1. Muon's speed determination using DQM database
Liceo Cavour Roma
Muon's speed determination using  DQM database
Andrea Gennari, Sharyar Khan
Referente: Prof.ssa Angela Antonucci
Erice 6-8 Dicembre 2018

2. The problem
The aim of the work is to determine the cosmic rays speed using the data collected in the DQM database
The muons speed, that crossing the telescope can be determined using the length of the trace and the time that the particles take to cross the telescope exploit the formula v = length of the trace / flight time.
The calculation data can be extracted from the DQM database by selecting the telescope of interest and setting some limitations that allow to use only the data really useful for the calculation.
It is necessary to analyze the variability of the results according to the parameters that influence their value.

3. Phases of the Work
Calculate the cosmic rays speed using the length of the trace and the flight time from DQM data
Analyze the correspondence between the experimental and the simulated data coming from the same telescope
Analyze the variation of the speed of cosmic rays as the angle of incidence changes, with respect to the vertical
Analyze the variability of cosmic rays velocity using data from different telescopes

4. DQM Database
By connecting to the Data Request the processing data can be obtained

5. Data Request
Using the form in the figure, the data of interest and the values of the parameters that can determine the variability of the data, can be requested

6. Data Request
In the CUT box, restrictions can be set for the extracted data.
ChiSquare<10 && TimeOfFlight>0 && Theta<10 && Theta>0 && Run<10 
With these limitations, the analysis is restricted to "good" traces; a positive flight time is required, to avoid the traces coming from the bottom that determine a negative time of flight. It is appropriate to insert a limitation for the angle to use the tracks that impact almost perpendicularly on the detector and finally we limit the run number to avoid an excessive number of data for the Excel sheet

7. Analysis of data compliance with theoretical predictions
The first analysis carried out concerned the comparison between experimental and theoretical data expected for the phenomenon and generated randomly (Montecarlo method).
A difference between these two sets of data could result in a correction of data to eliminate any systematic errors made in the collection of experimental data. The analysis was carried out on both the CERN01 and BOLOGNA01 telescope. For both telescopes, the experimental data and those indicated with MC were extracted. The results are expressed in graphical form. The two sets of data were made comparable using the same number of data (the experimental data are more numerous than those generated randomly)

8. CERN 01 (experimental data ID 864,Simulated data ID 944)
Average = 30 cm/ns
σ= 9 cm/ns
Average = 28 cm/ns
σ= 4 cm/ns
The histograms shape of the experimental and simulated frequencies is comparable and therefore it is not necessary to impose corrections.
We observed, for the CERN 01 telescope, a track length of less than 90 cm.

9. BOLOGNA 01 (dati sperimentali ID 1273, Dati simulati ID 1267)
Media = 31 cm/ns
Dev,.St= 5 cm/ns
Media = 31 cm/ns
Dev,.St=17 cm/ns
The histograms shape of the experimental and simulated frequencies is comparable and therefore it is not necessary to impose corrections.
The simulated data of BOLOGNA 01 show two peaks (frequencies at 26 and 36 cm/ns)

10. Dependence of the speed value on angle of the cosmic rays with respect to the normal to the detector
The analysis is carried out by comparing the histograms
The shape of the histograms is similar.
By limiting the width of the angle, they get values distributed around the average in a more symmetrical way; the standard deviation is greater.

11. Muon speed for different telescopes
Arezzo
AVERAGE 27
cm/ns σ 4

12. Muon speed for different telescopes
L’Aquila
AVERAGE
29 cm/ns σ
4 cm/ns

13. Muon speed for different telescopes
Lodi
AVERAGE
31 cm/ns σ
22 cm/ns

14. Muon speed for different telescopes
Bologna 01
AVERAGE
30 cm/ns σ
5 cm/ns

15. Comparison of the speed value for different telescopes The analysis is carried out by comparing the histograms
The telescopes of Arezzo and L'Aquila reach higher peak values

16. Comparison of average muon velocity values
The distribution of the averages obtained from the different telescopes is represented in the following histogram
Media cm/ns
Dev.St cm/ns
Cern 01 28 4
Bologna 01 31 17
Arezzo 27
l'Aquila 29
Lodi 22
Bologna 30 5
AVERAGE 29
cm/ns
σ /√n 3

17. Muon speed
The analysis of the data carried out on the DQM data makes it possible to state that the velocity of the muons is:
V=(2.9 ± 0.3) 108 m/s

18. Conclusions
Using the data collected in the DQM database it was possible to determine the velocity of the muons analyzing , for selected telescopes, the data related to the length of the trace and to the time of flight .
The comparison between the experimental and simulated data allowed to exclude corrections on the experimental data
The data were selected using tracks compatible with muonic traces, the most possible vertical with respect to the detector
The variability of the data was analyzed by comparing data with and without limitations with respect to the perpendicularity of the trace and between data from different telescopes
The averages of the velocities obtained from the various telescopes were analyzed and a small sample distribution of the averages was constructed
The final result V = (2.9 ± 0.3) 108 m/s is compatible with the expected result given that the values greater than m/s have no physical significance.

19. Thanks for the attention