Electroweak and QCD studies in the forward region with LHCb
Simone Bifani ∗
University College Dublin
School of Physics, Science Centre North
Belfield, Dublin 4 (Ireland)
Measurements of the Z 0 and W production cross-sections constitute important tests of the
Standard Model at the LHC energies. NLO predictions have relative errors of between a few
percents and ∼ 10%, depending on rapidity, where the dominant uncertainty is due to the
knowledge of the PDFs. The forward acceptance of the LHCb experiment can provide unique
measurements to constrain the PDFs in previously unexplored regions of the (x, Q 2 ) space.
Determinations of cross-sections and ratios of Z 0 and W bosons using L = (16.5 ± 1.7) pb −1
of LHCb data at √ s = 7 TeV collected during 2010 are reported.
The LHCb 1 experiment at the CERN Large Hadron Collider (LHC) has been designed to
study heavy flavour physics in the forward region (1.9 < η < 4.9). Part of this range (|η| < 2.5)
is common to the ATLAS and CMS general purpose detectors. The rest is unique to LHCb.
Since production in this kinematic range involves the interaction of one valence quark carrying
a large fraction of the proton momentum (high-x) and a sea quark with small fraction of the
momentum (low-x), proton Parton Density Functions (PDFs) can be probed in two distinct
regions of the (x, Q 2 ) space, one of which is previously unexplored.
While electroweak theory can currently describe the fundamental partonic processes of electroweak
boson production at the LHC at NLO with an accuracy at the percent level, a large
uncertainty on the theoretical predictions arise from the present knowledge of the proton PDFs.
The accuracy strongly depends on the rapidity range (Fig. 1): in kinematic regions where PDF
uncertainties are low, precise measurements of electroweak bosons provide a stringent test of
the Standard Model in a new energy regime; in regions where PDFs are less known, production
studies can input valuable information to constrain new PDF fits.
The following electroweak measurements at LHCb include the analysis of the Z 0 and W
boson production at √ s = 7 TeV using L = (16.5±1.7) pb −1 of data collected during 2010 2 . By
looking at inclusive jet distributions and dijet characteristics in the forward region, additional
information on proton PDFs will be collected: details are not discussed here but can be found
elsewhere 3 .
∗ On behalf of the LHCb Collaboration
Figure 1: Percentage uncertainties due to MSTW08 4 PDF set on the production cross-sections (left) and ratios
(right) of Z 0 and W bosons: errors are larger at the high rapidity, but ratios are less sensitive to PDFs.
2 Z 0 → µ + µ − selection
Z 0 events are selected by requiring two well reconstructed muons with a transverse momentum,
pT , greater than 20 GeV/c and lying in the pseudo-rapidity range between 2.0 and 4.5. The
di-muon invariant mass distribution of such candidates is shown in Fig. 2 (Left). To further
identify Z 0 → µ + µ − events, the invariant mass is required to be consistent with Z 0 production
by imposing the mass constraint 81 GeV/c 2 < mµµ < 101 GeV/c 2 . 833 candidate events satisfy
Several background sources are considered and studied using both data and simulation:
Z 0 → τ + τ − where both taus decay leptonically inside the LHCb geometrical acceptance to a
muon; heavy flavour events with two semi-leptonic decays; generic QCD events where pions or
kaons either decay in flight or punch-through the detector to be falsely identified as muons. The
total background contamination in the signal region is estimated to be 1.2 ± 1.2 events.
3 W → µνµ selection
The signature for W bosons is characterised by a single isolated high transverse momentum
lepton and minimal other activity in the event. As the background contamination is expected
to be larger than in Z 0 events, additional criteria to the pT > 20 GeV/c and 2.0 < η < 4.5
requirements are imposed on consistency with the primary vertex, muon isolation and event
activity. Semi-leptonic B and D meson decays are suppressed by requiring the impact parameter
significance of the muon with respect to the primary vertex to be less than 2. Isolation is imposed
by demanding that the summed transverse energy in a cone of radius R = ∆η 2 + ∆φ 2 = 0.5
around the muon is less than 2 GeV/c. As the neutrino cannot be reconstructed inside LHCb,
extra requirements are placed on the rest of the event to select candidates consistent with W
production: the invariant mass of tracks in the event other than the muon must be less than
20 GeV/c 2 ; the vector summed pT of all tracks apart from the muon must be less than 10 GeV/c.
7624 W + → µ + νµ and 5732 W − → µ − ¯νµ candidates pass these requirements.
A detailed background study is performed: Z 0 → µ + µ − where one of the muons goes outside
the LHCb geometrical acceptance; W → τντ and Z 0 → τ + τ − where one tau decays leptonically
inside the detector to a muon; b and c events containing semi-leptonic decays with a muon in
the final state; generic QCD events where pions or kaons are mis-identified as muons (decay in
flight or punch-through).
