Quantum Mechanical Interference in Charmed Meson Decays

Physics Society Talk (Sept/20/00): Pg 1

Quantum Mechanical InterferenceQuantum Mechanical Interferencein Charmed Meson Decaysin Charmed Meson Decays

TOO BORING


Everything you Need to KnowEverything you Need to KnowAbout Three Body InteractionsAbout Three Body Interactions

I’ll get arrested


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


Tevatron (1000 GeV)FermilabFermilab


At the “Interaction Point”At the “Interaction Point”

Beam particles collide

e e

c t = 0

e

e

q

q

c



Hardonization

c t ~ 10-23 sec

QCD

c



Hardonization

c t ~ 10-23 sec

QCD

c = (ud)

= (ud)

= (ud)

D*+= (cd)

D0= (cu)



t ~ 10-23 sec

D*+

Mesons leave the scene of the crime

D0 10-15 m



Mesons start to decay strongly

D*+

t ~ 10-20 sec

D0

10-11 mD0



Weakly decaying mesons are next

10-4 m

t ~ 10-12 sec

K

K

D0

D0


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


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!)



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 2

K mass (GeV)

m(D0)=1.86 GeV

detectorresolution

K

D0



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



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



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


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


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


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.


A tiny bit of Math !A tiny bit of Math !

Invariant mass

This bump is described by a something called a

Breit-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


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.


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:

Ci

LiRLRC

1

Amp


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:


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 !!


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 !!

+ -+

-

-

+


OK…that’s nice, but therehas to be a better way to see these phases at work!!


Finally there: Three body decays !!Finally there: Three body decays !!

M

Start with a fairly heavy(charmed) meson like D0

D0


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


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)


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

c

a at rest

b

a

c at rest

ba

c


Figuring out the PhysicsFiguring out the Physics

mab2

mbc2

mx2

mb

mc

ma

M

mx

This is like ridge with a Breit-Wigner shape


mab2

mbc2 m

b

mc

ma

Mm

ymy2


mab2

mbc2

mz2

mb

mc

ma

M

mz


Interference Between Intermediate StatesInterference Between Intermediate States

mab2

mbc2

Addition Movie

mbc2

+ + + + + + + +

- - - - - -

+ +

+ +

+ +

+

- -

- -

- - Phases


More Phases are Possible (more physics)More Phases are Possible (more physics)

mab2

mbc2

mbc2

+ + + + + + + +

- - - - - -

+ +

+ +

+ +

+

- -

- -

- - Phases

Phase Movie

ei


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 !


Looking at real data:Looking at real data:

D0 K- Seven resonances are needed

to represent the data

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Quantum Mechanical Interference in Charmed Meson Decays