Multiplicity difference between heavy and light quark jets revisited XXXV Int. Symposium on Multiparticle Dynamics Krom ěří ž, Czech Republic, August , 2005 Fabrizio Fabbri INFN - Bologna Work by Yuri L. Dokshitzer, Fabrizio Fabbri, Valery A. Khoze and Wolfgang Ochs 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 Conclusions Presented by N.B. Detailed description of the present work in hep-ph/

10/8/2005F. Fabbri - ISMD 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 M Q and energy E Q >> M Q is suppressed inside the forward angular cone with opening angle Θ o = M Q / E Q Dead cone + LPHD ⇨ expect difference between the companion multiplicity of primary light hadrons in QQ ̄ and qq ̄ initiated jets in e + e - annihilation Yu.L.Dokshitzer, V.A.Khoze and S.I.Troyan, Proc. of the 6 th Int. Conf. on Physics in Collisions, Chicago, 1986 and J. Phys. G17 (1991) 1481, DEAD CONE phenomenon Total multiplicity companion multiplicity decay products of Q-flavoured hadrons At c.m.s. energy W = 2 Ejet one obtains the pQCD prediction B.A.Schumm, Yu.L.Dokshitzer, V.A.Khoze and D.S.Koetke Phys. Rev. Lett. 69 (1992) 3025 The const. is different for c- and b-quark initiated events and depends on the type of light hadrons h.

10/8/2005F. Fabbri - ISMD In the MLL Approximation the companion multiplicity in e + e -  QQ ̄ events can be related to the particle yield in the light quark events e + e -  qq ̄ ( q = u,d,s ) Thus the difference in the mean charged multiplicities, δ qℓ, between Q and q - initiated events at fixed annihilation energy W depends only on the heavy quark mass M, and remains W-independent B.A.Schumm, Yu.L.Dokshitzer, V.A.Khoze and D.S.Koetke Phys. Rev. Lett. 69 (1992) 3025 for b quarks

10/8/2005F. Fabbri - ISMD 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

10/8/05 - ISMD 2005F. Fabbri - INFN Bologna5 Naive model prediction Experimental measurements of δ b ℓ at different c.m.s. energies in e + e - annihilation Original MLLA prediction δ b ℓ = 5.5 ± 0.8 Schumm, Dokshitzer, Khoze, Koetke (1992) weighted average 3.12 ± 0.14 Naïve model strongly disfavoured Data show NO energy dependence ( supporting the MLLA prediction ) Compilation from OPAL paper + VENUS and prelim. DELPHI at 206 GeV MLLA expectation high compared to data

10/8/2005F. Fabbri - ISMD Presented by K. Hamacher at ISMD 2004 First preliminary data from 3-jet event analysis (DELPHI exp.) show energy independence and a value of δ b ℓ consistent with the precise result from VENUS 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 q ̄ energy p * ┴ = gluon transverse momentum With W qq ̄ = 2 E * q one gets N QQ ̄ g (W) – N qq ̄ g (W) = N QQ ̄ (W QQ ̄ ) - N qq ̄ (N qq ̄ )

10/8/2005F. Fabbri - ISMD Why the original MLLA numerical prediction (1992) needs a revision ? This value relies on the experimentally measured quantities All together they have a sizeable impact on the original MLLA result. Not enough time to go through all details (see hep-ph/ for this) Only major points in the following - New relevant exp. results since the 1992 analysis - Some small errors and inconsistencies spotted in the literature - Improved analysis of old data on mean charged multiplicities and

10/8/2005F. Fabbri - ISMD ± ± 0.7 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) This value should be changed according to the present analysis Average number of charged particles coming from the decay of two B-hadrons Mean charged multiplicity of e + e - → qq ̄ (q = u,d,s) events at energy scale W o b = √e M b Which terms need revision ?

