Forward jet and particle production at low x Leif Jönsson representing H1 and ZEUS

1. Forward jet and particle production at low xLeif JönssonrepresentingH1 and ZEUS Outline of the talk: ● Introduction ● QCD models ● Inclusive jet production ● Forward jet production ● Forward pion production ● Summary and conclusion

2. Introduction • Collisions between electrons and protons offer the ideal possibility to study the partonic structure of matter. • The big advantage is the possibility to vary the ’hardness’ of the interaction by changing the energy and virtuality of the probing photon • The dependence of the parton distributions on the energy fraction, x, and photon virtuality, Q2, is one of the most interesting and challenging problems in QCD. • At small enough x the DGLAP parton evolution description is expected to become inadequate since ln(1/x) terms in the evolution equation will become increasingly important. Significant progress has been made in the theoretical description of the parton evolution but there are still a number of problems to be solved. • Nevertheless the DGLAP scheme has been succesful in describing F2(x,Q2) down to small x and thus signatures for new parton dynamics is expected to be more visible in hadronic final states. • At low Q2 the partonic content of the photon can be probed by the interacting parton of the proton. • HERA offers the highest energies available today for such studies.

3. Matrix elements and higher order corrections Boson-gluon fusion: ● Dominates in the low x region ● Probes the gluon content of the proton ● Calculated in perturbation theory ● Most calculations have been performed up to NLO (DISENT, DISASTER, MEPJET, JetViP) Use evolution equations to simulate higher order emission fj = fo + fi·Pij,k ●fi and fj are the parton density functions for the mother and daughter propagator ●f0 is the input gluon density function ●Pij,k is the probability for the splitting ij,k

4. QCD models DGLAP (collinear approximation) ● QCD expansion by resumming terms of the type (αSlnQ2)n ●Strict ordering in virtuality of the propagators m2 >> kn2>> …>>k12 >> k02 which means strict ordering in transverse momenta of the propagators m2 >> ktn2>>… >> kt12 >> kt02 ● Good approximation at high Q2 values Resolved photons ●The photon can interact via its partonic content  two DGLAP chains

5. QCD models contd. BFKL (kt-factorization) ● Evolution equation includes terms of the type (αSln1/x)n ● These terms become important at small x-values ● Strict ordering in the longitudinal momentum, ln(1/x), of the propagators, ln(1/x)  x02 >> x12 >> ... >> xn2 >> xBj2 ●no ordering in transverse momenta CCFM ●CCFM combines in a consistent manner the properties of DGLAP and BFKL since it resums terms of both the form (αSln1/x)n and (αSln1/(1-x))n ●CCFM evolution is valid both at large and small x ●The CCFM evolution is based on angular ordering of the emitted partons: Ξ >> ξn >> ξn-1 ... >> ξo ●Virtual corrections in the gluon vertex are automatically taken into account (resummed to all orders)

6. QCD models contd. The Colour Dipole Model (CDM) ●Gluon emission originates from colour dipoles which radiate independently.

7. Single inclusive jet measurements Jet search is performed with the longitudinally invariantkT-algorithm requiring: ● Et,jet > 6 GeV ● -1 < hjet < 3 in the laboratory frame Restricted to events with: ● Q2 > 25 GeV2 and y > 0.04 The analysis is performed for two cases: ● The full phase space as defined above ● The ’dijet phase space’, cos gh < 0, hjet < 0 Data are compared to predictions from: ● LEPTO (LO QCD Matrix elements + parton showers) ●Ariadne (colour dipole model) ●DISENT (NLO matrix elements + CTEQ6 pdf)

8. Single inclusive jet cross sections, full phase space ● The CDM model (ARIADNE) gives a very good description of the data, both as a function of hjet and xBj. ● The LO MC model (LEPTO) exhibits slight deviations from data in the very forward rapidity region and in the small x region ● The NLO calculation (DISENT O(aS) deviates rapidly from data as one moves toward the forward region and can also not describe the small x behaviour ● RAPGAP without parton cascade gives similar results as DISENT  NLO is not enough; higher order corrections are necessary

9. Single inclusive jet cross sections, dijet phase space ●The CDM model (ARIADNE) again gives the best description of the data ● The LO MC model (LEPTO) clearly undershoots data over the full rapidity range and in the small x region ● The NLO calculation (DISENT) does not reproduce the shape of the rapidity distribution but is in good agreement with the xBj distribution ● Notice: the scale uncertainties are very big which excludes firm conclusions

10. Forward jet selection ● Ptjet > 3.5 GeV (5 GeV) ● 7.0o < Θjet < 20.0o ● Suppress the DGLAP evolution by choosing the momentum transferred by the virtual photon equal to the transverse momentum of the first propagator in the ladder (forward jet; 0.5< pt2/Q2<2) ● Enhance BFKL by choosing Bjorken-x much smaller than the momentum fraction of the first propagator in the ladder (xjet>0.035 where xjet=Ejet/Ep)

