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B. Measurement of the muon’s speed                       To  find  the  mean  value  of  these  time
                                                                  measurements,  along  with  its  corresponding
          The  distribution  of  time  measurements  for  a       standard deviation, a gaussian curve was adjusted
          separation  of  50cm  between  the  detectors,  is      to this distribution, meaning the curve had to follow
          presented  in fig.  (19).  The scale of the bins  in the   the equation
          horizontal  axis  was  converted  into  time  units  with                  − (   )
                                                                                      1   −   2
          the  help  of  the  calibration  previously  made  (fig.          (  ) =      2      ,      (15)
          (10)): every channel represents (1/83.6183)    .
                                                                  Where    is the mean value of the distribution,    is
                                                                  the standard deviation, and    is the amplitude. As
                                                                  in  the  previous  experiment,  the  curve_fit  function
                                                                  from  the  Python  library  SciPy  was  used  for  this
                                                                  purpose. In fig. (21) the best curve fit is shown. The
                                                                  mean  value  of  the  distribution  was  found  to  be
                                                                     = 15.685    ,  with  standard  deviation     =
                                                                                                               1
                                                                   1
                                                                  0.785    .






          Figure 19. Time distribution for    = 50    .
                                     1
           Based  on  the  irregularity  of  the  distribution,  the
          possibility  of  the  presence  of  a  non-constant
          background  was  considered.  To  identify  it,  only
          data  from  short  and  large  times  was  considered,
          since  the  peak  in  the  middle  of  the  distribution
          wouldn’t  allow  to  isolate  the  background.  The
          model for the background curve fit was

                               −                                  Figure  21.  Gaussian  curve  fit  for  the     = 50    
                                                                                                          1
                      (  ) =       ,       (14)                   distribution.
                                   
                                                                   On  the  other  hand,  the  distribution  of  the  time
          Where    ,      and      were  parameters.  Once  the   measurements for a separation of    = 100     is
          background was obtained as a function of time, it       shown in the fig. (22)              2
          was  subtracted  from  the  data,  and  the  resulting
          distribution within the range from 12     to 19     is
          shown in fig. (20).


















          Figure  20.  Time  distribution  for     = 50      after   Figure 22. Time distribution for    = 100    .
                                                                                             2
                                           1
          background subtraction.
              17
                            Tlahuizcalli ISSN: 2448-7260                    Año 10 Núm. 30 septiembre-diciembre 2024
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