Quantum Mechanical Interference in Charmed Meson Decays

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Quantum Mechanical Interferencein Charmed Meson
Decays
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Everything you Need to KnowAbout Three Body
Interactions
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Since Relativity is Cooland Quantum Mechanics is
Coolwe conclude thatRelativity Quantum
Mechanicsmust be VERY Cool
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Fermilab
Tevatron (1000 GeV)
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At the Interaction Point

• Beam particles collide

c
e
e-
c
t 0
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At the Interaction Point

• Hardonization

c
t 10-23 sec
c
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At the Interaction Point

• Hardonization

p (ud)
D (cd)
c
p- (ud)
p- (ud)
t 10-23 sec
c
D0 (cu)
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At the Interaction Point

• Mesons leave the scene of the crime

p
D
p-
p-
t 10-23 sec
10-15 m
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At the Interaction Point

• Mesons start to decay strongly

p
p
D0
D
p-
t 10-20 sec
p-
10-11 m
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At the Interaction Point

• Weakly decaying mesons are next

p
K-
D0
p
g
p
p0
g
p-
t 10-12 sec
p-
p-
10-4 m
K
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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
K-
p-
g
t 10-8 sec
p-
g
p-
100 m
K
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Event Reconstruction
K- p

• Suppose we are looking for

• 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 knowthe energy and momentum of
  each particle.

K-
p
The mass does not depend on which reference
frame I use !!!(special relativity is cool!)
D0
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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
detectorresolution
D0
Kp mass (GeV)
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Event Reconstruction

• Some reality We usually dont 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
Kp mass (GeV)
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Event Reconstruction

• More reality There are many other tracks in
  every event, and we dont know which belong to
  the D0 !
• From each event we will have one right and many
  wrong invariant mass combinations.

signal
combinatoricbackground
Kp mass (GeV)
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Event Reconstruction

• Actual reality Not every event will contain a
• From some events we will have no right
  combinations.
• More background

signal
totalbackground
Kp mass (GeV)
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Here comes Heisenberg !

• Not all resonances (i.e. particles) have the
  same width

p-
p
r0
Kp mass (GeV)
pp mass (GeV)
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Here comes Heisenberg !

• Uncertainty Principle DEDt gt h

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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.
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A tiny bit of Math !
This bump is described by a something called
a Breit-Wigner lineshape
GR Width of resonance
Intensity( events)
MR Mass of resonance
mpp inv. mass of each event(independent
variable)
pp Invariant mass
We observe Intensity Amp2
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Complex Number Has both Magnitude and Phase
Mean Width areeasy to measure
Phase is hard to seesince amplitude is squared
to produce observable quantity.
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Think of an LRC circuit (looks very similar in
a mirror sort of way) This can help you visualize
what the Phase means
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Getting at the Underlying Physics
Mean Width areeasy to measure
Magnitude
Phase is hard to seesince amplitude is squared
to produce observable quantity.
Phase
pp Invariant mass
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How we can see phases interference
When there are two (or more) paths to the same
final state. Since we add the amplitudes
beforewe square to get intensity,
interferencebetween the amplitudes (caused
byphase differences) will show up whenwe make
measurements !!
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The same works thing with particles !!
p-
r0
p
p-
w0
p
Same initial final states, just different in
the middle) These two amplitudes can interfere !
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OKthats nice, but therehas to be a better way
to see these phases at work!!
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Finally there Three body decays !!
D0
M
Start with a fairly heavy(charmed) meson like D0
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Finally there Three body decays !!
p0
mc
M
K-
ma
p
mb
Study cases in which it decays into three
daughters (for example K- p p0)
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p0
mc
There are now several invariant masses we can
calculate
(Ec,Pc)
D0
M
(Ea,Pa)
K-
(Eb,Pb)
ma
p
M2 (EaEbEc)2 - (PaPbPc)2 Boringwe
already know its a D0.
mb
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Dalitz Plot
b
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Figuring out the Physics
mx2
mbc2
mab2
This is like ridge with a Breit-Wigner shape
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mbc2
my2
mab2
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mz2
mbc2
mab2
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Interference Between Intermediate States
mbc2
mbc2
Addition Movie
mab2
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More Phases are Possible (more physics)
mbc2
eif
mbc2
Phase Movie
mab2
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More Physics
mx2
mbc2
mab2
Now suppose X is a vector resonance (L1)We can
measure the L of the intermediate state !
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Looking at real data
Seven resonances are needed to represent the data
D0 ? K- p p0