Measurement of angular correlations based on secondary vertex reconstruction at

Abstract

A measurement of the angular correlations between beauty and anti-beauty hadrons (

\textB[`(\textB)] {\text{B}}\overline {\text{B}} ) produced in pp collisions at a centre-of-mass energy of 7 TeV at the CERN LHC is presented, probing for the first time the
region of small angular separation. The B hadrons are identified by the presence of displaced secondary vertices from their
decays. The B hadron angular separation is reconstructed from the decay vertices and the primary-interaction vertex. The differential

\textB[`(\textB)] {\text{B}}\overline {\text{B}} production cross section, measured from a data sample collected by CMS and corresponding to an integrated luminosity of 3.1 pb−1, shows that a sizable fraction of the

\textB[`(\textB)] {\text{B}}\overline {\text{B}} pairs are produced with small opening angles. These studies provide a test of QCD and further insight into the dynamics of

\textb[`(\textb)] {\text{b}}\overline {\text{b}} production.

KeywordsHadron-Hadron Scattering

Full text

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JHEP03(2011)136
Published for SISSA bySpringer
Received: February 18, 2011
Accepted: March 20, 2011
Published: March 28, 2011
Measurement of BB angular correlations based on
secondary vertex reconstruction at√s = 7TeV
The CMS collaboration
Abstract: A measurement of the angular correlations between beauty and anti-beauty
hadrons (BB) produced in pp collisions at a centre-of-mass energy of 7 TeV at the CERN
LHC is presented, probing for the first time the region of small angular separation. The
B hadrons are identified by the presence of displaced secondary vertices from their decays.
The B hadron angular separation is reconstructed from the decay vertices and the primary-
interaction vertex. The differential BB production cross section, measured from a data
sample collected by CMS and corresponding to an integrated luminosity of 3.1pb−1, shows
that a sizable fraction of the BBpairs are produced with small opening angles. These
studies provide a test of QCD and further insight into the dynamics of bb production.
Keywords: Hadron-Hadron Scattering
Open Access, Copyright CERN,
for the benefit of the CMS Collaboration
doi:10.1007/JHEP03(2011)136

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JHEP03(2011)136
Contents
1Introduction1
2 The CMS detector2
3 Monte Carlo simulation and QCD predictions3
4Event selection and data analysis
4.1Analysis overview
4.2Vertex reconstruction and B candidate identification
4.3Efficiency and resolution
4.4Systematic uncertainties
4
4
5
6
8
5Results
5.1
5.2
11
11
13
Differential distributions in ∆R and ∆φ
Comparisons with theoretical predictions
6Summary14
1Introduction
Beauty quarks are abundantly produced through strong interactions in pp collisions at the
CERN Large Hadron Collider (LHC). The hadroproduction of bb pairs is measured to have
a large cross section (of the order of 100µb) at a centre-of-mass energy of 7 TeV [1–3]. De-
tailed b quark production studies provide substantial information about the dynamics of the
underlying hard scattering subprocesses within perturbative Quantum Chromodynamics
(pQCD). In lowest order pQCD, i.e. in 2 → 2 parton interaction subprocesses, momen-
tum conservation requires the b and b quarks to be emitted in a back-to-back topology.
However, higher order 2 → 2 + n (n ≥ 1) subprocesses with additional partons (notably
gluons) emitted, give rise to different topologies of the final state b quarks. Consequently,
measurements of bb angular and momentum correlations provide information about the
underlying production subprocesses and allow for a sensitive test of pQCD leading-order
(LO) and next-to-leading order (NLO) cross sections and their evolution with event energy
scales. Studies of b quark production at the LHC may provide insight into the hadronisa-
tion properties of heavy quarks at these new energy scales, as well as better knowledge of
the heavy quark content of the proton. In addition, identification of b quarks and precision
measurements of their properties are crucial ingredients for new physics searches in which
bb hadroproduction is expected to be one of the main backgrounds.
In this paper, angular correlations between pairs of beauty hadrons, hereafter referred
to as “B hadrons”, are studied with the Compact Muon Solenoid (CMS) detector, probing
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for the first time the region of very small angular separation at√s = 7 TeV. Measurements
of BB-pair production are presented differentially as a function of the opening angle for
different event scales, characterised by the leading jet transverse momentum. The extra-
polation back to the angular separation of the b quarks, which requires modeling of heavy
quark fragmentation and hadronisation, is not considered in this analysis. The results are
given for the visible kinematic range defined by the phase space at the hadron level.