11. ’Typical’ forward jet event Experimental difficulties: ● Acceptance limitations ● Interference with the proton remnant  angular cut necessary

12. Forward jet data ● DGLAP direct too low ● DGLAP direct + resolved and CDM in agreement with data ● CASCADE too high Pgg(z,q,kt) = aS(q2)/(1-z) + aS(kt2)/z · Dns(z,q2,kt) Fit s = dkt2dxgA(xg,kt2,q)s(g*g*qq) to data on F2(x,Q2) Fit performed to F2(x,Q2) from H1 1994

13. New fits of the unintegrated gluon density • ● Adjust the input pdf’s to fit data • on F2(x,Q2) from H1 and ZEUS taken • in 1994 and 1996/97, in the region • Q2 > 4.5 GeV2 and x < 5·10-3 • ● CCFM is based on angular ordering • but requires no ordering in kt of the • propagator, which means that kt can • take any kinematically allowed value • need for a cut, ktcut • ● If kt < ktcut no real emission is allowed in CASCADE and the evolution in angle is continued until kt > ktcut • ● What is the effect of the ktcut? ● JS2001 has a soft cut ktcut> 0.25 GeV, and Q0 = 1.4 GeV, where Q0 is the collinear cut for real emissions ● In the new fits ktcut = Q0 .

14. New fits of the unintegrated gluon density J2003 set 1: ktcut = Q0 = 1.33 GeV Only singular terms in the splitting function J2003 set 2: ktcut = Q0 = 1.18 GeV Includes also non-singular terms in the splitting function ● It is clearly seen that the behaviour of the unintegrated gluon density, in the low x region for small values of kt, depends on how the soft region, kt < ktcut, is treated.

15. Forward jet data contd. J2003-1: Pgg(z,q,kt) = aS(q2)/(1-z) + aS(kt2)/z · Dns(z,q2,kt) Q0 = ktcut = 1.33 GeV J2003-2: Pgg(z,q,kt) = aS(kt2)[(1-z)/z + z(1-z)/2]·Dns + aS(q2)[z/(1-z)+z(1-z)/2] Q0 = ktcut = 1.18 GeV (fits to F2(x,Q2) from H1 1994&1996/97and ZEUS 1994&1996/97)

16. Forward pion production Select p0 mesons via their two-photon decayusing the calorimeter Require: ● 5o < Θp < 25o ● xp = Ep/Ep > 0.01 ● p*T,p > 2.5 GeV Advantage: ● Extends the forward region to smaller angles and to smaller x Disadvantage: ● Smaller rates compared to jets ● Fragmentation effects more significant

17. x dependence of the forward po cross section ● DGLAP direct undershoots the data ● DGLAP direct + resolved gives the best description using m2 = Q2+4pt2 ● LO BFKL modified by KMO also reproduces the data ● CCFM too low at small x ● Agreement with forward jet data in the overlapping region

18. Transverse energy flow around forward po ●DGLAP direct + resolved gives the best description of the data compared to DGLAP direct and CASCADE ●The flat distribution of the data points outside the pion peak indicates that energy compensation occurs over the full phase space

19. Summary Inclusive jet production: ● NLO calculations (DISENT) give a reasonable description of the data except in the high h and low x regions. This is probably due to missing higher order corrections ● The LO DGLAP model (LEPTO) gives a similar description of the data with deviations at high h and low x values ● The colour dipole model (ARIADNE) gives an overall good agreement with data Forward jet production: ● NLO calculations (DISENT) are not able to reproduce the data ● The LO DGLAP model (RAPGAP DIR) does also not describe the data ● Inclusion of resolved photon contributions to the LO DGLAP model (RAPGAP DIR+RES) leads to good overall agreement ● The colour dipole model (ARIADNE) ● The CCFM model (CASCADE) gives a good description of data with the parameter settings from the fits to the improved data on F2

20. Summary contd. Forward pion production: ● The LO DGAP model (RAPGAP DIR) does not reproduce data ●The LO DGLAP model with resolved photons (RAPGAP DIR+RES) is in good agreement with data ● A modified LO BFKL calculation also describes the data ●The CCFM model with the splitting function restricted to singular terms and Q0 = 1.40 GeV and ktcut = 0.25 GeV undershoots data at low x but is consistent with fwd jet data in the overlapping x-region Conclusions ●Although the simple DGLAP model fails to describe data the inclusion of resolved photons leads to good agreement ●The CCFM model is able to reproduce most data but several problems still to be solved ● No clear evidence for new parton dynamics so far