Abstract
To sum high-energy leading logarithms in a consistent way, one has to impose the strong ordering in both projectile rapidity and dense target rapidity simultaneously, which results in a kinematically improved Balitsky-Kovchegov (BK) equation. We find that beyond this strong ordering region, the important sub-leading double logarithms arise at high order due to the incomplete cancellation between real corrections and virtual corrections in a t-channel calculation. Based on this observation, we further argue that these double logarithms are the Sudakov type ones, and thus can be resummed into an exponential leading to a Sudakov suppressed BK equation.
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].
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].
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].
Y.V. Kovchegov, Small-x F2 structure function of a nucleus including multiple Pomeron exchanges, Phys. Rev. D 60 (1999) 034008 [hep-ph/9901281] [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, 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].
T. Lappi and H. Mäntysaari, Direct numerical solution of the coordinate space Balitsky-Kovchegov equation at next to leading order, Phys. Rev. D 91 (2015) 074016 [arXiv:1502.02400] [INSPIRE].
E.A. Kuraev, L.N. Lipatov and V.S. Fadin, The Pomeranchuk Singularity in Nonabelian 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].
G.P. Salam, A Resummation of large subleading corrections at small x, JHEP 07 (1998) 019 [hep-ph/9806482] [INSPIRE].
M. Ciafaloni, D. Colferai and G.P. Salam, Renormalization group improved small x equation, Phys. Rev. D 60 (1999) 114036 [hep-ph/9905566] [INSPIRE].
M. Ciafaloni, D. Colferai, G.P. Salam and A.M. Stasto, Renormalization group improved small x Green’s function, Phys. Rev. D 68 (2003) 114003 [hep-ph/0307188] [INSPIRE].
G. Altarelli, R.D. Ball and S. Forte, Perturbatively stable resummed small x evolution kernels, Nucl. Phys. B 742 (2006) 1 [hep-ph/0512237] [INSPIRE].
M. Ciafaloni, D. Colferai, G.P. Salam and A.M. Stasto, A Matrix formulation for small-x singlet evolution, JHEP 08 (2007) 046 [arXiv:0707.1453] [INSPIRE].
K. Kutak, K. Golec-Biernat, S. Jadach and M. Skrzypek, Nonlinear equation for coherent gluon emission, JHEP 02 (2012) 117 [arXiv:1111.6928] [INSPIRE].
G. Beuf, Improving the kinematics for low-x QCD evolution equations in coordinate space, Phys. Rev. D 89 (2014) 074039 [arXiv:1401.0313] [INSPIRE].
E. Iancu, J.D. Madrigal, A.H. Mueller, G. Soyez and D.N. Triantafyllopoulos, Resumming double logarithms in the QCD evolution of color dipoles, Phys. Lett. B 744 (2015) 293 [arXiv:1502.05642] [INSPIRE].
E. Iancu, J.D. Madrigal, A.H. Mueller, G. Soyez and D.N. Triantafyllopoulos, Collinearly-improved BK evolution meets the HERA data, Phys. Lett. B 750 (2015) 643 [arXiv:1507.03651] [INSPIRE].
T. Lappi and H. Mäntysaari, Next-to-leading order Balitsky-Kovchegov equation with resummation, Phys. Rev. D 93 (2016) 094004 [arXiv:1601.06598] [INSPIRE].
B. Ducloué, E. Iancu, A.H. Mueller, G. Soyez and D.N. Triantafyllopoulos, Non-linear evolution in QCD at high-energy beyond leading order, JHEP 04 (2019) 081 [arXiv:1902.06637] [INSPIRE].
A.H. Mueller, B.-W. Xiao and F. Yuan, Sudakov Resummation in Small-x Saturation Formalism, Phys. Rev. Lett. 110 (2013) 082301 [arXiv:1210.5792] [INSPIRE].
A.H. Mueller, B.-W. Xiao and F. Yuan, Sudakov double logarithms resummation in hard processes in the small-x saturation formalism, Phys. Rev. D 88 (2013) 114010 [arXiv:1308.2993] [INSPIRE].
