We discuss the azimuthal angle decorrelation of Mueller-Navelet jets at
hadron colliders and forward jets in Deep Inelastic Scattering within the BFKL
framework with a NLO kernel. We stress the need of collinear improvements to
obtain good perturbative convergence. We provide estimates of these
decorrelations for large rapidity differences at the Tevatron, LHC and HERA.Comment: Talk given at 12th International Conference on Elastic and
  Diffractive Scattering: Forward Physics and QCD, Hamburg, DESY, Germany,
  21-25 May 200

Schwennsen, Florian

Vera, Agustin Sabio

English

arXiv

We discuss the azimuthal angle decorrelation of Mueller-Navelet jets at hadron colliders and forward jets in Deep Inelastic Scattering within the BFKL framework with a NLO kernel. We stress the need of collinear improvements to obtain good perturbative convergence. We provide estimates of these decorrelations for large rapidity differences at the Tevatron, LHC and HERA

Sabio Vera, Agustin

DESY Publication Database

Angular decorrelations in Mueller-Navelet jets and DIS

DESY

We discuss the azimuthal angle decorrelation of Mueller-Navelet jets at hadron colliders and forward jets in Deep Inelastic Scattering within the BFKL framework with a NLO kernel. We stress the need of collinear improvements to obtain good perturbative convergence. We provide estimates of these decorrelations for large rapidity differences at the Tevatron, LHC and HERA.We discuss the azimuthal angle decorrelation of Mueller-Navelet jets at hadron colliders and forward jets in Deep Inelastic Scattering within the BFKL framework with a NLO kernel. We stress the need of collinear improvements to obtain good perturbative convergence. We provide estimates of these decorrelations for large rapidity differences at the Tevatron, LHC and HERA

