The standard formulation of the high-energy evolution in perturbative QCD, based on the Balitsky-Kovchegov equation, is known to suffer from severe instabilities associated with radiative corrections enhanced by double transverse logarithms, which occur in all orders starting with the next-to-leading one. Over the last years, several methods have been devised to resum such corrections by enforcing the time-ordering of the successive gluon emissions. We observe that the instability problem is not fully cured by these methods: various prescriptions for performing the resummation lead to very different physical results and thus lack of predictive power. We argue that this problem can be avoided by using the rapidity of the dense target (which corresponds to Bjorken x) instead of that of the dilute projectile as an evolution time. This automatically ensures the proper time-ordering and also allows for a direct physical interpretation of the results. We explicitly perform this change of variables at NLO. We observe the emergence of a new class of double logarithmic corrections, potentially leading to instabilities, which are however less severe, since disfavoured by the typical BK evolution for “dilute-dense” scattering. We propose several prescriptions for resumming these new double-logarithms to all orders and find only little scheme dependence: different prescriptions lead to results which are consistent to each other to the accuracy of interest. We restore full NLO accuracy by completing one of the resummed equations (non-local in rapidity) with the remaining NLO corrections.
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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].
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].
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. 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. Ferreiro, E. Iancu, A. Leonidov and L. McLerran, Nonlinear gluon evolution in the color glass condensate: II, Nucl. Phys.A 703 (2002) 489 [hep-ph/0109115] [INSPIRE].
Y.V. Kovchegov, Small x F2structure 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].
I.I. Balitsky and L.N. Lipatov, The Pomeranchuk Singularity in Quantum Chromodynamics, Sov. J. Nucl. Phys.28 (1978) 822 [INSPIRE].Google Scholar
J. Kwiecinski, A.D. Martin and A.M. Stasto, A Unified BFKL and GLAP description of F2data, Phys. Rev.D 56 (1997) 3991 [hep-ph/9703445] [INSPIRE].
G.P. Salam, A Resummation of large subleading corrections at small x, JHEP07 (1998) 019 [hep-ph/9806482] [INSPIRE].
M. Ciafaloni and D. Colferai, The BFKL equation at next-to-leading level and beyond, Phys. Lett.B 452 (1999) 372 [hep-ph/9812366] [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].
A. Sabio Vera, An ‘All-poles’ approximation to collinear resummations in the Regge limit of perturbative QCD, Nucl. Phys.B 722 (2005) 65 [hep-ph/0505128] [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].
J.L. Albacete, Resummation of double collinear logs in BK evolution versus HERA data, Nucl. Phys.A 957 (2017) 71 [arXiv:1507.07120] [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].
A.M. Stasto, K.J. Golec-Biernat and J. Kwiecinski, Geometric scaling for the total γ∗p cross-section in the low x region, Phys. Rev. Lett.86 (2001) 596 [hep-ph/0007192] [INSPIRE].
E. Iancu, K. Itakura and L. McLerran, Geometric scaling above the saturation scale, Nucl. Phys.A 708 (2002) 327 [hep-ph/0203137] [INSPIRE].
A.H. Mueller and D.N. Triantafyllopoulos, The Energy dependence of the saturation momentum, Nucl. Phys.B 640 (2002) 331 [hep-ph/0205167] [INSPIRE].
S. Munier and R.B. Peschanski, Geometric scaling as traveling waves, Phys. Rev. Lett.91 (2003) 232001 [hep-ph/0309177] [INSPIRE].
S. Munier and R.B. Peschanski, Traveling wave fronts and the transition to saturation, Phys. Rev.D 69 (2004) 034008 [hep-ph/0310357] [INSPIRE].
G.P. Salam, An Introduction to leading and next-to-leading BFKL, Acta Phys. Polon.B 30 (1999) 3679 [hep-ph/9910492] [INSPIRE].