1. Costas Foudas, Imperial College, 1.5.02 Jet Production at High Transverse Energies at HERA Underline: Costas Foudas Imperial College c.foudas@ic.ac.uk Krakow 1.5.2002 (1) Introduction (2) Jet Production in NLO pQCD (3) Jet Measurements and  s (4) Summary and outlook

2. Costas Foudas, Imperial College, 1.5.02 Jet Events at HERA Jet signatures are clearly visible !!! Jet production has been measured at HERA for 0  Q 2  10 4 GeV 2 and 4  E T  100 GeV  jet =(-1)ln(tan(  jet /2))

3. Costas Foudas, Imperial College, 1.5.02 Jet Production in e-p scattering at HERA At LO pQCD two processes contribute to Jet production : Boson-gluon fusion (BGF) QCD Compton (QCDC) Sensitive to the gluon parton distribution function xg(x) and the strong coupling constant  s. Mainly at low x. Sensitive to the sea quarks, which are constrained from measurements of the proton structure, and  s.  = x(1 + M JJ 2 / Q 2 ): Fraction of the proton’s momentum carried by the emitted parton. ssss ssss Q 2 =-q 2 Q2Q2Q2Q2 X BJ = Q 2 2pq q Y=q.p/p.l

4. Costas Foudas, Imperial College, 1.5.02 Jet Production Cross Sections The Jet production Cross Section can be written in terms of the proton Parton Distribution Functions and the hard Scattering cross section as: d  (ep  jet+jet+X) =   q i (x,  F,  s )  i (  R,  s  F ) (1+  had )   q i (x,  F,  s )  i (  R,  s  F ) (1+  had ) 2 2 2 The cross section calculation is only The cross section calculation is only reliable if : reliable if :   R,  F Uncertainties are small (what is  R =?)   had Correction and uncertainty is small  PDF uncertainties are small FactorizationScale RenormalizationScale Parton to Hadron Corrections Hence, to test QCD and perhaps make a discovery, one must measure Jets at High Q 2 and high E T

5. Costas Foudas, Imperial College, 1.5.02 Renormalization Scale Uncertainties The uncertainties decrease with Q 2 and E T but they depend upon the choice of  R (Q 2 or E T or ?) 2

6. Costas Foudas, Imperial College, 1.5.02 PDF Uncertainties Ratios of cross sections are in general less sensitive to the PDF uncertainty !!!!

7. Costas Foudas, Imperial College, 1.5.02 Hadron to Parton Corrections At low Q 2 the corrections depend strongly on the choice of the jet finder but as Q 2 increases they converge. In all cases the hadronization corrections decrease with increasing Q 2.

8. Costas Foudas, Imperial College, 1.5.02 pQCD Predictions and Asymmetric Jet Cuts The predictions become unphysical when the two jets balance in E T !!! This is because there is no phase space for extra gluons to be emitted in the final state Use asymmetric jet cut: E T BRE (2) > 5 GeV and E T BRE (1) > 8 GeV

9. Costas Foudas, Imperial College, 1.5.02 Jet Data vs Monte Carlo Models Although the Monte Carlo reproduces well the shape of the measured cross sections (good for calculating corrections) It does not reproduce the jet absolute cross section.

10. Costas Foudas, Imperial College, 1.5.02 The DiJet cross section vs Q 2 The data agrees well with the predictions of pQCD within 10% for  2 R = Q 2 Large scale uncertainty at low Q 2. Only for Q 2 > 400 GeV 2 does it decrease below 10%. The data are more precise than the predictions. Need predictions with smaller uncertainty

11. Costas Foudas, Imperial College, 1.5.02 DiJet Cross Section vs  Within the theoretical and experimental uncertainties the measured DiJet cross section agrees with the pQCD predictions using xg(x) extracted from scaling violations and other data. Important test of the universality of xg(x)

12. Costas Foudas, Imperial College, 1.5.02 Dijet Double Differential Cross Section

13. Costas Foudas, Imperial College, 1.5.02 DiJet Cross Sections I 5  Q 2  5000 GeV 2 0.2  y  0.6 -1   lab  2.5 E T,1 +E T,2  17 GeV E T,1,2  5 GeV d  /d  is sensitive to the gluon PDF and is Described well by NLO+CTEQ5M1 d  /dM JJ described well except at low Q 2

14. Costas Foudas, Imperial College, 1.5.02 DiJet Cross Sections II d  /dE T described well except at low Q 2 d  /d  : The NLO corrections are large in the forward Region at low Q 2. NLO QCD describes d  /d  in the entire kinematical region

15. Costas Foudas, Imperial College, 1.5.02 3 Jets Cross Sections 3 Jet Cross sections are sensitive to a s already at LO pQCD  Important test of QCD 2 The shapes and angular distributions of the cross sections are sensitive to the dynamics of the interaction X 4 =E 4 /M 3jet X 3 =E 3 /M 3jet cos 3 = P B· P 3 |P B | · |P 3 | |P B | · |P 3 | cos  3 = (P 3  P B ) · (P 4  P 5 ) | P 3  P B | · | P 4  P 5 | | P 3  P B | · | P 4  P 5 |

16. Costas Foudas, Imperial College, 1.5.02 3 Jet Cross Section vs Q 2 The 3-jet cross section is in good agreement with the predictions of NLO pQCD including Hadronization corrections (-18 -22%)  R -uncertainties dominant below 50 GeV 2 ; a s -uncertainties dominate; Sensitivity to a s

17. Costas Foudas, Imperial College, 1.5.02 3-Jets to 2-Jets Rate The ratio is described Well by the predictions of NLO pQCD plus hadronization corr. (-18% -10%) Renoramlization scale Uncertainties reduced particularly at low Q 2 The ratio is sensitive to a s but it is insensitive to the gluon distribution in the proton.

