Heavy Quark Production at HERA

0.94 MB·

by  Ian C. Brock

Heavy Quark Production at HERA
9 Ian C. Brock – on behalf of the H1 and ZEUS Collaborations
0 Physikalisches Institut, Universit¨at Bonn, Bonn, Germany
0
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HeavyflavourproductionisoneofthekeycomponentsoftheHERAIIphysicsprogramme. Whilemostofthe

n resultspresenteduseleptonsorthereconstructionofcharmedmesonstoidentifyheavyflavourproduction,both
a
the H1 and ZEUS experiments now have working microvertex detectors that are being used more and more. In
J
this talk I will summarise a selection of the recent results obtained by the two collaborations.
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1

] 1. Introduction The measurements are usually separated into
x thedeepinelasticscattering(DIS),Q2 (cid:38)1GeV2,
e The study of heavy flavour production at or photoproduction, Q2 (cid:46) 1GeV2, regimes, de-
-
HERA provides an important test of pertur-
p pending on whether the scattered electron is de-
e bative Quantum Chromodynamics (pQCD) and tected in the in the main calorimeter or not.
h alsovaluableinformationforthemeasurementsto
The main production mechanism for heavy
[
be made at the LHC. I will discuss a small selec-
quarks is the so-called Boson Gluon Fusion

1 tion of the many measurements of heavy flavour
(BGF) process which is illustrated in Figure 1.
v production that have been made at HERA, con-
Inpracticehigherordercontributionsalsohaveto
5 centrating on the more recent results.
3
HERA running started in 1992 and the ac-
5 Boson-Gluon Fusion
celerator stopped running at the end of June
1
. 2007. HERA collided 27.5GeV electrons or e e
1
0 positrons1 with 920GeV (820GeV until the end g *
9 of 1997) protons, giving a centre-of-mass energy
0 of 318GeV. A long shutdown in 2000 and 2001 Q
: was used to upgrade the machine and the detec-
v
i tors,withtheaimofincreasingtheluminosityby Q-
X
aboutafactorof4. Theperiodupto2000isusu-
g
r ally called HERA I and after 2001 HERA II. By
a
theendoftherunningbothofthecollidingbeam p
X
experiments, H1 and ZEUS, had collected about
0.5fb−1 of data.
Several kinematic variables are used to charac-
terise the ep scattering process:
Figure 1. Feynman diagram of the boson gluon
• Q2, the negative squared four-momentum fusion process.
exchanged at the electron or positron ver-
tex;
• x, the Bjorken scaling variable; be taken into account. The photon can fluctuate
into a qq¯pair and one of the quarks then partici-
• y, the inelasticity;
pates in the hard interaction (resolved photopro-
• W, the invariant mass of the hadronic final duction); or in so-called excitation the scattering
state. from charm or beauty can take place with intrin-
1Hereafter unless explicitly stated both electrons and sic charm or beauty inside the proton or photon.
positronsarereferredtoaselectrons. Monte Carlo models usually include these pro-
1
2 Ian C. Brock
cess in addition to the direct boson-gluon fusion.
These higher order processes are also sometimes
referred to collectively as non-direct.
Next-to-leading oder (NLO) QCD calculations
exist for heavy quark production at HERA.
These are implemented for photoproduction in
the FMNR programme [1,2] and for DIS in the
HVQDIS programme [3]. The programmes in-
clude simple independent fragmentation of the
b or c quark, but on their own are not able to
give predictions for correlations between final-
state particles. The FMNR programme has been
interfaced[4]tothe Pythia MonteCarloandits
predictions have been used for studies of dimuon
final states.
Most heavy flavour measurements rely on the
central tracking detectors and are helped signifi-
cantly by the presence of a microvertex detector.
H1 had such a detector for some of the HERA I
running, while both ZEUS and H1 had such de-
tectors for the HERA II running period.
