Experimental results on the atmospheric muon charge ratio

The atmospheric muon charge ratio, defined as the number of positive over negative charged muons, is a highly informative observable both for cosmic rays and particle physics. It allows studying the features of high-energy hadronic interactions in the forward region and the composition of primary cosmic rays. In this review results from underground experiments measuring the charge ratio around 1 TeV are discussed. The measurements in the TeV energy region constrain the associated kaon production, which is particularly important e.g. for the calculation of the atmospheric neutrino flux.

The atmospheric muon charge ratio • The atmospheric muon charge ratio R µ ≡ N µ+ /N µ-is being studied and measured since many decades -Depends on the chemical composition and energy spectrum of the primary cosmic rays -Depends on the hadronic interaction features -At high energy, depends on the prompt component • It provides the possibility to check HE hadronic interaction models (E>1TeV) in the fragmentation region, in a phase space complementary to the collider's one • Since atmospheric muons are kinematically related to atmospheric neutrinos (same sources), R µ provides a benchmark for atmospheric ν flux computations (e.g. background for neutrino telescopes)

Naïf prediction
Feynman scaling Assuming Feynman scaling, the muon charge ratio prediction: Interpretation of the prominent features: • The result is valid only in the fragmentation region, enhanced in the SWM • But the steeply falling primary spectrum (γ ~ 1.7) in the SWM suppresses the contribution of the central region  scaling holds Each pion is likely to have an energy close to the one of the projectile (primary CR proton) and comes from its fragmentation (valence quarks)  positive charge (R µ > 1) • R µ does not depend on E µ (or E π ) nor on the target nature • R µ depends on the primary composition through δ 0

Feynman scaling validity
Elaborating the minimal model: • Introducing the neutron component in the primary flux (in heavy nuclei) and considering the isospin symmetries: primary proton excess Parameterization of the charge ratio • Considering the general form for the muon flux where we have made explicit the ε i (θ) dependence on θ • The correct variable to describe the evolution of R µ is therefore E µ cosθ * (assuming a constant primary composition) • The R µ evolution as a function of E µ cosθ * spans over the different sources  thickness. Thus, depending on the point of impact on CMS, the total material traversed by close-to-vertical muons changes from approximately 6 to 175 meters of water equivalent. The CMS experiment uses a right-handed coordinate system, with the origin at the nominal proton-proton collision point, the x axis pointing towards the center of the LHC ring, the y axis pointing upwards (perpendicular to the LHC plane), and the z axis pointing along the anticlockwise beam-direction, at geographic azimuth 280.8 • (approximately west). The angle between the CMS y axis and the zenith direction is 0.8 • . This small difference is neglected in the analysis, and the angle of the muons relative to the y axis is used to represent the zenith angle θ z .
At the center of the detector, the magnetic field is parallel subdetectors was instrumented and operating at the time. The details of the MTCC setup are described in [12,14]. About 25 million cosmic-muon events were recorded during the first phase of the MTCC with the magnet at a number of field values ranging from 3.67 to 4.00 T.
The CRAFT08 campaign was a sustained data-taking exercise in October and November 2008 with the CMS detector fully assembled in its final underground position. The full detector, ready for collecting data from LHC, participated in the run, with the magnet at the nominal field of 3.8 T. Approximately 270 million cosmicmuon events were recorded. Single

MINOS results
Measurements by two functionally identical detectors, one at shallow depth, one deep underground  Toroidal magnetic field: different acceptance for µ + and µ - Combination of data sets with opposite magnetic field orientations to minimize systematic errors 4 further than 3 cm outside the detector volume the track is rejected. The curvature of the track is known to be poorly determined, and the track is rejected, if any scintillator strips hit are further than 3 cm from the reconstructed position of the track, or if the track does not pass through a region of the detector where there is scintillator on each layer of steel.
Track reconstruction errors may occur when the event contains a large amount of activity which is not related to the track. These extra hits degrade the charge sign determination and can be generated by muon bremsstrahlung, natural radioactivity, or by electrical and optical cross-talk between the channels on the multi-anode PMT [16]. Events are rejected if more than 40% of the strips hit are not track-related. Muon tracks determined to be poorly reconstructed by internal consistency checks of the reconstruction algorithm are also removed from the data sample.

