1. Physics Society Talk (Sept/20/00): Pg 1 Quantum Mechanical Interference in Charmed Meson Decays TOO BORING

2. Physics Society Talk (Sept/20/00): Pg 2 Everything you Need to Know About Three Body Interactions I’ll get arrested

3. 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 Cool

4. Physics Society Talk (Sept/20/00): Pg 4 Tevatron (1000 GeV) Fermilab

5. Physics Society Talk (Sept/20/00): Pg 5 At the “Interaction Point” l Beam particles collide ee ee c t = 0  ee ee q q c

6. Physics Society Talk (Sept/20/00): Pg 6 At the “Interaction Point” l Hardonization c t ~ 10 -23 sec QCD c

7. Physics Society Talk (Sept/20/00): Pg 7 At the “Interaction Point” l Hardonization c t ~ 10 -23 sec QCD c   = (ud)   = (ud)   = (ud) D* + = (cd) D 0 = (cu)

8. Physics Society Talk (Sept/20/00): Pg 8 At the “Interaction Point” t ~ 10 -23 sec    D* + l Mesons leave the scene of the crime D0D0 10 -15 m

9. Physics Society Talk (Sept/20/00): Pg 9 At the “Interaction Point” l Mesons start to decay strongly D* +    t ~ 10 -20 sec D0D0  10 -11 m D0D0

10. Physics Society Talk (Sept/20/00): Pg 10 At the “Interaction Point” l Weakly decaying mesons are next   10 -4 m t ~ 10 -12 sec    KK KK     D0D0 D0D0

11. Physics Society Talk (Sept/20/00): Pg 11 What we need to detect l Finally we are left with the particles that live long enough to be detected. l In this case ç8 charged ç2 neutral   10 0 m t ~ 10 -8 sec    KK KK   

12. Physics Society Talk (Sept/20/00): Pg 12 Event Reconstruction  KK l If every event has exactly one of these decays and nothing else, and suppose we know which track is the K. KK l Suppose we are looking for D0D0 We can calculate the Lorenz invariant mass of the K  pair if we know the energy and momentum of each particle. The mass does not depend on which reference frame I use !!! (special relativity is cool!)

13. Physics Society Talk (Sept/20/00): Pg 13 Event Reconstruction l If we plot the invariant mass for a large number of such events in a histogram we measure the mass of the D 0 : 1.71.81.92 K  mass (GeV) m(D 0 )=1.86 GeV detector resolution  KK D0D0

14. Physics Society Talk (Sept/20/00): Pg 14 Event Reconstruction l Some reality: l Some reality: We usually don’t know which track is the K so we have to try both possible combinations. çFrom each event we will have one right and one wrong invariant mass combination. K  mass (GeV) 1.71.81.92 good guesses bad guesses D0D0

15. Physics Society Talk (Sept/20/00): Pg 15 Event Reconstruction l More reality: l More reality: There are many other tracks in every event, and we don’t know which belong to the D 0 ! çFrom each event we will have one right and many wrong invariant mass combinations. K  mass (GeV) “combinatoric” background signal 1.71.81.92

16. Physics Society Talk (Sept/20/00): Pg 16 Event Reconstruction l Actual reality: l Actual reality: Not every event will contain a çFrom some events we will have no right combinations. çMore “background” K  mass (GeV) 1.71.81.92 total background signal K   

17. Physics Society Talk (Sept/20/00): Pg 17 Here comes Heisenberg ! l Not all “resonances” (i.e. particles) have the same “width” 1.71.81.9 2 K  mass (GeV)  KK D0D0 0.60.70.8 2  mass (GeV)   00

18. Physics Society Talk (Sept/20/00): Pg 18 Here comes Heisenberg ! Uncertainty Principle:  E  t > h 0.60.70.8 2  mass (GeV) So if  t is small (short lifetime) then  E is big (large mass uncertainty) 1.71.81.9 2 K  mass (GeV) The  E of the D 0 is really much smaller than our measurement errors

19. Physics Society Talk (Sept/20/00): Pg 19 What we can measure: 0.60.70.8 2  invariant mass (GeV) With this kind of experimental data, we can measure the mass and width of a particle resonance.

