- Email: [email protected]
Gluon splitting to bb and cc at the Z resonance
ELSEVIER
PROCEEDINGS SUPPLEMENTS
Nuclear Physics B (Proc. Suppl.) 75B (1999) 241-245
Gluon Splitting to bb and
at the Z resonance
Tommaso Boccali a alstituto di Fisica Nucleare Sezione di Pisa, Via Livornese, 1291 1-56010 S.Piero a Grado (Pisa), Italy. Scuola Normale Superiore, P.zza dei Cavalieri, 7 1-56126 Pisa, Italy. The available experimental measurements for gb~ and gc~ are reviewed, including some very recent results. The measurements are combined having particular care in the cross-correlations between the two quantities. The combined values can be used to rescale the central value and the error for Rb.
1. I n t r o d u c t i o n The gluon splitting process to heavy quark pairs is one of the elementary processes in QCD, and can be sketched as in Fig. 1.
experimental input value for gb$ instead of the theoretical one. 2. T h e o r e t i c a l e s t i m a t e s
Theoretical estimates for the gluon splitting rates are available [1] at the next-to--leading logarithmic order, complemented with the full a ,2 matrix element. The rates are presented in Tab. 1 [2] as a function of a , ( M z ) . O~s 0.112
Figure 1. Gluon splitting in heavy flavours. The gluon splitting rates, gb~ and gce, are defined as the number of events in which a gluon splits to a heavy quark pair, divided by the total number of hadronic Z decays. These processes have gained popularity in the last years, when it has become clear that they constitute one of the most important background to the measurement of R~. In the following I will try to present a comprehensive summary of the available measurements, with particular attention to the preliminary ones that have been presented for the first time to this conference. Combining the experimental measurements, is now possible to have estimates for the rates with errors comparable if not smaller than those from theoretical calculations. In section 5 I will show how much the total error on Rb decreases using for the first time an
gc~ (%) 1%~+o.4s .vv_0.30
gb~ (lO-u) 2.0 4- 0.2
0.125
1 U~+0.69 2.6 4- 0.3 ~.~v--0.44 Table 1. Theoretical expectations for gluon splitting rates. It can be seen that the process is highly suppressed with respect to primary heavy flavour Z decays, mainly due to the high gluon virtuaJity necessary to create a quark-antiquark pair. Monte Carlo models are in general able to reproduce the expected rates; for what concerns the event spectra, it is generally believed that models based on Parton Shower better agree than those based on Matrix Element [3]. 3. gce e x p e r i m e n t a l
measurements
Up to now published results for gee were presented only by OPAL [4,5]. Preliminary results from A L E P H [6] and L3 [7] also exist.
0920-5632/99/$ - see front matter © 1999 ElsevierScience B.V. All rights reserved. Pll S0920-5632(99)00359-X
242
T. Boccali/Nuclear Physics B (Proc. Suppl.) 75b (1999) 241-245
Three different methods have been used to measure gc~: • fit to mass or energy in events with reconstructed D* • search for leptons in three jet events • use of neural networks and event shape variables. I will briefly describe each method. 3.1. gee w i t h r e c o n s t r u c t e d D* Those methods are based on the exclusive decay chain: D *+ -~ D°~r+ D O -~ K-~r +
(68%) (4%)
The reconstruction of these events is fairly accurate, due to the small phase space accessible to background. Moreover, the energy spectra of the reconstructed D* is different for primary and secondary (via gluon splitting) heavy quark production [6]. The background that better reproduces the characteristics of gluon splitting events is that from direct Z ~ bb, and it is rejected using b anti-tag methods such as the requirement of displaced secondary vertices or high Pc leptons. OPAL [4] extracts gee from a fit to the energy of the reconstructed D*, obtaining gc~ = (4.4 4. 1.4(stat) :h 1.5(syst))%
(1)
ALEPH uses a different approach. As already mentioned, the virtuality of the gluon is the limiting factor in gluon splitting events. This results in a privileged small angle between the two quarks from splitting. One thus expects the two charm quarks from g ~ c5 and one of the primary quarks to be in the same hemisphere, leaving only the other primary quark in the other hemisphere. This gives a large mass difference AM between hemispheres in gluon splitting events. ALEPH [6] performs a fit to the AM distribution, obtaining gc~ = (2.65 4- 0.74(stat) 4- 0.51(syst))%
(2)
The main systematics are in common to both analyses, and come from the different parametrizations of the heavy quarks fragmentation functions.