Measurements of the full range of BB angular separation demand good angular res-
olution and require the ability to resolve small opening angles when the two B hadrons
are inside a single reconstructed jet. The kinematic properties of B hadrons can be recon-
structed using jets, leptons from semileptonic decays of B hadrons or secondary vertices
(SV) originating from the decay of long-lived B hadrons. In this analysis, a method based
on an iterative inclusive secondary vertex finder that exploits the excellent tracking capa-
bilities of the CMS detector is introduced. One advantage of this method is the unique
capability to detect BB pairs even at small opening angles, in which case the decay pro-
ducts of the B hadrons tend to be merged into a single jet and the standard B jet tagging
techniques [4] are not applicable. Previously, studies of azimuthal bb correlations using
vertexing have been done at lower energy in pp collisions [5, 6].
In section 2, a brief overview of the subdetectors relevant for this analysis is given.
Section 3 describes the Monte Carlo (MC) simulations and the programs used for QCD
predictions. The event selection, the analysis details, and the determination of efficiencies
and systematic uncertainties are described in section 4. In section 5 we present the results
and compare the data with theoretical predictions.
2The CMS detector
A detailed description of the CMS detector can be found in ref. [7]. The central feature of
the CMS apparatus is a superconducting solenoid of 6 m inner diameter, with a 3.8 T axial
magnetic field. The subdetectors used in the present analysis are tracking detectors and
calorimeters, located within the field volume. The tracker consists of a silicon pixel and
silicon strip tracker covering the pseudorapidity range |η| < 2.5. The pixel tracker consists
of three barrel layers and two endcap disks at each barrel end. The strip tracker has 10
barrel layers and 12 endcap disks. The barrel and endcap calorimeters (|η| < 3) consist
of a lead-tungstate crystal electromagnetic calorimeter (ECAL) and a brass/scintillator
hadron calorimeter (HCAL). The ECAL and HCAL cells are grouped into towers, project-
ing radially outward from the interaction region, for triggering purposes and to facilitate
jet reconstruction. The CMS experiment uses a right-handed coordinate system, with the
origin at the nominal proton-proton collision point, the x-axis pointing towards the centre
of the LHC ring, the y-axis pointing upwards (perpendicular to the LHC plane), and the
z-axis pointing along the anticlockwise beam direction. The polar angle θ is measured
from the positive z-axis and the azimuthal angle φ is measured from the positive x-axis in
the xy plane. The radius r denotes the distance from the z-axis and the pseudorapidity is
defined by η = −ln(tan(θ/2)).
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3Monte Carlo simulation and QCD predictions
Different simulation programs at the LO and the NLO level have been utilized to describe
the b production process within perturbative QCD. Within the LO picture, three parton
level production subprocesses can be defined [8, 9], conventionally denoted by flavour cre-
ation (FCR), flavour excitation (FEX) and gluon splitting (GSP), and are implemented
in Monte Carlo event generators like pythia [10] and herwig [11]. These subprocesses
are related to different final state topologies. Notably, in FCR processes the bb pairs are
expected to be emitted in a back-to-back topology, which corresponds to a large angular
separation between the b and b quarks, whereas in GSP the pair emission follows a more
collinear topology, i.e. a small angular separation between the b and b quarks. At higher
orders in QCD, the FCR, FEX and GSP separation of production subprocesses becomes
meaningless and only the combination of the 2 → 2 and 2 → 2 + n (n ≥ 1) subpro-
cesses is relevant. Calculations of such processes are implemented in mc@nlo [12–14] or
fonll [15]. The MadGraph/madevent [16, 17] generator provides the possibility to sim-
ulate 2 → 2,3 subprocesses at tree-level, providing a hybrid solution between 2 → 2 at LO
and the NLO simulations. We use also the cascade [18] generator, which is based on off-
shell LO matrix elements using high-energy factorization [19] convolved with unintegrated
parton distributions.
The basic Monte Carlo event generator applied in this analysis is the LO pythia pro-
gram (version 6.422 [10]), which is used to determine selection efficiencies and to optimise
the vertexing algorithm for B hadron reconstruction. The event samples are generated
applying the standard pythia settings [10] with tune D6T [20] for the underlying event
and with the CTEQ6L1 [21] proton parton distribution functions (PDF). All events gener-
ated by the pythia program are processed with a detailed simulation of the CMS detector
response based on the geant4 package [22].
For comparison with theoretical predictions, events with two and three partons in the
final state are generated by means of the MadGraph/madevent4 program, where the
showering is performed with pythia, and the jet matching scheme used is “kT-MLM” [23].
The CTEQ6L1 [21] parton distribution functions are used, and the mass of the b quark is
set to mb= 4.75GeV.
For the events produced with the cascade generator, the CCFM set A [24] of parton
distributions is used. The calculations include the processes g∗g∗→ b¯b and g∗q → gq →
b¯bX. The matrix element of g∗g∗→ b¯b already includes a large fraction of the process
g∗g → gg → b¯bX [19, 25], therefore g∗g → gg → b¯bX is not added to avoid double counting.