CERN Document Server

arXiv:0710.1478v1  [hep-ph]  8 Oct 2007Angular decorrelations in Mueller-Navelet jets and DISAgustı´n Sabio Vera1y, Florian Schwennsen21 Physics Department, Theory Division, CERN, CH–1211 Geneva 23, Switzerland,2 II. Institut fu¨r Theoretische Physik, Universita¨t Hamburg, Luruper Chaussee 149 D–22761Hamburg, Germany.AbstractWe discuss the azimuthal angle decorrelation of Mueller–Navelet jetsat hadron colliders and forward jets in Deep Inelastic Scattering withinthe BFKL framework with a NLO kernel. We stress the need of collinearimprovements to obtain good perturbative convergence. We provideestimates of these decorrelations for large rapidity differences at theTevatron, LHC and HERA.1 BFKL cross sectionsIn this contribution we discuss the results recently obtained in [1] where azimuthal angle corre-lations in Mueller–Navelet jets [2] and forward jets at HERA using the Balitsky–Fadin–Kuraev–Lipatov (BFKL) equation in the next–to–leading (NLO) approximation [3] were investigated(related works can be found in [4]). In this section we focus on normalized differential crosssections for Mueller–Navelet jets, which are quite insensitive to parton distribution functions.This justifies the use of partonic cross sections which can be written asd^d2~q1d2~q2=22s21q21q22Zd!2ie!Yf! (~q1;~q2); (1)where s = sN c=, ~q1;2 are the transverse momenta of the tagged jets, and Y their relativerapidity. The Green’s function carries the bulk of the Y dependence and is the solution to theNLO BFKL equation,!   sK^ 0  2sK^ 1f^! = 1^; (2)which acts on the basis including the azimuthal angle, i.e.,h~qj;ni=1p2q2i  12ein: (3)As Y increases the azimuthal dependence is mainly driven by the kernel and therefore we useLO jet vertices which are simpler than the NLO ones [5]. The differential cross section in theazimuthal angle  = 1   2  , with  ibeing the angles of the two tagged jets, readsd^s;Y;p21;2d=22s4qp21p221Xn=   1einCn (Y); (4)y talk presented at EDS07whereCn (Y) =12Z 1  1d14+ 2 p21p22! ie(jnj;12+ i;s(p1p2))Y ; (5)and the NLO kernel can be written as (n;;s) = s0(n;)+ 2s1(n;) 08N c0(n;) (1 ): (6)The eigenvalue of the LO kernel is 0(n;) = 2 (1)    + n2   1  + n2, with  the logarithmic derivative of the Euler function. The action of K^ 1, in M S scheme, can be foundin [6]. The full cross section only depends on the n = 0 component,^ =32s2qp21p22C0(Y): (7)The average of the cosine of the azimuthal angle times an integer projects out the contributionfrom each of these angular components:hcos(m )ihcos(n)i=Cm (Y)Cn (Y)(8)The normalized differential cross section is1^d^d=121Xn=   1einCn (Y)C0(Y)=12(1+ 21Xn= 1cos(n)hcos(n)i): (9)The BFKL resummation is not stable at NLO for zero conformal spin. A manifestation of thislack of convergence is what we found in the gluon–bremsstrahlung scheme where our NLOdistributions have an unphysical behavior whenever the n = 0 conformal spin appears in the cal-culation. To solve this problem we imposed compatibility with renormalization group evolutionin the DIS limit following [7] for all conformal spins. The new kernel with improvements to allorders reads [1]! = s(1+ A ns)2 (1)   +jnj2+!2+ Bns  1  +jnj2+!2+ Bns+ 2s(1(jnj;) 08N c0(n;) (1 ) A n0(jnj;)!+ 0 +jnj2+  01  +jnj2 0(jnj;)2+ Bn );(10)where A n and Bn are collinear coefficients [1]. After this collinear resummation our observableshave a good physical behavior and are independent of the renormalization scheme. It is veryimportant to remark that the asymptotic behavior of the BFKL resummation is convergent for nonzero conformal spins. In this sense the ideal distributions to investigate experimentally are thoseof the form hcos(m )i=hcos(n)iwith m ;n 6= 0, we will see that in this case the differencebetween the LO and higher orders results is small.2 Phenomenology for Mueller–Navelet jetsThe D; [8] collaboration analyzed data for Mueller–Navelet jets at p s = 630 and 1800 GeV.For the angular correlation LO BFKL predictions were first obtained in [9] and failed to de-scribe the data estimating too much decorrelation. An exact fixed NLO analysis using JETRADunderestimated the decorrelation, while HERWIG was in agreement with the data.YC1C02 3 4 5 6.2.4.6.811YC2C12 3 4 5 6.2.4.6.811Fig. 1: Top: hcosi = C1=C0 and Bottom: < cos2>< cos>=C2C1, at a pp collider withps = 1.8 TeV for BFKL at LO(solid) and NLO (dashed). The results from the resummation presented in the text are shown as well (dash–dotted).In Fig. 1 we compare the Tevatron data for hcosi = C1=C0 with our LO, NLO andresummed predictions. For Tevatron’s cuts, where the transverse momentum for one jet is 20GeV and for the other 50 GeV, the NLO calculation is instable under renormalization schemechanges. The convergence of our observables is poor whenever the coefficient associated to zeroconformal spin, C0, is involved. If we eliminate this coefficient by calculating the ratios definedin Eq. (8) then the predictions are very stable, see Fig. 1.The full angular dependence studied at the Tevatron by the D;collaboration was publishedin [8]. In Fig. 2 we compare this measurement with the predictions obtained in our approach.For the differential cross section we also make predictions for the LHC at larger