3.2. gce with leptons Those methods try to select gluon splitting events using the decays g ~ cg ~ h , X . Events are clustered in 3 jets, with the assumption that the two charm quarks from splitting are close enough in angle to generate a single jet. Moreover, the jet from splitting is likely to be the least energetic one, due to the energy spectrum of the gluon. Signal selection is thus obtained by requesting a lepton in the least energetic jet in 3-jet events. The main background comes from leptons from b quarks decays: those events are rejected using b anti-tag and a cut on the mass of the third jet. OPAL [5] and L3 [7] perform very similar analyses, and look at both electrons and muons. Averaging those two channels, they find: OPAL L3
gc~ = (2.27:h0.28(stat):h0.41(syst))%(3)
gc~ = (2.68 4-0.64(stat) 4- 0.59(syst))%
(4)
The analyses being very similar, the systematic errors are in common and come mainly from semileptonic BR of heavy quarks, fragmentation functions and efficiencies for fake leptons. 3.3. gce w i t h N e u r a l N e t w o r k s L3 [7] presented to this conference a new analysis using event shape variables in input to a neural network. Events with 3 jets are initially selected, and jets are ordered in energy; in this way, gluon splitting generated jets should be the second or the third. The variables chosen are: • Mjet2 + Mjet3 -- Mjetl • 3 different Fox-Wolfram momenta • the fraction of the energy of the second jet within a cone of 8 ° around its axis. The output of the neural network is presented in Fig. 2. An additional cut requests the presence of a minimum number of tracks displaced from the primary vertex; this is done to enrich the sample in events with gluon splitting to heavy flavours. L3 obtains: gee = (2.05 + 0.19(stat) 4. 0.48(syst))%
(5)
T. Boccali/Nuclear Physics B (Proc. Suppl.) 75B (1999) 241-245
0.1
L3 -
0.075 C
--
g-> H e a v y Q u a r k s
--
Background
J t I . .I I
iii
o P O
0.05
u.
0.025
tl
,, i i i
Jo12
0.4
0.6
0.8
Neural Network output
Figure 2. Output of L3 neural network. where the main contributions to the systematic error come from g --+ bb subtraction and from calibration of calorimetric response. 4. gb$ e x p e r i m e n t a l m e a s u r e m e n t s
The measurement of gb~ are particularly challenging: the rate is about ten times smaller, and the uncertainties in heavy flavour physics contribute a bigger systematic error, that can be controlled only if high purity is obtained. These problems explain why in heavy flavour measurements it was generally chosen to use for gb~ a theoretical value, tuned to the ratio to the more precise measurements of gcc: 2
R ~ gb_~_~_ m c _ 0.13 ± 0.04 gce m~
(6)
Using gee = (2.38 =t=0.48)%, one gets gb~, = (3.1 ± 1.1) x 10 -3
(7)
This is the value used up to now in input to the Rb analysis, and it depends on the input for gee. An experimental measurement has been published by D E L P H I [8], but a number of other measurements exist in preliminary or final state. All of them have been presented to this conference for the first time. Two different approaches have been used to measure gb~" One can search generic g -~ bb events, without any request for the flavour of the primary quarks; otherwise one could search specifically for the final state Z ~ bbbb, accessible only to gluon splitting to b events.
