Transcript PPT

Quantum Mechanical Interference
in Charmed Meson Decays
TOO BORING
Physics Society Talk (Sept/20/00): Pg 1
Everything you Need to Know
About Three Body Interactions
I’ll get arrested
Physics Society Talk (Sept/20/00): Pg 2
Since Relativity is Cool
and Quantum Mechanics is Cool
we conclude that
Relativity + Quantum Mechanics
must be VERY Cool
Physics Society Talk (Sept/20/00): Pg 3
Fermilab
Tevatron (1000 GeV)
Physics Society Talk (Sept/20/00): Pg 4
At the “Interaction Point”

Beam particles collide
e+
ec
ec
g
q
q
e+
t=0
Physics Society Talk (Sept/20/00): Pg 5
At the “Interaction Point”

Hardonization
QCD
c
c
t ~ 10-23 sec
Physics Society Talk (Sept/20/00): Pg 6
At the “Interaction Point”

Hardonization
p+= (ud)
D*+= (cd)
QCD
c
p-= (ud)
c
p- = (ud)
t ~ 10-23 sec
D0= (cu)
Physics Society Talk (Sept/20/00): Pg 7
At the “Interaction Point”

Mesons leave the scene of the crime
p+
D*+
pp-
t ~ 10-23 sec
D0
10-15 m
Physics Society Talk (Sept/20/00): Pg 8
At the “Interaction Point”

Mesons start to decay strongly
p+
p+
D0
D*+
pt ~ 10-20 sec
p-
D0
10-11 m
Physics Society Talk (Sept/20/00): Pg 9
At the “Interaction Point”

Weakly decaying mesons are next
p+ p +
D0
p0
p-
p+
Kg
g
t ~ 10-12 sec
pp-
D0
10-4 m
K+
Physics Society Talk (Sept/20/00): Pg 10
What we need to detect


Finally we are left with the particles that live long enough to
be detected.
In this case
8 charged
2 neutral
p+ +
p
p+
Kpg
p-
g
pK+
t ~ 10-8 sec
100 m
Physics Society Talk (Sept/20/00): Pg 11
Event Reconstruction

Suppose we are looking for D 0  K- p+

If every event has exactly one of these decays and nothing
else, and suppose we know which track is the K.

We can calculate the Lorenz invariant mass of the Kp pair if we know
the energy and momentum of each particle.
E 2  P 2 + m2
m  EK + Ep 
2
2

 2
-  p K + pp 
K-
p+
The mass does not depend on which
reference frame I use !!!
(special relativity is cool!)
D0
Physics Society Talk (Sept/20/00): Pg 12
Event Reconstruction

If we plot the invariant mass for a large number of such
events in a histogram we measure the mass of the D0 :
m(D0)=1.86 GeV
K-
p+
detector
resolution
D0
1.7
1.8
1.9
2
Kp mass (GeV)
Physics Society Talk (Sept/20/00): Pg 13
Event Reconstruction

Some reality: We usually don’t know which track is the K so we
have to try both possible combinations.
From each event we will have one right and one wrong
invariant mass combination.
good guesses
bad guesses
D0
1.7
1.8
1.9
2
Kp mass (GeV)
Physics Society Talk (Sept/20/00): Pg 14
Event Reconstruction

More reality: There are many other tracks in every event, and
we don’t know which belong to the D0 !
From each event we will have one right and many wrong
invariant mass combinations.
signal
“combinatoric”
background
1.7
1.8
1.9
2
Kp mass (GeV)
Physics Society Talk (Sept/20/00): Pg 15
Event Reconstruction

Actual reality: Not every event will contain a D 0  K- p+
From some events we will have no right combinations.
More “background”
signal
total
background
1.7
1.8
1.9
2
Kp mass (GeV)
Physics Society Talk (Sept/20/00): Pg 16
Here comes Heisenberg !

Not all “resonances” (i.e. particles) have the same “width”
K-
p+
p-
p+
r0
D0
1.7
1.8
1.9
Kp mass (GeV)
2
0.6
0.7
0.8
2
pp mass (GeV)
Physics Society Talk (Sept/20/00): Pg 17
Here comes Heisenberg !
Uncertainty Principle: DEDt > h
So if Dt is small (short lifetime) then
DE is big (large mass uncertainty)
0.6
0.7
0.8
pp mass (GeV)
2
The DE of the D0 is
really much smaller than
our measurement errors
1.7
1.8
1.9
2
Kp mass (GeV)
Physics Society Talk (Sept/20/00): Pg 18
What we can measure:
pp invariant mass (GeV)
With this kind of experimental data,
we can measure the mass and width
of a particle resonance.
0.6
0.7
0.8
2
Physics Society Talk (Sept/20/00): Pg 19
A tiny bit of Math !
This bump is described by a something called a
Breit-Wigner lineshape:
Amp
B -W

