OUTP-8--P Three-jet DIS final states from k -epenent parton showers University of Oxfor E-mail: hautmann@thphys.ox.ac.uk H. Jung DESY E-mail: jung@mail.esy.e Experimental measurements of angular correlations in three-jet final states have recently been performe in DIS. Next-to-leaing-orer QCD results for these observables are affecte by large theoretical uncertainties in the kinematic region of the ata. We iscuss the effects of multiple QCD raiation at higher orer using parton-shower methos base on transverse-momentum epenent parton istributions an matrix elements. We present Monte-Carlo results for azimuthal two-jet an three-jet istributions, an iscuss the comparison with experimental ata. PoS(RAD COR 7) 8th International Symposium on Raiative Corrections October -5, 7 Florence, Italy Speaker. c Copyright owne by the author(s) uner the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. http://pos.sissa.it/
The stuy of haronic final states with multiple jets at the Tevatron, HERA an LHC colliers relies both on perturbative multi-jet calculations (see [] for a recent overview) an on realistic event simulation by parton-shower Monte-Carlo generators (see e.g. [, ]). These complex processes, characterize by multiple har scales, are potentially sensitive to effects of QCD initial-state raiation that epen on the finite transverse-momentum tail of partonic matrix elements an istributions [, ]. In perturbative multi-jet calculations truncate to fixe orer in! s [], finite-k contributions are taken into account partially, orer-by-orer, through higher-loop corrections. On the other han, in stanar shower Monte-Carlos such as HERWIG [5] an PYTHIA [6], base on collinear evolution of the initial-state jet, finite-k contributions are not inclue, but rather correspon to corrections [7, 8] to the angular or transverse-momentum orering implemente in the parton-branching algorithms. In this article we iscuss the role of initial-state raiative effects in the stuy of angular correlations for multi-jet processes, concentrating on the case of three-jet DIS prouction, for which new experimental ata have recently appeare [9] an next-to-leaing-orer (NLO) calculations are available []. In the first part we recall the experimental results [9] an observe that while inclusive jet cross sections are reliably preicte by NLO perturbation, jet correlations are affecte by significant higher-orer corrections, increasing as the momentum fraction x ecreases, giving large theoretical uncertainties at NLO. Sizeable contributions arise from regions [] with three well-separate har jets in which the partonic lines along the ecay chain in the initial state are not orere in transverse momentum. In the secon part we move on to the escription of multi-jet correlations by parton showers that incorporate finite-k corrections to the transverse-momentum orering []. The results compare well with experimental ata, an give quite istinctive features of the associate jet istributions compare to stanar showers such as HERWIG.. Jet istributions from NLO calculations DIS multi-jet istributions associate with Q > GeV an < x < have recently been measure by the ZEUS collaboration [9], an compare with next-to-leaing-orer calculations []. Results for i-jet istributions are shown in Fig. [9]. The plot on the left in Fig. ) x (pb/gev "/Q ata - GeV < Q < 5 GeV jet, < # / - - - ZEUS 8 pb ijets NLOjet: O(! & C s ) ha NLOjet: O(! ) & C s ha jet energy scale uncertainty /6 < µ /(Q +ET ) < r - (a) x Bj "/Q x (pb/gev ) ata - - - GeV < Q < GeV jet, < # / - ZEUS 8 pb ijets NLOjet: O(! ) s NLOjet: O(! ) s jet energy scale uncertainty /6 < µ /(Q +ET ) < r - & C ha & C ha (b) - x Bj x (pb) jet, "/ ata - 7 6 5 <..7 < x Bj -.5.5.5 <.5. < x Bj.5.5.5 <..5 < x Bj.5.5.5 % $ jet, PoS(RAD COR 7) Figure : (left) Bjorken-x epenence an (right) azimuth epenence of i-jet istributions at HERA as measure by ZEUS[9]. shows the x-epenence of the i-jet istribution integrate over < #/, where is the az-
imuthal separation between the two high-e T jets. The plot on the right shows the i-jet istribution in for ifferent bins of x. The overall agreement of ata with NLO results is within errors. However, the variation of the preictions from orer-! s to orer-! s is significant. Given the large ifference between orer-! s an orer-! s results, the theoretical uncertainty at NLO appears to be unerestimate by the error ban obtaine from the conventional metho of varying the renormalization/factorization scale. The stability of preictions for the jet observables in Fig. epens on a number of physical processes. Part of these concern nonperturbative ynamics, incluing jet clustering an haronization, part concern raiative corrections at higher orer. Fixe-orer calculations beyon NLO are not within present reach for