243
4.1. G e n e r i c gb~ m e a s u r e m e n t s The idea beyond the analyses from D E L P H I [8] and ALEPH [9] is the search of events in which the two b quarks from splitting produce two different jets in the hadronization process. Events with 4 hadronic jets are thus selected, and lifetime tags are requested on those jets that are supposed to come from b quarks in signal events. D E L P H I [8] assumes that those jets are the two closer in angle, due to the usual phase space restrictions for the gluon, and then cuts on the lifetime of those two jets are applied. Two additional topological cuts are useful to improve the purity of the sample: a request on the rapidity of the first jet with respect to the thrust axis and a cut on the acoplanarity of plane formed by the first two jets with respect to the other two. From an initial statistic of 1.4 million hadronic events, 22 are selected with an estimated signal purity of 40%. The result is gb~ = (2.1 ± 1.0(stat) ± 0.9(syst)) x 10 -3
(8)
The main systematic errors come from model dependence in signal simulation (a comparison is performed between Matrix Element and Parton Shower models) and from discrepancies between data and Monte Carlo simulation in cut efficiencies. A L E P H [9] uses a different approach, searching events in which the two jets from splitting are those with highest lifetime. Having done this, one can cut on the lifetimes of those jets, and then perform angular selections. Events are selected if the angle between the two jets from splitting is small, and the angle between the other two (that should come from primary quarks) is large. Doing so 222 events are selected among the full LEP 1 statistics, with a purity of 45%. A L E P H measures: gb~, = (2.77 =k 0.42(stat) =t: 0.57(syst)) x 10 -3
(9)
Here the main systematics come from model dependence and from uncertainties in heavy flavour physics parameters (lifetimes, BR, charged track multiplicities). The expected data composition is shown in Fig. 3 just before the cut on the angle between the two jets supposed to come from primary quarks.
T Boccali/Nuclear Physics B (Proc. Suppl.) 75B (1999) 241-245
244
further suppressed requiring angular cuts. The result is
120
ALEPH
D g-" ~ i g - ~ ~'¢ •
gb~ = (3.6 + 0.6(stat) + 0.8(syst)) x 10 -3
(11)
This analysis uses the same events than the generic one from ALEPH, but the statistical correlation of the samples is negligible; unfortunately that is not true for what concerns the systematic errors, which are fully correlated.
Data
5. C o m b i n e d r e s u l t s
0 -1
-0.75
-0.5
-0.25
0
0.25
0.5
0."/5
1
Cos(e34) Figure 3. Data composition of selected events.
In order to obtain the best estimates gb~ and gee measurements are combined together: the problem is complicated by the fact that one has not only to take into account the correlations between measurements of the same quantity, but also cross correlations between gbb and gc~. The procedure chosen to use requires parametrizing each measured value as a function of the input rate. In this way a consistent set of measurements is obtained, and can be combined using a BLUE [11] technique. The combined values from the BLUE output are reused in input to rescale values and errors, and this is reiterated until convergence. The parametrizations for the measured values
4.2. Z -~ bbbb a n a l y s e s In principle events with four b quarks in the final state could come at L E P 1 only from gluon splitting to bb. Those events are indeed quite easy to select: they generate usually three or four jet topologies, and background can be rejected using lifetime selections on all the jets. D E L P H I [10] and A L E P H [9] presented analyses using Z -+ bbbb events, but with different approaches. D E L P H I [10] selects events with three hadronic jets, in the hypothesis that the two b quarks from splitting hadronize in the same jet. Then simply requesting high lifetime for all the three jets permits to select 4 - b events with high purity. From 1994 and 1995 statistic, DELPHI selects 140 events, with a purity of about 30%. The result is:
where Ai, Bi, Cj and D j are given from the measured efficiencies; the index i runs over gce measurements, j over gb~ ones. With Yc~ ~best and Ybb ^best the best estimates obtained from the previous iteration are indicated. This technique gives the results:
gb~ "- (3.0 ± 1.0(stat) ± 0.8(syst)) × 10 -3
g~e
=
(2.36±0.39)%
(13)
gb5
=
(2.78±0.63) × 10 -3
(14)
(10)
The main systematic errors come from modeling in signal simulation and g ~ c~ events. This last systematic error is more relevant in this analysis due to the request of three hadronic jets, that can't reject efficiently gluon splitting to charm events. A L E P H [9] uses a different approach selecting events with 4 hadronic jets, the same used for the generic analysis. The lifetime cut is imposed to the first three jets. Moreover background is then
are:
(gce)~ =
Ai ~best 1 + ~Bi
(gb~)J = Cj + D j Yce-bes'(12)
The single measurements contribute to this result in a non obvious way, which takes into account both the total error and the correlations. The weights from BLUE are presented in Tab. 2. As naively expected from the total errors, gc~ combined value is dominated by OPAL measurement with electrons and L3 with neural network, while gb~ is largely dominated by the first A L E P H analysis.
