Research Article
On the Impact of Tsallis Statistics on Cosmic Ray Showers
M. Abrahão,
1
W. G. Dantas,
1
R. M. de Almeida,
1
D. R. Gratieri,
1
andT.J.P.Penna
2,3
1
EEIMVR, Universidade Federal Fluminense, Volta Redonda, RJ, Brazil
2
ICEx, Universidade Federal Fluminense, Volta Redonda, RJ, Brazil
3
INCT-SC, National Institute of Science and Technology, CNPq, Rio de Janeiro, RJ, Brazil
Correspondence should be addressed to R. M. de Almeida; rmenezes@id.u.br
Received June ; Accepted September
Academic Editor: Sally Seidel
Copyright © M. Abrah˜ao et al. is is an open access article distributed under the Creative Commons Attribution License,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. e
publication of this article was funded by SCOAP
.
We investigate the impact of the Tsallis nonextensive statistics introduced by intrinsic temperature uctuations in -Air ultrahigh
energy interactions on observables of cosmic ray showers, such as the slant depth of the maximum
max
and the muon number on
the ground
𝜇
. e results show that these observables are signicantly aected by temperature uctuations and agree qualitatively
with the predictions of Heitler model.
1. Introduction
e Pierre Auger Observatory [, ] has led to great discov-
eries in the eld of ultrahigh energy cosmic rays (UHECRs)
such as the conrmation of suppression of the cosmic ray ux
at energies above 4×10
19
eV [], rst observed by the HiRes
Collaboration [], limits on photon [–], and neutrino [–
] uxes at ultrahigh energies and a hint of large scale
anisotropies at energies above 8×10
18
eV []. Nevertheless,
many questions related to these particles are still open.
Particularly interesting is the behavior of the slant depth of
the shower maximum with energy. Understood in terms of
the LHC-tuned shower models, the HiRes [] and Telescope
Array Collaborations [] reported a light mass composition
at energies above 10
18
eV, while the Auger results suggest a
gradual shi to a heavier composition, with a large fraction
of protons at 10
18
eV, changing to a heavier composition at
10
19.5
eV []. However, we should interpret these results with
caution, since measurements of shower properties performed
by the Auger Collaboration have revealed inconsistencies
between data and present shower models. For instance, the
Pierre Auger Collaboration has reported the rst hybrid
measurement of the average muon number in inclined air
showers at ultrahigh energies, suggesting a muon decit
in simulations of about 30%to80
+17
−20
(sys)%at10
19
eV,
depending on the hadronic interaction model []. Hence, the
measured behavior of the slant depth of the shower maximum
evolution could be understood as a hint of new hadronic
interaction physics at energy scales beyond the reach of LHC.
In this work, we will deal with hadronic interactions in a
statistical model, as rst introduced by Hagedorn [] ideas in
the sixties. Recently a power-law function based on the Tsallis
statistics [] has been widely used in tting the transverse
momentum (
𝑇
) and pseudorapidity () distributions mea-
sured in high energy collisions [–], while several studies
have been devoted to discuss these results in the literature
[–]. e Tsallis statistics, which is frequently present to
model dierent branches of science, is oen used to describe
systems which display properties like memory eects, long
range interactions, intrinsic uctuations, (multi)fractal phase
space, and so on. It consists in replacing the classical
Boltzmann-Gibbs entropy (
BG
) by the form proposed by
Tsallis:
𝑞
=
1−
∑
𝑖
𝑞
𝑖
−1
𝑞→1
⇒
BG
=−
𝑖
𝑖
ln
𝑖
,
()
where
𝑖
is the probability of a particle occupying the state
and is the Tsallis index. is denition comprises the
Boltzmann-Gibbs entropy as a particular case, where =
1. On the other hand, a straight consequence from this
Hindawi Publishing Corporation
Advances in High Energy Physics
Volume 2016, Article ID 4676024, 7 pages
http://dx.doi.org/10.1155/2016/4676024