Gluon Splitting to C¯C and B¯B in Hadronic Z0 Decays

Gluon splitting to c¯cand bb¯ in hadronic Z0 decays: Experimental results

Stefan Schmitt

DESY Deutsches Elektron Synchrotron, Notkestrasse 85, 22607 Hamburg, Germany E-mail: [email protected]

Abstract Several measurements of the rates of gluon splitting to heavy quarks in hadronic Z0 decays are presented and compared to theoretical predictions. Averages are calculated taking into account correlated sources of systematic uncertainties.

1. Introduction 2. Gluon splitting to c¯cquark pairs

In hadronic Z0 decays, charm (c) or bottom (b) Results for gluon splitting to charm quarks are quark pairs are produced either directly, or by gluon available from the ALEPH [5], L3 [6] and OPAL [7] splitting g → QQ.¯ The rate for the latter process collaborations. The new OPAL analysis supersedes 0 per hadronic Z decay is denoted gQQ¯ (Q = b, c), previous results [8, 9]. The ALEPH and L3 results quoted here are preliminary. 0 → → ¯ Γ Z q¯qg, g QQ D⋆± g ¯ = . ALEPH reconstructs mesons in the decay QQ Γ (Z0 → hadrons) chain D⋆± → D0π±, D0 → K∓π±. These D⋆± mesons originate from various sources, one of them Theoretical calculations of the rates g and g c¯c c¯c being gluon splitting to c¯c. The event is divided are available [1, 2] and include the re-summation of large logarithmic terms. The predicted rates into two hemispheres, based on the thrust axis. The D⋆± depend on the strong coupling constant and the mesons from gluon splitting are preferentially heavy quark mass. However, as the tree-level found in the hemisphere with the larger invariant part of the calculations is only performed up to mass, with relatively small energies. In contrast, leading order, no renormalisation scheme is defined, the mesons from direct c¯cproduction are found with resulting in relatively large uncertainties on the about equal probability in both hemispheres and predicted rates. Numerical values are given in have larger energies. theor The OPAL and the L3 analyses start with [1, 2, 3], predicting rates in the range gc¯c = − × −2 theor − × a selection of three-jet events. For the OPAL (1.05 2.54) 10 and gbb¯ = (1.8 2.9) −3 analysis, in each event a candidate gluon jet is 10 . Several experimental measurements of the ⋆± rate of gluon splitting to charm and bottom quarks selected. Within this jet, D mesons or leptons have been performed and will be summarised here, from charm decays are identified, both originating testing these predictions. Gluon splitting to heavy with a high probability from gluon splitting to charm quark pairs. Optimised gluon-candidate quarks is also an important source of background ⋆± for the precise measurements of the partial decay selections are used for the lepton and the D 0 width of the Z to heavy quarks, Rc and Rb [4]. analysis, respectively. Experimentally, events with gluon splitting to The L3 collaboration identifies leptons from heavy quarks are observed as events with three or charm decays in the lowest-energetic jet. In an four jets. In the latter case, the heavy quarks from independent analysis, events from gluon splitting gluon splitting are resolved in separate jets, while are selected with a dedicated neural network, based in the three-jet case, only one broad gluon jet is on event-shape observables. reconstructed. The other two jets correspond to The results of the individual analyses are shown the two primary quarks from the Z0 decay. in Figure 1. As the individual measurements are In Section 2 and 3, experimental results are found to be consistent, their average is calculated presented for gc¯c and gbb¯, respectively. In Section using a common value for background from gluon 4, the averaging procedure developed for the use in splitting to bb¯ and taking care of correlated this paper is described in more detail. systematic uncertainties. This is described in more 2

0.01 0.02 0.03 0.04 0.05 0.001 0.002 0.003 0.004

ALEPH D* ALEPH ALEPH-CONF 99-051 Phys. Lett. B434 (1998) 437 ± ± ± ± gcc=0.0323 0.0048 0.0053 gbb=0.00277 0.00042 0.00057 OPAL D* DELPHI CERN-EP 99-098 Phys. Lett. B405 (1997) 202 ± ± ± ± gcc=0.0408 0.0122 0.0069 gbb=0.0021 0.0011 0.0009

OPAL leptons DELPHI from R4b CERN-EP 99-098 CERN-EP/99-81 ± ± ± ± gcc=0.0311 0.0022 0.0041 gbb=0.0033 0.001 0.0008 L3 leptons OPAL L3 note 2415 OPAL note PN383 ± ± ± ± gcc=0.0311 0.0101 0.0069 gbb=0.00215 0.00043 0.0008 L3 event-shape SLD theory

L3 note 2415 theory hep-ex/9905057 ± ± ± ± gcc=0.0227 0.0037 0.0052 gbb=0.00307 0.00071 0.00066 average average

0.01 0.02 0.03 0.04 0.05 0.001 0.002 0.003 0.004 ± ± ± ± gcc = 0.0307 0.0018 (stat) 0.0036 (syst) gbb = 0.00247 0.00028 (stat) 0.00048 (syst)