T Boccali/Nuclear Physics B (Proc. Suppl.) 75B (1999) 241-245
OPAL e [5] OPAL # [5] OPAL D* [4] ALEPH D* [6] L3 e [7] L3 # [7] L3 NN [7] DELPHI [8] ALEPH [9] DELPHI 45 [10] ALEPH 4b [9]
gee
gb~
47.5% 6.0% 3.3% 2.7% 0.6% 0.4% 39.5% 13% 65% 15% 6%
Table 2. Weights from the BLUE technique 6. C o n c l u s i o n s It is instructive to show the individual values of the available experimental measurements as in section 5. In Fig. 4 the spreads around the combined values are presented. It is clear how no inconsistency is present.
9°°
(%)
OPAL e OPAL OPAL ~* ALEPH D* L3 e NEW L3 L,3 '~N NEW COMBINED NEW
0
2
3
4
5
6
7
g~b (10 -~) DELPHI DELPHI 4b
NEW
-~ ~ ~
ALEPH
FINAL
~
~X~
~
,~'~
A L E P H
4b
,
FINAL
COMBINED
REFERENCES 1. 2. 3. 4. 5. 6.
[ . i i
, [ i
1
11. 12. ,
,
,
, ,~._~
2
8. 9. 10.
,
~ , ~
0
Rb analyses used gee and R as the free parameters to take into account systematics from gluon splitting. This leads indirectly to the value for gb~, showed in equation (7). With the new direct measurements, I can rescale both central value and error for Rb. The best value presented at the Summer Conferences in 1997 using LEP and SLD data was Rb = 0.2170 4- 0.0009 [12]. If I rescale this to the new input values, I get Rb = 0.2171 + 0.0008, which is roughly a 10% decrease in the total error. To conclude, the biggest achievement obtained from the new set of measurements is the combined average for gb[,: the experimental value (14) is more precisely known than the old estimate (7). Is therefore now possible to use use the value gb~ = (2.784-0.63) × 10 -3 as input to heavy flavour measurements.
7.
1
3
4
,
i
I
5
Figure 4. Spread of measured values. The bars represent theoretical expectations for as = 0.112 (on the left) and c~s = 0.125 (on the right). Superimposed are the theoretical allowed region for gb~, and 9c~ for the two different c~, values presented in Tab. 1. Both gb~, and gce combined values clearly privilege the higher value c~, = 0.125.
245
M.H. Seymour, Nucl. Phys. B 436 (1995) 163. S. Frixione et al., CERN-TH-97-16, Feb 1997. M.H. Seymour, private communications. OPAL Coll., Zeit. fur Physik C67 (1995) 27. OPAL Coll., Phys. Lett. B 353 (1995) 595. ALEPH Coll., Contr. to the XXVIII ICHEP, Warsav, 1996. L3 Coll., L3 Note 2273, Sub. to XXIX ICHEP, Vancouver, 1998. DELPHI Coll., Phys. Lett. B 405 (1997) 202. ALEPH Coll., CERN-EP/98-103, Sub. to Phys. Lett. B. DELPHI Coll., DELPHI Note 98-77, Sub. to XXIX ICHEP, Vancouver, 1998. L. Lyons et al., Phys. Rev. D 43 (1990) 982. The LEP Coll., CERN-PPE/97-154.
