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JHEP03(2018)043
Published for SISSA by Springer
Received: November 6, 2017
Accepted: February 12, 2018
Published: March 8, 2018
Measurements of the branching fractions of
Λ
+
c
→ pπ
−
π
+
, Λ
+
c
→ pK
−
K
+
, and Λ
+
c
→ pπ
−
K
+
The LHCb collaboration
E-mail: stephen.ogilvy@cern.ch
Abstract: The ratios of the branching fractions of the decays Λ
+
c
→ pπ
−
π
+
, Λ
+
c
→
pK
−
K
+
, and Λ
+
c
→ pπ
−
K
+
with respect to the Cabibbo-favoured Λ
+
c
→ pK
−
π
+
decay
are measured using proton-proton collision data collected with the LHCb experiment at a
7 TeV centre-of-mass energy and corresponding to an integrated luminosity of 1.0 fb
−1
:
B(Λ
+
c
→ pπ
−
π
+
)
B(Λ
+
c
→ pK
−
π
+
)
= (7.44 ± 0.08 ± 0.18)%,
B(Λ
+
c
→ pK
−
K
+
)
B(Λ
+
c
→ pK
−
π
+
)
= (1.70 ± 0.03 ± 0.03)%,
B(Λ
+
c
→ pπ
−
K
+
)
B(Λ
+
c
→ pK
−
π
+
)
= (0.165 ± 0.015 ± 0.005)%,
where the uncertainties are statistical and systematic, respectively. These results are the
most precise measurements of these quantities to date. When multiplied by the world-
average value for B(Λ
+
c
→ pK
−
π
+
), the corresponding branching fractions are
B(Λ
+
c
→ pπ
−
π
+
) = (4.72 ± 0.05 ± 0.11 ± 0.25) ×10
−3
,
B(Λ
+
c
→ pK
−
K
+
) = (1.08 ± 0.02 ± 0.02 ± 0.06) ×10
−3
,
B(Λ
+
c
→ pπ
−
K
+
) = (1.04 ± 0.09 ± 0.03 ± 0.05) ×10
−4
,
where the final uncertainty is due to B(Λ
+
c
→ pK
−
π
+
).
Keywords: Branching fraction, Charm physics, Flavor physics, Hadron-Hadron scatter-
ing (experiments), Spectroscopy
ArXiv ePrint: 1711.01157
Open Access, Copyright CERN,
for the benefit of the LHCb Collaboration.
Article funded by SCOAP
3
.
https://doi.org/10.1007/JHEP03(2018)043
JHEP03(2018)043
Contents
1 Introduction 1
2 Detector and simulation 3
3 Candidate selection 4
3.1 Λ
0
b
→ Λ
+
c
(phh
0
)µ
−
ν
µ
selection 4
3.2 Prompt Λ
+
c
→ phh
0
selection 5
3.3 Selection efficiencies 5
4 Signal yield determination 7
4.1 Λ
0
b
→ Λ
+
c
(phh
0
)µ
−
ν
µ
yield determination 7
4.2 Prompt Λ
+
c
→ phh
0
yield determination 8
5 Systematic uncertainties 10
6 Results 13
The LHCb collaboration 18
1 Introduction
Nonleptonic decays of charmed baryons are a useful environment in which to study the
interplay of the weak and strong interactions. Measurements of their branching fractions
are of great importance in understanding the internal dynamics of the decays. The last few
years have seen advances in the study of Λ
+
c
→ phh
0
decays, where hh
0
∈ {K
−
π
+
, K
−
K
+
,
π
−
π
+
, π
−
K
+
}. Until recently, measurements of the absolute branching fraction of the
Λ
+
c
→ pK
−
π
+
decay suffered from model dependence, relying on assumptions concern-
ing several B, Λ
+
c
and D
+
branching fraction ratios and decay widths. The first model-
independent measurements of the absolute branching fraction of the Λ
+
c
→ pK
−
π
+
de-
cay have been made by the Belle [1] and BESIII [2] collaborations. The precision of a
number of Λ
+
c
decay branching fractions has also been improved at the B factories [2–5],
while the first measurement of a doubly Cabibbo-suppressed (DCS) charmed-baryon decay,
Λ
+
c
→ pπ
−
K
+
, has been performed by the Belle collaboration [6].