The signal yield is estimated by fitting the lepton pT spectrum to the shapes expected for
signal (simulation) and each background class (simulation and data-driven by anti-cuts) in 5 bins
Number of events per 1 GeV/c 2
L = 16.5 pb-1, √s = 7 TeV
Dimuon invariant mass [GeV/c 2 ]
Number of events per 2 GeV/c
L = 16.5 pb-1, √s = 7 TeV
QCD bkgs (data)
Tau bkgs (MC)
Z µµ (MC)
20 30 40 50 20 30 40 50 50
Muon transverse momentum [GeV/c]
Figure 2: (Left) Di-muon invariant mass of Z 0 candidates: data points are fitted to a Crystal Ball function (signal)
on an exponential (background). (Right) pT distribution for negative (left) and positive (right) charged muons.
of the lepton pseudo-rapidity. The W selected candidates and the result of the fit are shown in
Fig. 2 (Right). The fit estimates that (34 ± 1)% of the sample is composed by W + → µ + νµ,
(26 ± 1)% by W − → µ − ¯νµ and (31 ± 1)% is due to the QCD background.
The Z 0 and W production cross-sections are measured with the kinematic requirements
that the muons have a pT > 20 GeV/c and a pseudo-rapidity lying in the range 2.0 < η < 4.5
(81 GeV/c 2 < mµµ < 101 GeV/c 2 for Z 0 determinations) according to †
NCandidates − NBackground
εT rigger · εT racking · εµ−ID · εSelection · L
where all involved efficiencies (trigger, tracking, muon identification and selection) are measured
directly from data and cross-checked with simulation: no evidence for charge bias or η, φ, pT
dependences are observed 2 .
Background estimates, efficiency measurements and luminosity determination are considered
as sources of systematic error.
Inclusive production cross-sections for Z 0 , W + and W − bosons are determined to be:
σ Z 0 →µ + µ − = (73±4±7) pb σ W + →µ + νµ = (1007±48±101) pb σ W − →µ − ¯νµ = (680±40±68) pb
where the first error is statistical and systematic combined and the second comes from the
The differential Z 0 cross-section in 5 bins of the boson rapidity and the W charge asymmetry
in 5 bins of lepton pseudo-rapidity are shown in Fig. 3. In the forward region, unlike for
ATLAS and CMS, the asymmetry distribution changes sign, showing the differing helicities of
the couplings of the leptons.
Results are compared to NLO predictions made using the FEWZ 5 (Z 0 ) and MCFM 6 (W )
generators with the MSTW08 4 PDF set (Fig. 4).
Cross-sections and ratios of Z 0 and W bosons are measured using L = (16.5 ± 1.7) pb −1 of
LHCb data at √ s = 7 TeV collected during 2010. While the luminosity uncertainty (10%) dominates
the precision of all cross-section determinations, ratios are independent of that, providing
a more accurate test of the Standard Model. All results are consistent with NLO predictions.
† Results are not extrapolated to 4π to minimise the dependence on theory when correcting to unmeasured
L=16.5 pb-1,!s = 7 TeV
FEWZ NLO+MSTW2008 PDFs
/d ! -d "
/d ! +d "
MCFM NLO s=7
0 1 2 3 4
Figure 3: (Left) Differential cross-section for Z 0 production in bins of boson rapidity. (Right) W charge asymmetry
in bins of lepton pseudo-rapidity. The points are the measured data (statistical and systematic errors combined)
compared to the NLO prediction with the MSTW08 4 PDF set; the yellow band is the theoretical uncertainty.
Figure 4: Z 0 , W + and W − cross-section measurements and ratios compared to the NLO prediction with the
MSTW08 4 PDF set: the inner uncertainty bar combines the statistical and systematic errors; the outer bar
includes the luminosity determination error (cross-sections only); the yellow band is the theoretical uncertainty.
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