PROCEEDINGS SUPPLEMENTS
Nuclear Physics B (Proc. Suppl.) 75B (1999) 241-245
Gluon Splitting to bb and
at the Z resonance
Tommaso Boccali a alstituto di Fisica Nucleare Sezione di Pisa, Via Livornese, 1291 1-56010 S.Piero a Grado (Pisa), Italy. Scuola Normale Superiore, P.zza dei Cavalieri, 7 1-56126 Pisa, Italy. The available experimental measurements for gb~ and gc~ are reviewed, including some very recent results. The measurements are combined having particular care in the cross-correlations between the two quantities. The combined values can be used to rescale the central value and the error for Rb.
1. I n t r o d u c t i o n The gluon splitting process to heavy quark pairs is one of the elementary processes in QCD, and can be sketched as in Fig. 1.
experimental input value for gb$ instead of the theoretical one. 2. T h e o r e t i c a l e s t i m a t e s
Theoretical estimates for the gluon splitting rates are available [1] at the next-to--leading logarithmic order, complemented with the full a ,2 matrix element. The rates are presented in Tab. 1 [2] as a function of a , ( M z ) . O~s 0.112
Figure 1. Gluon splitting in heavy flavours. The gluon splitting rates, gb~ and gce, are defined as the number of events in which a gluon splits to a heavy quark pair, divided by the total number of hadronic Z decays. These processes have gained popularity in the last years, when it has become clear that they constitute one of the most important background to the measurement of R~. In the following I will try to present a comprehensive summary of the available measurements, with particular attention to the preliminary ones that have been presented for the first time to this conference. Combining the experimental measurements, is now possible to have estimates for the rates with errors comparable if not smaller than those from theoretical calculations. In section 5 I will show how much the total error on Rb decreases using for the first time an
gc~ (%) 1%~+o.4s .vv_0.30
gb~ (lO-u) 2.0 4- 0.2
0.125
1 U~+0.69 2.6 4- 0.3 ~.~v--0.44 Table 1. Theoretical expectations for gluon splitting rates. It can be seen that the process is highly suppressed with respect to primary heavy flavour Z decays, mainly due to the high gluon virtuaJity necessary to create a quark-antiquark pair. Monte Carlo models are in general able to reproduce the expected rates; for what concerns the event spectra, it is generally believed that models based on Parton Shower better agree than those based on Matrix Element [3]. 3. gce e x p e r i m e n t a l
measurements
Up to now published results for gee were presented only by OPAL [4,5]. Preliminary results from A L E P H [6] and L3 [7] also exist.
0920-5632/99/$ - see front matter © 1999 ElsevierScience B.V. All rights reserved. Pll S0920-5632(99)00359-X
242
T. Boccali/Nuclear Physics B (Proc. Suppl.) 75b (1999) 241-245
Three different methods have been used to measure gc~: • fit to mass or energy in events with reconstructed D* • search for leptons in three jet events • use of neural networks and event shape variables. I will briefly describe each method. 3.1. gee w i t h r e c o n s t r u c t e d D* Those methods are based on the exclusive decay chain: D *+ -~ D°~r+ D O -~ K-~r +
(68%) (4%)
The reconstruction of these events is fairly accurate, due to the small phase space accessible to background. Moreover, the energy spectra of the reconstructed D* is different for primary and secondary (via gluon splitting) heavy quark production [6]. The background that better reproduces the characteristics of gluon splitting events is that from direct Z ~ bb, and it is rejected using b anti-tag methods such as the requirement of displaced secondary vertices or high Pc leptons. OPAL [4] extracts gee from a fit to the energy of the reconstructed D*, obtaining gc~ = (4.4 4. 1.4(stat) :h 1.5(syst))%
(1)
ALEPH uses a different approach. As already mentioned, the virtuality of the gluon is the limiting factor in gluon splitting events. This results in a privileged small angle between the two quarks from splitting. One thus expects the two charm quarks from g ~ c5 and one of the primary quarks to be in the same hemisphere, leaving only the other primary quark in the other hemisphere. This gives a large mass difference AM between hemispheres in gluon splitting events. ALEPH [6] performs a fit to the AM distribution, obtaining gc~ = (2.65 4- 0.74(stat) 4- 0.51(syst))%
(2)
The main systematics are in common to both analyses, and come from the different parametrizations of the heavy quarks fragmentation functions.
