Testing BFKL evolution with Mueller-Navelet jets

1. 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

2. 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

3. J J 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 • BFKL resummation of large αS ln(x1 x2 s / k1k2) X Balitsky, Fadin, Kuraev and Lipatov (2007) Introduction : BFKL evolution linear pQCD evolutions: weakly-coupled regime • DGLAP evolution towards larger momentum scalekT well known, works very well to describe hard processes in hadronic collisions - BFKL evolution towards larger center-of-mass energysstrong 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

4. next-order diagrams: their contribution goes as and is as large need ressumation of leading logs (LL)  BFKL equation with n gluons: 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

5. 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

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

7. - 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 Salam (1998), Ciafaloni, Colferai and Salam (1999) for double vector meson production in γ*-γ* scattering there is a full computation and the result is unstable when varying the renormalization scheme Ivanov and Papa (2006) - the problem comes from Green function, and it can be cured Ciafaloni, Colferai, Salam, Stasto, Altarelli, Ball, Forte, Brodsky, Lipatov, Fadin, … (1999-now) we will use Salam’s schemes, the only ones used so far for phenomenological studies Peschanski, Royon and Schoeffel (2005), Kepka, Marquet, Peschansi and Royon (2007) 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

8. the NLL Green function (in our approach with LO impact factors) effective kernel now running coupling (with symmetric scale) from to : the ω integration leads to the implicit equation 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

9. there is some arbitrary: different schemes S3, S4, … regularisation implicit equation Strategy: in practice, each value k1k2 leads to a different effective kernel in this work, we extended those schemes to p≠ 0 : with 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

10. 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

11. 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

12. Some results for (1/σ) dσ/dΔΦ fixed R = 1 and several Δη fixed Δη = 10and several R LL-BFKL NLL-BFKL the decorrelation increases when R deviates from 1 the decorrelation increases with the rapidity interval Δη

13. Scale/Scheme dependence 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

14. prospects for future measurements: - at the Tevatron with new CDF detectors called miniplugs possibilities for Δη =12 with ET cut = 5 GeV the CDF miniplugs cannot measure pT well but are suited for azimuthal angle measurements - at the LHC feasibility study in collaboration with Christophe Royon (D0/Atlas) and Ramiro Debbe (Star/Atlas) predictions for future measurements at CDF 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)