physics society talk (sept/20/00): pg 1 quantum mechanical interference in charmed meson decays too...
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Physics Society Talk (Sept/20/00): Pg 3 Since Relativity is Cool and Quantum Mechanics is Cool we conclude that Relativity + Quantum Mechanics must be VERY CoolTRANSCRIPT
Physics Society Talk (Sept/20/00): Pg 1
Quantum Mechanical InterferenceQuantum Mechanical Interferencein Charmed Meson Decaysin Charmed Meson Decays
TOO BORING
Physics Society Talk (Sept/20/00): Pg 2
Everything you Need to KnowEverything you Need to KnowAbout Three Body InteractionsAbout Three Body Interactions
I’ll get arrested
Physics Society Talk (Sept/20/00): Pg 3
Since Relativity is CoolSince Relativity is Cooland Quantum Mechanics is Cooland Quantum Mechanics is Cool
we conclude thatwe conclude that
Relativity + Quantum MechanicsRelativity + Quantum Mechanicsmust be VERY Coolmust be VERY Cool
Physics Society Talk (Sept/20/00): Pg 4
Tevatron (1000 GeV)FermilabFermilab
Physics Society Talk (Sept/20/00): Pg 5
At the “Interaction Point”At the “Interaction Point”
Beam particles collide
e e
c t = 0
e
e
q
q
c
Physics Society Talk (Sept/20/00): Pg 6
At the “Interaction Point”At the “Interaction Point”
Hardonization
c t ~ 10-23 sec
QCD
c
Physics Society Talk (Sept/20/00): Pg 7
At the “Interaction Point”At the “Interaction Point”
Hardonization
c t ~ 10-23 sec
QCD
c = (ud)
= (ud)
= (ud)
D*+= (cd)
D0= (cu)
Physics Society Talk (Sept/20/00): Pg 8
At the “Interaction Point”At the “Interaction Point”
t ~ 10-23 sec
D*+
Mesons leave the scene of the crime
D0 10-15 m
Physics Society Talk (Sept/20/00): Pg 9
At the “Interaction Point”At the “Interaction Point”
Mesons start to decay strongly
D*+
t ~ 10-20 sec
D0
10-11 mD0
Physics Society Talk (Sept/20/00): Pg 10
At the “Interaction Point”At the “Interaction Point”
Weakly decaying mesons are next
10-4 m
t ~ 10-12 sec
K
K
D0
D0
Physics Society Talk (Sept/20/00): Pg 11
What we need to detectWhat 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
100 m
t ~ 10-8 sec
K
K
Physics Society Talk (Sept/20/00): Pg 12
Event ReconstructionEvent Reconstruction
K
If every event has exactly one of these decays and nothing else, and suppose we know which track is the K.
D0 K Suppose we are looking for
D0
m E E p pK K2 2 2
We can calculate the Lorenz invariant mass of the K pair if we knowthe energy and momentum of each particle.
222 mPE
The mass does not depend on which reference frame I use !!!
(special relativity is cool!)
Physics Society Talk (Sept/20/00): Pg 13
Event ReconstructionEvent Reconstruction
If we plot the invariant mass for a large number of such events in a histogram we measure the mass of the D0 :
1.7 1.8 1.9 2K mass (GeV)
m(D0)=1.86 GeV
detectorresolution
K
D0
Physics Society Talk (Sept/20/00): Pg 14
Event ReconstructionEvent Reconstruction
Some reality: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.
K mass (GeV)1.7 1.8 1.9 2
good guesses
bad guesses
D0
Physics Society Talk (Sept/20/00): Pg 15
Event ReconstructionEvent Reconstruction
More reality: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.
K mass (GeV)
“combinatoric”background
signal
1.7 1.8 1.9 2
Physics Society Talk (Sept/20/00): Pg 16
Event ReconstructionEvent Reconstruction
Actual reality:Actual reality: Not every event will contain a From some events we will have no right combinations. More “background”
K mass (GeV)1.7 1.8 1.9 2
totalbackground
signal
D0 K
Physics Society Talk (Sept/20/00): Pg 17
Here comes Heisenberg !Here comes Heisenberg !
Not all “resonances” (i.e. particles) have the same “width”
1.7 1.8 1.9 2
K mass (GeV)
K
D0
0.6 0.7 0.8 2
mass (GeV)
0
Physics Society Talk (Sept/20/00): Pg 18
Here comes Heisenberg !Here comes Heisenberg !
Uncertainty Principle: Et > h
0.6 0.7 0.8 2
mass (GeV)
So if t is small (short lifetime) then E is big (large mass uncertainty)
1.7 1.8 1.9 2
K mass (GeV)
The E of the D0 is really much smaller than our measurement errors
Physics Society Talk (Sept/20/00): Pg 19
What we can measure:What we can measure:
0.6 0.7 0.8 2
invariant mass (GeV)
With this kind of experimental data, we can measure the mass and width of a particle resonance.