3.2. gce with leptons Those methods try to select gluon splitting events using the decays g ~ cg ~ h , X . Events are clustered in 3 jets, with the assumption that the two charm quarks from splitting are close enough in angle to generate a single jet. Moreover, the jet from splitting is likely to be the least energetic one, due to the energy spectrum of the gluon. Signal selection is thus obtained by requesting a lepton in the least energetic jet in 3-jet events. The main background comes from leptons from b quarks decays: those events are rejected using b anti-tag and a cut on the mass of the third jet. OPAL [5] and L3 [7] perform very similar analyses, and look at both electrons and muons. Averaging those two channels, they find: OPAL L3
gc~ = (2.27:h0.28(stat):h0.41(syst))%(3)
gc~ = (2.68 4-0.64(stat) 4- 0.59(syst))%
(4)
The analyses being very similar, the systematic errors are in common and come mainly from semileptonic BR of heavy quarks, fragmentation functions and efficiencies for fake leptons. 3.3. gce w i t h N e u r a l N e t w o r k s L3 [7] presented to this conference a new analysis using event shape variables in input to a neural network. Events with 3 jets are initially selected, and jets are ordered in energy; in this way, gluon splitting generated jets should be the second or the third. The variables chosen are: • Mjet2 + Mjet3 -- Mjetl • 3 different Fox-Wolfram momenta • the fraction of the energy of the second jet within a cone of 8 ° around its axis. The output of the neural network is presented in Fig. 2. An additional cut requests the presence of a minimum number of tracks displaced from the primary vertex; this is done to enrich the sample in events with gluon splitting to heavy flavours. L3 obtains: gee = (2.05 + 0.19(stat) 4. 0.48(syst))%
(5)
T. Boccali/Nuclear Physics B (Proc. Suppl.) 75B (1999) 241-245
0.1
L3 -
0.075 C
--
g-> H e a v y Q u a r k s
--
Background
J t I . .I I
iii
o P O
0.05
u.
0.025
tl
,, i i i
Jo12
0.4
0.6
0.8
Neural Network output
Figure 2. Output of L3 neural network. where the main contributions to the systematic error come from g --+ bb subtraction and from calibration of calorimetric response. 4. gb$ e x p e r i m e n t a l m e a s u r e m e n t s
The measurement of gb~ are particularly challenging: the rate is about ten times smaller, and the uncertainties in heavy flavour physics contribute a bigger systematic error, that can be controlled only if high purity is obtained. These problems explain why in heavy flavour measurements it was generally chosen to use for gb~ a theoretical value, tuned to the ratio to the more precise measurements of gcc: 2
R ~ gb_~_~_ m c _ 0.13 ± 0.04 gce m~
(6)
Using gee = (2.38 =t=0.48)%, one gets gb~, = (3.1 ± 1.1) x 10 -3
(7)
This is the value used up to now in input to the Rb analysis, and it depends on the input for gee. An experimental measurement has been published by D E L P H I [8], but a number of other measurements exist in preliminary or final state. All of them have been presented to this conference for the first time. Two different approaches have been used to measure gb~" One can search generic g -~ bb events, without any request for the flavour of the primary quarks; otherwise one could search specifically for the final state Z ~ bbbb, accessible only to gluon splitting to b events.