Unlike in the charmed-meson sector, there exist a large number of favoured internal
W -boson exchange decays which can be readily studied. Quark-level diagrams demon-
strating external W -emission, internal W -emission, and W -exchange are shown in fig-
ure 1. As can be seen, while W-boson exchange is not permitted in the decay Λ
+
c
→
pπ
−
K
+
, it is allowed in the decay Λ
+
c
→ pK
−
π
+
. The ratio of the branching fractions
B(Λ
+
c
→ pπ
−
K
+
)/B(Λ
+
c
→ pK
−
π
+
) is a useful variable with which to indirectly study the
– 1 –
JHEP03(2018)043
c s
d
u
u
u
u
u
d
d
W
+
p
π
+
K
−
Λ
+
c
(a)
c
d
s
u
u
u
u
u
d
d
W
+
p
K
+
π
−
Λ
+
c
(b)
c u
u
s
d
u
u
u
d
d
W
+
p
K
−
π
+
Λ
+
c
(c)
c u
u
d
s
u
u
u
d
d
W
+
p
π
−
K
+
Λ
+
c
(d)
c u
u
s
d
d
d
u
u
u
W
+
p
K
−
π
+
Λ
+
c
(e)
Figure 1. Weak decays of Λ
+
c
to a proton and two mesons, without hyperon mediation. Shown
are external W -emission for (a) Λ
+
c
→ pK
−
π
+
and (b) Λ
+
c
→ pπ
−
K
+
, internal W -emission for
(c) Λ
+
c
→ pK
−
π
+
and (d) Λ
+
c
→ pπ
−
K
+
, and W -exchange for (e) Λ
+
c
→ pK
−
π
+
.
role of W -boson exchange in hadronic decays. In the absence of flavour-SU(3) symme-
try breaking, the ratio can naively be expected to be equal to tan
4
θ
c
[7], where θ
c
is the
Cabibbo mixing angle [8]. Taking the most recent measurements of |V
ud
| and |V
us
| [9] yields
a value tan
4
θ
c
≈ 0.285%. The Belle measurement for B(Λ
+
c
→ pπ
−
K
+
)/B(Λ
+
c
→ pK
−
π
+
)
corresponds to (0.82 ± 0.12) tan
4
θ
c
.
In this paper we report measurements of the ratios of the branching fractions
B(Λ
+
c
→ pK
−
K
+
)
B(Λ
+
c
→ pK
−
π
+
)
,
B(Λ
+
c
→ pπ
−
π
+
)
B(Λ
+
c
→ pK
−
π
+
)
and
B(Λ
+
c
→ pπ
−
K
+
)
B(Λ
+
c
→ pK
−
π
+
)
.
– 2 –
JHEP03(2018)043
These measurements are carried out using a data sample, corresponding to an integrated
luminosity of 1.0 fb
−1
of pp collision data, collected with the LHCb detector at a centre-
of-mass energy of
√
s = 7 TeV. The Λ
+
c
candidates are reconstructed in semileptonic (SL)
decays of Λ
0
b
→ Λ
+
c
µ
−
X, where X is any particle in this decay that is not reconstructed.
These decays have a low level of background due to the use of high-purity muon triggers
and the displacement of the Λ
+
c
production point from the primary pp collision. As a
powerful cross-check, the same measurements, although with a lower precision, are carried
out using a sample of Λ
+
c
produced in the primary pp interaction vertex (PV), referred to
as the prompt sample.
2 Detector and simulation
The LHCb detector [10] is a single-arm forward spectrometer covering the pseudorapidity
range 2 < η < 5, designed for the study of particles containing b or c quarks. The detector
includes a high-precision tracking system consisting of a silicon-strip vertex detector sur-
rounding the pp interaction region, a large-area silicon-strip detector located upstream of
a dipole magnet with a bending power of about 4 Tm, and three stations of silicon-strip
detectors and straw drift tubes placed downstream of the magnet. The tracking system
provides a measurement of momentum, p, of charged particles with a relative uncertainty
that varies from 0.5% at low momentum to 1.0% at 200 GeV/c. The minimum distance of
a track to a primary vertex, the impact parameter (IP), is measured with a resolution of
(15 + 29/p
T
) µm, where p
T
is the component of the momentum transverse to the beam,
in GeV/c. Different types of charged hadrons are distinguished using information from
two ring-imaging Cherenkov (RICH) detectors [11], allowing for an effective discrimination
between the different Λ
+
c
→ phh
0
final states. Photons, electrons and hadrons are iden-
tified by a calorimeter system consisting of scintillating-pad and preshower detectors, an
electromagnetic calorimeter and a hadronic calorimeter. Muons are identified by a system
composed of alternating layers of iron and multiwire proportional chambers.
