# Presentation: 226796

## Testing BFKL evolution with Mueller-Navelet jets

- Cyrille Marquet
- RIKEN BNL Research Center

- based on C. Marquet and C. Royon, arXiv:0704.3409

- ISMD 2007, Berkeley, USA

## Contents

- Introduction: BFKL evolutionhigh-energy evolution with fixed hard-momentum scale in pQCD
- Mueller-Navelet jets: h h → Jet X Jeta jet in each of the forward directions and a large rapidity interval in between  large values of *x* probed in both hadrons, pdfs under control focus on the (BFKL) resummation of large logarithms ln(s/k1k2)
- BFKL ressumation: from LL to NLLa collinear-improved kernel is needed for meaningful predictions
- The observable: correlations in azimuthal anglethey provide clean experimental probes and are theoretically under control

## Introduction : BFKL evolution

- weakly-coupled regime

-  DGLAP evolution towards larger momentum scale *k**T*
- 	well known, works very well to describe hard processes in hadronic collisions
- - BFKL evolution towards larger center-of-mass energy *s**	*strong hints for the need of BFKL in forward jets are HERA

- idea: study the BFKL evolution with azimuthal correlations of Mueller-Navelet jets

- linear pQCD evolutions:

- Kepka, Marquet, Peschanski and Royon (2007)

## Why large logarithms ?

- consider 2 to 2 scattering with		(Regge limit):

- the exchanged particle has a very small
- longidudinal momentum
- the final-state particles are separated by a large rapidity interval

## The observable: Mueller-Navelet jets

- moderate values of *x*1, typically 0.05

- moderate values of *x*2, typically 0.05

- large rapidity
- interval Δ*η** *~ 8

-  *y*1 ~ 4

-  *y*2 ~ - 4

*k*1 >> QCD  collinear factorization of

*k*2 >> QCD  collinear factorization of

- pQCD: need ressumation of powers of αS Δ*η** *~ 1 in the partonic cross-section *gg *→ *JXJ*

- h+h  Jet+X+Jet

- Mueller and Navelet (1994)

## kT factorization and BFKL evolution

- - from  *hh *→ *JXJ* to *gg *→ *JXJ*: collinear factorization of the pdf’s

## Going to NLL-BFKL

- - for jet production, everything is known, but at NLO there are difficulties
- in merging kT and collinear factorizations

- for instance, with the photon I.F. (relevant in DIS) will probably take ~ 10 years
- the jet impact factors are known

- - it took ~ 10 years to compute the NLL Green function
- and the NLO impact factors are also very difficult to compute

- in progress, Bartels et al.

- Fadin and Lipatov (1998) Ciafaloni (1998)

- Bartels, Colferai and Vacca (2002)

- after 5 years, still no numerical results

## BFKL Green functions

- this allows to solve the equation and obtain the LL Green function

- the integral kernel of the LL-BFKL equation is conformal invariant:

- Lipatov (1986)

- discrete index
- called conformal spin

- Mellin transformation

## Salam’s regularisation schemes

- results, this is an artefact of the truncation of the perturbative series

- - to produce meaningful NLL-BFKL results, one has to add to	the higher order
- corrections which are responsible for the canceling the singularities

- in momemtum space, the poles correspond to the known DGLAP limits k1 >> k2 and
- k1 << k2 , this gives information/constraints on what add to the next-leading kernel

## Some formulae

- it is symmetric under the sustitution	           , the scale-dependent part of the kernel
- is antisymmetric and does not contribute

- the scale-invariant part of          :

- with

## The ΔΦ distribution

-  parameter-free predictions

- we used the following variables

- and we studied the normalized ΔΦ distribution

- given in terms of the coefficients

- ET cut = 20 GeV (Tevatron)
- 	 50 GeV (LHC)

- |y| < 0.5 for a symetric
- situation y1 ~ - y2

- important piece: contains the Δη and R dependencies

## Some results for (1/σ) dσ/dΔΦ

- fixed R = 1 and several Δη

- fixed Δη = 10 and several R

- LL-BFKL

- NLL-BFKL

- the decorrelation increases with
- the rapidity interval Δη

- the decorrelation increases
- when R deviates from 1

## Scale/Scheme dependence

- we also noticed that the uncertainty due to pdfs is negligible
- we suspect very little sensitivity to NLO impact factor
-  very interesting observable

- scheme dependence

- scale dependence

- Tevatron

- LHC

- almost no scheme dependence

- scale uncertainty quite large

## Conclusions

- - there is some data from the D0 collaboration at the Tevatron, but for rapidity intervals Δη smaller than 5

- - the correlation in azimuthal angle between two jets gets weaker as their separation in rapidity increases
- - we obtained parameter free predictions in the BFKL framework at next-leading accuracy, valid for large enough rapidity intervals

- see also Sabio Vera and Schwenssen (2007)

- - our predictions underestimate the correlation while pQCD@NLO predictions overestimate it