1. Parametrized Jet Energy Resolution Studies Darius Gallagher, Graham W. Wilson Univ. of Kansas Cornell Workshop, July 15 th 2003

2. Goal Verify intrinsic resolution limitations on jet energy measurement goal of 30%/  E jet in energy flow algorithm. Assume charged particles measured by tracker, photons measured by ECAL, neutral hadrons by HCAL. Check for wide range of energy and hadron producers –91 GeV and 1 TeV NB 91 GeV is a proxy for multi-jet events neare threshold –e + e -  q qbar –Normal mixture quarks, u, d, s, b, c, tau, (gluons in progress)

3. Parametrizations EM Energy resolution :  E /E = c 1 /  E(GeV)  c 2 HCAL Energy resolution :  E /E = c 3 /  E(GeV)  c 4 Tracker resolution :  pT /p T 2 = c 5 ( GeV -1 ) Central values : 10%/  E  1% 50%/  E  4% 5  10 -5 Keep 4 parameters fixed at central values, vary 5 th.

4. Method Event generator : Pandora-Pythia No acceptance cuts ISR and beamstrahlung turned off –With no resolution effects : delta function at center-of-mass energy Measure rms of the same 10,000 events as the resolution parameter is varied. –Quoted result scaled by  E

5. 3 different plot types 1) Total energy. Ignore effects of events with neutrinos by assuming neutrinos are measured perfectly (only really an issue for tau, b, c) 2) Visible energy. Assume neutrinos are not measured (good assumption!). 3) Neutrinoless. Assume events with neutrinos can be identified and ignore them. (NB efficiency of this cut can be low !) => 3 types x 5 parameters x 2 energies = 30 plots which are included here for reference.

6. Z to hadrons

7. “Total” Energy Plots

8. c1c1 Motivation for good ECAL stochastic resolution

9. c2c2

10. c3c3 Motivation for excellent HCAL stochastic resolution

11. c4c4

12. c5c5

13. Mean Energy Components at 91 GeV u d s c b Charged 57.2 55.0 57.3 56.5 55.6 Photons 25.2 25.3 20.4 22.8 22.9 Neutrinos 0.02 0.17 0.02 2.0 5.6 Klong 3.1 3.5 7.5 5.5 4.5 Neutrons 5.5 7.1 5.9 4.1 2.9 It would be good to know at what level we can trust these numbers ….

15. For taus : constant term starts to be important

18. Poor tracker resolution : hurts taus a lot

19. Visible Energy plots

20. Basically, better than 30%/  E only trivially achievable for light quarks.

25. Well – if it was hard at 91 GeV it’s even harder at 1 TeV

30. Neutrinoless plots Visible energy for events with no neutrinos. For b quarks particularly one can vertex tag b-quarks, identify leptons from the b-decay and infer the existence of neutrinos –So to some extent these are very relevant. NB no taus at all !

32. For ECAL, constant term is irrelevant to jet energy measurement for 91 GeV jets.

37. Even at 1 TeV, constant term not too important

39. HCAL constant term starts to be important

40. Poor tracker resolution is an issue (worse than 1 x 10 -4 )

41. Conclusions for jet energy measurements HCAL stochastic energy resolution by far the most important ECAL stochastic important for taus HCAL and ECAL constant terms start to be important at 1 TeV Tracking resolution has some margin – but can’t be degraded too much at 1 TeV. NB None of this addresses the hard part – the pattern recognition and separation of particles.