Physics Society Talk (Sept/20/00): Pg 20
A tiny bit of Math !A tiny bit of Math !
Invariant mass
This bump is described by a something called aBreit-Wigner lineshape:
Intensity(# events)
We observe Intensity = |Amp|2
RRRWB iMmM
22
1 Amp
MR = Mass of resonance
m = inv. mass of each “event”(independent variable)
R = Width of resonance
Physics Society Talk (Sept/20/00): Pg 21
RRRWB iMmM
22
1 Amp Complex Number:Has both Magnitude and Phase
m = MR
Invariant mass
Phase
Magnitude Mean & Width areeasy to measure
Phase is hard to seesince amplitude issquared to produceobservable quantity.
Physics Society Talk (Sept/20/00): Pg 22
RRRWB iMmM
22
1 Amp
Think of an LRC circuitThink of an LRC circuit (looks very similar in a mirror sort of way)
This can help you visualize what the “Phase” means:
CiLiR
LRC
1 Amp
Physics Society Talk (Sept/20/00): Pg 23
Invariant mass
Phase
Magnitude Mean & Width areeasy to measure
Phase is hard to seesince amplitude issquared to produceobservable quantity.
Getting at the Underlying Physics:Getting at the Underlying Physics:
Physics Society Talk (Sept/20/00): Pg 24
How we can see phases: interferenceHow we can see phases: interference
When there are two (or more) “paths”to the same final state.
Since we add the amplitudes beforebeforewe square to get intensity, interferencebetween the amplitudes (caused byphase differences) will show up whenwe make measurements !!
Physics Society Talk (Sept/20/00): Pg 25
Same initial & final states, just different in the middle)
These two amplitudes can interfere !
The same works thing with particles !!The same works thing with particles !!
+ -+ -
-
+
Physics Society Talk (Sept/20/00): Pg 26
OK…that’s nice, but therehas to be a better way to see these phases at work!!
Physics Society Talk (Sept/20/00): Pg 27
Finally there: Three body decays !!Finally there: Three body decays !!
M
Start with a fairly heavy(charmed) meson like D0
D0
Physics Society Talk (Sept/20/00): Pg 28
Finally there: Three body decays !!Finally there: Three body decays !!
mb
mc
ma
Study cases in which it decays into three daughters (for example K)
K
M
Physics Society Talk (Sept/20/00): Pg 29
mb
mc
ma
There are now several invariant masses we can calculate:
K
D0
M
M2 = (Ea+Eb+Ec)2 - (Pa+Pb+Pc)2 Boring…we already know it’s a D0.
mab2 = (Ea+Eb)2 - (PPa+PPb)2
mbc2 = (Eb+Ec)2 - (PPb+PPc)2 These are very
useful mac
2 = (Ea+Ec)2 - (PPa+PPc)2
(Ea,PPa)
(Eb,PPb)
(Ec,PPc)
Physics Society Talk (Sept/20/00): Pg 30
mb
mc
ma
M
Dalitz PlotDalitz Plot
mab2
mbc2
All events end up uniformlydistributed in this enclosed area. Unless there is Unless there is additional physics.additional physics.
mab2 , mbc
2 and mac2 are simply related:
mab2 + mbc
2 + mac2 = constant
= M2 + ma2 + mb
2 + ma2
Only two are independent
b
b
a
b at rest
ca at rest
b
ac at rest
ba
c
Physics Society Talk (Sept/20/00): Pg 31
Figuring out the PhysicsFiguring out the Physics
mab2
mbc2
mx2
mb
mc
ma
M
mx
This is like ridge with a Breit-Wigner shape
Physics Society Talk (Sept/20/00): Pg 32
mab2
mbc2 m
b
mc
maM
mymy
2
Physics Society Talk (Sept/20/00): Pg 33
mab2
mbc2
mz2
mb
mc
maM
mz
Physics Society Talk (Sept/20/00): Pg 34
Interference Between Intermediate StatesInterference Between Intermediate States
mab2
mbc2
Addition Movie
mbc2
+ + + + + + + +
- - - - - -
+ +
+ +
+ +
+- -
- - -
- Phases
Physics Society Talk (Sept/20/00): Pg 35
More Phases are Possible (more physics)More Phases are Possible (more physics)
mab2
mbc2
mbc2
+ + + + + + + +
- - - - - -
+ +
+ +
+ +
+- -
- - -
- Phases
Phase Movie
ei
Physics Society Talk (Sept/20/00): Pg 36
More PhysicsMore Physics
mab2
mbc2
mx2
mb
mc
ma
M
mx
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 37
Looking at real data:Looking at real data:
D0 K- Seven resonances are needed to represent the data