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Forward-backward asymmetry of b-¯b events at the Z
P. Antilogus
To cite this version:
Forward/Backward asymmetry of events at the
P.ANTILOGUS
Universit´e Claude Bernard de Lyon, IPN Lyon, IN2P3-CNRS, F-69622 Villeurbanne Cedex, France
E-mail: Pierre.Antilogus@cern.ch
Forward/Backward asymmetry of events (
) provides the most precise measurement of
!"!
at LEP I. In this note we will review :
#
The different techniques used to measure .
#
The recent improvements implemented by the LEP experiments in their $
analysis.
#
The corrections applied to
% to extract
&!'! . The value obtained for() * +
&!'!
from
is in favour of a high value for the Higgs mass compared to what is obtained with other observables like -,%. or /10 . This difference is commented.
1 Introduction
Particles not produced at LEP, like the top or the Higgs, can have measurable effects on electroweak observables through the radiative corrections they induce. In the same
way than LEP was able to predict the top mass with a precision of2 103-465 before its
discovery at the TEVATRON, the present electroweak data give throng constrains on
the Higgs mass (798 = 88:<;>=
?
=>;
3-4"5 ,798A@ 1963-4"5 at 95% cl)B . All measurements
sensitive to the fermions couplings to the play an important role in these
con-strains. The asymmetric forward-backward production of fermions in the decays
are among them. In this paper the measurement of the forward-backward
asymme-try performed at LEP I will be presented. It provides today, with 7DC andE$FHG , the
main constrain on7 8 .
1.1 Fermions asymmetries andI JLKNMPO
Q RTS+U RTVV
In the Standard Model (SM) the differential cross-section in function of the polar
angleO between theW
?
and the fermion X directions for the processW
: W ?ZY X X at [ \^] 7D_ is `ba `<c6d IeO 2gfih c6d I M Ojh k l E VHmn obp c"d IeO q
All the results/numbers quoted in this note are updated to their summer 2001 values
with E VHmn obp ] l r<s R s V
which can be expressed in terms of the real part of the effective vector and axial-vector
neutral current couplings of fermionX ,tbu%v andt
B v : s V ] w t u%vt B v tbu6v M hxt B v M ] w y{z v y"| v y{z v y"| v M h}f
In the case of the left-right cross section asymmetry (E FHG ) or ~ polarisation
measurements, the results can be directly expressed in term ofs
R
alone.
At firstI>JKMPO
QRTS+U
RTVV was introduced for
pole analysis as the ratio of effective
vector and axial-vector couplings of , including loops, for the on mass shell
Y : ? vertex : t u6 t B ] f r I>JKMPO Q RTS+U RTVV
Then for each fermion,I JLKNMPO
V RTVV is: t u%v t B v ] f rj V I JLKM$O V R V%V
Within the SMI JLKM$O
V
R V%V can be corrected to I>JKMPO
Q RTS+U
RTVV . All the measurements, like
asymmetries, expressed in term of ratio of these effective vector and axial-vector
cou-plings, can be translated in a value ofI JLKNMPO
Q RTS+U
RTVV . It can be noticed than I JK(M$O
Q R S U RTVV , in
the SM, is the most sensitive quantity to798 . For example with7982f{H3-4"5
7D8 7 8 2 rHr I JLK(M$O Q RTS+U R V%V I JLKM$O Q RTS+U R V%V to be compared to 7 8 7 8 2f l H 7DC 79C
All fermions asymmetries don’t have the same sensitivity toI JKMPO
Q R S U RTVV ,
7D8 . s1 for
the quarks is large (s 2 0.93 ands1 2 0.67 ) compared tos
Q
for the leptons (
s
Q
2 0.15 ). For this reason the quarks, and more precisely the high quark
asym-metry, provide a better sensitivity toI>JKMPO
Q RTS+U RTVV : E$ obp 2f k I JK(MPO Q RTS+U RTVV , E op 2 r r I JK(MPO Q RTS+U RTVV and E$ obp 2 I>JK(MPO QRTS+U
RTVV . Nevertheless the sensitivity to I>JKMPO
QRTS+U RTVV for
E$
obp comes from
s
R
. In the SMs is some how saturated/almost independent of
the radiative correction : it is2 7 time less sensitive to a change inI JLKM$O
Q RTS+U R V%V than
s
R
.
