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Solar Precision Measurements with Super Kamiokande

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					 BONSAI: (Low Energy) Vertex
Reconstruction for DUSEL LBNE




 Michael Smy   DUSEL LBNE Collaboration
 UC Irvine      Meeting, January 26th 2010
           BONSAI Reconstruction
   • BONSAI is the Super-K low energy vertex
     reconstruction software
   • BONSAI is not Super-K proprietary (or
     owned by anybody else, for that matter)
   • it is a maximum likelihood fit based almost
     entirely on relative PMT hit timing
   • in SK, it can reconstruct electrons above 3
     MeV
   • In SK, it is tested with electrons from a linear
     accelerator (4.4MeV<E<19MeV)
Michael Smy, UC Irvine
Michael Smy, UC Irvine
                    I. Initial Search Grid
• define list of “good hits” (meaning all
  pairs obey Dt<Dx and/or high charge hits)
• draw quadruples from this list: each
  quadruple defines a point in space
• reduce number of quadruples by giving
  preference to clusters in absolute time
• reduce number of points by averaging
  close neighbors
Michael Smy, UC Irvine
         Four-Hit Combinations
      • need to Solve                  ( x i  v )  ( xi  v )  0
        or with q  v  v              q  2 x i  v  x i  xi  0
      • choose                                           q
                  x1  0                                  
                            1 0 0 0 0 0   vx 
                                                        
                            0 1 0 0 a x bx   v y 
       and convert to 
                             0 0 1 0 a y by            v   0
                           
                            0 0 0 1 a b  ct            z
                                                z    z
                                                          
                                                        1
      • solve (ct )2 (a 2  1)  2a  b (ct )  b2  0  
                                  
                              
                         v  b  a (ct )
Michael Smy, UC Irvine
                          I Initial Searchgrid

                         total # of quadruples        • problem: Nquadruple
                                                        proportional to N4
                                                      • need to limit the
                                                        combinations
                            desired # of quadruples




             smallest reasonable # of quadruples


Michael Smy, UC Irvine
                   I Initial Searchgrid
     I.   time-order selected hits
     II.  select time window to achieve desired # of
          four-hit combinations within that window
     III. do all combinations within that time window




                         t1   t2 t3 t4t5 t6 t7 t8t9t10t11t12t13t14   t15   t16   time

     IV. average over “close” points in three steps:
         60cm, 150cm (BONSAI), and 400cm (Clusfit)
Michael Smy, UC Irvine
             II. Minimization
                         Branch Optimization
                         Navigating Successive
                         Annealing Iterations
                                trace all branches
                                   for a range of
                                     likelihoods!


