ATLAS Collaboration / Nuclear Physics B 907 (2016) 717–763 725
where x =|(m − m
0
)/σ |. This functional form, introduced to take into account the non-
Gaussian tails of resonant signals, describes both the data and MC signals well. The signal
position, m
0
, and width, σ , as well as the number of D
∗+
mesons are free parameters of the fit.
The threshold function has the form A ·(m −m
π
+
)
B
·exp[C ·(m −m
π
+
) +D ·(m −m
π
+
)
2
],
where m
π
+
is the pion mass and A, B, C and D are free parameters. The fitted D
∗±
yields are
N(D
∗±
) = 2140 ±120 (stat) and N(D
∗±
) = 732 ±34 (stat) for the low-p
T
and high-p
T
ranges,
respectively. Small admixtures (< 1%) to the reconstructed signals from the D
∗+
→ D
0
π
+
decays with D
0
decays to final states other than K
−
π
+
are taken into account in the accep-
tance correction procedure (Section 7). The combined value of the fitted mass differences is
145.47 ± 0.03 (stat) MeV, in agreement with the world average. The widths of the signals are
∼0.6MeV, in agreement with the MC expectations.
6.2. Reconstruction of D
+
mesons
The D
+
mesons are reconstructed from the decay D
+
→ K
−
π
+
π
+
. In each event, two
tracks from same-charge particles each with p
T
> 0.8 GeV are combined with a track from
the opposite-charge particle with p
T
> 1GeVto form a D
+
candidate. At least one of the two
particles with the same charge is required to have p
T
> 1GeV. Only three-track combinations
successfully fitted to a common vertex are kept. The pion mass is assigned to each of the two
tracks from same-charge particles and the kaon mass is assigned to the third track, after which
the candidate invariant mass, m(Kππ), is calculated using the track momenta refitted to the
common ve
rtex. To suppress combinatorial background the following requirements are used:
• χ
2
< 12, where χ
2
is the D
+
candidate vertex fit quality.
•|d
0
(D
+
)| < 0.15 mm.
•|z
0
(D
+
) sin θ(D
+
)| < 0.3mm.
• L
xy
(D
+
) > 1.2mm. The large value of the requirement on L
xy
(D
+
) is motivated by the
relatively large lifetime of the D
+
meson [47] and the large combinatorial background.
• cos θ
∗
(K) > −0.8, where θ
∗
(K) is the angle between the kaon in the Kππ rest frame and
the Kππ line of flight in the laboratory frame.
• cos θ
∗
(π) > −0.85, where θ
∗
(π) is the angle between the pion in the Kππ rest frame and
the Kππ line of flight in the laboratory frame.
To suppress background from D
∗+
decays, combinations with m(Kππ) − m(Kπ) <
153 MeV are removed. The background from D
+
s
→ φπ
+
, with φ → K
+
K
−
, is suppressed
by rejecting any three-track D
+
candidate comprised of a pair of tracks of oppositely charged
particles which, when assuming the kaon mass for both tracks, has a two-track invariant mass
within ±8 MeV of the world average φ mass [47]. MC studies indicate that the suppression
of the D
∗+
→ D
0
π
+
decays has a negligible effect on the D
+
signal, and the suppression of
the D
+
s
→ φπ
+
decays rejects less than 2% of the signal. The remaining small background
from D
+
s
→ K
+
K
−
π
+
decays is subtracted using the simulated reflection shape normalised to
the measured D
+
s
rate (Section 6.3). Smaller contributions, affecting mass ranges outside the
expected D
+
signal, from the decays D
+
s
→ π
+
π
−
π
+
, D
+
→ K
+
K
−
π
+
, D
+
→ π
+
π
−
π
+
and D
+
→ π
+
π
−
π
+
π
0
are subtracted using the simulated reflection shapes normalised to the
measured D
+
and D
+
s
rates.
Fig. 2 sho
ws the m(Kππ) distributions for low-p
T
and high-p
T
D
+
candidates after all
requirements. Sizeable signals are seen around the world average value of the D
+
mass,