From the SM model point of viewE$
obp , E$
obp , the
~ polarisation andE F)G measure
the same things : the value ofI>JKMPO
Q RTS+U RTVV through s Q ors R
according to lepton uni-versality.
1.2 TheI JKMPO Q R S U
RTVV measurements
In regard of the previous section, the different values ofI>JKMPO
QRTS+U
RTVV extracted form the
data are not really satisfactory in the SM frame work. As shown in figure 1, there is a
poor agreement (2 w %) between the leptonic measurements ofs
Q
(like inE$
obp or E$FHG ) and the indirect hadronic measurements ofs
Q (like in E op ). Fixing s Q to
its leptonic measurements underline further this point : the couplings extracted that
way are quite away from the SM prediction (see figure 2).
2 E$
obp ( E$
obp ) measurements
2.1 Experimental techniques
To perform theE
op measurement the following informations are required :
A flavour tag to select the
P
event
The polar angle/”axis” of the
production
A charge tag to sign this
“axis” along the direction
Among the quarks only the and quarks can be easily tagged. Many methods to tag
decays in
or
quarks have been developed. They rely on different properties of the heavy quarks production and decay:
The hadrons have a long fly distance (&~ 2 w mm). The charm, present
in the decay products, further increases the distance between the interaction
region and the secondary vertices. Such decay chain gives vertices clearly shifted from the primary vertex and produces tracks with high impact
param-eters (see figure 4). Typical working point in E$
obp analysis using lifetime tag
corresponds to an efficiency in 2 0.7 - 0.9 for a purity2 0.7 - 0.9. This
work-ing point is slightly different to the one used in analysis for which a higher
purity is required.
sin
2θ
lepteff <LEP + SLD> Summer 2001 0.23152 ± 0.00017 A FB b-quark 0.23226 ± 0.00031 A FB c-quark 0.23272 ± 0.00079 < ¡ Q ¢ FB > 0.2324 ± 0.0012 Al Pol.(£τ ) ¤ 0.23137 ± 0.00033 AFB leptons 0.23099 ± 0.00053 SLD A ¥ LR ¦ ,A § l 0.23098 ± 0.00026 χ ¨2 /dof=12.8/5; Prob( © χ ¨2 )=.025 ª m « t = 174.3 ± 5.1 GeV ∆α¬ had = 0.02761 ± 0.00036 102 ® 0.23 ¯ 0.231 ¯ 0.232 ¯ 0.233 ¯ sin ° 2 θ ±lept eff m H [ GeV ] 150 200 mt GeV Figure 1: Values of &!'! extracted from different measurements. If in average this sub-sample of electroweak observables predicts a Higgs mass slightly above 100²´³Tµ , the masspreferred by each measurement cover a large range. The main discrepancy is observed be-tween the ,%. measurement at SLC and the
measurement at LEP I. The overall
com-patibility between all these measurements is only 2.5%. -0.35 -0.33 -0.31 -0.29 -0.54 -0.52 -0.50 -0.48 g¶Ab gVb Preliminary 68.3 · 95.5 99.5 % CL SM Figure 2: Values of¸ q{¹ and ¸6º ¹ extracted from » ,¼-½ (¾D¸ º ¹+¿ ¸ q ¹) and ( ¾D¸ º ¹ÁÀ ¸ q ¹).
The SM is excluded at almost 99.5 % cl.
0 Â 2500 5000 Ã 7500 Ä 10000 Å 12500 Å 15000 10 Å 20 Æ 30 Ç 40 È 50 Ã b É → Ê c Ë → Ê l Ì b É → Ê l fake l Í c Ë uds Î Data
L3
Muon momentum (GeV/c)
Number of muons 0 Ï 2000 Ð 4000 6000 Ñ 0 Ï 1 Ò 2 Ð 3 Ó 4 Ô 5 Õ 6 Ñ b Ö → × c Ø → × l b Ö → × l Ù fake l Ú c Ø uds Û Data
L3
Muon transverse momentum (GeV/c)
Number of muons
Figure 3: Distribution of theÜ momentum,Ý , (left) and transverse momentum relative to the closest jet, ÝÞ , (right) for different sources. Due to the hard fragmentation and high mass of the , an excess of events
at highÝ orÝ Þ fromàßÜ is observed. In theÜ
L3 analysis
á the following cuts are applied : ÝjâäãH²´³Tµ
À{å and
ÝÞæâèç{²´³ µ À{å .
