nucl. Phys. A 683, 649 (2001) [hep-ph/0001260]
Y.V. Kovchegov, Phys. Rev. D 72, 094009 (2005) [hep-ph/0508276]
K.G. Boreskov, A.B. Kaidalov, V.A. Khoze, A.D. Martin, M.G. Ryskin, Eur. Phys. J. C 44, 523 (2005) [hep-ph/0506211]
M. Kozlov, E. Levin, Nucl. Phys. A 739, 291 (2004) [hep-ph/0401118]
I. Gradstein, I. Ryzhik, Tables of Series, Products, and Integrals, (Verlag MIR, Moskau, 1981)
A. Kovner, M. Lublinsky, JHEP 0611, 083 (2006) [hep-ph/0609227]
A. Kovner, M. Lublinsky, H. Weigert, hep-ph/0608258
J. Jalilian-Marian, Y.V. Kovchegov, Phys. Rev. D 70, 114017 (2004)
J. Jalilian-Marian, Y.V. Kovchegov, Phys. Rev. D 71, 079901 (2005) [hep-ph/0405266]
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Levin, E., Prygarin, A. Pomeron calculus in zero transverse dimensions: Summation of pomeron loops and generating functional for multiparticle production processes. Eur. Phys. J. C 53, 385–399 (2008). https://doi.org/10.1140/epjc/s10052-007-0458-5
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DOI: https://doi.org/10.1140/epjc/s10052-007-0458-5