Eur. Phys. J. C (2015) 75:292
DOI 10.1140/epjc/s10052-015-3522-6
Regular Article - Theoretical Physics
Mueller–Navelet jets at LHC: BFKL versus high-energy DGLAP
F. G. Celiberto
1,a
, D. Yu. Ivanov
2,3,b
, B. Murdaca
1,c
, A. Papa
1,d
1
Dipartimento di Fisica, Università della Calabria, and Istituto Nazionale di Fisica Nucleare, Gruppo Collegato di Cosenza, Arcavacata di Rende,
87036 Cosenza, Italy
2
Sobolev Institute of Mathematics, 630090 Novosibirsk, Russia
3
Novosibirsk State University, 630090 Novosibirsk, Russia
Received: 5 May 2015 / Accepted: 10 June 2015 / Published online: 26 June 2015
© The Author(s) 2015. This article is published with open access at Springerlink.com
Abstract The production of forward jets separated by a
large rapidity gap at LHC, the so-called Mueller–Navelet
jets, is a fundamental testfield for perturbative QCD in the
high-energy limit. Several analyses have already provided us
with evidence about the compatibility of theoretical predic-
tions, based on collinear factorization and BFKL resumma-
tion of energy logarithms in the next-to-leading approxima-
tion, with the CMS experimental data at 7 TeV of center-
of-mass energy. However, the question if the same data can
be described also by fixed-order perturbative approaches has
not yet been fully answered. In this paper we provide numer-
ical evidence that the mere use of partially asymmetric cuts
in the transverse momenta of the detected jets allows for a
clear separation between BFKL-resummed and fixed-order
predictions in some observables related with the Mueller–
Navelet jet production process.
1 Introduction
It is widely believed now that the inclusive hadroproduction
of two jets featuring transverse momenta of the same order
and much larger than the typical hadronic masses and being
separated by a large rapidity gap Y , the so-called Mueller–
Navelet jets [1], is a fundamental testfield for perturbative
QCD in the high-energy limit, the jet transverse momenta
providing us with the hard scales of the process.
At the LHC energies, the theoretical description of this
process lies at the crossing point of two distinct approaches:
collinear factorization and BFKL [2–5] resummation. On one
side, at leading twist the process can be seen as the hard scat-
tering of two partons, each emitted by one of the colliding
a
e-mail: francescogiovanni.celiberto@fis.unical.it
b
e-mail: d-ivanov@math.nsc.ru
c
e-mail: beatrice.murdaca@fis.unical.it
d
e-mail: papa@cs.infn.it; alessandro.papa@fis.unical.it
hadrons according to the appropriate parton distribution func-
tion (PDF); see Fig. 1. Collinear factorization takes care of
systematically resumming the logarithms of the hard scale,
through the standard DGLAP evolution [6–8] of the PDFs
and the fixed-order radiative corrections to the parton scat-
tering cross section.
The other resummation mechanism at work, justified by
the large center-of-mass energy
√
s available at LHC, is the
BFKL resummation of energy logarithms, which are so large
as to compensate the small QCD coupling and must therefore
be accounted for to all orders of perturbation. These energy
logarithms are related with the emission of undetected par-
tons between the two jets (the larges s, the larger the num-
ber of partons), which lead to a reduced azimuthal correla-
tion between the two detected forward jets, in comparison to
the fixed-order DGLAP calculation, where jets are emitted
almost back-to-back.
In the BFKL approach energy logarithms are system-
atically resummed in the leading logarithmic approxima-
tion (LLA), which means all terms (α
s
ln(s))
n
, and in the
next-to-leading logarithmic approximation (NLA), which
means resummation of all terms α
s
(α
s
ln(s))
n
. The process-
independent part of such resummation is encoded in the
BFKL Green’s function, obeying an iterative integral equa-
tion, whose kernel is known at the next-to-leading order
(NLO) both for forward scattering (i.e. for t = 0 and color
singlet in the t-channel) [9,10] and for any fixed (not grow-
ing with energy) momentum transfer t and any possible two-
gluon color state in the t-channel [11–17].
To get the cross section for Mueller–Navelet jet production
and other related observables, the BFKL Green’s function
must be convoluted with two impact factors for the transition
from the colliding parton to the forward jet (the so-called
“jet vertices”). They were first calculated with NLO accu-
racy in [18,19] and the result was later confirmed in [20]. A
simpler expression, more practical for numerical purposes,
was obtained in [21] adopting the so-called “small-cone”
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