A further set of QCD events is produced by means of the mc@nlo generator (version
3.4 [14] with standard scale settings and b-quark mass mb= 4.75GeV), which matches
NLO QCD matrix element calculations with parton shower simulations as implemented in
herwig (version 6.510) [11]. The proton PDF set used is CTEQ6M [21]. For the NLO
generated events, no full CMS detector simulation is done. Subsequent to the parton show-
ering and hadronisation process, the generated stable particles in the events are clustered
into jets with the anti-kTjet algorithm [26].
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(GeV) (GeV)
TT
leading jet pleading jet p
5050100 100150150200200250250300 350300 350400400450450500 500
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00020 202040 404060 606080 8080100100100 120120120 140140140
efficiency
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efficiency
> 15 GeV
U
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> 30 GeVE
> 50 GeVE
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efficiency
Figure 1. The measured transverse momentum distributions of the leading jet in the event (left)
and measured efficiency to trigger an event on the high-level trigger as a function of jet pT(right),
for three different trigger thresholds.
4Event selection and data analysis
The data sample used in this analysis was collected by the CMS experiment during 2010
at a centre-of-mass energy of√s = 7 TeV and corresponds to an integrated luminosity
of 3.1 ± 0.3pb−1. Only data from runs when the CMS detector components relevant for
this analysis were fully functional and when stable beam conditions were present are used.
Events from non-collision processes are rejected by requiring a primary (“collision”) vertex
(PV) [27, 28] with at least four well reconstructed tracks. Background from beam-wall and
beam halo events, and events faking high energy deposits in the HCAL, are filtered out
based on pulse shape, hit multiplicity and timing criteria [29].
4.1Analysis overview
The analysis relies on the single-jet trigger in both the hardware-level (L1) and the software
high-level (HLT) components of the CMS trigger system [7]. We require at least one HLT
jet with uncorrected transverse calorimetric energy EU
50GeV. Figure 1 shows the leading jet transverse momentum (pT) spectra with particle flow
jets [30] and the corresponding trigger efficiency dependence on pT. The efficiencies, also
shown in figure 1, are determined using events selected with a lower EU
The event sample is then divided into three energy scale bins corresponding to the pT
ranges where the different jet triggers are over 99% efficient. These correspond to samples
where the transverse momenta of the leading jet, using corrected jet energies [31], exceed
56, 84 and 120GeV, respectively. The effective integrated luminosity, taking into account
the trigger prescale factors, corresponds to 0.031, 0.313 and 3.069pb−1, respectively, for
the three samples, including some overlap.
The visible kinematic range for the measurements is defined at the B hadron level by
the requirements |η(B)| < 2.0 and pT(B) > 15GeV for both of the B hadrons. The leading
jet used to define the energy scale is required to be within |η(jet)| < 3.0.
Tabove a trigger threshold of 15, 30 or
T(prescaled) trigger.
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In this analysis, the HLT triggered events are required to have at least one recon-
structed jet with a corrected pTabove a threshold, a reconstructed PV, and in addition at
least two reconstructed secondary vertices (SV). For the offline jet reconstruction, particle
flow objects [30] are clustered with the anti-kTjet algorithm [26, 32] with a distance pa-
rameter RkT= 0.5. For further BB angular analysis, these generic secondary vertices are
required to originate from B hadron decays, as described in the following paragraphs.
The flight direction of the original B hadron is approximated by the vector− →
the PV (position of B hadron production) and the SV (position of the B hadron decay).
The length |− →
by S3D= D3D/σ(D3D), where σ(D3D) is the uncertainty of D3D.
In an event with two SVs, which are considered to originate from a bb pair, the angular
correlation variables between the B and B hadrons are calculated using their flight direc-
tions. Typical variables used for the characterization of the angular correlations between
the two hadrons are the difference in azimuthal angles (∆φ) and the difference in polar
angles, usually expressed in terms of pseudorapidity (∆η), or the combined separation
variable ∆R =
The kinematic regions with ∆R < 0.8 and with ∆R > 2.4 are used for comparisons or
normalisations of the simulation. The cross sections integrated over these two regions will
be denoted by σ∆R<0.8and by σ∆R>2.4, and the ratio by ρ∆R= σ∆R<0.8/σ∆R>2.4. This is
inspired by the theoretical predictions, since at low ∆R values the gluon splitting process
is expected to contribute significantly, whereas at high ∆R values flavour creation prevails.
SV , joining
SV | is the three-dimensional flight distance (D3D) and its significance is given
?∆η2+ ∆φ2.
4.2Vertex reconstruction and B candidate identification
The primary vertex is reconstructed from tracks of low impact parameter with respect
to the nominal interaction region. In cases of multiple interactions in the same bunch
crossing (pile-up events), the primary interaction vertex is chosen to be the one with the
largest squared transverse momentum sum ST=?p2
Next, the events are required to have at least two reconstructed secondary vertices.