10/8/2005F. Fabbri - ISMD NO direct measurements of N qq ̄ ch (8 GeV) ⇩ - Interpolate existing data on TOTAL mean charged multiplicity - Subtract multiplicity contribution of c-quarks (c-quark fraction at 8 GeV is 40%) 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 W o b = √e M b at which the mean charged multiplicity generated by light quarks must be evaluated is then √s = (8.0 ± 0.25) GeV - 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) We did the following NEW method compared to the original MLLA analysis ⇩ fit result

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

10/8/2005F. Fabbri - ISMD Cross check the result by fitting data (corrected at the u,d,s level) down to 1.4 GeV. - c- and b-quark contribution subtracted from the data - energy dependence of the flavor composition taken into account - use δ cl = 1.0 and δ bl = 3.1 (exp. averages) Mean charged multiplicity for e + e¯ → qq ̄ (q = u,d,s) events One example Fit in the range 1.4 – 11 GeV Same fitting curve extrapolated to 91.2 GeV data above 11 GeV not used for the fit ! = 6.6 ± 0.35 Completely consistent with the previous result This time get light flavor multiplicity directly from the fit

10/8/2005F. Fabbri - ISMD Finally the (revised) MLLA prediction for b-quark jets becomes 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 ( α s ) 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.Sj ö strand (private comm.) (default version - generation of light quarks only - no ISR) N.B. About 1 unit lower than the original 1992 prediction 5.5 ± ± ± 0.34

10/8/2005F. Fabbri - ISMD Experimental results and revised MLLA prediction Theory still above the experimental average … but definitely in a better quantitative agreement (2005) N.B. Derived results on δ bl at energies below 91 GeV have been reevaluated in the present analysis δ bl = 4.4 ± 0.4 MLLA 2005

10/8/2005F. Fabbri - ISMD Can the remaining discrepancy be attributed to the Next-to-MLLA contributions ? Large angle two soft gluon systems (dipole configurations) They have been evaluated in the present work, and to make a long (and quite technical) story short the expression for the companion multiplicity difference (not claimed to be complete at this order ) becomes Detailed presentation of this result in appendix A of hep-ph/ 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 (1-z) rescaling of the argument of the dead cone subtraction (which improves the description of the small angle emission from the heavy quark)

10/8/2005F. Fabbri - ISMD Results on charm quark jets Following the same approach as for b-quark jets we reevaluate also δ cℓ and find δ cℓ = 1.5 ± 0.4 very similar to the value of 1.7 ± 0.4 found in the original analysis. Numerical estimate of these next-to-MLLA terms Assuming Λ = 250 MeV one get for n f = 3 α s (M b ) = 0.23 from the 1-loop formula The predicted value of δ bl including these contributions becomes δ bl ≈ 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.

10/8/2005F. Fabbri - ISMD The measurement of the process γ γ → H → bb ̄ is one of the important goals of a future linear e + e - collider. Multiplicities associated with the Higgs particle 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 γ γ → bb ̄ g and gg → bb ̄ g (for which the M b 2 /m H 2 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 M H ) 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 the two

10/8/2005F. Fabbri - ISMD Conclusions The experimental results from e + e - annihilation in the energy range 29 – 206 GeV nicely confirm the energy independence of the multiplicity difference, δ bℓ and δ cℓ, between heavy and light quark initiated jets, as predicted within the MLLA + LPHD framework. The numerical value of this difference is derived in terms of a few experimentally measured quantities. The earlier prediction for δ bℓ needed revision in the light of new experimental results and the improvement in the understanding of the experimental data. The updated MLLA result is now δ bℓ = 4.4 ± 0.4 in better agreement with experiment than in the previous analysis. ( δ cℓ = 1.5 ± 0.4, only marginally changed with respect to earlier prediction ) Dominant Next-to-MLLA correction terms are also evaluated and shown to be largely responsible of the remaining difference between the theoretical prediction and the experimental results.

10/8/2005F. Fabbri - ISMD An important contribution to this topic could be provided by a precise measurement of δ cℓ at √s = 8 GeV, possibly already within the experimental reach by analysing radiative events at BaBar and Belle. Further measurements of δ bℓ and δ cℓ at a future linear collider would also be important, as well as further analyses of 3-jet QQ ̄ g events which are expected to show the same multiplicity difference as that in 2-jet QQ ̄ events at the corresponding c.m.s. energy. An interesting application of our results to improve Higgs detection against background (in the decay channel H → bb ̄ ) is also discussed.