243
4.1. G e n e r i c gb~ m e a s u r e m e n t s The idea beyond the analyses from D E L P H I [8] and ALEPH [9] is the search of events in which the two b quarks from splitting produce two different jets in the hadronization process. Events with 4 hadronic jets are thus selected, and lifetime tags are requested on those jets that are supposed to come from b quarks in signal events. D E L P H I [8] assumes that those jets are the two closer in angle, due to the usual phase space restrictions for the gluon, and then cuts on the lifetime of those two jets are applied. Two additional topological cuts are useful to improve the purity of the sample: a request on the rapidity of the first jet with respect to the thrust axis and a cut on the acoplanarity of plane formed by the first two jets with respect to the other two. From an initial statistic of 1.4 million hadronic events, 22 are selected with an estimated signal purity of 40%. The result is gb~ = (2.1 ± 1.0(stat) ± 0.9(syst)) x 10 -3
(8)
The main systematic errors come from model dependence in signal simulation (a comparison is performed between Matrix Element and Parton Shower models) and from discrepancies between data and Monte Carlo simulation in cut efficiencies. A L E P H [9] uses a different approach, searching events in which the two jets from splitting are those with highest lifetime. Having done this, one can cut on the lifetimes of those jets, and then perform angular selections. Events are selected if the angle between the two jets from splitting is small, and the angle between the other two (that should come from primary quarks) is large. Doing so 222 events are selected among the full LEP 1 statistics, with a purity of 45%. A L E P H measures: gb~, = (2.77 =k 0.42(stat) =t: 0.57(syst)) x 10 -3
(9)
Here the main systematics come from model dependence and from uncertainties in heavy flavour physics parameters (lifetimes, BR, charged track multiplicities). The expected data composition is shown in Fig. 3 just before the cut on the angle between the two jets supposed to come from primary quarks.
T Boccali/Nuclear Physics B (Proc. Suppl.) 75B (1999) 241-245
244
further suppressed requiring angular cuts. The result is
120
ALEPH
D g-" ~ i g - ~ ~'¢ •
gb~ = (3.6 + 0.6(stat) + 0.8(syst)) x 10 -3
(11)
This analysis uses the same events than the generic one from ALEPH, but the statistical correlation of the samples is negligible; unfortunately that is not true for what concerns the systematic errors, which are fully correlated.
Data
5. C o m b i n e d r e s u l t s
0 -1
-0.75
-0.5
-0.25
0
0.25
0.5
0."/5
1
Cos(e34) Figure 3. Data composition of selected events.
In order to obtain the best estimates gb~ and gee measurements are combined together: the problem is complicated by the fact that one has not only to take into account the correlations between measurements of the same quantity, but also cross correlations between gbb and gc~. The procedure chosen to use requires parametrizing each measured value as a function of the input rate. In this way a consistent set of measurements is obtained, and can be combined using a BLUE [11] technique. The combined values from the BLUE output are reused in input to rescale values and errors, and this is reiterated until convergence. The parametrizations for the measured values
4.2. Z -~ bbbb a n a l y s e s In principle events with four b quarks in the final state could come at L E P 1 only from gluon splitting to bb. Those events are indeed quite easy to select: they generate usually three or four jet topologies, and background can be rejected using lifetime selections on all the jets. D E L P H I [10] and A L E P H [9] presented analyses using Z -+ bbbb events, but with different approaches. D E L P H I [10] selects events with three hadronic jets, in the hypothesis that the two b quarks from splitting hadronize in the same jet. Then simply requesting high lifetime for all the three jets permits to select 4 - b events with high purity. From 1994 and 1995 statistic, DELPHI selects 140 events, with a purity of about 30%. The result is:
where Ai, Bi, Cj and D j are given from the measured efficiencies; the index i runs over gce measurements, j over gb~ ones. With Yc~ ~best and Ybb ^best the best estimates obtained from the previous iteration are indicated. This technique gives the results:
gb~ "- (3.0 ± 1.0(stat) ± 0.8(syst)) × 10 -3
g~e
=
(2.36±0.39)%
(13)
gb5
=
(2.78±0.63) × 10 -3
(14)
(10)
The main systematic errors come from modeling in signal simulation and g ~ c~ events. This last systematic error is more relevant in this analysis due to the request of three hadronic jets, that can't reject efficiently gluon splitting to charm events. A L E P H [9] uses a different approach selecting events with 4 hadronic jets, the same used for the generic analysis. The lifetime cut is imposed to the first three jets. Moreover background is then
are:
(gce)~ =
Ai ~best 1 + ~Bi
(gb~)J = Cj + D j Yce-bes'(12)
The single measurements contribute to this result in a non obvious way, which takes into account both the total error and the correlations. The weights from BLUE are presented in Tab. 2. As naively expected from the total errors, gc~ combined value is dominated by OPAL measurement with electrons and L3 with neural network, while gb~ is largely dominated by the first A L E P H analysis.