An inclusive secondary vertex finding (IVF) technique, completely independent of jet
reconstruction, is applied for this purpose. This technique reconstructs secondary ver-
tices by clustering tracks around the so-called seeding tracks characterized by high three-
dimensional impact parameter significance Sd= d/σ(d), where d and σ(d) are the impact
parameter and its uncertainty at the PV, respectively. The tracks are clustered to a seed
track based on their compatibility given their separation distance in three dimensions, the
separation distance significance (distance normalised to its uncertainty), and the angu-
lar separation. The clustered tracks are then fitted to a common vertex with an outlier-
resistant fitter [33, 34]. The vertices sharing more than 70% of the tracks compatible within
the uncertainties are merged. As a final step, all tracks are assigned to either the primary
or the secondary vertices on the basis of the significance of the track to vertex distance.
In this analysis, a SV is required to be made up of at least three tracks, to have
a maximal two-dimensional flight distance Dxy = |− →
dimensional flight distance significance S2D= Dxy/σ(Dxy) > 3, and to possess a vertex
Ti, where the sum runs over all tracks
associated with the vertex. Residual effects from pile-up events are found to be negligible.
SVxy| < 2.5 cm, a minimal two-
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mass mSV < 6.5GeV. Here, σ(Dxy) is the uncertainty on Dxy. The four-momentum of the
vertex pSV = (ESV,? pSV) is calculated as the sum pSV =?piover all tracks fitted to that
ergy Ei. The vertex mass mSV is calculated as m2
the reconstructed B hadron candidate is then identified with the SV four-momentum, and
thus the variables pT(B),η(B) for the B hadron candidates are readily calculated from pSV.
Events with at least two secondary vertices may originate from any of the following
processes: a) true ’signal’ BB events; b) true BB events where at least one B hadron
is not correctly reconstructed (SV from other sources); c) QCD events with light quark
and gluon jets, which enter through misidentification of vertices not originating from B
decay; d) direct cc production with long lived D hadrons; e) sequential B → D → X decay
chains, where B hadrons decay to long lived D hadrons, and both B and D vertices are
reconstructed. The BB signal events contain a fraction from top quark pair production of
less than 1% [35, 36].
Often, both the B and D decay vertices are reconstructed by the IVF. Such topologies
need to be distinguished from events with two quasi-collinear B hadrons. To achieve this,
an iterative merging procedure is applied to vertices with ∆R < 0.4. The procedure is
optimised to yield a single B candidate associated with a decay chain B → D → X, while
successfully retaining two B candidates also in events where two real B hadrons are emitted
nearly collinearly. The vertices are merged into a single B candidate if the invariant mass
of the sum over all tracks is below 5.5GeV and cosβ > 0.99, where β is the angle between
the line connecting the two vertices and the sum of the momenta of the tracks associated
to the vertex at largest distance from the PV.
All B candidates are retained if they have a minimal 3D flight distance significance
S3D> 5, a pseudorapidity |η(SV)| < 2, a transverse momentum pT(SV) > 8GeV, and a
vertex mass mSV> 1.4GeV. The quality of the B candidate reconstruction technique is
illustrated in figure 2 for events with a leading jet having pT> 84GeV (all selection cuts
apart from those on the shown quantities are applied). The simulation describes the data
very well in terms of vertex mass and 3D decay length significance distribution.
Only those events which have exactly two B hadron candidates and which have a vertex
mass sum m1+ m2> 4.5GeV are retained. A total of 160, 380 and 1038 events pass all
these requirements for the three leading jet pTbins, respectively from the lowest to the
highest. The overall contributions from events with three or more B candidates is found
to be negligible (less than 1%).
vertex, with pi= (Ei,? pi), using the pion mass hypothesis for every track to obtain its en-
SV= E2
SV−? p2
SV. The four-momentum of
4.3Efficiency and resolution
This analysis uses selection efficiency corrections as a function of the leading jet pTand the
∆R between the two SVs. The corrections are determined from the simulated pythia event
samples. They extrapolate from the measured vertex momenta to the visible phase space
of long-lived B hadrons, defined by |η(B)| < 2.0, and pT(B) > 15GeV. The momentum
measured by the vertex candidate represents of the order of 50% of the true B hadron
momentum. The overall event reconstruction efficiencies (including both B hadron decays)
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vertex mass (GeV)vertex mass (GeV)
001122334455667788
number of B candidates
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number of B candidates
Figure 2. Properties of the reconstructed B candidates: vertex mass distribution (left) and flight
distance significance distribution (right). The inset in the right plot shows a zoom of the flight
distance significance distribution with narrower bins and linear scale. The data are shown by the
solid points. The decomposition into the different sources, beauty, charm and light quarks, is shown
for the pythia Monte Carlo simulation. The simulated distributions are normalised to the total
number of data events. All selection cuts apart from those on the shown quantities are applied.
are found to be 7.4%, 9.3% and 10.7%, on average, for the three jet pTbins, respectively
from the lowest to the highest.
