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arXiv:0909.5236v1 [hep-ph] 28 Sep 2009

Jet gap jet events at Tevatron and LHC

Christophe Royon∗

CEA/IRFU/Service de physique des particules, CEA/Saclay, 91191 Gif-sur-Yvette cedex, France

E-mail: royon@hep.saclay.cea.fr

We investigate diffractive events in hadron-hadroncollisions, in which two jets are produced and

separated by a large rapidity gap. Using a renormalisation-group improved NLL kernel imple-

mented in the HERWIG Monte Carlo program, we show that the BFKL predictions are in good

agreement with the Tevatron data, and present predictions which could be tested at the LHC.

The 2009 Europhysics Conference on High Energy Physics,

July 16 - 22 2009

Krakow, Poland

∗Speaker.

c ? Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlikeLicence.

http://pos.sissa.it/

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Jet gap jet events at Tevatron and LHC

Christophe Royon

In a hadron-hadron collision, a jet-gap-jet event features a large rapidity gap with a high−ET

jet on each side (ET≫ΛQCD). Across the gap, the object exchanged in the t−channel is color

singlet and carries a large momentum transfer, and when the rapidity gap is sufficiently large the

natural candidate in perturbative QCD is the Balitsky-Fadin-Kuraev-Lipatov (BFKL) Pomeron [1].

Of course the total energy of the collision√s should be big (√s ≫ ET) in order to get jets and a

large rapidity gap.

Following the success of the forward jet and Mueller Navelet jet BFKL NLL studies [2],

we use the implementation of the BFKL NLL kernel inside the HERWIG [3] Monte Carlo to

compute the jet gap jet cross section, compare our results with the Tevatron measurement and

make predictions at the LHC [4].

1. BFKL NLL formalism

The production cross section of two jets with a gap in rapidity between them reads

dσpp→XJJY

dx1dx2dE2

T

where√s is the total energy of the collision, ETthe transverse momentum of the two jets, x1and

x2their longitudinal fraction of momentum with respect to the incident hadrons, S the survival

probability, and f the effective parton density functions [4]. The rapidity gap between the two jets

is ∆η=ln(x1x2s/p2

T).

The cross section is given by

dσgg→gg

dE2

T

16π

in terms of the gg → gg scattering amplitude A(∆η,p2

In the following, we consider the high energy limit in which the rapidity gap ∆η is assumed

to be very large. The BFKL framework allows to compute the gg → gg amplitude in this regime,

and the result is known up to NLL accuracy

∞

∑

p=−∞

with the complex integral running along the imaginary axis from 1/2−i∞ to 1/2+i∞, and with

only even conformal spins contributing to the sum, and ¯ α = αSNC/π the running coupling.

Letus give some moredetails onformula 1.3. The NLL-BFKLeffects are phenomenologically

taken into account by the effective kernels χef f(p,γ, ¯ α). The NLL kernels obey a consistency

condition which allows to reformulate the problem in terms of χef f(γ, ¯ α). The effective kernel

χef f(γ, ¯ α) is obtained from the NLL kernel χNLL(γ,ω) by solving the implicit equation χef f=

χNLL(γ, ¯ α χef f) as a solution of the consistency condition.

In this study, we performed a parametrised distribution of dσgg→gg/dE2

implemented in the Herwig Monte Carlo since performing the integral over γ in particular would

be too much time consuming in a Monte Carlo. The implementation of the BFKL cross section in

a Monte Carlo is absolutely necessary to make a direct comparison with data. Namely, the mea-

surements are sensititive to the jet size (for instance, experimentally the gap size is different from

the rapidity interval between the jets which is not the case by definition in the analytic calculation).

= S fef f(x1,E2

T)fef f(x2,E2

T)dσgg→gg

dE2

T

,

(1.1)

=

1

??A(∆η,E2

T).

T)??2

(1.2)

A(∆η,E2

T) =16Ncπα2

CFE2

s

T

?

dγ

2iπ

[p2−(γ −1/2)2]exp?¯ α(E2

[(γ −1/2)2−(p−1/2)2][(γ −1/2)2−(p+1/2)2]

T)χef f[2p,γ, ¯ α(E2

T)]∆η?