Several different methods have been used by
the collaborations to identify the production of
heavy quarks. Each of them has its advantages
and disadvantages and often cover different kine-
matic ranges. Traditionally the identification of
D∗ mesons and semileptonic decays have been
used most often. With the advent of microver-
tex detectors lifetime information is being used
more and more often. This works best for events
withhighenergyjets,whiletaggingwithsemilep-
tonic decays to electrons or double tags enables
one to go to lower transverse momenta.
Figure2. ∆M =m(Kππ)−m(Kπ)distributions
2. D∗ Production
for the photoproduction (top) and DIS (bottom)
TheH1collaborationhasmadeaseriesofmea- samples. The points show the data, the curves
surements of D∗ production both in the photo- in the lower figure, the results of a fit to the dis-
production [5] (96pb−1 of data taken in 2006 tribution. The dotted line shows the background
and 2007) and the DIS [6] (347pb−1 from the shape. The kinematic cuts are indicated.
HERAIIrunningperiod)regimes. Forthesemea-
surements they make use of their new Fast Track
Trigger,whichenableseventswithD∗ candidates
to be selected early in the trigger chain. In both
photoproduction and DIS clear signals are seen
asillustratedinFigure2. Thekinematiccutsare
indicated in the figures.
Differential cross-sections as a function of a
Heavy Quark Production at HERA 3
wide range of variables have been determined.
The cross-section as a function of Q2 is shown
in Figure 3. The measurements are compared to
Figure 4. D∗ production cross-section in DIS as
a function of η(D∗) compared to NLO QCD pre-
dictions. For further details see the caption of
Figure 3. D∗ production cross-section as a func-
Figure 3.
tion of Q2. The data (points) are compared to
NLO QCD predictions with two different PDFs.
The lower plot shows the NLO QCD prediction
scaled by the ratio of the data to NLO QCD vis-
ible cross-sections. The range of variation of the
quarkmassandfactorisationandrenormalisation
scales are indicated in the figure.
the predictions of the HVQDIS programme us-
ing two different Parton Distribution Functions
(PDF). The different PDFs show a very similar
behaviour as a function of Q2.
Incontrastthecross-sectionasafunctionofthe
pseudorapidity, η, shows a clear dependence (see
Figure4),demonstratingthesensitivityofcharm
production to the gluon structure function.
Makingthesamecomparisonforphotoproduc-
Figure 5. D∗ production cross-section in pho-
tion one sees that the NLO QCD prediction un-
toproduction as a function of η(D∗) compared
derestimates the data in the forward direction
to the NLO QCD prediction. The band shows
(see Figure 5). Comparing the data to Monte
Carlopredictions,theCascadegenerator,which the uncertainty in the prediction. The range of
variationofthequarkmassandfactorisationand
is based upon k -factorisation, is able to pro-
T
renormalisation scales are indicated in the figure.
vide a better description of the data in DIS than
RAPGAPwithtwodifferentPDFs(seeFigure6).
However, in photoproduction Pythia, using the
4 Ian C. Brock
rate b-quark events from background. The cross-
sections as a function of the transverse momen-
tum and pseudorapidity of the muon are shown
in Figures 7 and 8. Both the charm and beauty
Figure 6. D∗ production cross-section in DIS as
a function of η(D∗). The data are compared to
thedifferentMonteCarlogeneratorsasindicated
in the figure.
massless scheme for the generation of the heavy
Figure 7. b-quark production cross-section in di-
quarks, provides the best description of the data,
jet photoproduction as a function of the trans-
whileCascadeandPythiainthemassivemode
versemomentumofthemuon. Themeasurement
both undershoot the data in the forward direc-
is compared to an earlier ZEUS publication [9]
tion.
and the NLO QCD prediction. The uncertainty
on the prediction is indicated by the band.
