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 evolution high-energy evolution with fixed hard-momentum scale in pQCD Mueller-Navelet jets: h h → Jet X Jet a 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 NLL a collinear-improved kernel is needed for meaningful predictions The observable: correlations in azimuthal angle they provide clean experimental probes and are theoretically under control

Introduction : BFKL evolution linear pQCD evolutions: weakly-coupled regime DGLAP evolution towards larger momentum scale kT 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 Kepka, Marquet, Peschanski and Royon (2007) idea: study the BFKL evolution with azimuthal correlations of Mueller-Navelet jets BFKL resummation of large αS ln(x1 x2 s / k1k2) x1 ~ x2 close to 1: large values of x probed in both hadrons, the pdf’s are under control, no small-x effects a jet in each of the forward directions and a large rapidity interval in between Balitsky, Fadin, Kuraev and Lipatov (2007) J X

in practice, NLL-BFKL is needed 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 their contribution goes as and is as large next-order diagrams: with n gluons: need ressumation of leading logs (LL)  BFKL equation in practice, NLL-BFKL is needed

The observable: Mueller-Navelet jets Mueller and Navelet (1994) moderate values of x1, typically 0.05 k1 >> QCD  collinear factorization of y1 ~ 4 h+h  Jet+X+Jet large rapidity interval Δη ~ 8 y2 ~ - 4 k2 >> QCD  collinear factorization of moderate values of x2, typically 0.05 pQCD: need ressumation of powers of αS Δη ~ 1 in the partonic cross-section gg → JXJ

kT factorization and BFKL evolution - from hh → JXJ to gg → JXJ: collinear factorization of the pdf’s - from gg → JXJ to gg → X: kT factorization of the BFKL Green function final-state particles leading-order impact factors (I. F.) kT factorization is also proved at NLL but there are many complications Green function, this is what resums the powers of αS Δη this simple formula holds at LL Fadin et al. (2005-2006)

Going to NLL-BFKL - it took ~ 10 years to compute the NLL Green function and the NLO impact factors are also very difficult to compute Fadin and Lipatov (1998) Ciafaloni (1998) for instance, with the photon I.F. (relevant in DIS) will probably take ~ 10 years the jet impact factors are known in progress, Bartels et al. Bartels, Colferai and Vacca (2002) - for jet production, everything is known, but at NLO there are difficulties in merging kT and collinear factorizations after 5 years, still no numerical results - it has been argued that a complete NLL-BFKL calculation would be flawed: the truncation of the perturbative series is spurious, it contains singularities which would not be there with all orders for double vector meson production in γ*-γ* scattering there is a full computation and the result is unstable when varying the renormalization scheme Salam (1998), Ciafaloni, Colferai and Salam (1999) Ivanov and Papa (2006) - the problem comes from Green function, and it can be cured we will use Salam’s schemes, the only ones used so far for phenomenological studies Ciafaloni, Colferai, Salam, Stasto, Altarelli, Ball, Forte, Brodsky, Lipatov, Fadin, … (1999-now) Peschanski, Royon and Schoeffel (2005), Kepka, Marquet, Peschansi and Royon (2007)

BFKL Green functions the integral kernel of the LL-BFKL equation is conformal invariant: Lipatov (1986) this allows to solve the equation and obtain the LL Green function discrete index called conformal spin Mellin transformation now running coupling (with symmetric scale) the NLL Green function (in our approach with LO impact factors) from to : the ω integration leads to the implicit equation effective kernel

Salam’s regularisation schemes - has spurious singularities in Mellin (γ) space, they lead to unphysical 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 regularisation Strategy: implicit equation there is some arbitrary: different schemes S3, S4, … in practice, each value k1k2 leads to a different effective kernel in this work, we extended those schemes to p ≠ 0 : with

the scale-invariant part of : Some formulae the scale-invariant part of : with only the scale-invariant part of the NLL-BFKL kernel contributes to our observable: it is symmetric under the sustitution , the scale-dependent part of the kernel is antisymmetric and does not contribute

The ΔΦ distribution we used the following variables and we studied the normalized ΔΦ distribution |y| < 0.5 for a symetric situation y1 ~ - y2 given in terms of the coefficients ET cut = 20 GeV (Tevatron) 50 GeV (LHC) important piece: contains the Δη and R dependencies  parameter-free predictions

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 scale dependence Tevatron LHC almost no scheme dependence scale uncertainty quite large we also noticed that the uncertainty due to pdfs is negligible we suspect very little sensitivity to NLO impact factor  very interesting observable

Conclusions - 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 - there is some data from the D0 collaboration at the Tevatron, but for rapidity intervals Δη smaller than 5 - our predictions underestimate the correlation while pQCD@NLO predictions overestimate it see also Sabio Vera and Schwenssen (2007) feasibility study in collaboration with Christophe Royon (D0/Atlas) and Ramiro Debbe (Star/Atlas) the CDF miniplugs cannot measure pT well but are suited for azimuthal angle measurements with new CDF detectors called miniplugs possibilities for Δη =12 with ET cut = 5 GeV prospects for future measurements: - at the LHC - at the Tevatron predictions for future measurements at CDF