Y in Fig. 3. Weestimated several uncertainties in our approach which are represented by gray bands.1NdNdφφpi10−110−210−31.5−.5 1−11NdNdφφpi10−110−210−31.5−.5 1−1Fig. 2: 1NdNdin a pp collider atps=1.8 TeV using a LO (stars), NLO (squares) and resummed (triangles) BFKLkernel. Plots are shown for Y = 3 (top) and Y = 5 (bottom).1σdσdφφpi−110−111Fig. 3: 1ddin our resummation scheme for rapidities Y = 7, 9, 11 from top to bottom. The gray band reflects theuncertainty in s0 and in the renormalization scale .3 Forward jets at HERAIn this section we apply the BFKL formalism to predict the decorrelation in azimuthal anglebetween the electron and a forward jet associated to the proton in Deep Inelastic Scattering(DIS). When the separation in rapidity space between the scattered electron and the forwardjet is large and the transverse momentum of the jet is similar to the virtuality of the photonresolving the hadron, then the dominant terms are of BFKL type. This process is similar tothat of Mueller–Navelet jets, the only difference being the substitution of one jet vertex by theelectron vertex describing the coupling of the electron to the BFKL gluon Green’s function via aquark–antiquark pair. Azimuthal angles in forward jets were studied at LO in [10]. We improvedtheir calculation by considering the NLO BFKL kernel.In the production of a forward jet in DIS it is necessary to extract a parton with a largelongitudinal momentum fraction xFJ from the proton. When the jet is characterized by a hardscale it is possible to use conventional collinear factorization to describe the process and the jetproduction rate may be written as(s) =ZdxFJ fe(xFJ;2F )^(^s); (11)with ^(^s)denoting the partonic cross section, and the effective parton density [11] beingfe(x;2F ) = G (x;2F )+49XfhQ f(x;2F )+Q f(x;2F )i; (12)where the sum runs over all quark flavors, and F stands for the factorization scale.The final expression for the cross section at hadronic level is of the formddY d= C0(Y )+ C2(Y )cos2; (13)withCn(Y ) =22s2ZcutsdxFJdQ2dyfe(xFJ;Q2)B(n)(y;Q2;Y ) xFJ  Q 2eYys!; (14)where the index in the integral sign refers to the cuts20G eV2< Q2< 100G eV2; 0:05 < y < 0:7; 510  3> xBj> 410  4: (15)The integration over the longitudinal momentum fraction xFJ of the forward jet involves a deltafunction fixing the rapidity Y = lnxFJ=xBj and B (n) is a complicated function which can befound in [1].Since the structure of the electron vertex singles out the components with conformal spin0 and 2, the number of observables related to the azimuthal angle dependence is limited whencompared to the Mueller–Navelet case. The most relevant observable is the dependence of theaverage < cos2 > = C2=C0 with the rapidity difference between the forward jet and outgoinglepton. It is natural to expect that the forward jet will be more decorrelated from the leptonic sys-tem as the rapidity difference is larger since the phase space for further gluon emission opens up.This is indeed what we observe in our numerical results shown in Fig. 4. We find similar resultsto the Mueller–Navelet jets case where the most reliable calculation is that with a collinearly–improved kernel. The main effect of the higher order corrections is to increase the azimuthalangle correlation for a given rapidity difference, while keeping the decrease of the correlation asY grows.YC2C0.02.04.06.082 3 4 5 61.1Fig. 4: < cos2 > at the ep collider HERA at leading (solid), next to leading order (dashed), and for resummedkernel (dash-dotted).References[1] A. Sabio Vera, Nucl. Phys. B746, 1 (2006). hep-ph/0602250;A. Sabio Vera and F. Schwennsen, Nucl. Phys. B776, 170 (2007). hep-ph/0702158;F. Schwennsen (2007). hep-ph/0703198;A. Sabio Vera and F. Schwennsen (2007). arXiv:0708.0549 [hep-ph].[2] A. H. Mueller and H. Navelet, Nucl. Phys. B282, 727 (1987).[3] V. S. Fadin and L. N. Lipatov, Phys. Lett. B429, 127 (1998). hep-ph/9802290;M. Ciafaloni and G. Camici, Phys. Lett. B430, 349 (1998). hep-ph/9803389.[4] C. Marquet and C. Royon, Nucl. Phys. B739, 131 (2006). hep-ph/0510266;O. Kepka, C. Royon, C. Marquet, and R. Peschanski (2006). hep-ph/0609299;O. Kepka, C. Royon, C. Marquet, and R. Peschanski (2006). hep-ph/0612261;C. Marquet and C. Royon (2007). arXiv:0704.3409 [hep-ph].[5] J. Bartels, D. Colferai, and G. P. Vacca, Eur. Phys. J. C24, 83 (2002). hep-ph/0112283;J. Bartels, D. Colferai, and G. P. Vacca, Eur. Phys. J. C29, 235 (2003). hep-ph/0206290.[6] A. V. Kotikov and L. N. Lipatov, Nucl. Phys. B582, 19 (2000). hep-ph/0004008.[7] G. P. Salam, JHEP 07, 019 (1998). hep-ph/9806482;M. Ciafaloni, D. Colferai, G. P. Salam, and A. M. Stasto, Phys. Rev. D68, 114003 (2003).hep-ph/0307188;A. Sabio Vera, Nucl. Phys. B722, 65 (2005). hep-ph/0505128.[8] D0 Collaboration, S. Abachi et al., Phys. Rev. Lett. 77, 595 (1996). hep-ex/9603010.[9] V. Del Duca and C. R. Schmidt, Phys. Rev. D49, 4510 (1994). hep-ph/9311290;W. J. Stirling, Nucl. Phys. B423, 56 (1994). hep-ph/9401266.[10] J. Bartels, V. Del Duca, and M. Wusthoff, Z. Phys. C76, 75 (1997). hep-ph/9610450.[11] B. L. Combridge and C. J. Maxwell, Nucl. Phys. B239, 429 (1984).

Angular decorrelations in Mueller-Navelet jets and DIS

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