multi-jet processes in haronic collisions. Resumme calculations of contributions from multiple infrare emissions are performe in []. These contributions are enhance in the region where the two high-e T jets are nearly back-to-back, an are also taken into account by parton-shower methos as in HERWIG [5]. Note however that sizeable corrections in Fig. arise for ecreasing, where the two jets are not close to back-to-back an one has effectively three well-separate har jets []. The corrections increase as x ecreases. By analyzing the angular istribution of the thir jet, Ref. [] fins significant contributions from configurations where the transverse momenta in the initial-state shower are not orere. These contributions are not inclue in stanar parton showers, e.g. HERWIG [5] an PYTHIA [6]. The next section escribes results of parton-shower calculations that take these contributions into account.. Parton showers with k -branching an jet correlations Corrections to the initial-state shower ue to non-orering in k can be incorporate in Monte- Carlo event generators [,, 5, 6], with logarithmic accuracy for x, by implementing unintegrate parton istributions efine through high-energy factorization [8]. Although none of the above generators are as evelope as stanar Monte-Carlos like HERWIG [5] or PYTHIA [6], they have the potential avantage of a more accurate treatment of the initial-state raiative effects that the observations of Sec. suggest to be relevant for multi-jet correlations. Fig. shows results [] for the azimuthal istribution of i-jet an three-jet cross sections obtaine by the k -shower Monte-Carlo CASCADE [6] an by HERWIG [5], compare with the measurement [9]. The shape of the istribution is ifferent for the two Monte-Carlos. CASCADE gives large ifferences from HERWIG in the region where the azimuthal separations between the leaing jets are small. It becomes closer to HERWIG as increases. This is consistent with the expectation that both Monte-Carlos give reasonable approximations near the back-to-back region. The escription of the measurement by CASCADE is goo, whereas HERWIG is not sufficient to escribe the measurement in the small region. In the k -shower calculation both the parton istributions (unintegrate pf s, fitte from experiment) an the har matrix elements (ME s, compute perturbatively) are transverse-momentum epenent. The parton branching inclues regions that are not orere in k along the initial-state ecay chain. Fig. shows ifferent approximations to the azimuthal ijet istribution normalize PoS(RAD COR 7) Besies angular correlations, sizeable uncertainties at NLO also affect other associate istributions such as momentum correlations. On the other han, NLO results are much more stable for inclusive jet cross sections [9]. See [] an references therein for more iscussion of these effects.
"/x (pb) 7 6 5 "/x (pb) 7 6 5.7 - < x < - - < x < 5-5 - < x < -.7 - < x < - - < x < 5-5 - < x < - (theo-at)/at (theo-at)/at - - Figure : Angular jet correlations [] obtaine by CASCADE an HERWIG, compare with ZEUS ata [9]: (left) i-jet cross section; (right) three-jet cross section. to the back-to-back cross section. The soli re curve is the full result. The ashe blue curve is obtaine from the same unintegrate pf s but not incluing the transverse-momentum epenence of the har ME. We see that the high-k component in the har ME is essential to escribe jet correlations particularly for small. The otte violet curve is obtaine from the unintegrate pf without any resolve branching, corresponing to nonperturbative, preominantly low-k moes. The results of Fig. illustrate that the k -epenence in the unintegrate pf alone is not sufficient to escribe jet prouction quantitatively. /" "/x - - -.7 - < x < - - < x < 5-5 - < x < - Figure : Azimuthal istribution normalize to the back-to-back cross section []: (soli re) full result (u-pf ME); (ashe blue) no finite-k correction in ME (u-pf ME collin. ); (otte violet) u-pf with no resolve branching. PoS(RAD COR 7) Jet multiplicities an jet momentum correlations are analyze in [] along lines similar to those iscusse above for azimuthal istributions. The largest ifferences between HERWIG an the k -showering are foun in the contribution of high multiplicities an correlations in the transversemomentum imbalance between the leaing jets. In summary, the results give a consistent parton-shower picture of istributions associate to multi-jet prouction, incluing correlations. This is expresse in terms of unintegrate pf s convolute with transverse-momentum epenent har kernels. The physical picture reflects the The u-pf s are efine gauge-invariantly [8] for small x. General operator efinitions, incluing the region x, an issues of lightcone singularities are iscusse e.g. in [7, 8] an references therein.
