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Chapter Inclusive Jet Cross Section
Chapter Inclusive Jet Cross Section
Figure 1: One-jet cross sections in NLO: ET (top) and η (bottom) distributions compared
j et
j et
Figure Inclusive di erential jet cross sections d dE and d d compared
to H1 (left) and ZEUST (right) data.
j et
with the next to leading order calculations Solid line calculations done with JETSAM
j et
Figure Inclusive di erential jet cross sections d dE and d d compared
T
program based on the results of M Klasen G Kramer and S G Salesch using
with the next to leading order calculations Solid line calculations done with JETSAM
GRV HO photon structure function and dash dotted line using AFG P Aurenche et al
program based on the results of M Klasen G Kramer and S G Salesch using
photon structure function Dashed line calculations of P Aurenche J Ph Guillet and
GRV HO photon structure function and dash dotted line using AFG P Aurenche et al
M Fontannaz Op en symbols are the data p oints after correction for underlying event
photon structure function Dashed line calculations of P Aurenche J Ph Guillet and
tegrateenergy either over η (top) or ET (bottom). The agreement between the two
M Fontannaz Op en symbols are the data p oints after correction for underlying event calculationsenergy and theory and data is excellent for the AFG structure functions (dashed curves) except in the forward region at low ET . This discrepancy vanishes after hadronization corrections (empty data points). At larger ET , the effect of hadronization and the discrepancy in the forward region are re- duced. The GRV photon structure function (full curves) underestimates the H1 data. However, the ZEUS data4 (right hand side of fig. 1) are overestimated when using the GRV structure function (full curves) except in the forward re- gion and can be better described by the GS structure function (dashed curves).
Next, we turn to two-jet cross sections, where only ZEUS 1993 data4 and our predictions5 with NLO direct and LO resolved contributions were avail- a 1 able so far. We compare the distribution in η = 2 (η1 + η2) integrated over ∗ ET > 6 GeV and the difference of the two rapidities |η | = |η1 − η2| < 0.5
aFor a comparison of our predictions to ZEUS 1994 data see L. Feld’s contribution to these proceedings.
2 Figure 2: Two-jet cross sections in NLO: η distributions compared to ZEUS data for different photon structure functions (left) and jet definitions (right).
OBS for xγ > 0.75 using CTEQ(3M) structure functions in the proton. The ZEUS data are again overestimated by the GRV structure function (dashed and dashed-dotted curves) and adequately described by the GS structure func- OBS tion (dotted curve) (left hand side of fig. 2). Since we are at large xγ , the direct process dominates with the resolved process still contributing 15% of the total cross section, and we can distinguish mainly the quark densities in the photon. Even with LO resolved contributions, the scheme dependence is cancelled as can be seen when comparing the GRV predictions in MS scheme (dashed curve) and in DISγ scheme (dashed-dotted curve).
An important prerequisite for pinning down the photon structure function is a good understanding of the jet final state. Here, ambiguities arise due to possible double counting of jets and restrictions in parton-parton separation. The right hand side of fig. 2 shows these uncertainties to be ±10%. They are reduced at larger ET similar to the hadronization corrections as demonstrated above for one-jet cross sections.
Finally, we present the first NLO predictions for resolved photoproduction of two jets, using again the phase space slicing method.6 The calculation was completed shortly after the workshop and checked with our old program in one-jet production.1 Fig. 3 shows the effect of the higher order contributions for η distributions in the direct dominated region (left) and the resolved domi- nated region (right). As expected from one-jet production, the corrections are large and range from 40% (“direct”) to 75% (“resolved”) in the central region. Whereas they are symmetric for the latter, they increase rapidly from the back- OBS ward to the forward region for xγ > 0.75 thus improving the description of the data in the forward region.
3 OBS Figure 3: Resolved two-jet cross sections in NLO and LO: η distributions for xγ > 0.75 OBS (left) and xγ ∈ [0.3; 0.75] (right).
Acknowledgments
It is a pleasure to thank G. Kramer and T. Kleinwort for their collaboration on the calculations and L. Feld and J. Butterworth for helpful discussions concerning the jet definitions. I would also like to thank A. Vogt and the con- venors for the invitation. This work is supported by BMBF, Bonn, Germany under contract 057HH92P(0) and EEC Program ”Human Capital and Mo- bility” through Network ”Physics at High Energy Colliders” under Contract CHRX-CT93-0357 (DG12 COMA).
References
1. M. Klasen, G. Kramer, S.G. Salesch, Z. Phys. C 68, 113 (1995). 2. A. Bouniatian, Ph.D. Thesis, DESY FH1K-95-04 (1995). 3. P. Aurenche, J.Ph. Guillet, M. Fontannaz, Phys. Lett. B 338, 98 (1994). 4. ZEUS Collaboration, Phys. Lett. B 342, 417 (1995), 348, 665 (1995). 5. M. Klasen, G. Kramer, Phys. Lett. B 366, 385 (1996). 6. M. Klasen, T. Kleinwort, G. Kramer, to be published.
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