J. Zhou, The evolution of the small x gluon TMD, JHEP 06 (2016) 151 [arXiv:1603.07426] [INSPIRE].
B.-W. Xiao, F. Yuan and J. Zhou, Transverse Momentum Dependent Parton Distributions at Small-x, Nucl. Phys. B 921 (2017) 104 [arXiv:1703.06163] [INSPIRE].
J. Zhou, Scale dependence of the small x transverse momentum dependent gluon distribution, Phys. Rev. D 99 (2019) 054026 [arXiv:1807.00506] [INSPIRE].
L. Zheng, E.C. Aschenauer, J.H. Lee and B.-W. Xiao, Probing Gluon Saturation through Dihadron Correlations at an Electron-Ion Collider, Phys. Rev. D 89 (2014) 074037 [arXiv:1403.2413] [INSPIRE].
A. van Hameren, P. Kotko, K. Kutak and S. Sapeta, Small-x dynamics in forward-central dijet decorrelations at the LHC, Phys. Lett. B 737 (2014) 335 [arXiv:1404.6204] [INSPIRE].
A. van Hameren, P. Kotko, K. Kutak and S. Sapeta, Broadening and saturation effects in dijet azimuthal correlations in p-p and p-Pb collisions at \( \sqrt{s} \) = 5.02 TeV, Phys. Lett. B 795 (2019) 511 [arXiv:1903.01361] [INSPIRE].
D. Boer, P.J. Mulders, J. Zhou and Y.-j. Zhou, Suppression of maximal linear gluon polarization in angular asymmetries, JHEP 10 (2017) 196 [arXiv:1702.08195] [INSPIRE].
H. Dong, D.-X. Zheng and J. Zhou, Sea quark Sivers distribution, Phys. Lett. B 788 (2019) 401 [arXiv:1805.09479] [INSPIRE].
I. Balitsky and A. Tarasov, Rapidity evolution of gluon TMD from low to moderate x, JHEP 10 (2015) 017 [arXiv:1505.02151] [INSPIRE].
I. Balitsky and A. Tarasov, Gluon TMD in particle production from low to moderate x, JHEP 06 (2016) 164 [arXiv:1603.06548] [INSPIRE].
I. Balitsky and G.A. Chirilli, Conformal invariance of transverse-momentum dependent parton distributions rapidity evolution, Phys. Rev. D 100 (2019) 051504(R) [arXiv:1905.09144] [INSPIRE].
S. Marzani, Combining QT and small-x resummations, Phys. Rev. D 93 (2016) 054047 [arXiv:1511.06039] [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].
L.D. McLerran and R. Venugopalan, Gluon distribution functions for very large nuclei at small transverse momentum, Phys. Rev. D 49 (1994) 3352 [hep-ph/9311205] [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].
V.V. Sudakov, Vertex parts at very high-energies in quantum electrodynamics, Sov. Phys. JETP 3 (1956) 65 [Zh. Eksp. Teor. Fiz. 30 (1956) 87] [INSPIRE].
J.M. Cornwall and G. Tiktopoulos, Infrared Behavior of Nonabelian Gauge Theories, Phys. Rev. D 13 (1976) 3370 [INSPIRE].
V.V. Belokurov and N.I. Usyukina, On Exponentiation Of The Singlet Quark Form-Factor In The Leading Logarithm Approximation, Phys. Lett. B 94 (1980) 251 [INSPIRE].
A. Sen, Asymptotic Behavior of the Sudakov Form-Factor in QCD, Phys. Rev. D 24 (1981) 3281 [INSPIRE].
J.C. Collins, Foundations of perturbative QCD, Cambridge University Press, Cambridge U.K. (2011).
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1906.06825
Rights and permissions
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.
About this article
Cite this article
Zheng, Dx., Zhou, J. Sudakov suppression of the Balitsky-Kovchegov kernel. J. High Energ. Phys. 2019, 177 (2019). https://doi.org/10.1007/JHEP11(2019)177
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2019)177