Measurement of the energy spectra relative to neutrons produced at very small angle in $\mathrm{\sqrt{s} = 13 ~ TeV}$ proton-proton collisions using the LHCf Arm2 detector

In the last years, several ground-based experiments have measured flux and composition of ultra high energy cosmic rays - i.e. cosmic rays having energies above $10^{18} ~ eV$ - up to the GZK cutoff region. Nevertheless, these analyses suffer of large uncertainties due to the fact that they must rely on hadronic interaction models, that exhibit very different behavior in the forward region due to the lack of high energy calibration data. To provide measurements that can be useful to tune these models is exactly the main aim of the LHC-forward (LHCf) experiment. Thanks to two small sampling calorimeter, Arm1 and Arm2, installed at $\pm 140 ~ m$ from LHC IP1, LHCf can detect neutral particles produced in the very forward region ($\eta > 8.4$) by proton-proton and proton-ion high energy collisions (proton-proton interaction at $\sqrt{s} = 14 ~ TeV$ is equivalent to the collision of a $10^{17} ~ eV$ proton with a proton at rest, hence it is possible to perform measurements at an energy close to the typical one of UHECRs). Detectors are optimized for the reconstruction of $\pi^0$ from its 2$\gamma$ decay, but they offer the possibility to study other secondary hadrons as well, despite with more limited performances. Neutrons, the most abundant hadrons reaching LHCf, have particular interest because it has been noted that a small change in the number of baryons produced very near to the first interaction point of a cosmic ray with the atmosphere can explain the muon excess problem, observed by Pierre Auger Observatory and Telescope Array. In this work we present the results relative to energy spectra of forward neutrons produced in $\sqrt{s} = 13 ~ TeV$ proton-proton collisions measured using the LHCf Arm2 detector. It is ideally divided into two parts: the first one is dedicated to detector calibration, the second one to analysis itself. Calibration of the energy scale for the reconstruction of hadronic showers was performed making use of both beam test data and MC simulations. This involved the estimation of scintillators absolute gains, position dependent correction factors and deposited energy to primary energy conversion coefficients. At the end, we obtained an uncertainty on the energy scale of about 3.5\%, energy and position resolution above $350 ~ GeV$ respectively better than 40\% and $1 ~ mm$, 70\% detection efficiency above $2 ~ TeV$. Analysis of data relative to proton-proton collisions at $\sqrt{s} = 13 ~ TeV$ with the Arm2 detector was divided in three different pseudorapidity regions: $8.81<\eta<8.99$, $8.99<\eta<9.22$, $\eta>10.76$. After some studies on simulations to set event selection criteria, we reconstructed energy spectra, applied necessary correction factors and estimated related systematic uncertainties. Being $\sigma_{E}/{E} \sim 40\%$, folded spectra are enough to test interaction models, but, in order to provide useful information for their tuning, deconvolution is needed. After applying iterative bayesian unfolding, unfolded spectra were finally compared to the most common models employed in cosmic rays physics. No one perfectly reproduces experimental data: in the most forward region a very large discrepancy was found, qualitatively explained only by QGSJet II-04; in the other two regions the agreement is generally better, especially in the case of EPOS-LHC. Finally, a test of Feynman scaling using Arm2 results relative to p-p collisions at $\sqrt{s} = 13 ~ TeV$ and Arm1-Arm2 combined ones in the case of $\sqrt{s} = 7 ~ TeV$ confirmed the validity of our analysis, that in the future will be extended to Arm1 as well.