Physics Letters B 760 (2016) 428–431
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
The effect of a rapidity gap veto on the discrete BFKL pomeron
Douglas A. Ross
a,∗
, Agustín Sabio Vera
b,c,∗
a
School of Physics & Astronomy, University of Southampton, Highfield, Southampton SO17 1BJ, UK
b
Instituto de Física Teórica UAM/CSIC, Nicolás Cabrera 15, E-28049 Madrid, Spain
c
Universidad Autónoma de Madrid, E-28049 Madrid, Spain
a r t i c l e i n f o a b s t r a c t
Article history:
Received
4 May 2016
Received
in revised form 7 July 2016
Accepted
8 July 2016
Available
online 14 July 2016
Editor:
J.-P. Blaizot
We investigate the sensitivity of the discrete BFKL spectrum, which appears in the gluon Green function
when the running coupling is considered, to a lower cut-off in the relative rapidities of the emitted
particles. We find that the eigenvalues associated to each of the discrete eigenfunctions decrease with
the size of the rapidity veto. The effect is stronger on the lowest eigenfunctions. The net result is a
reduction of the growth with energy for the Green function together with a suppression in the regions
with small transverse momentum.
© 2016 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP
3
.
1. Introduction
In perturbative QCD, the counterpart of the pomeron of Regge
theory is described in terms of a Green function G(Y , t, t
) de-
scribing
the rapidity , Y , dependence of the scattering amplitude
of a gluon with transverse momentum k
T
=
QCD
e
t/2
and a gluon
with transverse momentum k
T
=
QCD
e
t
/2
with a relative rapid-
ity
difference Y between the two gluons. It is obtained [1] by
resumming the leading rapidity contributions to all orders in per-
turbation
theory. At leading order, this is obtained by assuming a
cascade of gluons emitted between the two primary gluons in the
kinematic regime in which the emitted gluons have a large rapid-
ity
relative to the preceding emitted gluons. Schmidt [2] pointed
out that a significant reduction in the resultant Green function oc-
curs
if one imposes this restriction explicitly by demanding that
one only considers contributions to the scattering amplitude in
which emitted gluons have a minimum rapidity gap, b, relative to
the preceding emitted gluon. It was furthermore shown in ref. [3]
that
the large effect of imposing such a restriction simulates, to
a good approximation, the effect of the NLO corrections to the
BFKL Green-function with collinear summation as proposed by
Salam [4]. In particular the optimal match was found if one takes
the resummation scheme 4 of [4] and a rapidity gap veto (min-
imum
rapidity gap between adjacent emitted gluons) b ≈ 2. This
is consistent with the original presentation of this idea by Lipa-
tov
in [5]. A rapidity veto has been used in dif ferent works also
*
Corresponding authors.
E-mail
addresses: D.A.Ross@soton.ac.uk (D.A. Ross), a.sabio.vera@gmail.com
(A. Sabio Vera).
for non-linear evolution equations [6]. The mean distance in ra-
pidity
among emissions in the BFKL ladder, including higher order
collinear contributions, has been recently studied using the Monte
Carlo event generator BFKLex in [7].
The
purely perturbative QCD pomeron has the feature of a cut
in the complex angular momentum plane as opposed to a discrete
pole predicted by the phenomenologically successful Regge theory.
As long ago as 1986, Lipatov [8] pointed out that the cut can be
converted into a series of discrete poles if the running of the QCD
coupling is taken into account and that a phase-fixing condition
in the infrared region of transverse momentum arising from the
non-perturbative properties of QCD is imposed. This scenario has
been studied extensively in ref. [9].
In
this letter we combine these two approaches and show that
there is a very significant attenuation of the growth of the BFKL
amplitude with rapidity if the rapidity veto is imposed.
2. Discrete pomeron in leading order
We first reproduce the results for the discrete BFKL pomeron
in leading order (LO). For simplicity we neglect the effects of any
thresholds arising from massive particles in the running of the
coupling and write the running coupling as
¯
α
s
(t) ≡
C
A
π
α
s
(t) =
1
¯
β
0
t
. (2.1)
The Green function, G(Y , t, t
), then obeys the equation
∂
∂Y
G(Y , t, t
) =
dt
1
¯
β
0
t
K(t, t
)
1
¯
β
0
t
G(Y , t
, t
), (2.2)
http://dx.doi.org/10.1016/j.physletb.2016.07.025
0370-2693/
© 2016 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by
SCOAP
3
.
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