Exclusive B->JPsiMuMu Analysis
in CMSSW_3_1_2
Muon Efficiency and Fake Rate
Two Dimension Fit
1
outline
 Muon Efficiency and Fake rate
 new MC data sample
 comparison of three kinds muons’ efficiency
 muon to pi/K fake rate
 Two Dimension Fit
 CDF
J/ψ meson 2D fit
 David’s Note BtoJPsiK 2D fit
 To do list
2
Mu efficiency and fake rate
 MC Data Sample:
Single Muon 460000 events
Single Pion 230000 events
Single Kaon 410000 events
 Muon type:
Glb Ξ Global Muon
Trk Ξ Track Muon
Trk’ Ξ Track Muon with χ2<1.9, inner track hit >11
 Muon efficiency:

N reco ( MCTruthMatch)
N gen
 Muon fake: Using Single Pion and Kaon MC Datasample.
fake  
3
N Re co Global 
NGen  / K
Here, we correct our mistake about double counting of muons
With Pt
=[3,65]
GeV
Muon Efficiency
Barrel+Endcap
Barrel
Endcap
Barrel+Endcap
Barrel
Endcap
I.
II.
Barrel+Endcap
Barrel
Endcap
4
At low pt <5GeV, Endcap muon can get
highest efficiency, barrel + endcap lower, and
barrel the lowest. But at high pt range, the
contrary in the case.
At high pt range ,Global muon can get 96%
efficiency, Tracker muon 97%,and Tracker muon
with cuts 96%, and at low pt range Tracker
muon can get highest effieiency 77.5%, Tracker
muon with cuts 75.5% and Global muon only
63%. In a word, at high pt Global and Tracker
muon efficiency almost the same, but in low pt
Tracker muon can gain 12% higher efficiency
than Global muon.
Comparison of fake rate Pi
After correctdouble counting,
using new Single Pi MC sample
Barrel+Endcap
Barrel
Endcap
5
Comparison of fake rate K
After correct double counting, using new Single
Kaon MC sample
Barrel+Endcap
Barrel
Endcap
6
Two Dimension Fit for J/ψ (CDF)
 Unbinned extended maximum likelihood fit
N
ln L   ln F( x, m )
i 1
 N is total number of events in the mass range 2.85GeV<mμμ<3.55GeV
F  x, m   f Sig  FSig  x   M Sig  m   1  f Sig   FBkg  x   M Bkg  m 
 f
is the fraction of signal J/ψ events, FSig and FBkg are the PDLS
of Signal and BKG. MSig and MBkg is the mass spectrum for Signal
and BKG.
FSig  x   f B  FB  x   1  f B   FP  x 
parameters
F
 x   1  f  f  f  R  x, s 
  x, s    mc  x 
F
x

R
x



B
Signal PDL: fB,s
2
 x 
f
FP  x   R  x, s 
 5exp      x   R  x  x, s 
M : f , M,D,σ ,r2
Sig

Bkg
2

M

M Sig  G1  m  M ,  M 
BKG f  G  mPDL:
f , r,f
,f ,λ ,λ ,λ
  M  D +
 - sym + - sym
1 M : Mslope
2
M Bkg 

2
: fsig
max
min

m
 m
m 
slope 
 
2




2sym

  
 x 
exp      x   R  x  x, s 

  
sym
1
sym
f
6
f
 1
M
min
m max
  m 
lnL M
7
2


f sym
2sym
 x 
exp  
 x  R  x  x, s 
    
 sym 
 x 
exp 
  x  R  x  x, s 
    
sym


total 15
Fit results of CDF
8
Two Dimension Fit for BtoJPsiK(David Note)
 Unbinned extended maximum likelihood fit
 Five components of B+-> J/ψ K+ datasample:
 Signal, B+->J/ψπ+, prompt J/ψ, combinatorial bbar(BB),
feeddown bbar(B0-> J/ψ K*0,B±-> J/ψ K*±)
 Extended likelihood function:

 

L  exp   ni     ni Pi  M B ,  i  Pi c , i 
 i  j  i



 where i = [1…5], ni and Pi is the yield and PDF of each
component separately, j is the event No. of the fit.
9
PDF of B mass and c
c
MB
Component
Function
Parameter
Function
parameter
Signal
G1+G2+G3
{μi,σi}
(G1+G2)e-ct/λ
{μi,σi,λ}
J/ψπ
10
Same with Signal
G1+G2+G3
{μi,σi}
(G1+G2)e-ct/λ
{μi,σi,λ}
{σ,λ1,λ2}
{μi,σi,λ}
Peak B
G1+G2+e-αMB
{μi,σi,α}
G
(e-ct/λ1+e-ct/λ1)
Comb B
e-αMB
{α}
(G1+G2)e-ct/λ
Prompt J/ψ
e-αMB
{α}
G1  G2  e ct / 

{μi,σi,λ}
Fit Procedure
 First fit each component with pT > 9GeV MC
truth match data sample to determine the best
values of λs(except Signal) and all parameters.
MASS
11
PDL
Fit Procedure
 Then fix λs(except Signal) and all parameters, and fit all pt
bins sample of S+B to determine the B lifetime λB and yield
for each component. (4 yields + λB )
 T he last, fix all λs and all parameters, and fit data
sample(S+B) for yields in each bins of PT.
12
To do list
 Perform the two dimension fit referring to
David’s Note.

Code skeleton was ready, but parameters need to be
optimized
 QCD BKG may introduce new variables when we
fit the real data.
13