T Boccali/Nuclear Physics B (Proc. Suppl.) 75B (1999) 241-245
OPAL e [5] OPAL # [5] OPAL D* [4] ALEPH D* [6] L3 e [7] L3 # [7] L3 NN [7] DELPHI [8] ALEPH [9] DELPHI 45 [10] ALEPH 4b [9]
gee
gb~
47.5% 6.0% 3.3% 2.7% 0.6% 0.4% 39.5% 13% 65% 15% 6%
Table 2. Weights from the BLUE technique 6. C o n c l u s i o n s It is instructive to show the individual values of the available experimental measurements as in section 5. In Fig. 4 the spreads around the combined values are presented. It is clear how no inconsistency is present.
9°°
(%)
OPAL e OPAL OPAL ~* ALEPH D* L3 e NEW L3 L,3 '~N NEW COMBINED NEW
0
2
3
4
5
6
7
g~b (10 -~) DELPHI DELPHI 4b
NEW
-~ ~ ~
ALEPH
FINAL
~
~X~
~
,~'~
A L E P H
4b
,
FINAL
COMBINED
REFERENCES 1. 2. 3. 4. 5. 6.
[ . i i
, [ i
1
11. 12. ,
,
,
, ,~._~
2
8. 9. 10.
,
~ , ~
0
Rb analyses used gee and R as the free parameters to take into account systematics from gluon splitting. This leads indirectly to the value for gb~, showed in equation (7). With the new direct measurements, I can rescale both central value and error for Rb. The best value presented at the Summer Conferences in 1997 using LEP and SLD data was Rb = 0.2170 4- 0.0009 [12]. If I rescale this to the new input values, I get Rb = 0.2171 + 0.0008, which is roughly a 10% decrease in the total error. To conclude, the biggest achievement obtained from the new set of measurements is the combined average for gb[,: the experimental value (14) is more precisely known than the old estimate (7). Is therefore now possible to use use the value gb~ = (2.784-0.63) × 10 -3 as input to heavy flavour measurements.
7.
1
3
4
,
i
I
5
Figure 4. Spread of measured values. The bars represent theoretical expectations for as = 0.112 (on the left) and c~s = 0.125 (on the right). Superimposed are the theoretical allowed region for gb~, and 9c~ for the two different c~, values presented in Tab. 1. Both gb~, and gce combined values clearly privilege the higher value c~, = 0.125.
245
M.H. Seymour, Nucl. Phys. B 436 (1995) 163. S. Frixione et al., CERN-TH-97-16, Feb 1997. M.H. Seymour, private communications. OPAL Coll., Zeit. fur Physik C67 (1995) 27. OPAL Coll., Phys. Lett. B 353 (1995) 595. ALEPH Coll., Contr. to the XXVIII ICHEP, Warsav, 1996. L3 Coll., L3 Note 2273, Sub. to XXIX ICHEP, Vancouver, 1998. DELPHI Coll., Phys. Lett. B 405 (1997) 202. ALEPH Coll., CERN-EP/98-103, Sub. to Phys. Lett. B. DELPHI Coll., DELPHI Note 98-77, Sub. to XXIX ICHEP, Vancouver, 1998. L. Lyons et al., Phys. Rev. D 43 (1990) 982. The LEP Coll., CERN-PPE/97-154.