The validity of the ∆R-dependence of the efficiencies obtained from simulation is
checked using a data driven method based on event mixing, as illustrated below. It is found
that the ∆R-dependence is well described by the simulation, justifying this approach. The
differences are used to estimate the systematic uncertainties.
The resolution achieved in the ∆R reconstruction is estimated from simulation. The
comparison of the ∆R values reconstructed between the two vertices ∆RV V with the values
calculated between the original true B hadrons ∆RBB, determines the resolution. This is
illustrated in figure 3, which shows the two-dimensional distribution ∆RV V versus ∆RBB
and its projection onto the diagonal (∆RV V − ∆RBB). A fit to this projection directly
yields an average resolution better than 0.02 in ∆R for the core region, a value much
smaller than the ∆R bin width of 0.4.
In order to calculate differential cross sections, a ∆R-dependent purity correction is
applied. The contributions to purity due to migration are illustrated in figure 3 (left).
The total number of event entries off the diagonal is found to be about 3%. The largest
impurity occurs close to ∆RV V ≈ 3 as can be seen in the 2D plot. These events are due
to misreconstructed collinear events where only one B hadron is reconstructed, while a
fake vertex is found in the recoiling light quark jet. The largest effect on a single bin is
below 10% and this is taken into account in the purity correction. The uncertainty arising
from this correction is included in the systematic uncertainties. The average BB purity,
including all background contributions listed in section 4.2, is found to be 84%, with a
variation within about ±10% over the full ∆R range in the visible region for the three
leading jet pTbins.
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BBBB
R R
∆∆
000.5 0.511 1.51.522 2.52.5333.53.544 4.54.5
VV VV
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number of events
00
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250250
300300
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= 7 TeV, SimulationsCMS
number of events
Figure 3. Resolution of the ∆R reconstruction, obtained using simulation for the leading jet
pT> 84GeV sample. Left: ∆R values reconstructed between the two secondary vertices ∆RV V
versus the values between the original B hadrons ∆RBB, in the visible B hadron phase space (see
text). Right: projection onto the diagonal (∆RV V− ∆RBB). The numbers in the boxes represent
the number of events reconstructed in that particular bin.
4.4Systematic uncertainties
Uncertainties relevant to the shape of the differential distributions are crucial for this paper.
The consistency in shape between the data and the simulation is assessed and the systematic
uncertainties are estimated by data driven methods. The systematic uncertainties related to
the absolute normalisation are much larger than the shape dependent ones. They sum up to
a total of 47%, but do not affect the shape analysis (see below). The dominant contribution
originates from the B hadron reconstruction efficiency (±20%, estimated in [4]), which
amounts to a total of 44% for reconstructing two B hadrons.
In the following the shape dependent systematic uncertainties for the ∆R distributions
are discussed. The values are quoted in terms of the relative change of the integrated cross
section ratio ρ∆R= σ∆R<0.8/σ∆R>2.4. Very similar systematic uncertainties arise for the
∆φ distributions and, hence, they are not quoted separately.
• Algorithmic effects. The shape of the ∆R dependence of the efficiency α(∆R) is
checked by means of an event mixing method. This event mixing technique mimics
an event with two genuine SVs by merging two independent events, where each has
at least one reconstructed SV. The positions of the two PVs are required to be within
20µm in three-dimensional space. This mixed event is then analysed and the fraction
of cases where both original SVs are again properly reconstructed is used to determine
the ∆R dependence of the efficiency to find two genuine SVs in an event which had
the SVs already reconstructed. The shape of this efficiency α(∆R) is determined for
the data and for the simulated samples independently in bins of ∆R. The vertex
reconstruction efficiency as a function of ∆R for data and for simulation, and their
ratio are shown in figure 4. Since in this analysis the shape is the most relevant
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R R
∆∆
00 0.50.5111.5 1.5222.52.5333.53.544
relative efficiency
00
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>30 GeV)
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p Simulation (
< 80 GeV)
T
pSimulation (50 GeV <
Data
relative efficiency
R R
∆∆
00 0.50.511 1.51.5222.52.533 3.5 3.544
data/simulation scaled efficiencies
0.9 0.9
0.920.92
0.940.94
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0.98 0.98
11
1.021.02
1.04 1.04
1.06 1.06
1.081.08
1.11.1
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data/simulation scaled efficiencies
Figure 4. Study of the vertex reconstruction efficiency by the event mixing method. Shown as
a function of ∆R are the relative vertex reconstruction efficiency (left) α(∆R) (see text), and the
ratio (right) between the quantities α(∆R) determined from the data and from the simulation.
