Abstract
It is well known that the high-energy scattering of a meson from some hadronic target can be described by the interaction of that target with a color dipole formed by two Wilson lines corresponding to the fast quark-antiquark pair. Moreover, the energy dependence of the scattering amplitude is governed by the evolution equation of this color dipole with respect to rapidity. Similarly, the energy dependence of scattering of a baryon can be described in terms of evolution of a three-Wilson-line operator with respect to the rapidity of the Wilson lines. We calculated the evolution of the 3-quark Wilson loop operator in the Next-to-Leading Order (NLO), and we presented a quasi-conformal evolution equation for a composite 3-Wilson-line operator. Futhermore, we obtained the linearized version of that evolution equation describing the amplitude of the odderon exchange at high energies.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
I. Balitsky, Operator expansion for high-energy scattering, Nucl. Phys. B 463 (1996) 99 [hep-ph/9509348] [INSPIRE].
A. Kovner, M. Lublinsky and Y. Mulian, NLO JIMWLK evolution unabridged, JHEP 08 (2014) 114 [arXiv:1405.0418] [INSPIRE].
I. Balitsky, High-energy amplitudes in the next-to-leading order, arXiv:1004.0057 [INSPIRE].
J. Jalilian-Marian, A. Kovner, A. Leonidov and H. Weigert, The BFKL equation from the Wilson renormalization group, Nucl. Phys. B 504 (1997) 415 [hep-ph/9701284] [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].
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].
A. Kovner, J.G. Milhano and H. Weigert, Relating different approaches to nonlinear QCD evolution at finite gluon density, Phys. Rev. D 62 (2000) 114005 [hep-ph/0004014] [INSPIRE].
H. Weigert, Unitarity at small Bjorken x, Nucl. Phys. A 703 (2002) 823 [hep-ph/0004044] [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. Ferreiro, E. Iancu, A. Leonidov and L. McLerran, Nonlinear gluon evolution in the color glass condensate. 2, Nucl. Phys. A 703 (2002) 489 [hep-ph/0109115] [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].
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].
E.A. Kuraev, L.N. Lipatov and V.S. Fadin, Multi-Reggeon processes in the Yang-Mills theory, Sov. Phys. JETP 44 (1976) 443 [Erratum ibid. 45 (1977) 199] [Zh. Eksp. Teor. Fiz. 71 (1976) 840] [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, 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].
I. Balitsky and G.A. Chirilli, Next-to-leading order evolution of color dipoles, Phys. Rev. D 77 (2008) 014019 [arXiv:0710.4330] [INSPIRE].
I. Balitsky and G.A. Chirilli, NLO evolution of color dipoles in N = 4 SYM, Nucl. Phys. B 822 (2009) 45 [arXiv:0903.5326] [INSPIRE].
I. Balitsky and G.A. Chirilli, Rapidity evolution of Wilson lines at the next-to-leading order, Phys. Rev. D 88 (2013) 111501 [arXiv:1309.7644] [INSPIRE].
A. Kovner, M. Lublinsky and Y. Mulian, Jalilian-Marian, Iancu, McLerran, Weigert, Leonidov, Kovner evolution at next to leading order, Phys. Rev. D 89 (2014) 061704 [arXiv:1310.0378] [INSPIRE].
J. Bartels, High-energy behavior in a non-Abelian gauge theory. 2. First corrections to T (n → m) beyond the leading LNS approximation, Nucl. Phys. B 175 (1980) 365 [INSPIRE].
J. Kwiecinski and M. Praszalowicz, Three gluon integral equation and odd c singlet Regge singularities in QCD, Phys. Lett. B 94 (1980) 413 [INSPIRE].
Y. Hatta, E. Iancu, K. Itakura and L. McLerran, Odderon in the color glass condensate, Nucl. Phys. A 760 (2005) 172 [hep-ph/0501171] [INSPIRE].
R.E. Gerasimov and A.V. Grabovsky, Evolution equation for 3-quark Wilson loop operator, JHEP 04 (2013) 102 [arXiv:1212.1681] [INSPIRE].
A.V. Grabovsky, Connected contribution to the kernel of the evolution equation for 3-quark Wilson loop operator, JHEP 09 (2013) 141 [arXiv:1307.5414] [INSPIRE].
M. Praszalowicz and A. Rostworowski, Problems with proton in the QCD dipole picture, Acta Phys. Polon. B 29 (1998) 745 [hep-ph/9712313] [INSPIRE].
J. Bartels and L. Motyka, Baryon scattering at high energies: wave function, impact factor and gluon radiation, Eur. Phys. J. C 55 (2008) 65 [arXiv:0711.2196] [INSPIRE].
J. Bartels, V.S. Fadin, L.N. Lipatov and G.P. Vacca, NLO corrections to the kernel of the BKP-equations, Nucl. Phys. B 867 (2013) 827 [arXiv:1210.0797] [INSPIRE].
A. Kovner, M. Lublinsky and Y. Mulian, NLO JIMWLK evolution unabridged, JHEP 08 (2014) 114 [arXiv:1405.0418] [INSPIRE].
I. Balitsky and G.A. Chirilli, Photon impact factor in the next-to-leading order, Phys. Rev. D 83 (2011) 031502 [arXiv:1009.4729] [INSPIRE].
I. Balitsky and G.A. Chirilli, Photon impact factor and k T -factorization for DIS in the next-to-leading order, Phys. Rev. D 87 (2013) 014013 [arXiv:1207.3844] [INSPIRE].
V.S. Fadin, R. Fiore and A.V. Grabovsky, Matching of the low-x evolution kernels, Nucl. Phys. B 831 (2010) 248 [arXiv:0911.5617] [INSPIRE].
A. Kovner, M. Lublinsky and Y. Mulian, Conformal symmetry of JIMWLK evolution at NLO, JHEP 04 (2014) 030 [arXiv:1401.0374] [INSPIRE].
V.S. Fadin, R. Fiore, A.V. Grabovsky and A. Papa, Connection between complete and Moebius forms of gauge invariant operators, Nucl. Phys. B 856 (2012) 111 [arXiv:1109.6634] [INSPIRE].
V.S. Fadin, R. Fiore and A.V. Grabovsky, On the discrepancy of the low-x evolution kernels, Nucl. Phys. B 820 (2009) 334 [arXiv:0904.0702] [INSPIRE].
V.S. Fadin and A. Papa, A proof of fulfillment of the strong bootstrap condition, Nucl. Phys. B 640 (2002) 309 [hep-ph/0206079] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1405.0443
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Balitsky, I., Grabovsky, A.V. NLO evolution of 3-quark Wilson loop operator. J. High Energ. Phys. 2015, 9 (2015). https://doi.org/10.1007/JHEP01(2015)009
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP01(2015)009