1. Update on the analysis of muon angular distributions in equatorial coordinates
F.Riggi
Dept. of Physics and INFN, Catania

2. Already discussed in past meetings: ● Motivations to search for cosmic ray anisotropies in the low energy regime (sub - TeV primary energies) with EEE telescopes ● Survey of results from other large experiments (IceCube, Milagro, Tibet- Array,…) ● How to transform from local (θ, ϕ) coordinates to equatorial (Right Ascension, Declination) coordinates ● CORSIKA simulations to estimate the muon angle w.r.t primary axis ● GEANT simulations to estimate multiple scattering effects of muons in the building ● Corrections for telescope geometrical acceptance and time exposure ● Preliminary analysis of small data sets

3. Update on recent activities: ● To take into account in a better and «natural» way the time exposure and the geometrical acceptance of a cosmic ray detector, the scrambling method is usually employed by several Collaborations (IceCube, Auger,…) ● For each event a «data» map in (Right Ascension, Declination) is built with the following variables (θ, ϕ, t_event) ● A «reference» map in (Right Ascension, Declination) is also built with the variables (θ, ϕ, t_random), where t_random is chosen among the measured events along one day. To reduce statistical errors on the reference map, usually a certain number of «fake» events are generated for each real event. ● A corrected map is then built by the ratio (Data Map) / (Reference Map) ● This takes into account both the real geometrical acceptance of the telescope and possible non uniform time exposure along each day.
The scrambling method

4. Such method has been now implemented for the EEE telescopes and a new analysis carried out on a data sample of about 20 million events. At the same time, some loose cuts on the track quality have been introduced in the analysis to get rid of unrealistic track parameters Χ2 < 10 0 < Time-of-flight < 20 ns 20 cm/ns < Track length/Time of flight < 40 cm/ns For each experimental event, 20 fake events were generated in our case
The scrambling method

5. Data map
Reference map
Corrected map

6. Corrected map (1 day) ~0.9 Mevents
3 x 3 degrees grid
Events/cell ~ 300 (5% stat.)
Cell-to-cell variations compatible with stat.errors

7. Corrected map (4 days ) ~3.5 Mevents

8. Corrected map (22 days) ~20 Mevents
With about 20 M events fluctuations are in the order of 1 % (about 8-10 kevents/cell).

9. Present status: ● Procedure for data analysis well tested on different data sets ● Scrambling method implemented to take into acount geometrical acceptance and time exposure of the telescope ● About 20 M events analyzed, with statistical uncertainties in each cell of the order of a 1% ● Anisotropies at the level of a few % may be excluded by the present analysis, in agreement with results obtained at higher primary energies ● To search for smaller effects (i.e. 0.1% anisotropies) a large increase (factor x100) in statistics required (2 x 109 events), which could be achieved in principle by a combined analysis of different telescopes

10. Next to be done: ● Check some additional data set from different telescopes ● Increase somehow the statistics (no large improvement in statistical accuracy expected however) ● Finalize the paper draft to be submitted to the Collaboration