3. Beauty in Photoproduction
The ZEUS collaboration recently reported two
new measurements of b-quark production in pho- contributions are left free in the fit. The fig-
toproduction. The first measurement uses semi- uresalsoshowtheresultsofananalysisusingthe
leptonic decays to muons [7] to identify heavy HERAIdata[9], whichonlyusedprel forsepara-
T
quarkdecays,whilethesecondoneuseselectrons tion. For this earlier analysis the charm content
[8]. Dijeteventsareselectedbyrequiringatleast was fixed. Good agreement between the analyses
two jets with |η| < 2.5 and a transverse mo- isseen. ThepredictionsoftheNLOQCDpredic-
mentum(muonmeasurement)orenergy(electron tion are also in good agreement with the data.
measurement)greaterthan7GeVforthehighest The second measurement identifies electrons
transverse energy and 6GeV for the 2nd highest from the semileptonic decays of heavy quarks us-
transverse energy jet. inganintegratedluminosityof120pb−1 collected
The first measurement uses 124pb−1 of data during the HERA I running period. Electron
collected in 2005 and requires a well identified identification uses the measurement of the spe-
muon with p > 2.5GeV and −1.6 < η < 2.3. cific energy loss, dE/dx, in the Central Track-
T
The microvertex detector is used to measure the ing Detector, CTD, the fraction of the energy
impactparameter(δ)ofidentifiedmuons. Thisis deposited in the electromagnetic calorimeter as
combined with the transverse momentum of the well as the ratio of the energy deposited in the
muon with respect to the jet axis (prel) to sepa- calorimeter to the momentum measured in the
T
Heavy Quark Production at HERA 5
ss
nitnit 11
UU b e X
y y
bitrarbitrar1100−−11 Bckg e X
ArAr
1100−−22
1100−−33
00 00..55 11 11..55 22 22..55 33 33..55 44
prel (GeV)
ss
nitnit
UU
y y 1100−−11
arar
bitrbitr
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00 00..55 11 11..55 22 22..55 33
∆∆φφ ((rraadd))
Figure 8. b-quark production cross-section in di-
jet photoproduction as a function of the pseudo-
rapidity of the muon. The measurement is com-
pared to an earlier ZEUS publication [9] and the Figure 9. Variables used to separate semilep-
NLO QCD prediction. The uncertainty on the tonic heavy quark decays from background. The
prediction is indicated by the band. solidlineshowsthedistributionforelectronsfrom
semileptonicb-quarkdecays,thedashedlineforc-
quark decays and the dotted line the background
(Bkg).
tracking detectors. Semileptonic decays are sep-
arated from background using prel and the az-
T
imuthal angle between the electron direction and
themissingtransversemomentumvector,∆φ. As
illustrated in Figure 9, prel can separate b-quark
T
fromc-quarkdecays,while∆φseparatessemilep-
tonic decays from background.
The variables are combined using a likelihood
ratio method, which is optimised for the iden-
tification of electrons from semileptonic b-quark
decays. Thedistributionofthelikelihoodratiois
shown in Figure 10. The distribution is fit using
the expected distributions for beauty, charm and
background to determine the fractions of events
Figure 10. The distribution of the likelihood ra-
from each source. The fit provides a very good
tio for electron candidates, N , in data com-
description of the data. cand
pared to the Monte Carlo expectation after the
The visible ep cross sections (at hadron level)
scaling the predictions to best fit the data. The
for b-quark and c-quark production and the sub-
arrow indicates the region included in the fit
sequent semileptonic decay to an electron with
(−2lnT <10). The shaded areas show the fitted
pe > 0.9GeV in the range |ηe| < 1.5 in photo-
T contributions from b quarks, c quarks and back-
production events with Q2 < 1GeV2 and 0.2 <
ground as denoted in the figure.
y <0.8andatleasttwojetswithE >7(6)GeV,
T
6 Ian C. Brock
√
|η| < 2.5 were determined separately for s =
√
300GeV and s = 318GeV. For the complete
data set (96–00) the cross-sections evaluated at
√
s=318GeV are
σvis =(cid:0)125±11(stat.)+10(syst.)(cid:1)pb,
b −11
σvis =(cid:0)278±33(stat.)+48(syst.)(cid:1)pb.
c −24
These cross-sections are in agreement with the
corresponding NLO QCD predictions:
σNLO =(cid:0)88+22(cid:1)pb,
b −13
σNLO =(cid:0)380+48(cid:1)pb.
c −24
The cross-sections as a function of the trans-
verse momentum and pseudorapidity of the elec-
tron are shown in Figure 11. Good agreement
with the NLO QCD prediction is seen. The data
alsoagreewellwiththePythiapredictionscaled
byafactorof1.75forb-quarkproductionand1.28
for c-quark production.