The simulated α(∆R) distribution (left) is shown for two energy scales, characterized by ˆ pT, the
pythia parameter describing the transverse momentum in the hard subprocess. The ratio (right)
is rescaled to unity to estimate the accuracy of the simulated shape.
property, the values in figure 4 (right) have been rescaled to the mean value. This
ratio exhibits good consistency in shape between simulation and data over the full
∆R range, including the region of small ∆R. The differences are found to be within
2% and are taken as systematic uncertainties.
• B hadron momenta. The mean reconstruction efficiency for an observed ∆R value
strongly depends on the kinematic properties of the B hadron pair. It depends on the
pTof each B hadron and predominantly on the softer of the two. Since all efficiency
corrections are taken from the MC simulation, it is important to verify that the
kinematic behaviour of the BB pairs is also properly modelled by the simulation.
Confidence in the Monte Carlo modelling is provided by comparing the transverse
momentum distributions of the reconstructed B candidates derived from data and
from Monte Carlo simulation. The distributions of the reconstructed pTof the harder
and of the softer of the two hadrons, their asymmetry, as well as the ∆R dependence
of the average reconstructed pT of the softer hadron for the three leading jet pT
regions, are shown in figure 5. The differences between the data and the simulation,
convolved with the pT-dependent efficiency, are found to have an effect on the final
result of between 4% and 8%. These values are used to estimate the systematic
uncertainties reported in table 1 as “B hadron kinematics”.
• Uncertainty on the Jet Energy Scale (JES). The JES influences the ∆R shape of
the two B hadrons. Its effect on the pTof the leading jet is estimated assuming a
linear rise of the pTdependency of the relative cross section ratio (see below). Given
that the higher pTscales exhibit a larger relative contribution to the cross section
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000.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.911
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T

00.511.52 2.533.54
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> 56 GeV
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p

0 0.511.52 2.533.54
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> 84 GeV
T
Jet
p

00.511.522.533.54
10
15
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40
PYTHIA
Data
> 120 GeV
T
Jet
p
Figure 5. Distributions of the reconstructed pTof the two B hadrons: pTof the harder B hadron
(top left); pTof the softer B hadron (top right); asymmetry (bottom left) of the pTof the harder
and the softer B hadron; average pT(bottom right) of the softer B hadron as a function of ∆R for
data (solid dots) and pythia simulation (green bars) for the three leading jet pTregions.
at low ∆R, the actual ∆R shape is distorted by this effect. The uncertainty on the
JES is determined by assuming a ±3% [31] uncertainty on average for the energy
region relevant for this analysis. An additional ±5% is added to take into account
the differences in the jet energy corrections between b and light jets as estimated in
the simulation. This yields a variation in the ∆R shape within 6%, which is taken
as systematic uncertainty.
• Phase space correction. The measurements of vertices are corrected to the visible
phase space of the B hadrons defined by |η(B)| < 2.0 and pT(B) > 15GeV, using the
pythia Monte Carlo simulation. In the analysis only reconstructed B hadrons above
a pT of 8GeV are considered. The uncertainty arising from this choice has been
estimated by varying the pTcut on the reconstructed vertex from 8 to 10GeV, re-
computing the MC correction and repeating the final measurement. The uncertainty
is found to be 2.8%.
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JHEP03(2011)136
Source of uncertainty in shapeChange in ρ∆R= σ∆R<0.8/σ∆R>2.4(%)
Leading jet pTbin (GeV)
> 56
> 84
2.02.0
8.07.0
6.06.0
2.82.8
0.61.3
10.69.9
13.013.0
16.816.4
> 120
2.0
4.0
6.0
2.8
2.1
8.3
13.0
15.4
Algorithmic effects (data mixing)
B hadron kinematics (pTof softer B)
Jet energy scale
Phase space correction
Bin migration from resolution
Subtotal shape uncertainty
MC statistical uncertainty
Total shape uncertainty
Table 1. Systematic uncertainties affecting the shape of the differential cross section as a function
of ∆R, for the three leading jet pTregions. The values are quoted in terms of percentage changes of
the integrated cross section ratio ρ∆R. In the figures, these values are included for each bin. Very
similar systematic uncertainties are assumed for the ∆φ distributions.
• Migration. The bin-to-bin migrations in the sample are small because, as shown
in figure 3, the core of the vertex resolution in ∆R (0.02) is much smaller than
the chosen bin width (0.4).The migrations are taken into account through the
efficiency corrections. The off-diagonal contributions (predominantly at ∆RV V ≈
π from misreconstructed collinear gluon splitting events, with one vertex from the
recoiling jet) are subtracted on a bin-to-bin basis. An uncertainty of up to 2.1% on
this purity correction is obtained by increasing the small angle ∆R < 0.8 contribution
by 50% (compatible with the measured results, as presented below).
• Monte Carlo statistics. An additional bin-to-bin systematic uncertainty results from
the limited number of simulated events. An uncertainty of 13% is used, conservatively
taking the maximum value of either the statistical uncertainty of the simulation or
half of the largest bin-to-bin fluctuation observed in the correction function between
any of the ∆R bins. This uncertainty is mostly relevant for figures 6 and 8; its effect
is reduced in figure 7.