Figure 1. Experimental results for gluon splitting to Figure 2. Experimental results for gluon splitting to charm quark pairs bottom quark pairs

detail in Section 4. The result is: depend on the b-quark mass and other parameters is used to extract the rate gbb¯ from this measurement gc¯c =0.0307 ± 0.0018(stat) ± 0.0036(sys) . of R4b. OPAL selects four-jet events with two b-tagged This is 1.3σ away from the upper edge of the jets that are close in phase-space. In addition, four- theoretical prediction. jet events with three b-tagged jets are selected. A simultaneous fit of the rates gbb¯ and R4b is 3. Gluon splitting to bb¯ quark pairs performed. The results of these five analyses are shown in . Figure 2 and are consistent with each other. Taking New measurements of gluon splitting to bottom into account a common value for background from quark pairs are available from the DELPHI [10], gluon splitting to charm quarks, and considering OPAL [11] and SLD [12] collaborations in addition other correlated sources of systematic uncertainties, to older analyses by DELPHI [13] and ALEPH the result is: [14]. The OPAL and SLD results quoted here are g ¯ =0.00247 ± 0.00028(stat) ± 0.00048(sys) preliminary. bb The analyses performed by ALEPH and SLD, consistent with theoretical predictions. The as well as the old DELPHI analysis, all follow averaging procedure is described in the next similar strategies. Events with four jets are Section. selected. Within these events, the signal is It is also interesting to look at the rates of events enriched by requiring two low-energetic jets, each with four bottom quarks, R4b. This quantity is one satisfying a b-tag requirement, with a small measured by DELPHI and OPAL opening angle. The b-identification is based on DELPHI ± ± × −3 R4b = (0.60 0.19 0.14) 10 , vertexing information, sensitive to long-lived b- OPAL ± ± × −3 hadron decays. R4b = (0.53 0.20 0.23) 10 . The new DELPHI analysis is based on three- The two measurements agree within errors. jet events, where the gluon decay products are not resolved in two separate jets. All three jets are 4. Averaging procedure required to have a b-tag. Using these events, the rate of events with four b-quarks R4b is measured. To calculate the averages for gc¯c and gbb¯, sources gbb¯ A QCD prediction for R4b , which does only weakly of systematic uncertainties that are correlated 3

between the various measurements have to be 2 4.5 10 ×

considered. cc g For the gc¯c measurements, the following sources 4 of common systematic uncertainties are taken into ¯ 90% account: gluon splitting to bb, modelling of heavy 3.5 70% quark fragmentation to hadrons, comparisons of 50% various Monte Carlo generators for signal and 3 background, dependence on Rb, and branching ratios for bottom and charm to leptons. 2.5 For the gbb¯ measurements the following sources of common systematic uncertainties are considered: gluon splitting to c¯c, choice of Monte Carlo model 2

for the signal, dependence on the b-quark mass, = 0.15-0.3 GeV modelling of charm production and decays, and 1.5 Λ MS

modelling of bottom production and decays. = 1.2-1.8 GeV c For a given value of gbb¯ with error σ, the 1 m g central values of the individual c¯c measurements m = 4.5-5 GeV are re-adjusted and new uncertainties from gluon b 0.5 ¯ 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 splitting to bb are calculated. Then the weighted × 2 gbb 10 average of these gc¯c measurements is calculated, 2 2 −1 with weights w = σstat + σsys . The statistical and the uncorrelated systematic uncertainties of the Figure 3. Areas allowed by theory and the individual measurements are added quadratically measurements in the gbb¯ − gc¯c plane using these weights while the correlated systematic . uncertainties are added linearly. An analogous procedure is then applied to gbb¯, with the new result for gc¯c as input, and these two steps are iterated Figure 3 illustrates how this result is consistent with several times, until the results are stable. theoretical predictions at a conﬁdence level of 70% To study correlations of gc¯c and gbb¯, a for high values of the charm quark mass and the symmetric error matrix is calculated using the strong coupling constant. ansatz: References 2 − − σgc¯c δgc¯c σgbb¯ δgbb¯ σgc¯c − − 2 . δgc¯c σgbb¯ δgbb¯ σgc¯c σgbb¯ [1] M. H. Seymour, Nucl. Phys. B436 (1995) 163 [2] D. J. Miller and M. H. Seymour, Here σgc¯c and σgbb¯ are the total uncertainties on gc¯c Phys. Lett. B435 (1998) 213 and gbb¯, while δgc¯c is the contribution to σgc¯c from [3] S. Frixione et al., CERN-TH/97-016. ¯ gluon splitting to bb and δgbb¯ is the contribution to [4] The LEP/SLD Heavy Flavour Working

σgbb¯ from gluon splitting to c¯c. The sign reﬂects Group, LEPHF/99-01 the fact that the measurements of gbb¯ and gc¯c are (see www.cern.ch/LEPEWWG/heavy/) anti-correlated. [5] ALEPH Collab., ALEPH-CONF 99-051 [6] L3 Collab., L3 note 2415 [7] OPAL Collab., G. Abbiendi et. al., 5. Summary CERN-EP/99-089, sub. to Eur. Phys. J. C [8] OPAL Collab., R. Akers et al., Z. Phys. C67 Several new measurements of gluon splitting to (1995) 27 heavy quarks have been presented. Averages of the [9] OPAL Collab., R. Akers et al., experimental results for gluon splitting to charm Phys. Lett. B353 (1995) 595 quarks, gc¯c, and bottom quarks, gbb¯, are calculated [10] DELPHI Collab., P. Abreu et al., taking into account correlations. The results are: CERN-EP/99-81, sub. to Phys. Lett. B ± [11] OPAL Collab., OPAL note PN383 gc¯c = 0.0307 0.0040 [12] SLD Collab., SLAC-PUB-8169 ± gbb¯ = 0.00247 0.00056 [13] DELPHI Collab., P. Abreu et al., Phys. Lett. B405 (1997) 202 with a correlation coeﬃcient [14] ALEPH Collab., R. Barate et al., − Phys. Lett. B434 (1998) 437 C (gc¯c,gbb¯)= 0.43 .