How simple can it be Two decays i pi 0 gt g g ii K 0 gt pi pi Mother particle momenta P 1 2 4 8 16 GeV Daughter momentum cut p1 p2 gt 05 ID: 383877
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Slide1
First look at mass constraint
[How simple can it be?]
Two decays:
i
)
pi
0
-> g
g
ii) K
0
-> pi+ pi-
- Mother particle
momenta
: P = 1, 2, 4, 8, 16
GeV
- Daughter momentum cut: p1, p2 > 0.5
GeV
- Simple ATLAS resolution smearing
- Very simple refitting of mass:
change p1 and p2 by the
same scale
(angular resolution not considered)
Note that a complete treatment involves relatively complex and slow chi-square fitting! Slide2
Plots
.
1. Mother particle momentum resolution (r)
for truth
, reconstructed, and
refitted daughters
r = (
p
meas
–
p
true
) /
p
true
This will hopefully improve after refitting
2.
Invariant
mass
for truth
, reconstructed, and
refitted daughters.
After refitting
M
should equal
MtruthSlide3
i
)
pi
0
-> g
g
M
2
= (E
1
+E
2
)
2
– P
2
=>
M
2
= 2 E
1
E
2
( 1 –
cos
A )
for
massless
photons
=>
M
2
= p
1
p
2
k
p
=
E
, and we wont change
A
“Refit”: simply scaling
p1
and
p2
by
M
pi0
/
M
will constrain the invariant mass to
M
pi0
Here we assume p
1
p
2
(true-
ish
given that we have a 0.5
GeV
momentum cut) and so we don’t care too much about weighting the scale for different resolutions.Slide4
P = 1
GeV
T
ruth
T
ruth
Recon
Recon
Refit
RefitSlide5
P = 2
GeV
T
ruth
T
ruth
Recon
Recon
Refit
RefitSlide6
P = 4
GeV
T
ruth
T
ruth
Recon
Recon
Refit
RefitSlide7
P = 8
GeV
T
ruth
T
ruth
Recon
Recon
Refit
RefitSlide8
P = 16
GeV
T
ruth
T
ruth
Recon
Recon
Refit
RefitSlide9
ii) K
0
-> pi+ pi-
M
2
= (E1+E2
)2 – P2
=> M2 = 2 E1 E
2 ( 1 – cos A )
for massless pions!!!
=> M2 = p
1
p
2
k
p
=
E!!
, and we wont change
A
“Refit”: simply scaling
p1
and
p2
by
M
K0
/
M
will constrain the invariant mass to
M
K
0
Here we assume p
1
p
2
(true-
ish
given that we have a 0.5
GeV
momentum cut) and so we don’t care too much about weighting the scale for different resolutions.
BUT we assume
massless
pions
! So this will not work so well.Slide10
P = 1
GeV
T
ruth
T
ruth
Recon
Recon
Refit
RefitSlide11
P = 2
GeV
T
ruth
T
ruth
Recon
Recon
Refit
RefitSlide12
P = 4
GeV
T
ruth
T
ruth
Recon
Recon
Refit
RefitSlide13
P = 8
GeV
T
ruth
T
ruth
Recon
Recon
Refit
RefitSlide14
P = 16
GeV
T
ruth
T
ruth
Recon
Recon
Refit
RefitSlide15
Conclusion
Simple scaling works well for the pi0 because E
1
and E
2
are similar (after energy cuts).
Weighting the scale seems to be not very important. - But I didnt
compare yet with the standard mass constraint method (Ahmet?) - Try a simple weighting scheme?
When we have massive daughters this method is not so good (the invariant mass doesn’t constrain properly). Try adding the mass effects in a simple way?
Ahmet does the scaling in the c.o.m
frame, again without weights This works well!