Multiplicity difference between heavy and light quark jets revisited

XXXV Int. Symposium on Multiparticle DynamicsKroměříž, Czech Republic, August 9 - 15, 2005

Fabrizio FabbriINFN - Bologna

Work by Yuri L. Dokshitzer, Fabrizio Fabbri, Valery A. Khoze and Wolfgang Ochs

Brief introduction

MLLA prediction for the multiplicity of light hadronsaccompanying 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/0508074

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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

Dead cone + LPHD ⇨ expect difference between the companion multiplicity

of primary light hadrons in QQ ̄ and qq̄ initiated jets in e+e- annihilation

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 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.KoetkePhys. 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 .

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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- qq ̄ (q = u,d,s)

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

B.A.Schumm, Yu.L.Dokshitzer, V.A.Khoze and D.S.KoetkePhys. Rev. Lett. 69 (1992) 3025

for b quarks

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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) 2580A.V.Kisselev, V.A.Petrov and O.P.Yushchenko, Z. Phys. C41 (1988) 521

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Naive model prediction

Experimental measurements of δbℓ at different c.m.s. energies in e+e- annihilation

Original MLLA prediction δbℓ = 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

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Presented by K. Hamacher at ISMD 2004

First preliminary data from 3-jet event analysis (DELPHI exp.) show energy independence and a value of δbℓ consistent with the precise resultfrom 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 Wqq ̄ = 2 E*q one gets

NQQ ̄g (W) – Nqq ̄g (W) = NQQ ̄ (WQQ ̄ ) - Nqq ̄ (Nqq ̄ )

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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/0508074 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

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11.0 ± 0.2

5.5 ± 0.7

From recent (2001) combined results of LEP and SLD

this value becomes 11.1 ± 0.18practically unchanged with respect to that used for the original MLLA analysis (1992)

This value should be changedaccording to the present analysis

Average number of charged particles coming from the decay of two B-hadrons

Mean charged multiplicityof e+e- → qq̄ (q = u,d,s) eventsat energy scale Wo

b = √e Mb

Which terms need revision ?

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NO direct measurements of Nqq ̄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 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

- 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 theoriginal MLLA analysis

⇩ fit result

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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 δcl

We assume δcℓ = 1.0 also at 8 GeV and finally obtain

Experimental resultsfrom direct measurement ( 1992 average was 2.2 ± 1.2 )

( It was 5.5 ± 0.7 )Important to have precise measurements of δcl at low energies,in particular at √s = 8 GeV, to verify our hypothesis.

Detailed discussion of this pointin appendix B of hep-ph/0508074

Revised low energy data points

What about analysing radiative events at BaBar and Belle ?

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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 δcl = 1.0 and δbl = 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

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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 (αs) effects 6.5 S.Lupia and W. Ochs - Phys. Lett. B418 (1998) 214for 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)

N.B. About 1 unit lower than the original 1992 prediction 5.5 ± 0.811.1 ± 0.18 6.7 ± 0.34

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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 δbl

at energies below 91 GeV

have been reevaluated in

the present analysis

δbl = 4.4 ± 0.4

MLLA 2005

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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, andto make a long (and quite technical) story short theexpression for the companion multiplicity difference (not claimed to be complete at this order ) becomes

Detailed presentation ofthis result in appendix Aof hep-ph/0508074

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)

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Results on charm quark jets

Following the same approach as for b-quark jets we reevaluate also δcℓ

and find

δcℓ = 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 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.

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The measurement of the process γ γ → H → bb̄ 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 → bb̄g (for which the Mb2/mH

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 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 the two

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Conclusions

The experimental results from e+e- annihilation in the energy range 29 – 206 GeV nicely confirm the energy independence of the multiplicity difference, δbℓ and δcℓ , 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 δbℓ 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

δbℓ = 4.4 ± 0.4

in better agreement with experiment than in the previous analysis.

( δcℓ = 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.

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An important contribution to this topic could be provided by a precise measurement of δcℓ at √s = 8 GeV, possibly already within the experimental reach by analysing radiative events at BaBar and Belle. Further measurements of δbℓ and δcℓ at a future linear collider would also

be important, as well as further analyses of 3-jet QQ̄g events which are expected to show the same multiplicity difference as that in 2-jet QQ̄ 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.