Work done in collaboration with Stefano Frixione

1. Jet and Di-jet production in Photon–Photon collisions Leonardo Bertora 1,2 INFN, Sezione di Genova 1 Università di Genova, DiFi 2 1 Work done in collaboration with Stefano Frixione Leonardo Bertora, 2004 April 14

2. Real photon + - Bremmstrahlung at e e colliders (LEP) If are small, typically below 30 mrad, both the leptons are “untagged”. Real photon production In this case, the photon virtuality averaged is of order , and we can consider both photons as real. Before interacting a real photon can fluctuate in a hadronic state, revealing a “structure”. In a high energy domain , QCD has to be able to describe photon hard interactions. Leonardo Bertora, 2004 April 14

3. Situation Photon – Photon Hard Collisions Motivations: • Hard production of jets is a complementary method (with respect to DIS) to study the “structure” of the photon • It is rich test for QCD (since the beginning of history…Han-Nambu integer charges model) Experimental Situation: • OPAL, hep-ex/0301013 • L3, see Photon2003 proceedings • DELPHI, see Photon2001 proceedings • Future Linear Collider … LEPII Theoretical results: • As of now only the theoretical prediction by Klasen, Kleinwort, Kramer (KKK) (hep-ph/9611450 and hep-ph/9712256) is available Leonardo Bertora, 2004 April 14

4. Motivations Any prediction has to be checked ! Factorization theorem • We are not able to compute differential cross section analytically • We fight against large unphysical oscillations and the computer precision • A general method should be adopted in order to cancel out divergences analytically, and finite remainders can be numerical (MC) integrated • We use subtraction method, KKK used slicing one • … double test: a different computation with a different method Leonardo Bertora, 2004 April 14

5. About subtraction method: Real emission plus virtual correction Neglected O() terms Large-number cancellations without any approximation and large-number cancellation (beware of narrow bins) Leonardo Bertora, 2004 April 14

6. The structure of the “home made” computation NLO terms + + … + • We have recalculated and checked (with respect to KKK’s) matrix elements • We implemented a “partons generator” (hep-ph/9512328 and hep-ph/9706545) divided in three classes of Feynman diagrams: double resolved, single resolved, direct diagrams • We have to rely on non-perturbative inputs such as PDFs and …paper in preparation Leonardo Bertora, 2004 April 14

7. The first check A first check: A comparison with OPAL 1997 (one inclusive jet) KKK Inclusive Jet Production in Photon-Photon Collision at sqrt(s)=130 and 136 GeV, Opal coll., Zeit. Fur Physik(1997) Ok, at least we are on the right path… Leonardo Bertora, 2004 April 14

8. Scheme DI-MS But we need self consistence tests!!! Unfortunately they are very boring! Let’s try to see their physical meaning: what about the true point-like photon contribution to the cross section? Each class of diagrams is separately divergent: We have removed analytically the infinities modulo finite, scheme dependent, terms Thus colored histos do not have a real physical meaning Changing the factorization scheme Leonardo Bertora, 2004 April 14

9. Try another way… Changing the factorization scale Changing the PDF Leonardo Bertora, 2004 April 14

10. Dangerous regions: Recall our simple model to deal with the final state direct contribution in the dangerous region Let’s try to understand where our troubles come from Dangerous regions: PYTHIA HERWIG 350% Zoom OPAL Failure of the perturbative computation Let’s try to understand where our troubles come from Leonardo Bertora, 2004 April 14

11. Phi angle • Symmetric cuts on Et imply large log corrections • Opal coll. have chosen to impose: Observation: • In NLO computation • In the limit we run into IR divergences! Cuts on the phase space for di-jet observables Dangerous regions II: NLO Limit Opal Phase Space Et min … thus even if in principle Opal’s choice could be dangerous, in practice it is far from the singularity sources! Leonardo Bertora, 2004 April 14

12. Results:Theo.vs.Opal KKK Data from Di-Jet Production in photon-photon collisions at sqrt(s) from 189 to 209 GeV, OPAL coll., hep-ex/0301013 Leonardo Bertora, 2004 April 14

13. Results:opal2 Results:Theo.vs.Opal II Data from Di-Jet Production in photon-photon collisions at sqrt(s) from 189 to 209 GeV, OPAL coll., hep-ex/0301013

14. Results:l3 Results:Theo.vs.L3 Good shape, but not really good normalization Wrong shape and normalization: Preliminary data seem to confirm L3-hadron production discrepancy with NLO prediction L3 Preliminary Leonardo Bertora, 2004 April 14

15. Conclusions Conclusions: • We implemented a computer code to compute jet and di-jet observables using the subtraction method; our results are in agreement with the predictions by KKK. • The comparisons of our results with OPAL data are really satisfactory for inclusive observables. The comparison with L3 data is troublesome! • Finally, we analyzed some theoretical QCD (NLO) difficulties to describe well particular exclusive observables measured by OPAL. Theoretical uncertainties for inclusive observables are under control. Leonardo Bertora, 2004 April 14

16. Results:opalB PHYTIA KKK NLO/(1+dhadr) KKK KKK Data from Di-Jet Production in photon-photon collisions at sqrt(s) from 189 to 209 GeV, OPAL coll., hep-ex/0301013 L. Bertora

17. Results:opalc Data from Di-Jet Production in photon-photon collisions at sqrt(s) from 189 to 209 GeV, OPAL coll., hep-ex/0301013