פרקים נבחרים בפיסיקת החלקיקים

1. פרקים נבחרים בפיסיקת החלקיקים אבנר סופר אביב 2007 5

2. Introduction to mixing and the recent evidence for D0-D0bar mixing from BaBar • Flavor eigenstates D0 = D0 = • Note: opposite convention for down-type heavy quark states: B0 = B0 = • They are not necessarily the mass eigenstates, due to the diagrams Short-distance effects Long-distance effects (Dominate for K, B mixing) (expected to dominate for D0) c u c u d b d b

3. Schrödinger's equation: Mass eigenstates: Mass eigenstates Mass matrix Off-diagonal mass matrix elements

4. Time evolution of flavor eigenstates • Time evolution can only be written in terms of the mass eigenstates (which diagonalize the mass matrix). So invert • A state that at time t=0 is a D0 (bar) has the time evolution • where (eigenvalues of the mass matrix)

5. Time-dependent mixing probabilities • The right state for the right job: • Time evolution – mass eigenstates • Detection experiments – flavor eigenstates (typically) • From (last page): • Obtain the probability amplitude to start at time 0 with a flavor eigenstate and obtain the same (or the opposite) state at time t:

6. Understanding g(t) Over time, a D0 can mix into a D0bar and vice versa

7. Approximating g(t) Different cases: • Bs-Bs mixing: x large y significant • Bd-Bd mixing: x significant y small • D0-D0 mixing: x and y small, expand g(t) to leading order: Go back 2 slides to understand what it means for the mixing rates

8. d s u u c c d s p+ K+ u u u u p- D0 D0 K- How to observe mixing • Detecting flavor: • So expect to identify the flavors in the time-evolved state using, e.g. • Except that there is also a doubly Cabibbo suppressed (DCS) decay: So in reality:

9. Mixing + direct decay small So now: small Use leading order expressions

10. What we’re looking for • Need to determine from the data: • G=1/t • r(t-t’) • x’2, y’ • Note that t is the proper time (in the D rest frame). • Since the D is moving, need to calculate t = d/gbc,where d = the flight distance from the D production point to itsdecay point Detectorresolution function

11. The analysis strategy • Use D*+D0p+ decays to identify initial D0 flavor (at time 0) • Right sign (RS) D0K-p+ decays determine: • Average lifetime t = 1/G • signal PDF resolution parameters r(t – t’) • In wrong-sign (WS) D0K+p- sample: • Use proper time distribution to distinguish between DCS and mixing • Use m(Kp), Dm = m(D*) – m(D) distribution to separate background from signal RS signal:

12. y beam spot interaction point x Reconstruction & cuts • Require particle ID for K, p • D momentum > 2.5 GeV • Vertex probability > 0.1% • –2 < t < 4 ps • dt < 0.5 ps • Cut on m(Kp) and Dm RS signal dt distribution

13. Signal and background kinematic behavior

14. Simultaneous RS+WS kinematic fit RS signal: 1,141,500±1200 combinations WS signal: 4030±90 combinations

15. Right-sign sample proper-time fit Gives resolution function r(t, t’)and D lifetime t, which is consistent with world average Fit quality per bin: Pull = (data – fit) / error

16. data – no mixing fit: mixing fit – no mixing fit: Wrong-sign sample proper-time fit

17. best fit best fit, x’2 ¸ 0 X (0,0) > How significant is the mixing? • 1-s contours

18. Significance of individual flavors x'2– = -0.020+-0.041% y’– = 0.963+0.614% x'2+ = -0.024+-0.043% y'+ = 0.982+0.637%

19. Cross-check: fit Monte Carlo x’2 = (2.0  18)x10-5 y’ = (-2.2  3.0)x10-3

20. Cross-check: fit RS data

21. What does it mean? • Maturity of a test of the SM – new physics can enter in the box diagram • Compare to other particles: • t(KL) ~ 5  10-8 s, t(KS) ~ 10-10 s. y ~ 1 • B0-B0: x = 0.78, expected y ~ 0.004 • Bs-Bs: x = 26, expected y ~ 0.1 • 4-s evidence for D-Dbar mixing • x’2 and y’ ~ at SM expectation • No evidence for CP violation

22. BaBar 2 BaBar 3 Comparing with other experiments BaBar 1 statistical contours from BaBar and Belle (400 fb-1) best fit results are within 2(statistical) (0,0) Belle 2 statistical

23. History of discoveries Pdg.lbl.gov

24. More history