4. Beauty Correlations
The identification of both heavy-quark decays
in an event has several advantages: the back-
groundisreducedsubstantiallyandthekinematic
range accessible is larger. The disadvantage is
a significant reduction of statistics. If both b-
quark jets can be identified, dijet correlations
can be directly measured which probe next-to-
leading order effects. The ZEUS collaboration
Figure 11. Differential cross sections as a func-
used the HERA I data sample to select events
tion of a), c) the transverse momentum and b),
with E > 8GeV and two identified muons [10].
T d) the pseudorapidity of the electrons. Plots a)
Separating the samples according to the relative
andb)areforb-quarkproductionwhilec)andd)
charge of the muons as well as their invariant
are for c-quark production. The measurements
mass allows much of the background to be evalu-
are shown as points. The inner error bar shows
ated directly from the data.
thestatisticaluncertaintyandtheoutererrorbar
The extracted cross-section is shown in Fig-
showsthestatisticalandsystematicuncertainties
ure12. ItiscomparedwiththeNLOQCDpredic-
added in quadrature. The solid line shows the
tion as well as with a leading order Monte Carlo.
NLO QCD prediction after hadronisation correc-
Given the limited statistics it is not possible to
tions,withthetheoreticaluncertaintiesindicated
say whether the NLO calculation provides a bet-
by the band; the dashed line shows the scaled
ter description of the data. prediction from Pythia.
5. Fb¯b and Fcc¯
2 2
TheH1collaborationhaveusedtheimpactpa-
rametersignificancetodetermineFb¯b andFcc¯for
2 2
Heavy Quark Production at HERA 7
Figure 12. The dimuon cross-section as a func-
tion of the azimuthal angle between the muons
in dijet events. The data (points) are compared
to the NLO QCD prediction calculated using the
Figure 13. Distribution of the signed impact pa-
FMNRxPYTHIAinterfaceaswellastotheRAP-
rameter for the data (points) and the contribu-
GAP prediction scaled by a factor of 1.84. The
tions from b, c and light quarks, evaluated using
inner error bar shows the statistical uncertainty
Monte Carlo events.
and the outer error bar shows the statistical and
systematic uncertainties added in quadrature.
12GeV2 < Q2 < 650GeV2 and 0.0002 < x <
0.032 using 56pb−1 of data taken in 2006 [11].
The distribution of the impact parameter in the
transverse plane is shown in Figure 13.
In order to separate beauty and charm from
background the two tracks with the most signifi-
cant impact parameters (S and S respectively)
1 2
are selected, rejecting events where the signs of
the impact parameters differ. The significance is
defined as δ/σ(δ), where σ(δ) is the error on δ.
Events with one good track are used to make the
S distribution; all other events are used for the
1
S distribution.
2
The contents of the negative significance bins
are subtracted from the corresponding positive
significance bins. This yields the distribution of
S shown in Figure 14. The charm contribution
2
dominates the distribution. At high significance Figure14. Distributionofthesecondhighestsig-
thebeautycontributionbecomeslarger. Thedata nificanceandthecontributionsfromb,candlight
are split into bins in Q2 and x and the contribu- quarks, evaluated using Monte Carlo events.
tions of beauty and charm are determined sepa-
ratelyineachbinusingaleastsquaressimultane-
8 Ian C. Brock
ousfittotheS andS distributions. Theoverall
1 2
normalisation is determined by also including in
the fit the total number of inclusive events with-
outanycutontheimpactparametersignificance.