The online event selection is performed by a trigger, which consists of a hardware
stage, based on information from the calorimeter and muon systems, followed by a software
stage which is divided into two parts. The first employs a partial reconstruction of the
candidates from the hardware trigger and a cut-based selection, while the second utilises a
full event reconstruction and further, often more complex, selection criteria on candidates.
Selection requirements can be made on whether a trigger decision was satisfied by any
given object in the event (including non-signal objects). In the offline selection, trigger
decisions are associated with reconstructed particles. Therefore requirements can be made
on whether the signal candidate was responsible for satisfying the trigger decision, or if
another nonsignal object in the event satisfied the trigger decision, or a combination of
the two. The detailed trigger requirements for the semileptonic and prompt samples are
described in section 3.
In the simulation, pp collisions are generated using Pythia [12, 13] with a specific
LHCb configuration [14]. The heavy flavour decays are described by EvtGen [15] with the
decay kinematics of the Λ
+
c
→ phh
0
generated according to a phase-space distribution. The
– 3 –
JHEP03(2018)043
interaction of the generated particles with the detector, and its response, are implemented
using the Geant4 toolkit [16] as described in ref. [14].
3 Candidate selection
The different production mechanisms in the SL and prompt processes necessitate two dis-
tinct selections, which are verified to result in statistically independent samples of Λ
+
c
candidates. The selections are developed using a fraction of the Λ
+
c
→ pK
−
π
+
data cor-
responding to 10% of the integrated luminosity, chosen randomly. This sample is then
discarded from measurements of the ratios of branching fractions, with an appropriate
scaling factor applied to the final results.
3.1 Λ
0
b
→ Λ
+
c
(phh
0
)µ
−
ν
µ
selection
The trigger selection at the hardware stage and the first software stage is focussed upon
the muon in the Λ
0
b
decay, such that the dependence of the selection upon the Λ
+
c
decay
product kinematics is reduced. This results in the ratios of trigger acceptance efficiencies
between the Λ
+
c
→ phh
0
modes being uniform at these stages of the trigger. The muon can-
didate is required to have a p
T
> 1.7 GeV/c and to be responsible for the decision of both
the hardware trigger and the first stage of the software trigger. The latter uses additional
detector information to confirm that the muon has a high p
T
and is significantly displaced
from the primary vertex. In the second stage of the software trigger, a general algorithm
designed for identifying semileptonic b-hadron decays selects Λ
0
b
→ Λ
+
c
(phh
0
)µ
−
ν
µ
candi-
dates, requiring a high p
T
muon that is significantly displaced from the PV. This muon
must then form a displaced secondary vertex with between one and three other tracks.
This vertex must have at least one track with p
T
> 1.7 GeV/c and χ
2
IP
with respect to
any PV greater than 16, where χ
2
IP
is defined as the difference in the fit χ
2
of a given PV
reconstructed with and without the considered particle.
The candidates selected by the trigger are then filtered to improve the signal purity.
Charged hadrons are selected with a momentum p > 2.0 GeV/c, and p
T
> 0.3 GeV/c. All
tracks must have χ
2
IP
> 9 such that they are significantly displaced from any PV in the
event, and have a good fit quality. Three such tracks must then form a high-quality vertex
with a flight-distance-significance greater than 100 (defined as the measured flight distance
from any PV divided by its uncertainty). The p
T
of the three-particle combination must
also be greater than 1.8 GeV/c.
Particle identification (PID) is applied to each charged hadron in order to select ex-
clusive samples of each final state, and to reject backgrounds from other multibody charm
decays. Tight PID selection criteria are enforced on the proton and kaon candidates in
order to suppress possible backgrounds from misidentified c-hadron decays, with a weaker
requirement placed upon the pion candidates.
Muon candidates must have a high-quality track fit, and have χ
2
IP
> 9, p > 3 GeV/c and
p
T
> 0.8 GeV/c. A moderate PID requirement is also enforced to reduce the background
from π − µ misidentification. Finally, the muon and Λ
+
c
candidates are required to form
a common vertex with a fit χ
2
lower than 6. The invariant mass of the three tracks in
– 4 –
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