The é and ê hadrons have high semi-leptonic branching ratios (2 10% for
prompt decay in orW ), they take most of the beam energy (@ëèì}íjîï2}N*
and@ëèìíjð2N ), and, due to their high mass, they produce leptons with a
high transverse momentum (ñ(ò ). For these reasons semi-leptonic tagging using
theñ andñ(ò of the leptons can give pure sample of or quarks (see figure 3).
The charm content of and events can be directly identified by exclusive
reconstruction ofêèó"ôHê decays. The energy and fly distance of theseêèó'ôê
allow a distinction between and events.
The usual choice for the polar angle is the thrust axis. This choice induces specific QCD corrections but doesn’t result in any significant systematics.
The charge of the initial quark can be extracted :
in a exclusive way using the correlation between the quark and its decay
prod-ucts ( Y W ? hxë , Y êèó : , etc).
in an inclusive way by a jet charge method where the sign of the quark charge is estimated by a momentum weighted mean of the charged tracks present in the
Forward/Backward hemispheres : öõP÷ îeø ] õ$÷ îeøù+úTûjü ú ô õP÷ î<ø´ûjü ú where ý
is typically chosen between 0.5 and 1 (see figure 5). This method uses the
fact than tracks of high momentum in a jet are more likely coming from the
decay itself.
10-6 10-5 10-4 10-3 10-2 -8 -6 -4 -2 0 2þ 4 6 8 tagging variable B rate V V OPAL 1994 data Monte Carlo b ÿ Monte Carlo c Monte Carlo uds
ÿ
Figure 4: This OPAL -tag variable which includes
decay length significance of a secondary vertex, shows at high value a strong enrichment. The
events with a-tag value below zero are the results
of resolution effects. This last type of events can be used to tune the simulation to the data resolution.
0.5 1 -2 0 2 dN/dQ FB <QFB> QFB δf σf σf σFB 0 0.5 1 -2 0 2 Qx dN/dQ TOT sum quark backward
quark forward QTOT
σf σf
Figure 5: Three experimental observables are used
in jet charge analysis :
which holds informations on the asymmetry and the charge separation ( ! ) , & ¿ which holds informations on charge bias and resolution (
!
) and
(not plotted here) which holds informa-tions on the charge separation and correlation. Such distributions allow to perform a fine tuning of the simulation before extracting the asymmetry itself.
in a semi-inclusive way by selecting a sub sample of tracks with a given prop-erty: for example with all the tracks associated to a secondary vertex a “vertex charge” can be built holding information on the charge of the particle at the origin of this vertex.
2.2 ImprovedE
op measurements
Many combinations of the different flavour and charge tagging techniques described in the previous section have been used. In this section the last developments in the usage of these tools will be presented.
New lepton analysis
In lepton analysis a few observables have been used on top of the pureñ ,ñ ò tags.
Im-proved sample purity has been obtained using missing energy/ neutrino tag (ALEPH
= ,OPAL
) or lifetime tag (ALEPH
= ,DELPHIM ,OPAL
). Better charge tagging has
Figure 6: The distribution of the -tag variable used
in the ALEPH inclusive analysis shows before tuning of the simulation a clear excess of events in the
region (shadowed area).
0.7 0.72 0.74 0.76 0.78 0.8 0.82 0.84 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 wb wb b-simulation wb DATA single tag DELPHI 0.86 0.88 0.9 0.92 0.94 0.96 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 cos(Θthrust ) wb D wbD b-simulation wbD DATA double tag
Figure 7: The probability to identify correctly the
charge of the quark in the DELPHI inclusive
anal-ysis for events where only one hemisphere has been tagged (upper plot) and when the two hemispheres have been tagged with opposite charge (lower plot). The difference between data and simulation shows the difficulty for the simulation to describe correctly all the information used. The direct calibration in the data of the charge tagging power overcomes this problem.
been reached using differences between Y
L Y? and Y L Y : in
ob-servables like the jet charge of the opposite hemisphere to the lepton (DELPHIM ) or
the energy taken by the tracks nearer the lepton (OPAL ). If all these observables
improved the statistical precision of the results, they require in general specific mea-surements/calibrations to keep the systematics under control.
