Quantum Mechanical Interference in Charmed Meson Decays

1. TOO BORING Quantum Mechanical Interferencein Charmed Meson Decays

2. I’ll get arrested Everything you Need to KnowAbout Three Body Interactions

3. Since Relativity is Cooland Quantum Mechanics is Coolwe conclude thatRelativity + Quantum Mechanicsmust be VERY Cool

4. Fermilab Tevatron (1000 GeV)

5. q e+ g e- q At the “Interaction Point” • Beam particles collide c e+ e- c t = 0

6. QCD At the “Interaction Point” • Hardonization c t ~ 10-23 sec c

7. QCD At the “Interaction Point” • Hardonization p+= (ud) D*+= (cd) c p- = (ud) p-= (ud) t ~ 10-23 sec c D0= (cu)

8. D0 At the “Interaction Point” • Mesons leave the scene of the crime p+ D*+ p- p- t ~ 10-23 sec 10-15 m

9. D0 At the “Interaction Point” p+ • Mesons start to decay strongly p+ D0 D*+ p- t ~ 10-20 sec p- 10-11 m

10. D0 At the “Interaction Point” p+ • Weakly decaying mesons are next K- D0 p+ g p+ p0 g p- t ~ 10-12 sec p- p- 10-4 m K+

11. 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+

12. Event Reconstruction • Suppose we are looking for 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 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

13. 1.7 1.8 1.9 2 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)

14. 1.7 1.8 1.9 2 Event Reconstruction • Some reality: We usually don’t know which track is the Kso 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)

15. 1.7 1.8 1.9 2 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 Kp mass (GeV)

16. K- p+ 1.7 1.8 1.9 2 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)

17. K- p+ D0 1.7 0.6 1.8 0.7 0.8 1.9 2 2 Here comes Heisenberg ! • Not all “resonances” (i.e. particles) have the same “width” p- p+ r0 Kp mass (GeV) pp mass (GeV)

18. So if Dt is small (short lifetime) then DE is big (large mass uncertainty) The DE of the D0 is really much smaller than our measurement errors 0.6 1.7 0.7 1.8 0.8 1.9 2 2 pp mass (GeV) Kp mass (GeV) Here comes Heisenberg ! Uncertainty Principle: DEDt > h

19. 0.6 0.7 0.8 2 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.

20. 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 = |Amp|2

21. mpp = MR Magnitude Phase pp Invariant mass Complex Number: Has both Magnitude and Phase Mean & Width areeasy to measure Phase is hard to seesince amplitude is squared to produce observable quantity.

22. Think of an LRC circuit(looks very similar in a mirror sort of way) This can help you visualize what the “Phase” means:

23. 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

24. 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 !!

25. - + - + - + 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 !

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

27. Finally there: Three body decays !! D0 M Start with a fairly heavy(charmed) meson like D0

28. 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)

29. mab2 = (Ea+Eb)2 - (Pa+Pb)2 mbc2 = (Eb+Ec)2 - (Pb+Pc)2These are very useful mac2 = (Ea+Ec)2 - (Pa+Pc)2 p0 mc There are now several invariant masses we can calculate: (Ec,Pc) D0 M (Ea,Pa) K- (Eb,Pb) ma p+ M2 = (Ea+Eb+Ec)2 - (Pa+Pb+Pc)2Boring…we already know it’s a D0. mb

30. c mc a at rest M All events end up uniformly distributed in this enclosed area. Unless there is additional physics. ma mbc2 mb b b at rest b b a mab2 a c at rest c a mab2 , mbc2 and mac2 are simply related: mab2 + mbc2 + mac2 = constant = M2 + ma2 + mb2 + ma2 Only two are independent Dalitz Plot b

31. mc M mx ma mb Figuring out the Physics mx2 mbc2 mab2 This is like ridge with a Breit-Wigner shape

32. mc M ma my mb mbc2 my2 mab2

33. mc M mz ma mb mz2 mbc2 mab2

34. Phases - - - - - - + + + + + + + - - - - - - + + + + + + + + Interference Between Intermediate States mbc2 mbc2 Addition Movie mab2

35. Phases - - - - - - + + + + + + + - - - - - - + + + + + + + + More Phases are Possible (more physics) mbc2 eif mbc2 Phase Movie mab2

36. mc M mx ma mb More Physics mx2 mbc2 mab2 Now suppose X is a vector resonance (L=1)We can measure the L of the intermediate state !

37. Looking at real data: Seven resonances are needed to represent the data D0 K-p+ p0