B. Charge Sign Quality Selection
Two selection variables are used to further increase the degree of confidence in the assigned curvature and charge sign of the track. The Kalman filter [21] used in the track curvature fitting provides an uncertainty σ(q/p) on the measured value of q/p, where q is the charge and p the momentum of the track. The first charge sign quality selection is based on the value of (q/p)/σ(q/p) determined by the track fitter. The second selection variable BdL is defined to be equivalent to N charge sign determination. Events which have passed all the selections described in this section are used in the calculation of the atmospheric muon charge ratio described in the next section.  where the primary trigger was satisfied, but there was not enough activity to resolve the eightfold ambiguity from the optical summing of the scintillator strips.  FIG. 8: The atmospheric muon charge ratio as a function of E µ cosθ*. The y-axis uncertainties are the statistical and systematic uncertainties added in quadrature. The MINOS Near Detector data, re-binned in five equal cosθ* intervals, are plotted for are considerably narrower than the corresponding E surf ace distributions. The b(E) radiative term yields the largest contribution to the width of the measured E surf ace µ cos θ distribution for the MINOS Far Detector. In the Near Detector distribution, the largest contribution is the larger ratio of maximum detectable momentum to energy loss in the overburden.  We have used Equation 14 and the measured muon charge ratio to study r π and r K . We have done chi-squared fits in E  Charge ratio of multiple muon events • The smaller value of the charge ratio of multiple muons is due to the convolution of two effects: larger n/p ratio in the all-nucleon spectrum ⊗ different x F region Feynman x: x F ≅ E secondary /E primary n/p ratio in primary cosmic rays  he charge ratio in bins of E µ cos q ⇤ . Here reported are the energy bin range, the most probable value of the energy distribution in the bin aluated using the full Monte Carlo simulation described in [9]), the average zenith angle, the charge ratio and the statistical and systematic ties. ERA as a function of re fitted to R µ (p µ ) = jected at the Earth ding technique for pt, only pion and are considered. We d in [7] to infer the o a positive muon, t consider any enhe primary compoge ratio depend on Fig. 2. The prompt muon component does not significantly contribute to R µ up to E µ cos q ⇤ < ⇠ 10 TeV. Recently, an enlightening analytic description of the muon charge ratio considering an explicit dependence on the relative proton excess in the primary cosmic rays, d 0 = (p n)/(p + n), was presented in [2]: Here p and n fluxes are defined as where the index i runs over the primary ions (H, He, CNO, Mg-Si, Fe) and E N is the primary nucleon energy. The contributions from decays of pions and kaons are included in the kinematic factors A i , B i , e i (i = p, K) described in [2,11]. An analogous contribution from charm decay is foreseen at high energies but still not observed. The spectrum weighted moments Z i j [2] are contained in b and a K : Taking into account an explicit dependence on δ 0 = (p -n)/(p + n): (Gaisser, Astropart. Phys. 35 (2012)

Conclusions
• The measurement of the atmospheric muon charge ratio R µ provides relevant information for both particle-and astrophysics • R µ was measured in a wide energy range, from O(1 GeV) up to O(10 TeV) • The results of CMS, MINOS and OPERA show a rise of R µ vs E µ cos θ *  increasing kaon contribution • The OPERA measurement in the highest energy region:  Found a strong reduction of the charge ratio for multiple muon events  R µ for single muons compatible with the expectation from a simple π-K model  No significant contribution of the prompt component up to E µ cos θ * ∼ 10 TeV  Extracted relevant parameters on the primary composition (δ 0 ) and the associated kaon production in the forward fragmentation region (Z pK+ moment) Dependencies of R µ • R µ exhibits a zenith dependence if: a) Muon contributions from different sources with different R µ b) At least one source has a zenith dependence (e.g. π and K due their relatively long lifetimes) • In the past several authors applied corrections to convert inclined to vertical R µ measurements • This procedure has a limit: it assumes no other sources apart from π and K and it assumes Z pπ and Z pK are known • The projection on the vertical via E µ cosθ is safer  capability to explore new (isotropic) components and to derive Z pπ and Z pK from data