3.1 Two-pion correlation function analysis
The one-dimensional femtoscopic analysis presented in this paper was performed using the
invariant momentum difference q, which corresponds to the magnitude of the relative three-
momentum in the pair rest frame (PRF). The measured CFs are defined as the ratio of the
q distributions for same-event (A) and mixed-event (B) pion pairs times a normalization
factor (ξ) [3],
C(q; N
rec
ch
, S
T
) = ξ(N
rec
ch
, S
T
) ·
A(q; N
rec
ch
, S
T
)
B(q; N
rec
ch
, S
T
)
. (3.3)
For the event mixing, pools of eight events of similar multiplicity and sphericity are formed.
In addition, it is also required that events in a mixed event pool have their vertex positions
within 2 cm from each other in the beam direction. The mixed event distributions were
then made by pairing up pions from different events in a mixed event pool. Identical
selection criteria are applied to the same-event and mixed-event pion pairs, and both A(q)
and B(q) are constructed in the same S
T
interval.
Both distributions are normalized in the range 0.7 < q < 0.8 GeV/c, which is well
outside the relevant quantum statistical (QS) domain (q ∝ 1/R ≈ 0.3 GeV/c) and below
the onset of the high-q rise associated with energy and momentum conservation.
Figure 1 shows good agreement between the measured correlation functions for
opposite-sign pion pairs in pp collisions at
√
s = 7 TeV and PYTHIA simulations, which in-
clude the ALICE detector response, for spherical and jet-like events at similar multiplicity.
Opposite-sign CFs do not include Bose-Einstein correlations but do include backgrounds,
such as those induced by mini-jets, which are also found in same-sign pair analyses [7].
They also show features due to two-body decays like K
0
S
and ρ → π
+
π
−
at about 412 and
723 MeV/c in q respectively, and a wide three-body decay peak from ω → π
+
π
−
π
0
.
The C(q) in spherical events are relatively flat at unity, while the low S
T
CFs exhibit
a very pronounced slope. This finding supports previous assumptions about the mini-
jet origin of background correlations in interferometry analyses [7] and demonstrates that
PYTHIA describes two-pion correlations well in the absence of Bose-Einstein correlations.
Figure 2 shows a comparison of CFs for same-sign pion pairs from data and PYTHIA
simulations for the two sphericity intervals at similar reconstructed multiplicity. The MC
includes neither quantum-statistical correlations nor final-state interactions (FSI).
Similar to the opposite-sign CF at S
T
> 0.7 shown in figure 1, the spherical-event same-
sign CF is rather flat outside the QS correlation region (q < 0.5 GeV/c). This indicates that
the background is small in spherical events for same-sign pairs. The shape of the same-sign
C(q) in spherical events is compatible with the expectation from Bose-Einstein correlations.
There are no novel features like peaks or depressions and the correlation function does not
extend outside the theoretically predicted values 1 ≤ C(q) ≤ 2. On the other hand, for
jet-like events, the CF exhibits a pronounced slope over the full q range, indicating the
presence of background. The CF shape is well described by PYTHIA outside the QS
correlation region. Moreover, it is observed that the large-q correlation increases with
k
T
and decreases with multiplicity, which is consistent with previous findings in [7]. These
results suggest that the primary source of background correlations in two-pion femtoscopic
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