Such improved techniques decreased the statistical error up to 20% (50%) for
E$ obp (
E$
obp ) with in general constant if not better systematics.
New inclusive analysis
ALEPH; and DELPHI
provided in 2001 results with highly inclusive techniques.
The interest of these approaches is to measure directly in the data both ,the sample
purity and the charge separation, using more of the available information than the usual “ -tagging + jet charge” techniques.
For the same sample, the total error onE$
obp is reduced by 1.2 in DELPHI and 1.7
in ALEPH compared to the classical jet charge analysis. These results are obtained by :
adding charge/ flavour informations like secondary vertex charge or lepton/K
identification combined with their reconstructedñ ,ñò and charge.
0 5000 10000 15000 20000 25000 30000 35000 40000 -1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1 DELPHI
Jet Charge distribution for the Barrel ( b-tagging )
Number of lepton candidates
0 5000 10000 15000 20000 25000 30000 35000 40000 -1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1 DELPHI
Jet Charge distribution for the Barrel ( b-tagging )
Number of lepton candidates
Figure 8: Distribution for -tagged event in the DELPHI lepton analysis of “the jet-charge opposite
hemi-sphere”
“the charge of the lepton”. Prompt leptons from produce events with a negative value for such
product : the two hemispheres have a with opposite charge. Nevertheless mixing or ß
å
ß
events (quoted as “$ß ,wrong” in the plot) may end up to events with a positive value for such product.
Figure on the left : before calibration of the jet charge shape. Figure on the right : after calibration.
“distinguishing” between the different é hadrons to take advantage of
differ-ences in their decay/charge properties : é
: has a good vertex charge
informa-tion insteadé
n
has some charge information in the fragmentation tracks to tag
the sign of the /
quark.
The E
op obtained with such analysis have statistical correlations with other
E$ obp
measurements performed on the same data sample. Such correlations have been taken
into account in the LEP average, for example a statistical correlation of 2 20% is
observed between such analysis and lepton analysis.
Calibration in the data
Of course the simulation cannot describe properly all the variables used in these anal-ysis : sample composition or charge separation have to be measured directly in the data. The interest in the analysis described above rely not only on their improved statistical sensitivity but even more on their relative low sensitivity to the availability of a precise simulation description.
For example all LEP experiments observe a2 w
% data/MC discrepancy in the
distribution of the -tagging variable (see figure 6). To extract the sample composition
in different bins of -tag, an analysis of the number of single (2
V
) /double (2!
M
V )
0 " 0.02 " 0.04 " 0.06 " 0.08 " 0.1 " 0 " 0.1 " 0.2 " 0.3 " 0.4 " 0.5 " 0.6 " 0.7 " 0.8 " <δ > <δ> <δ> thrust>0.90 <δ> no jetcharge <δ> thrust>0.90 + no jetcharge <δ> correlation (single tag)
-0.02 0 " 0.02 " 0.04 " 0.06 " 0.08 " 0.1 " 0 " 0.1 " 0.2 " 0.3 " 0.4 " 0.5 " 0.6 " 0.7 " 0.8 " flav # hem $ <β > <β> <β> thrust>0.90 <β> no jetcharge <β> thrust>0.90 + no jetcharge <β> correlation (double tag)
DELPHI
%
Figure 9: The hemisphere charge correlation as
pre-dicted by the simulation when one hemisphere (upper plot) or two hemispheres with opposite charge (lower plot) are tagged. The correlations are plotted as a function of the neural net variable used to select
with a defined charge. Beside the full flavour net-work (point) results using modified flavour netnet-work are shown.
tagged hemispheres can be performed to extract the efficiency ( V
) to tag each flavour
X .
In the DELPHI lepton analysis, the jet charge of the opposite hemisphere to the lepton is used. The shape of the jet charge (
a
,
) like always is measured in the
data (see figure 5). The calibration gives, almost by construction, a good data/MC agreement (see figure 8) for the overall sample but also for subsamples with different
lepton- charge correlation selected by a givenñ ,ñ(ò cuts. This last point is interesting
as it indicates than the origin of the different leptons is well understood.
