Multiplicity difference between heavy and light quark jets revisited

1. XXXV Int. Symposium on Multiparticle Dynamics Kroměříž, Czech Republic, August 9 - 15, 2005 Multiplicity difference between heavy and light quark jets revisited Work by Yuri L. Dokshitzer, Fabrizio Fabbri, Valery A. Khoze and Wolfgang Ochs Presented by Fabrizio Fabbri INFN - Bologna Brief introduction MLLA prediction for the multiplicity of light hadrons accompanying heavy quark pair production in e+e¯ Why a revision ? Estimate of Next-to-MLLA terms N.B. Detailed description of the present work in hep-ph/0508074 Conclusions

2. Within the framework of pQCD essential differences between heavy and light (u,d,s) quark jets are expected due to dynamical restriction on the phase space of primary gluon radiation in the heavy quark case Gluon radiation off an energetic heavy quark Q , with mass MQ and energy EQ >> MQ is suppressed inside the forward angular cone with opening angle Θo =MQ / EQ Yu.L.Dokshitzer, V.A.Khoze and S.I.Troyan, Proc. of the 6th Int. Conf. on Physics in Collisions, Chicago, 1986 and J. Phys. G17 (1991) 1481, 1602. Dead cone + LPHD ⇨ expect difference between the companion multiplicity of primary light hadrons in QQ̄ and qq̄ initiated jets in e+e- annihilation At c.m.s. energy W = 2 Ejet one obtains the pQCD prediction The const. is different for c- and b-quark initiated events and depends on the type of light hadrons h . decay products of Q-flavoured hadrons Total multiplicity B.A.Schumm, Yu.L.Dokshitzer, V.A.Khoze and D.S.Koetke Phys. Rev. Lett. 69 (1992) 3025 companion multiplicity F. Fabbri - ISMD 2005

3. In the MLL Approximation the companion multiplicity in e+e-QQ̄ events can be related to the particle yield in the light quark events e+e-  qq̄ (q = u,d,s) B.A.Schumm, Yu.L.Dokshitzer, V.A.Khoze and D.S.Koetke Phys. Rev. Lett. 69 (1992) 3025 Thus the difference in the mean charged multiplicities, δqℓ, between Q and q - initiated events at fixed annihilation energy W depends only on the heavy quark mass M, and remains W-independent for b quarks F. Fabbri - ISMD 2005

4. This predicted energy independence is in marked contrast with the expectation of the so called Naïve Model, which predicts instead a gradually growing difference of the type The naïve model is based on the idea of the reduction of the energy scale P.C.Rowson et al., Phys. Rev. Lett. 54 (1985) 2580 A.V.Kisselev, V.A.Petrov and O.P.Yushchenko, Z. Phys. C41 (1988) 521 F. Fabbri - ISMD 2005

5. Experimental measurements of δbℓ at different c.m.s. energies in e+e- annihilation Compilation from OPAL paper + VENUS and prelim. DELPHI at 206 GeV Original MLLA prediction δbℓ= 5.5 ±0.8 Schumm, Dokshitzer, Khoze, Koetke (1992) weighted average 3.12 ± 0.14 Naive model prediction Data show NO energy dependence ( supporting the MLLA prediction ) Naïve model strongly disfavoured MLLA expectation high compared to data F. Fabbri - INFN Bologna

6. Another interesting consequence of QCD coherence is that the particle multiplicity in 3-jet events can be written in MLLA as the sum of quark and gluon jet multiplicities E*q = q or q̄ energy p*┴ = gluon transverse momentum With Wqq̄ = 2 E*q one gets NQQ̄g (W) – Nqq̄g (W) = NQQ̄ (WQQ̄ ) - Nqq̄ (Nqq̄ ) First preliminary data from 3-jet event analysis (DELPHI exp.) show energy independence and a value of δbℓconsistent with the precise result from VENUS Presented by K. Hamacher at ISMD 2004 F. Fabbri - ISMD 2005

7. Why the original MLLA numerical prediction (1992) needs a revision ? This value relies on the experimentally measured quantities and All together they have a sizeable impact on the original MLLA result. Not enough time to go through all details (see hep-ph/0508074 for this) Only major points in the following F. Fabbri - ISMD 2005

8. Which terms need revision ? Average number of charged particles coming from the decay of two B-hadrons 11.0 ± 0.2 Mean charged multiplicity of e+e-→ qq̄ (q = u,d,s) events at energy scale Wob = √e Mb From recent (2001) combined results of LEP and SLD this value becomes 11.1 ± 0.18 practically unchanged with respect to that used for the original MLLA analysis (1992) 5.5 ± 0.7 This value should be changed according to the present analysis F. Fabbri - ISMD 2005