18. Costas Foudas, Imperial College, 1.5.02 3-Jets Cross Sections The NLO pQCD predictions describe well also the X BJ and M 3jet distributions.

19. Costas Foudas, Imperial College, 1.5.02 3-Jets Cross sections vs  3 and  3 The shapes of the NLO predictions are different than those of phase space curves and in agreement with the data. Jet 3 prefers the proton Or photon directions. NLO QCD and Phase Space predictions have different shape due to the Bremsstrahlung nature of the process The data prefers  3  0 or  3  The predictions are in reasonable agreement with the data !!

20. Costas Foudas, Imperial College, 1.5.02 3-Jets Cross Sections vs X 4 and X 3 The data are well described By the NLO pQCDpredictions

21. Costas Foudas, Imperial College, 1.5.02 Measuring a S from the Jet data ZEUS measured the ratio of dijet (d  2+1 ) over the total cross section (d  tot ) and extracted a S by fitting extracted a S by fitting. The cross section falls by 4 orders of magnitude and the predictions of pQCD are in very good agreement with the data.

22. Costas Foudas, Imperial College, 1.5.02 The a s evolution with Q 2 Both a precise determination of the strong coupling constant and a test of its energy-scale dependence.  S =0.1166  0.0019 -0.0033- 0.0044. (stat.) (exp.) (th.) +0.0024+0.0057 At  R = M Z these measurements result to:

23. Costas Foudas, Imperial College, 1.5.02 Dijet Cross sections at High Q 2 After the fit the cross sections as a function of the jet pseudorapidity and jet transverse energy were compared with the NLO pQCD Predictions using the a S found from the fit. The measured cross sections agree well with the NLO pQCD predictions calculated using DISENT

24. Costas Foudas, Imperial College, 1.5.02 Extracting a s from Inclusive Jets  s (M Z ) = 0.1186  0.0059 (tot.)  s (M Z ) = 0.1186  0.0030 +0.0039 +0.0033 -0.0045 -0.0023

25. Costas Foudas, Imperial College, 1.5.02 Jet Photoproduction at High E T Direct Photon diagram Resolved Photon diagram Scale = E T jet x  =  E t e -  /2yE e Fractional photon momentum Direct  x  = 1 Resolved  x  < 1 Resolved  Direct

26. Costas Foudas, Imperial College, 1.5.02 Dijet Photoproduction I Q 2  1 GeV 2 0.1  y  0.9 E Tmax  25 GeV E Tsecond  15 GeV -0.5    2.5 40% from gluons in the proton The NLO pQCD Calculations using PDFs coming from F 2 at lower scales agree reasonably well with the data  Universal PDFs

27. Costas Foudas, Imperial College, 1.5.02 Dijet Photoproduction II The dijet data are shown for two different E T ranges Representing different factorization scales for the proton and photon PDFs. The NLO pQCD predictions agree well with the data and change very little if the GRV or the AFG photon PDFs are used. In contrast the renormalization scale uncertainties are significant….

28. Costas Foudas, Imperial College, 1.5.02 Dijet Photoproduction III%-Difference Between the measured cross Sections and the NLO pQCD predictions Correlateduncertainty Renormalization scale uncertainty

29. Costas Foudas, Imperial College, 1.5.02 High Mass Dijets I M JJ = 2E T1 E T2 (cosh(  1-  2)-cos(  1-  2)) The cross section falls by 3 orders of magnitude.  Renormalization scale uncertainties less than 15%. less than 15%.  Hadronization uncertainties within 5% !!! within 5% !!!  Uncertainty due to proton and photon PDFs > 6%, 10% (norm) photon PDFs > 6%, 10% (norm)  The shape of the distributions is described well by QCD but the data are above the calculations (still consistent) 47  M JJ  160 GeV

30. Costas Foudas, Imperial College, 1.5.02 High Mass Dijets II **** cos  * = tanh(1/2(  1 -  2 ))  = (1+|cos  * |) /(1-|cos  * |) 1111 2222 Renormalization scale uncertainties less than 5%. Gluon exchange  uniform Quark exchange  1/(1+  ) Good agreement  Dynamics is OK

31. Costas Foudas, Imperial College, 1.5.02 Limits for Resonance decaying to Two Jets Having the experimental and theoretical uncertainties under control,the dijet data are then used to search for a resonance P above 60 GeV decaying to two jets:  p  P +X  Jet+Jet+X The d  /dM jj is compared to the NLO QCD predictions normalized to the data.

32. Costas Foudas, Imperial College, 1.5.02 Summary and Outlook Jet data at high E T have been used at HERA-I to test QCD and make precise measurements of the gluons and  SJet data at high E T have been used at HERA-I to test QCD and make precise measurements of the gluons and  S The detector and theory systematic errors have been well understood and we have learned that jet measurements can be made to better than 10% level if the E T is high enough (high Q 2 is needed also)The detector and theory systematic errors have been well understood and we have learned that jet measurements can be made to better than 10% level if the E T is high enough (high Q 2 is needed also) Low Q 2 regime is rich but require more precise theoretical calculations. Low Q 2 regime is rich but require more precise theoretical calculations. HERA II will start soon !! One can expect a large increase of the high E T high Q 2 samples which will enable us to tag the proton PDFs at higher x, measure  S, BFKL, search for new physics. HERA II will start soon !! One can expect a large increase of the high E T high Q 2 samples which will enable us to tag the proton PDFs at higher x, measure  S, BFKL, search for new physics.