The results of the fit in each x−Q2 bin are con-
verted to a “reduced cross-section” using
d2σcc¯ xQ4
σ˜cc¯(x,Q2)= .
dxdQ22πα2(1+(1−y)2)
The reduced cross section for cc¯production as a
functionofxindifferentQ2 binsisshowninFig-
ure 15. Measurements made with the HERA I
data in the same kinematic range are also shown
in the figure. The results are in good agree-
ment with each other and can be combined, tak-
ing into account the correlated systematic errors.
The prediction using the Variable Flavour Num-
ber Scheme (VFNS) in the MRST04 PDF agrees
well with the data.
From the reduced cross-section Fcc¯ can be ex-
2
tracted:
y2
σ˜cc¯(x,Q2)=Fcc¯− Fcc¯.
2 (1+(1−y)2) L
The correction due to the longitudinal structure
function,Fcc¯,issmall. Thesameformulaewithc
L
replacedbybcanbeusedtoextractσ˜b¯b andFb¯b.
2
The measurements of Fcc¯ and Fb¯b are shown in
2 2
Figures 16 and 17, respectively. The rapid in-
crease in Fcc¯ as a function of Q2 at low x is
2
clearly visible. The Fb¯b measurements are con-
2
sistent with the same trend, but are less precise.
Figure 15. The reduced cross-section for cc¯pro-
duction in different Q2 bins as a function of x.
6. Conclusions
The inner errors bars show the statistical uncer-
tainty, the outer error bars represent the statisti-
ThemanyHERAmeasurementsofbeautypro-
calandsystematicuncertaintiesaddedinquadra-
duction in photoproduction are compared in Fig-
ture. Themeasurementsarecomparedwiththose
ure 18. The measurements presented here agree
from HERA I and the averaged data are also
well with the previous values, giving a consistent
shown. The measurements are compared to the
picture of b-quark production in ep collisions in
MRST04 prediction.
the photoproduction regime, and are well repro-
duced by the NLO QCD calculations. For all the
measurements leading order Monte Carlo predic-
tions also describe well the shapes of the distri-
butions.
There is a tendency for the charm measure-
mentstoovershootthepredictionsintheforward
Heavy Quark Production at HERA 9
Figure 16. Fcc¯ as a function of Q2 for different x Figure 17. Fb¯b as a function of Q2 for different
2 2
ranges. Also shown are measurements from the x ranges. Also shown is a preliminary measure-
H1 and ZEUS collaborations using D∗ mesons to mentfromtheZEUScollaborationusingthedata
identify the charm quarks. The inner errors bars from 2004. The inner errors bars show the sta-
show the statistical uncertainty, the outer error tisticaluncertainty,theoutererrorbarsrepresent
bars represent the statistical and systematic un- thestatisticalandsystematicuncertaintiesadded
certainties added in quadrature. in quadrature.
10 Ian C. Brock
REFERENCES
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T
ZEUS measurements as indicated in the figure. 5. H1 Coll., F. D. Aaron, et al., Measurement of
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the FMNR program with the theoretical uncer-
Scattering, DIS2008 (Apr. 2008).
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9. ZEUS Coll., S. Chekanov, et al., Bottom
In the near future a number of final HERA I
photoproduction measured using decays into
measurements will be published. With the
muons in dijet events in ep collisions at
√
HERA II data the kinematic range of the mea- s=318GeV, Phys. Rev. D 70 (2004) 012008.
surements can be extended and a combination arXiv:hep-ex/0312057.
of different tagging methods should increase the 10. I. Bloch, Measurement of beauty production
precision of the measurements. The improved from dimuon events at HERA / ZEUS, Ph.D.
HERA II forward tracking will allow much im- thesis, Hamburg University (2005).
proved studies of heavy quark production in the 11. H1 Coll., F. D. Aaron, et al., Measurement of
Fcc¯ and Fb¯b using the H1 vertex detector at
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Acknowledgements
It is a pleasure to thank the organisers for
making this an informative and enjoyable con-
ference. I would like to thank Cristi Diaconu,
Achim Geiser, Markus Ju¨ngst, Monica Turcato,
Andr´eSch¨oningandMatthewWingfortheirhelp
in preparing this talk.