growth of the k transmitte along the initial-state jet, an inclues corrections to the collinear orering implemente in stanar showers such as HERWIG an PYTHIA. We have consiere prouction of jets in the non-forwar region. Results for jet correlations are less epenent on etails of u-pf evolution moels than in the case of forwar-region observables. Owing to the large phase space available for jet prouction, the DIS kinematic region uner consieration may be relevant for unerstaning the extrapolation of initial-state showering effects to the LHC, espite the lower energy. Acknowlegments. We thank the organizers of the Symposium for the invitation, an gratefully acknowlege the hospitality an support of the Galileo Galilei Institute for Theoretical Physics. References [] Z. Bern et al., arxiv:8.9 [hep-ph], in Proceeings of the Workshop Physics at TeV Colliers" (Les Houches, 7). [] S. Höche, F. Krauss, N. Lavesson, L. Lönnbla, M. Mangano, A. Schälicke an S. Schumann, hep-ph/6; N. Lavesson an L. Lönnbla, arxiv:7.966 [hep-ph]. [] S. Alekhin et al., hep-ph/6, hep-ph/6: Proceeings of the Workshop HERA an the LHC", es. A. De Roeck an H. Jung. [] an H. Jung, arxiv:7.568 [hep-ph]. [5] G. Corcella et al., JHEP () [arxiv:hep-ph/6]; G. Corcella et al., arxiv:hep-ph/. [6] T. Sjöstran, S. Mrenna an P. Skans, JHEP 65 (6) 6. [7] G. Marchesini an B.R. Webber, Nucl. Phys. B86 (99) 5; M. Ciafaloni, Nucl. Phys. B96 (988) 9. [8] S. Catani, M. Ciafaloni an, Phys. Lett. B (99) 97; Nucl. Phys. B66 (99) 5; Phys. Lett. B 7 (99) 7. [9] S. Chekanov et al. [ZEUS Collaboration], Nucl. Phys. B 786 (7) 5 [arxiv:75.9 [hep-ex]]. [] Z. Nagy an Z. Trocsanyi, Phys. Rev. Lett. 87 () 8 [arxiv:hep-ph/5]. [] an H. Jung, preprint DESY-7-8, OUTP-7--P. [] Y. Delena, arxiv:76.7 [hep-ph]. [] S. Höche, F. Krauss an T. Teubner, arxiv:75.577 [hep-ph]. [] K. Golec-Biernat, S. Jaach, W. Placzek, P. Stephens an M. Skrzypek, hep-ph/77. [5] L. Lönnbla an M. Sjöahl, JHEP 55 (5) 8; JHEP () ; G. Gustafson, L. Lönnbla an G. Miu, JHEP 9 () 5. [6] H. Jung, Comput. Phys. Commun. () [arxiv:hep-ph/9]; H. Jung an G.P. Salam, Eur. Phys. J. C 9 () 5 [arxiv:hep-ph/]. [7] J.C. Collins, Acta Phys. Polon. B () ; arxiv:78. [hep-ph]; J.C. Collins an, JHEP () 6; Phys. Lett. B 7 () 9. [8], Phys. Lett. B 655 (7) 6 [arxiv:hep-ph/796]; arxiv:78.9 [hep-ph]. PoS(RAD COR 7) 5