                          simple search tree @ each grid point
Michael Smy, UC Irvine
     Fitter Controlled by Parameter File
BONSAI and Clusfit Shared Parameters                       Clusfit Parameters
-------------------------------------------------------    -------------------------------------------------------
PMT time resolution:                            3.00 ns    Clusfit grid constant:                       400.00 cm
                                                           Minimum wall distance for Clusfit vertex:   -100.00 cm
PMT coincidence time difference:                3.00 ns    Initial Clusfit Cherenkov cone opening angle: 23.00 deg
PMT pair maximal distance fraction:             0.1785     Initial Clusfit angle positive deviation:   none
PMT pair maximal time difference fraction:      0.1079     Initial Clusfit angle negative deviation:   none
                                                           Initial Clusfit angle goodness weight:         0.02
Maximum # of hits to do all 4-hit combin.:     10          Number of Clusfit passes:                      3
Initial grid constant:                         60.00 cm    First minimum goodness difference to skim:     0.05
Minimum wall distance for 4-hit vertices:    -300.00 cm    Second minimum goodness difference to skim:    0.02
                                                           Third minimum goodness difference to skim:     0.01
BONSAI Parameters                                          Final minimum goodness difference to skim:     0.01
-------------------------------------------------------    First goodness skim fraction:                  0.10
BONSAI grid constant:                         150.00 cm    Second goodness skim fraction:                 0.10
                                                           Third goodness skim fraction:                  0.10
Minimum wall distance for BONSAI vertex:     -100.00 cm    Final goodness skim fraction:                  0.10
Wall distance to invoke fine search:           50.00 cm    Grid search goodness time window:              8.00 ns
Initial Cherenkov cone opening angle:          44.75 deg   First search goodness time window:             6.00 ns
                                                           Second search goodness time window:            5.00 ns
Initial Cherenkov angle positive deviation:     8.00 deg   Third search goodness time window:             4.00 ns
Initial Cherenkov angle negative deviation:    19.12 deg   First search Clusfit minimum radius:         200.00 cm
Final minimum likelihood difference to skim:    0.01       Second search Clusfit minimum radius:         20.00 cm
                                                           Third search Clusfit minimum radius:           5.00 cm
Final likelihood skim fraction:                 0.08       First search Clusfit stop radius:            100.00 cm
Coarse Search Parameters-------------------------------    Second search Clusfit stop radius:            14.00 cm
Coarse search Cherenkov cone opening angle:    44.75 deg   Third search Clusfit stop radius:              8.00 cm
                                                           First Clusfit Cherenkov cone opening angle:   45.17 deg
Coarse search positive angle deviation:         8.00 deg   First Clusfit angle positive deviation:     none
Coarse search negative angle deviation:        19.12 deg   First Clusfit angle negative deviation:     none
Coarse search minimum likelihood diff to skim: 0.04        First Clusfit angle goodness weight:           0.05
                                                           Second Clusfit Cherenkov cone opening angle: 45.17 deg
Coarse search likelihood skim fraction:         0.08       Second Clusfit angle positive deviation:       7.60 deg
Coarse search start radius:                   200.00 cm    Second Clusfit angle negative deviation:       5.08 deg
Coarse search stop radius:                    100.00 cm    Second Clusfit angle goodness weight:          0.20
                                                           Third Clusfit Cherenkov cone opening angle:   45.17 deg
Fine Search Parameters---------------------------------    Third Clusfit angle positive deviation:        7.60 deg
Fine search Cherenkov cone opening angle:      44.75 deg   Third Clusfit angle negative deviation:        5.08 deg
Fine search positive angle deviation:           8.00 deg   Third Clusfit angle goodness weight:           0.20
Fine search negative angle deviation:          21.18 deg
Fine search minimum likelihood diff to skim:    0.05
Fine search likelihood skim fraction:           0.10
Fine search search minimum radius:            100.00 cm
                         BONSAI Reconstruction
                          of High Energy Events
• BONSAI is general, it can work for higher energy
  events also
• might be interesting if PMT coverage is sparse
• use also does not require permission by anybody
• BONSAI was used for the near detector of the K2K
  experiment (the “1kt” water Cherenkov detector)
• K2K Performance was tested by tagging cosmic ray
  muons traveling inside a PVC pipe to emulate muon
  neutrino interactions (five different “vertices” are
  emulated):
Michael Smy, UC Irvine
    Test with “1kt” Calibration Muons
                         BONSAI true z                     BONSAI true z
                                  Auto
                                   Fit                    Auto Fit
                                BONSAI                           BONSAI
                                true z                           true z
                                   Auto Fit             Auto Fit
                            BONSAI                       true z BONSAI
                            true z
                               Auto Fit          Auto Fit

                          BONSAI                 true z BONSAI
                         true z                Auto Fit
                            Auto Fit
                                               true z     BONSAI
                       BONSAI                 Auto
                     true z
                          Auto Fit            Fit

Michael Smy, UC Irvine
LBNE Std Config: Likelihood Function




Michael Smy, UC Irvine
                               ns
                         Gd Configuration: Resolution
Angular Deviation in o




                                    20 MeV Electrons




Michael Smy, UC Irvine                             Vertex Deviation in cm
          Direction Fit
• BONSAI’s direction fit is very primitive:
  sum up all hit directions
• better to do Hough transformation:
  – Take all two-hit combinations to give zero, one,
    or two candidates of particle direction assuming
    42o Cherenkov angle
  – find clusters in those particle direction
    candidates
    Hit-by-Hit Hough Transform
(viewed from reconstructed Vertex)
                              fake solution




                                          true solution




• Event direction in region of “maximal overlap”
• Constructed with hit pairs: two solutions
• Find Answer by combinatorical means
             Find Clusters
• scattering of hits transformed to scattering of
  direction center candidates
• combine “aligned” (within some maximum
  deviation angle) direction center candidates by
  vector sum
• find largest such sum
• goodness: length of vector divided by number of
  centers      combined direction:
               (length is goodness)

compare
                center candidates
length of


     with                     also report: quality=fraction of used centers
      Direction Resolution
Ariadne (Hough transform)
          goodness is a measure of
          multiple Coulomb scattering (mCs) of
          the electrons; better angular resolution
          can be achieved by selecting events
          with little mCs

     BONSAI Standard




                                                     degrees
                         Conclusion
     • BONSAI is working with WCSim
     • usual vertex bias in Cherenkov direction
     • 3D resolution ~50cm, 25o at 20 MeV
     • can be used for Supernova, SRNs, and solar
       neutrinos
     • could be an option for beam events, if PMT
       coverage is sparse
     • BONSAI is not owned by Super-K
     • for higher energy events, I still need to generate
       the likelihoods

Michael Smy, UC Irvine

				
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