On important point in the new ALEPH/DELPHI inclusive analysis is the mea-surement of the charge separation in the data them self. In DELPHI only hemispheres
with a good charge separation are used. The charge tagging power is measured in
the data by a single/double tag techniques. Up to 93% right charge tagging has been obtained (see figure 7). In ALEPH all -tagged events have been used and a charge separation up to 74% has been observed. In this last analysis a classical (see figure 5) calibration of the shape of the jet charge has been performed.
In analysis using such kind of self-calibration (for the jet charge , -tagging , ... ) the dominant systematics are in general still coming from what has to be taken from the simulation. For example the hemisphere correlations or the behaviour of non-events induce the main contribution to the systematics in the inclusive analysis.
Nevertheless lots of efforts have been done to define correctly the size of such systematics. For example (see figure 9) in the new DELPHI inclusive analysis the source of the charge correlation between the hemispheres has been investigated in the simulation and identified to the jet charge information. Such correlation in the jet charge being well understood and studied in data as shown in the pure jet charge
Table 1: Corrections applied to the QCD
cor-rected asymmetry ( '&)()* ) : ,+ % -&.(* ¿ /10 > .2/ Source E$ obp E$ obp [ \^] 7 _ -0.0013 -0.0034 QED corr. +0.0041 +0.0104 43b -0.0003 -0.0008 Total +0.0025 +0.0062
Table 2: The following reduction coefficients,5 ½, of the
theoretical QCD correction,687 q:9
½ , have been estimated
(example of summer 97 analysis): 6';
q:< ½ 5 ½6 7 q:9 ½ and ; q:< =?> 9 0 çe@6 ; q:< ½ 2 -&.(* Exp. $ôHW ê ó Jet Ch. ALEPH .74A .07 DELPHI .52A .06 .46A .14 .24A .46 OPAL .69A .13 .29A .13 .36A .32
DELPHI analysisB , a systematic associated to this hemisphere correlation can be
correctly defined.
3 The corrections :E$
obp Y E mn obp
To extract from the measured asymmetries the pole asymmetry/I>JK MPO
Q RTS+U
RTVV , corrections
have to be applied (see table 1) :
energy shift from 91.263-465 (energy used to average theE
op ) to 7 _
initial state radiation
and interference
QCD corrections (done separately for each measurement)
The effect of the QCD corrections received lots of attention over the last years. This effort converged only in 1999. The main conclusion of these studies is than the visibility of the hard gluon emission, which dominate the theoretical QCD correc-tions, is a function of the experimental method used to extract the asymmetry. For example
experimental cuts ( ex : lower cut on the lepton momentum remove events with hard gluon )
event weight ( ex : events with hard gluon may end up in “area” of high
back-ground and get a lower weight in theE
op extraction )
generate changes in the QCD corrections to apply. As shown table 2 the scaling down of the QCD corrections due to these effects is not negligible. For this reason,
even if the theoretical QCD corrections for the ( ) is CDBFE
] N l GA NHIH (CD%B?E ] r f l A IJ l
), the common error in the LEP average from the QCD
corrections is only2 0.0002 forE
A FB 0,bb_ LEP K Summer 2001 < L A M FB 0,bb _ > N =0.0990 O ± P 0.0017 OPAL jet-ch Q ☞1991-95 0.1028 O ± P 0.0049 ±P 0.0046 L3 jet-ch ☞1994-95 0.0949 O ± 0.0101 ± 0.0056 DELPHI NN R ✍1992-95 0.0995 O ± P 0.0036 ±P 0.0022 DELPHI jet-ch ☞1992-95 0.1011 O ± 0.0044 ± 0.0015 ALEPH jet-ch M ☞1991-95 0.1012 O ± P 0.0025 ±P 0.0012 OPAL leptons Q ✍1990-95 0.0938 O ± 0.0040 ± 0.0022 L3 leptons K ☞1990-95 0.0999 O ± P 0.0060 ±P 0.0035 DELPHI leptons ✍1991-95 0.1012 O ± 0.0052 ± 0.0020 ALEPH leptons M ✍1991-95 0.0979 O ± P 0.0038 ±P 0.0022
Include Total Sys 0.0007 With Common Sys 0.0003
S mtT = 174.3 ± 5.1 GeV ∆αU had V = 0.02761 ± 0.00036 102 0.09 W 0.1 W 0.11 W A M FB 0,bb _ mH X[ GeV ] 150 200 m Y t[GeV]
Figure 10: The 9 most precise measurements of
and the overall LEP I average. The total (full
line) and systematic (doted line) errors are plotted. The first printed error corresponds to the statistic the second to the systematic. The different measurements of
are in very good agreement and give an
av-erage ofZ\[Z^]^_^`abZ\[Z^ZHç^c . The error of 0.0017
in-clude a total systematic of only 0.0007 with a com-mon part (systematics present in more than one mea-surement) of 0.0003 : the individual measurements and the final average are dominated by the statistical error. This final
is not significantly correlated
to any other quantity than ,dd
and even there the
correlation is small : 16 %.
