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Introduction

To play with the truth objects is a good idea to understand the structures of data

AOD truth (SpclMC)

Herwig (athena 12.0.6)

• data trig1_misal1_mc12.005200.T1_McAtNlo_Jimmy.recon.AOD.v12000601_tid005997
  • MC@NLO generate only 4-momentum of t and anti-t, all the other work is down by Herwig
• Characteristics
  • Documentation particles only 6. -6. 2201(ud_0), 2203(uu_1). don't understand the latter 2
  • status of 6: 123(124)->143(144) ->3 ->155
    • event ratio, (status 123):(status 124) =12.4:87.6.
    • 1 events -6 decay style different: status 124 stop, and then new -6 status 155 decay
  • status of 24: 123->195
    • 2% events: w from l radiation with status 2: w->lv->(wv)v

Pythia (athena 12.0.6)

• definition of is the angle between the direction of lepton in w rest fram and the direction of w in top rest frame.

Because of the angle moemtum reservation, the spin of w defines the secondary objects' total angle momentum. The wave function of w in its own rest frame is an engenfunction of spin operator in a specific direction, which is the direction the leptons to be emited. ?. The w spin distribution in directions is discribed by its flying direction in the rest frame of its parent particle, so here the w direction in top rest frame is used as an axis.

• Dataset CSC 5200 Truth cospsi_true changes according to cut on l pt:
  

But cut on the eta of lepton doesn’t distort the distribution shape

Cut on the pt of neutrino also distort w pola distribution:

• cospsi_true changes according to the cut on nu pt:
  

summary：w polarization distribution is distorted by lepton and neutrino pt cut, because the cut remove low pt lepton and neutrino which is backard comparing with w flying direction so some PSI is suppressed.

A and Ad

• The effection from the cut on the A and Ad ( truth and reco)

1.   Divide truth pt of lepton so as to there are same events (5000) in each pt interval.
2.   Check the mean of -3cosphilep_lej_true and -9coslep_true*coshad_lej_true as the function of pt_l_true  (ask Mttbar<550GeV)
3.   Do the same to reco values, and use reconstructed pt_l, the reconstructed one is corrected with correction function and ask Mttbar<550GeV

• A_Ad_in_different_lpt_interval:
  

1. up trueth, down reconstruction  2. left Ad right A  3.the interval and events are  (for A)
pt_l_true>20000.000000 && pt_l_true<25568.000000  mean: 0.133228 events: 5038
pt_l_true>25568.000000 && pt_l_true<31040.000000 mean: 0.218282 events: 5010
pt_l_true>31040.000000 && pt_l_true<36704.000000 mean: 0.142326 events: 5002
pt_l_true>36704.000000 && pt_l_true<42704.000000 mean: 0.150123 events: 5006
pt_l_true>42704.000000 && pt_l_true<49760.000000 mean: 0.148801 events: 5028
pt_l_true>49760.000000 && pt_l_true<57872.000000 mean: 0.18008 events: 5010
pt_l_true>57872.000000 && pt_l_true<67904.000000 mean: 0.0954169 events: 5008
pt_l_true>67904.000000 && pt_l_true<83360.000000 mean: 0.242128 events: 5013
pt_l_true>83360.000000 && pt_l_true<95952.000000 mean: -0.0157556 events: 2397
pt_l>20000.000000 && pt_l<25568.000000 mean: 1.02116 events: 194.779
pt_l>25568.000000 && pt_l<31040.000000 mean: 0.625692 events: 190.005
pt_l>31040.000000 && pt_l<36704.000000 mean: 0.708421 events: 140.993
pt_l>36704.000000 && pt_l<42704.000000 mean: 0.534248 events: 130.514
pt_l>42704.000000 && pt_l<49760.000000 mean: 0.357269 events: 133.531
pt_l>49760.000000 && pt_l<57872.000000 mean: 0.187895 events: 106.536
pt_l>57872.000000 && pt_l<67904.000000 mean: -0.733406 events: 91.5522
pt_l>67904.000000 && pt_l<83360.000000 mean: -0.384124 events: 74.6901
pt_l>83360.000000 && pt_l<95952.000000 mean: -1.50455 events: 26.7938

• To sum all event from each pt sliding point to 500GeV:
• A and Ad from different lpt to 500GeV:
  

Summary:
1.   The investigation indicates that the truth information on hard process read out from AOD truth container is not correct, at least not correct on spin correlations as in sn-2005-052. 
2.   for the reconstructed spin correlation of t and tbar, we have the coslep:coshad_lej in the following, (the shape doesn’t change, after corrected with correction function). Actually the shape for truth is similar except that for coslep:coshad_lej  1:-1, it is not the least bin, which has been suppressed to least in reconstruction.
a)   We suppose, top is flying in one direction:  in the rest frame of the top, w will fly in each direction with the same probability away from the top, because top is not polarized,   and the least energy jet in top rest frame is from quark which flies in the inverse direction with the w, that is towards the top because they are inverse-boosted by the w.  Then the lease energy quark is boosted by the top again, the quark flying in the direction of top is boosted (coshad_lej->1) , other wise is inverse boosted (coshad_lej-1) and more are cut by the selection of pt_jet>30GeV. So coshad_lej1 has more events. 
b)   For lepton, in top rest fram, lepton is not always inverse-boosted by w, in fact, 50% is boosted. In this case, only 25% of events, lepton is inverse-boosted by w and top (twice), they are cut with a smaller selection pt_l>20GeV.  So still coslep1 still has more events but the asymmetry is smaller than jet.

• sn-atlas-2005-052.pdf: scientific note on w pola and tt correlation study with atlfast

Plots code

truth electron:

truth muon:

truth jets:

truth etmiss:

truth wt mass:

truth w t:

truth ttbar:

truth angle distrubution:

truth in 2, 10, 30 bins: