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Quantum Mechanical Interference in Charmed Meson Decays TOO BORING Physics Society Talk (Sept/20/00): Pg 1 Everything you Need to Know About Three Body Interactions I’ll get arrested Physics Society Talk (Sept/20/00): Pg 2 Since Relativity is Cool and Quantum Mechanics is Cool we conclude that Relativity + Quantum Mechanics must be VERY Cool Physics Society Talk (Sept/20/00): Pg 3 Fermilab Tevatron (1000 GeV) Physics Society Talk (Sept/20/00): Pg 4 At the “Interaction Point” Beam particles collide e+ ec ec g q q e+ t=0 Physics Society Talk (Sept/20/00): Pg 5 At the “Interaction Point” Hardonization QCD c c t ~ 10-23 sec Physics Society Talk (Sept/20/00): Pg 6 At the “Interaction Point” Hardonization p+= (ud) D*+= (cd) QCD c p-= (ud) c p- = (ud) t ~ 10-23 sec D0= (cu) Physics Society Talk (Sept/20/00): Pg 7 At the “Interaction Point” Mesons leave the scene of the crime p+ D*+ pp- t ~ 10-23 sec D0 10-15 m Physics Society Talk (Sept/20/00): Pg 8 At the “Interaction Point” Mesons start to decay strongly p+ p+ D0 D*+ pt ~ 10-20 sec p- D0 10-11 m Physics Society Talk (Sept/20/00): Pg 9 At the “Interaction Point” Weakly decaying mesons are next p+ p + D0 p0 p- p+ Kg g t ~ 10-12 sec pp- D0 10-4 m K+ Physics Society Talk (Sept/20/00): Pg 10 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+ Kpg p- g pK+ t ~ 10-8 sec 100 m Physics Society Talk (Sept/20/00): Pg 11 Event Reconstruction Suppose we are looking for D 0 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 know the energy and momentum of each particle. E 2 P 2 + m2 m EK + Ep 2 2 2 - p K + pp K- p+ The mass does not depend on which reference frame I use !!! (special relativity is cool!) D0 Physics Society Talk (Sept/20/00): Pg 12 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+ detector resolution D0 1.7 1.8 1.9 2 Kp mass (GeV) Physics Society Talk (Sept/20/00): Pg 13 Event Reconstruction 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. good guesses bad guesses D0 1.7 1.8 1.9 2 Kp mass (GeV) Physics Society Talk (Sept/20/00): Pg 14 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 1.7 1.8 1.9 2 Kp mass (GeV) Physics Society Talk (Sept/20/00): Pg 15 Event Reconstruction Actual reality: Not every event will contain a D 0 K- p+ From some events we will have no right combinations. More “background” signal total background 1.7 1.8 1.9 2 Kp mass (GeV) Physics Society Talk (Sept/20/00): Pg 16 Here comes Heisenberg ! Not all “resonances” (i.e. particles) have the same “width” K- p+ p- p+ r0 D0 1.7 1.8 1.9 Kp mass (GeV) 2 0.6 0.7 0.8 2 pp mass (GeV) Physics Society Talk (Sept/20/00): Pg 17 Here comes Heisenberg ! Uncertainty Principle: DEDt > h So if Dt is small (short lifetime) then DE is big (large mass uncertainty) 0.6 0.7 0.8 pp mass (GeV) 2 The DE of the D0 is really much smaller than our measurement errors 1.7 1.8 1.9 2 Kp mass (GeV) Physics Society Talk (Sept/20/00): Pg 18 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. 0.6 0.7 0.8 2 Physics Society Talk (Sept/20/00): Pg 19 A tiny bit of Math ! This bump is described by a something called a Breit-Wigner lineshape: Amp B -W 1 M R2 - mpp2 - iM R R R = Width of resonance MR = Mass of resonance Intensity (# events) mpp = inv. mass of each “event” (independent variable) pp Invariant mass We observe Intensity = |Amp|2 Physics Society Talk (Sept/20/00): Pg 20 Amp B -W 1 2 M R2 - mpp - iM R R Complex Number: Has both Magnitude and Phase mpp = MR Mean & Width are easy to measure Magnitude Phase is hard to see since amplitude is squared to produce observable quantity. Phase pp Invariant mass Physics Society Talk (Sept/20/00): Pg 21 Think of an LRC circuit (looks very similar in a mirror sort of way) This can help you visualize what the “Phase” means: 1 1 Amp LRC Amp B -W 2 2 i M R - mpp - iM R R R + iL C Physics Society Talk (Sept/20/00): Pg 22 Getting at the Underlying Physics: Mean & Width are easy to measure Magnitude Phase is hard to see since amplitude is squared to produce observable quantity. Phase pp Invariant mass Physics Society Talk (Sept/20/00): Pg 23 How we can see phases: interference When there are two (or more) “paths” to the same final state. 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 !! Physics Society Talk (Sept/20/00): Pg 24 The same works thing with particles !! pr0 p+ - + + + - - p0 p+ Same initial & final states, just different in the middle) These two amplitudes can interfere ! Physics Society Talk (Sept/20/00): Pg 25 OK…that’s nice, but there has to be a better way to see these phases at work!! Physics Society Talk (Sept/20/00): Pg 26 Finally there: Three body decays !! D0 M Start with a fairly heavy (charmed) meson like D0 Physics Society Talk (Sept/20/00): Pg 27 Finally there: Three body decays !! p0 m c M K- m a Study cases in which it decays into three daughters (for example K- p+ p0) p+ mb Physics Society Talk (Sept/20/00): Pg 28 p0 m There are now several invariant masses we can calculate: D0 (Ea,Pa) K- (Ec,Pc) c M (Eb,Pb) m a M2 = (Ea+Eb+Ec)2 - (Pa+Pb+Pc)2 mab2 = (Ea+Eb)2 - (Pa+Pb)2 mbc2 = (Eb+Ec)2 - (Pb+Pc)2 mac2 = (Ea+Ec)2 - (Pa+Pc)2 Boring…we already know it’s a D0. p+ mb These are very useful Physics Society Talk (Sept/20/00): Pg 29 Dalitz Plot c mc a at rest M b mbc2 b ma b a All events end up uniformly distributed in this enclosed area. Unless there is additional physics. c b b at rest a mb c at rest mab2 a mab2 , mbc2 and mac2 are simply related: mab2 + mbc2 + mac2 = constant = M2 + ma2 + mb2 + ma2 Only two are independent Physics Society Talk (Sept/20/00): Pg 30 Figuring out the Physics mx2 mc M mbc2 ma mx mb mab2 This is like ridge with a Breit-Wigner shape Physics Society Talk (Sept/20/00): Pg 31 ma mbc2 my2 M mc my mb mab2 Physics Society Talk (Sept/20/00): Pg 32 m z2 mc ma mz M mbc2 mb mab2 Physics Society Talk (Sept/20/00): Pg 33 mbc2 ------ mbc2 +++++++ Interference Between Intermediate States Phases -----++++++++ Addition Movie mab2 Physics Society Talk (Sept/20/00): Pg 34 mbc2 ------ mbc2 +++++++ More Phases are Possible (more physics) -----++++++++ Phases eif Phase Movie mab2 Physics Society Talk (Sept/20/00): Pg 35 More Physics mx2 mc M mbc2 ma mx mb mab2 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 36 Looking at real data: D0 K- p+ p0 Seven resonances are needed to represent the data Physics Society Talk (Sept/20/00): Pg 37