3.1 Results summary
There is eleven different measurements ofE$
obp performed at LEP I by the four LEP
experiments. To take into account correctly in the average the statistical and system-atical correlations of these results, the LEP/SLD Heavy Flavour Working group has
developed an averaging proceduree which includes many measured quantities
con-nected to the electroweak measurements in the and sectors at the . In practice
the average is performed for 18 observables and for a total of 99 measurements. The
main measurements and the LEP average forE
op are quoted in figure 10.
4 Conclusion
Since 1994-1995 some discrepancies betweenI JKMPO
Q R S U
RTVV extracted from
E FHG andE op
measurements have been observed. Over the last 10 years, LEP I data collected
be-tween 1990 and 1995 have been analysed and re-analysed to improve theE
op
mea-surement and to further check its associated systematics. Nevertheless, today , using
E$ obp ,
and the measurement ofs
Q
in the leptonic sector
, the value extracted for
the effectivetbu
¹ and
t
B
¹ are compatible with the Standard Model prediction by less
than 1% (see figure 2). If this is not enough to claim a discovery, this should trig our
attention.
Even if some E
op measurements are still preliminary no significant change or
improvement are expected with the LEP and SLC data.
The present7 C andE F)G measurements are compatible with the SM, even if
both predict a “too” low Higgs mass,2 1.5 sigma below the LEP II 95% exclusion
limit of 114.13-465 . If SUSY could explain such low798 prediction, no discrepancy
between theI JLKNMPO
Q RTS+U RTVV , 7 8 extracted from E F)G andE
op are expected in the usual
theoretical frame works.
Before the start of LHC, to investigate further these results, improved
measure-ment of79C (LEP II+ TEVATRON :
79C 34 Y 25f94"5 ) ,7 Uhg>S (TEVATRON : 7 Uhg>S 5.1Y 23-4"5 ) andikj ; DBFE lnm _,o ( BES +”QCD” : 0.00036 Y 0.0002-0.0001 ) are expected. References
1. L3 collaboration, M. Acciari et al. , Phys. Let. B448, 152 (1999). 2. DELPHI collaboration, P. Abreu et al. , Z. Phys. C65, 569 (1995).
DELPHI collaboration,Measurement of the Forward-Backward Asymmetries of
W : W ? Y Y and W : W ? Y Y
using prompt leptons , DELPHI
2000-101 CONF 400.
3. ALEPH collaboration, D. Buskulic et al. , Phys. Lett. B384, 414 (1996)
ALEPH collaboration,Measurement of the and forward-backward
asymme-try using leptons,ALEPH 99-076 CONF 99-048.
4. OPAL Collaboration, G.Alexander et al., Z. Phys. C70, 357 (1996) // OPAL Collaboration, Updated Measurement of the Heavy Quark Forward-Backward
Asymmetries and Averageé Mixing Using Leptons in Multi-hadronic Events,
OPAL Physics Note PN226.
5. ALEPH collaboration, Measurement ofE
op using inclusive -hadron decays,
CERN EP/2001-047
6. DELPHI collaboration, Determination ofE$
obp using inclusive charge
recon-struction and lifetime tagging at LEP I, DELPHI 2001-020 CONF 468. 7. DELPHI collaboration, P. Abreu et al. , Eur. Phys. J. C9, 367 (1999). 8. D.Abbaneo , NIM A378, 101 (1996)