9. For our purposes, appropriate to use the two-loop pole mass (M b)pole = 4.7 – 5.0 GeV S.Eidelman et al., Phys. Lett. B592 (2004) 1 ⇨scale Wob = √e M b at which the mean charged multiplicity generated by light quarks must be evaluated is then √s = (8.0 ± 0.25) GeV NO direct measurements of Nqq̄ch (8 GeV) ⇩ - Interpolate existing data on TOTAL mean charged multiplicity - Subtract multiplicity contribution of c-quarks (c-quark fraction at 8 GeV is 40%) We did the following - Use all existing data in the energy range (1.4 GeV – 91.2 GeV) - Fit the data points over increasingly wider energy ranges 7 – 14 GeV ; 7 – 44 GeV ; 7 – 62 GeV and 7 – 91.2 GeV - Use different fitting parameterisations to test stability and consistency of the interpolated value at 8 GeV (data above 10 GeV corrected for b-quark effects) NEW method compared to the original MLLA analysis ⇩ fit result F. Fabbri - ISMD 2005

10. NEWLY evaluated correction for c-quark contamination (much more precise data from LEP and SLC available since the original analysis) Detailed discussion of this point in appendix B of hep-ph/0508074 Data show remarkable energy independence also for δcl New experimental weighted average Experimental results from direct measurement ( 1992 average was 2.2 ± 1.2 ) We assume δcℓ = 1.0 also at 8 GeV and finally obtain Revised low energy data points Important to have precise measurements ofδcl at low energies, in particular at √s = 8 GeV, to verify our hypothesis. ( It was 5.5 ± 0.7 ) F. Fabbri - ISMD 2005

11. Cross check the result by fitting data (corrected at the u,d,s level) down to 1.4 GeV. This time get light flavor multiplicity directly from the fit Mean charged multiplicity for e+e¯→ qq̄ (q = u,d,s) events = 6.6 ± 0.35 Completely consistent with the previous result Same fitting curve extrapolated to 91.2 GeV data above 11 GeV not used for the fit ! One example Fit in the range 1.4 – 11 GeV - c- and b-quark contribution subtracted from the data - energy dependence of the flavor composition taken into account - use δcl = 1.0 and δbl = 3.1 (exp. averages) F. Fabbri - ISMD 2005

12. These results are also consistent with several global QCD fits to data on total mean multiplicities 3NLO-fit (to data above 10 GeV) 7.3 I.M.Dremin and J.W.Gary - Phys. Lett. B459 (1999) 341 Numerical solution of the MLLA evolution eq. + full O(αs) effects 6.5 S.Lupia and W. Ochs - Phys. Lett. B418 (1998) 214 for light quarks and the prediction from Pythia 6.2 M.C. 6.5 T.Sjöstrand (private comm.) (default version - generation of light quarks only - no ISR) Finally the (revised) MLLA prediction for b-quark jets becomes 11.1 ± 0.18 6.7 ± 0.34 N.B. About 1 unit lower than the original 1992 prediction 5.5 ± 0.8 F. Fabbri - ISMD 2005

13. Experimental results and revised MLLA prediction MLLA 2005 δbl = 4.4 ± 0.4 (2005) N.B. Derived results on δbl at energies below 91 GeV have been reevaluated in the present analysis Theory still above the experimental average … but definitely in a better quantitative agreement F. Fabbri - ISMD 2005

14. Can the remaining discrepancy be attributed to the Next-to-MLLA contributions ? Next-to-MLLA correction terms are copious (hard to collect them all). There are, however, some specific contributions that are believed to be dominant, arising from Large angle two soft gluon systems (dipole configurations) (1-z) rescaling of the argument of the dead cone subtraction (which improves the description of the small angle emission from the heavy quark) Detailed presentation of this result in appendix A of hep-ph/0508074 F. Fabbri - ISMD 2005

15. Numerical estimate of these next-to-MLLA terms Assuming Λ = 250 MeV one get for nf = 3 αs (Mb) = 0.23 from the 1-loop formula The predicted value of δbl including these contributions becomes δbl ≈ 2.6 ± 0.4 The MLLA prediction is already close to the experimental data and the remaining difference is of the order of the expected next-to-MLLA contributions. Results on charm quark jets Following the same approach as for b-quark jets we reevaluate alsoδcℓand find δcℓ=1.5± 0.4 very similar to the value of 1.7 ± 0.4 found in the original analysis. F. Fabbri - ISMD 2005

16. Multiplicities associated with the Higgs particle The measurement of the processγγ → H → bb̄ is one of the important goals of a future linear e+e- collider. Analogously, but with initial gluons, the SM Higgs boson is expected to be produced in the central exclusive diffractive process pp → p + H + p In both cases, the 3-jet final state produced by the radiative processes γγ → bb̄g and gg → bb̄g (for which the Mb2/mH2 suppression does not apply) could induce a significant background fot the Higgs signal. The relative probability of the Mercedes like configuration in the final qq̄g state for background processes, becomes indeed unusually large. The results presented in this paper allow to evaluate the difference between the charged multiplicity of the signal and Mercedes-like events containing b-quarks, for both the above mentioned processes. For example the difference in multiplicity in the case of a 100 GeV Higgs boson (N.B. the difference rises with increasing MH ) between background events and signal events is evaluated to be ΔN = 6.8 ± 1.5 tracks. We may expect that such a large effect could help to discriminate thetwo F. Fabbri - ISMD 2005

17. Conclusions F. Fabbri - ISMD 2005

18. F. Fabbri - ISMD 2005