The shape-dependent systematic uncertainties are calculated and included binwise in
the figures, as indicated by the outer error bars which show statistical and systematic uncer-
tainties added in quadrature. They are summarised in table 1. The overall normalisation
uncertainties are not included in the error bars in the figures.
5Results
5.1Differential distributions in ∆R and ∆φ
The differential cross section of BB-pair production is measured as a function of the an-
gular separation variables ∆R and ∆φ between the two reconstructed B hadrons for three
different energy scales. The results are presented for the visible kinematic phase space of
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JHEP03(2011)136
R R R
∆∆∆
0000.50.50.51111.51.51.52222.5 2.52.5333 3.53.53.5444
(pb)
σ
d
σ
d
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∆
d
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×
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>84 GeV)
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>120 GeV)
T
Data (p
PYTHIA
Normalisation region
-1
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| < 3.0
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η
> 15 GeV, |
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T
p
(pb)
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(pb)
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0000.50.50.51111.5 1.51.52222.52.52.5333
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σ
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d d d
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-1
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| < 3.0
Jet
η |
| < 2.0
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η
> 15 GeV, |
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T
p
(pb)
φ ∆
φ ∆
(pb)
Figure 6. Differential BB production cross sections as a function of ∆R (left) and ∆φ (right) for
the three leading jet pTregions. For clarity, the pT> 56 and 84GeV bins are offset by a factor 4
and 2, respectively. For the data points, the error bars show the statistical (inner bars) and the
total (outer bars) uncertainties. A common uncertainty of 47% due to the absolute normalisation
on the data points is not included. The symbols denote the values averaged over the bins and
are plotted at the bin centres. The pythia simulation (shaded bars) is normalised to the region
∆R > 2.4 or ∆φ >3
bands indicate the statistical uncertainties of the predictions.
4π, as indicated by the shaded normalisation regions. The widths of the shaded
the B hadrons and the leading jet pTranges as defined in section 4.1. The cross sections
are determined by applying efficiency corrections and normalising to the total integrated
luminosity, according to
?dσvisible(pp → BB X)
dA
?
i
=Ni(data) · fi
∆Ai· L · ?i
,
(5.1)
where Ni(data) denotes the number of selected signal BB events in bin i, L the integrated
luminosity, ?ithe total efficiency, fithe purity correction factor, and ∆Aithe width of bin
i in variable A, with A being ∆R or ∆φ.
The measured cross sections are shown in figure 6 as a function of ∆R and ∆φ for
the three leading jet pT regions. The error bars on the data points include statistical
and uncorrelated systematic uncertainties. An uncertainty of 47% common to all data
points due to the absolute normalisation is not shown in the figure. The bars shown for
the pythia simulation in figure 6 are normalised to the region ∆R > 2.4 or ∆φ >3
where the theory calculations are expected to be more reliable, since the cross section is
anticipated to be dominated by leading order diagrams (flavour creation).
It is interesting to note that the cross sections at small values of ∆R or ∆φ are found to
be substantial. They exceed the cross sections observed at large angular separation values,
the configuration where the two B hadrons are emitted in opposite directions.
The scale dependence is illustrated in table 2 and figure 7, where the left panel shows
the ratio ρ∆Ras a function of the leading jet pT, a measure of the hard interaction scale.
4π,
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JHEP03(2011)136
Jet pT
Cut
(GeV) (GeV)
> 56
> 84
> 120
Jet pT
Cut
(GeV) (GeV)
> 56
> 84
> 120
ρ∆R= σ∆R<0.8/σ∆R>2.4
Data
pythia
(%) (%) (stat+sys)
7.4 84.9 1.42 ± 0.29 0.89 ± 0.02 1.53 ± 0.07
10.0 ± 4.8 5.7 ± 2.7 9.3 84.6 1.77 ± 0.26 1.51 ± 0.05 2.60 ± 0.09
2.9 ± 1.4 1.0 ± 0.5 10.7 83.2 2.74 ± 0.32 2.13 ± 0.07 3.64 ± 0.11
?pT?
σ∆R<0.8
(nb)
37 ± 18
σ∆R>2.4
(nb)
26 ± 12
????P?
MadGraph
(stat)(stat)
72
106
150
ρ∆φ= σ∆φ<1
Data
4π/σ∆φ>3
pythia
(stat)
4π
?pT?