(1.3)

Tso that it can be easily

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Jet gap jet events at Tevatron and LHC

Christophe Royon

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

10 15202530 3540 455055 60

ET

ratio

D0 Data

BFKL NLL/

NLO QCD

BFKL LL p=0 /NLO QCD

BFKL LL /NLO QCD

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0.009

0.01

456

∆η

ratio

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0.02

456

∆η

ratio

Figure 1: Comparisons between the D0 measurements of the jet-gap-jet event ratio with the NLL- and

LL-BFKL calculations. For reference, the comparison with the LL BFKL with only the conformal spin

component p = 0 is also given.

2. Comparison with D0 and CDF measurements

Let us first notice that the sum over all conformal spins is absolutely necessary. Consider-

ing only p = 0 in the sum of Equation 1.3 leads to a wrong normalisation and a wrong jet ET

dependence, and the effect is more pronounced as ∆η diminishes.

The D0 collaboration measured the jet gap jet cross section ratio with respect to the total

dijet cross section, requesting for a gap between -1 and 1 in rapidity, as a function of the second

leading jet ET, and ∆η between the two leading jets for two different low and high ETsamples

(15< ET<20 GeV and ET>30 GeV). To compare with theory, we compute the following quantity

Ratio =BFKL NLL HERWIG

Dijet Herwig

×

LO QCD

NLO QCD

(2.1)

inorder totakeinto account theNLOorder corrections onthedijet cross sections, where BFKLNLL

HERWIG and Dijet Herwig denote the BFKL NLL and the dijet cross section implemented in

HERWIG. The NLO QCD cross section was computed using the NLOJet++ program [5].

The comparison with D0 data [6] is shown in Fig. 1. We find a good agreement between the

data and the BFKL calculation. It is worth noticing that the BFKL NLL calculation leads to a

better result than the BFKL LL one (note that the best description of data is given by the BFKL LL

formalism for p = 0 but it does not make sense theoretically to neglect the higher spin components

and this comparison is only made to compare with previous LL BFKL calculations).

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Jet gap jet events at Tevatron and LHC

Christophe Royon

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2030 40 506070 80

average ET

ratio

CDF Data

BFKL LL (p=0) / LO QCD

BFKL NLL / LO QCD

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

1.82 2.2 2.42.6 2.83 3.2 3.4

∆η/2

ratio

BFKL LL / LO QCD

Figure 2: Comparisons between the CDF measurements of the jet-gap-jet event ratio with the NLL- and

LL-BFKL calculations. For reference, the comparison with the LL BFKL with only the conformal spin

component p = 0 is also given.

The comparison with the CDF data [6] as a function of the average jet ETand the difference in

rapidity between the two jets is shown in Fig. 2, and the conclusion remains the same: the BFKL

NLL formalism leads to a better description than the BFKL LL one.

3. Predictions for the LHC

Using the same formalism, and assuming a survival probability of 0.03 at the LHC, it is possi-

ble to predict the jet gap jet cross section at the LHC. While both LL and NLL BFKL formalisms

lead to a weak jet ETor ∆η dependence, the normalisation if found to be quite difference leading

to higher cross section for the BFKL NLL formalism.

References

[1] V. S. Fadin and L. N. Lipatov, Phys. Lett. B 429, 127 (1998); M. Ciafaloni, Phys. Lett. B 429, 363

(1998);

[2] O. Kepka, C. Royon, C. Marquet and R. B. Peschanski, Phys. Lett. B 655, 236 (2007); Eur. Phys. J. C

55, 259 (2008); C. Marquet and C. Royon, Phys. Rev. D 79, 034028 (2009).

[3] G. Marchesini et al., Comp. Phys. Comm. 67, 465 (1992).

[4] F. Chevallier, O. Kepka, C. Marquet, C. Royon, Phys. Rev. D79 (2009) 094019.

[5] Z. Nagy and Z. Trocsanyi, Phys. Rev. Lett. 87, 082001 (2001).

[6] B. Abbott et al., Phys. Lett. B 440, 189 (1998); F. Abe et al., Phys. Rev. Lett. 80, 1156 (1998).

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