1
M R2 - mpp2 - iM R R
R = Width of resonance
MR = Mass of resonance
Intensity
(# events)
mpp = inv. mass of each “event”
(independent variable)
pp Invariant mass
We observe Intensity = |Amp|2
Physics Society Talk (Sept/20/00): Pg 20
Amp
B -W 
1
2
M R2 - mpp
- iM R R
Complex Number:
Has both Magnitude and Phase
mpp = MR
Mean & Width are
easy to measure
Magnitude
Phase is hard to see
since amplitude is
squared to produce
observable quantity.
Phase
pp Invariant mass
Physics Society Talk (Sept/20/00): Pg 21
Think of an LRC circuit
(looks very similar in a mirror sort of way)
This can help you visualize what the “Phase” means:
1
1
Amp LRC 
Amp B -W  2
2
i
M R - mpp - iM R R
R + iL C
Physics Society Talk (Sept/20/00): Pg 22
Getting at the Underlying Physics:
Mean & Width are
easy to measure
Magnitude
Phase is hard to see
since amplitude is
squared to produce
observable quantity.
Phase
pp Invariant mass
Physics Society Talk (Sept/20/00): Pg 23
How we can see phases: interference
When there are two (or more) “paths”
to the same final state.
Since we add the amplitudes before
we square to get intensity, interference
between the amplitudes (caused by
phase differences) will show up when
we make measurements !!
Physics Society Talk (Sept/20/00): Pg 24
The same works thing with particles !!
pr0
p+
-
+
+
+
-
-
p0
p+
Same initial & final states,
just different in the middle)
These two amplitudes can interfere !
Physics Society Talk (Sept/20/00): Pg 25
OK…that’s nice, but there
has to be a better way to
see these phases at
work!!
Physics Society Talk (Sept/20/00): Pg 26
Finally there: Three body decays !!
D0
M
Start with a fairly heavy
(charmed) meson like D0
Physics Society Talk (Sept/20/00): Pg 27
Finally there: Three body decays !!
p0
m
c
M
K-
m
a
Study cases in which it
decays into three daughters
(for example K- p+ p0)
p+
mb
Physics Society Talk (Sept/20/00): Pg 28
p0
m
There are now several
invariant masses we can
calculate:
D0
(Ea,Pa)
K-
(Ec,Pc)
c
M
(Eb,Pb)
m
a
M2
=
(Ea+Eb+Ec)2
-
(Pa+Pb+Pc)2
mab2 = (Ea+Eb)2 - (Pa+Pb)2
mbc2 = (Eb+Ec)2 - (Pb+Pc)2
mac2 = (Ea+Ec)2 - (Pa+Pc)2
Boring…we already
know it’s a D0.
p+
mb
These are very useful
Physics Society Talk (Sept/20/00): Pg 29
Dalitz Plot
c
mc
a at rest
M
b
mbc2
b
ma
b
a
All events end up uniformly
distributed in this enclosed
area. Unless there is
additional physics.
c
b
b at rest
a
mb
c at rest
mab2
a
mab2 , mbc2 and mac2 are simply related:
mab2 + mbc2 + mac2 = constant
= M2 + ma2 + mb2 + ma2
Only two are independent
Physics Society Talk (Sept/20/00): Pg 30
Figuring out the Physics
mx2
mc
M
mbc2
ma
mx
mb
mab2
This is like ridge with a
Breit-Wigner shape
Physics Society Talk (Sept/20/00): Pg 31
ma
mbc2
my2
M
mc
my
mb
mab2
Physics Society Talk (Sept/20/00): Pg 32
m z2
mc
ma
mz
M
mbc2
mb
mab2
Physics Society Talk (Sept/20/00): Pg 33
mbc2
------
mbc2
+++++++
Interference Between Intermediate States
Phases
-----++++++++
Addition Movie
mab2
Physics Society Talk (Sept/20/00): Pg 34
mbc2
------
mbc2
+++++++
More Phases are Possible (more physics)
-----++++++++
Phases
eif
Phase Movie
mab2
Physics Society Talk (Sept/20/00): Pg 35
More Physics
mx2
mc
M
mbc2
ma
mx
mb
mab2
Now suppose X is a
vector resonance (L=1)
We can measure the L of
the intermediate state !
Physics Society Talk (Sept/20/00): Pg 36
Looking at real data:
D0

K-
p+
p0
Seven resonances are needed
to represent the data
Physics Society Talk (Sept/20/00): Pg 37