σ∆φ<1
(nb)
42 ± 20
11.5 ± 5.5 4.9 ± 2.3 9.3 84.6 2.37 ± 0.36 1.95 ± 0.25 3.41 ± 0.12
3.3 ± 1.6 0.9 ± 0.4 10.7 83.2 3.64 ± 0.46 2.73 ± 0.32 4.79 ± 0.15
Table 2. Input values used to calculate the BB production cross sections ratio ρ∆R, as shown
in figure 7, and the corresponding ratio ρ∆φ. Listed are the pTcut of the leading jet, average jet
pT, cross sections in the two ∆R and ∆φ regions (including the 47% uncertainty on the absolute
normalisation), average efficiency, average purity, and cross section ratio for the data, as well as for
the pythia and MadGraph simulations. Statistical and systematic uncertainties are included for
the data, while for the simulations only the statistical uncertainties are given.
4π
σ∆φ>3
(nb)
24 ± 12
4π
???
(%) (%) (stat+sys)
7.4 84.9 1.78 ± 0.36 1.15 ± 0.15 2.07 ± 0.10
?P?
MadGraph
(stat)
72
106
150
The right panel shows the asymmetry of the cross section contributions between small and
large ∆R values, (σ∆R<0.8− σ∆R>2.4) / (σ∆R<0.8+ σ∆R>2.4). The measured data clearly
indicate that the relative contributions of σ∆R<0.8significantly exceed those of σ∆R>2.4.
Similarly, the contributions of σ∆φ<1
addition, the data show that this excess depends on the energy scale, increasing towards
larger leading jet pTvalues.
4πare much larger compared to those of σ∆φ>3
4π. In
5.2Comparisons with theoretical predictions
The measured distributions are compared with various theoretical predictions, based on
perturbative QCD calculations, both at LO and NLO.
Within pQCD, a back-to-back configuration for the production of the BB pair (i.e.
large values of ∆R and/or ∆φ) is expected for the LO processes, while the region of phase
space with small opening angles between the B and B hadrons provides strong sensitiv-
ity to collinear emission processes. The higher-order processes, such as gluon radiation
which splits into bb pairs, are anticipated to have a smaller angular separation between
the b quarks. Naively, the flavour creation contribution is expected to be dominant in
most regions of the phase space, whereas the gluon splitting contributions should be rela-
tively small.
The measurements show that the BB production cross section ratio ρ∆Rincreases as
a function of the leading jet pTin the event (see figure 7). Larger pTvalues lead to more
gluon radiation and, hence, are expected to produce more gluon splitting into BB pairs.
This general trend is described by the theoretical calculations.
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JHEP03(2011)136
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T
leading jet p
70 8090100 110 120 130 140 150
R > 2.4
∆
σ
/
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∆
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4
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η
> 15 GeV, |
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p
(GeV)
T
leading jet p
708090100 110 120 130 140 150
R > 2.4
∆
σ
+
R < 0.8
∆
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R < 0.8
∆
σ
R > 2.4
∆
σ
-
-0.1
0
0.1
0.2
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0.7
PYTHIA
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| < 3.0
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η |
| < 2.0
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η
> 15 GeV, |
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T
p
Figure 7. Left: ratio between the BB production cross sections in ∆R < 0.8 and ∆R > 2.4,
ρ∆R = σ∆R<0.8 / σ∆R>2.4, as a function of the leading jet pT. Right: asymmetry between the
two regions, (σ∆R<0.8− σ∆R>2.4) / (σ∆R<0.8+ σ∆R>2.4). The symbols denote the data averaged
over the bins and are plotted at the mean leading jet pT of the bins. For the data points, the
error bars show the statistical (inner bars) and the total (outer bars) errors. Also shown are the
predictions from the pythia and MadGraph simulations, where the widths of the bands indicate
the uncertainties arising from the limited number of simulated events.
In order to provide a detailed comparison between the data and the theory predictions
in terms of shape, figure 8 presents the ratios, of the data as well as of the MadGraph,
mc@nlo and cascade models, with respect to the pythia predictions, for the three
different scales in leading jet pT. The values for the pythia simulation are normalised in
the region ∆R > 2.4 (or ∆φ >3
It is observed that none of the predictions describes the data very well. The data lie be-
tween the MadGraph and the pythia curves. The mc@nlo calculations do not describe
the shape of the observed ∆R distribution. In particular, at small values of ∆R, where
higher-order processes, notably gluon splitting, are expected to be large, the mc@nlo
predictions are substantially below the data. The ∆φ distribution is more adequately re-
produced by mc@nlo. The cascade predictions are significantly below the data in all
regions, both in the ∆R and ∆φ distributions.
4π).
6Summary
A first measurement of the angular correlations between BB pairs produced in pp colli-
sions at a centre-of-mass energy of 7 TeV is presented. The measurements are based on
data corresponding to an integrated luminosity of 3.1 ± 0.3pb−1recorded by the CMS
experiment during 2010. The detection of the B hadrons is based on the reconstruction
of the secondary vertices from their decays. The results are given in terms of normalised
differential production cross sections as functions of the angular separation variables ∆R
and ∆φ between the two B hadrons. The data exhibit a substantial enhancement of the
– 14 –