20. Physics Society Talk (Sept/20/00): Pg 20 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 M R = Mass of resonance m  = inv. mass of each “event” (independent variable)  R = Width of resonance

21. Physics Society Talk (Sept/20/00): Pg 21 Complex Number: Has both Magnitude and Phase m  = M R  Invariant mass Phase Magnitude Mean & Width are easy to measure Phase is hard to see since amplitude is squared to produce observable quantity.

22. Physics Society Talk (Sept/20/00): Pg 22 Think of an LRC circuit Think of an LRC circuit (looks very similar in a mirror sort of way) This can help you visualize what the “Phase” means:

23. Physics Society Talk (Sept/20/00): Pg 23  Invariant mass Phase Magnitude Mean & Width are easy to measure Phase is hard to see since amplitude is squared to produce observable quantity. Getting at the Underlying Physics:

24. Physics Society Talk (Sept/20/00): Pg 24 How we can see phases: interference When there are two (or more) “paths” to the same final state. before 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 !!

25. 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 !!       + - + - - +

26. Physics Society Talk (Sept/20/00): Pg 26 OK…that’s nice, but there has to be a better way to see these phases at work!!

27. Physics Society Talk (Sept/20/00): Pg 27 Finally there: Three body decays !! M Start with a fairly heavy (charmed) meson like D 0 D0D0

28. Physics Society Talk (Sept/20/00): Pg 28 Finally there: Three body decays !! mbmb mcmc mama Study cases in which it decays into three daughters (for example K      ) KK   M

29. Physics Society Talk (Sept/20/00): Pg 29 mbmb mcmc mama There are now several invariant masses we can calculate: KK   D0D0 M M 2 = (E a +E b +E c ) 2 - (P a +P b +P c ) 2 Boring…we already know it’s a D 0. PP m ab 2 = (E a +E b ) 2 - (P a +P b ) 2 PP m bc 2 = (E b +E c ) 2 - (P b +P c ) 2 These are very useful PP m ac 2 = (E a +E c ) 2 - (P a +P c ) 2 P (E a,P a ) P (E b,P b ) P (E c,P c )

30. Physics Society Talk (Sept/20/00): Pg 30 mbmb mcmc mama M Dalitz Plot m ab 2 m bc 2 All events end up uniformly Unless there is additional physics. distributed in this enclosed area. Unless there is additional physics. m ab 2, m bc 2 and m ac 2 are simply related: m ab 2 + m bc 2 + m ac 2 = constant = M 2 + m a 2 + m b 2 + m a 2 Only two are independent b b a b at rest c a at rest b a c at rest b a c

31. Physics Society Talk (Sept/20/00): Pg 31 Figuring out the Physics m ab 2 m bc 2 mx2mx2 mbmb mcmc mama M mxmx This is like ridge with a Breit-Wigner shape

32. Physics Society Talk (Sept/20/00): Pg 32 m ab 2 m bc 2 mbmb mcmc mama M mymy my2my2

33. Physics Society Talk (Sept/20/00): Pg 33 m ab 2 m bc 2 mz2mz2 mbmb mcmc mama M mzmz

34. Physics Society Talk (Sept/20/00): Pg 34 Interference Between Intermediate States m ab 2 m bc 2 Addition Movie m bc 2 + + + + - - - + + + + + + + - - - Phases

35. Physics Society Talk (Sept/20/00): Pg 35 More Phases are Possible (more physics) m ab 2 m bc 2 + + + + - - - + + + + + + + - - - Phases Phase Movie eiei

36. Physics Society Talk (Sept/20/00): Pg 36 More Physics m ab 2 m bc 2 mx2mx2 mbmb mcmc mama M mxmx Now suppose X is a vector resonance (L=1) We can measure the L of the intermediate state !

37. Physics Society Talk (Sept/20/00): Pg 37 Looking at real data: D 0  K -     Seven resonances are needed to represent the data