Alexey A. Petrov Wayne State University

1. Mixing and CP violation in charm Alexey A. Petrov Wayne State University • Table of Contents: • Introduction • Mixing: current/future experimental constraints • Mixing: theoretical expectations • CP violation in charm • Conclusions and outlook Alexey Petrov(Wayne State Univ.)

2. Introduction Murphy’s law: Modern charm physics experiments acquire ample statistics; many decay rates are quite large. THUS: It is very difficult to provide model-independent theoretical description of charmed quark systems. Alexey Petrov(Wayne State Univ.) 27

3. Introduction: charm and New Physics Charm transitions serve as excellent probes of New Physics • Processes forbidden in the Standard Model to all orders (or very rare) Examples: • Processes forbidden in the Standard Model at tree level Examples: • Processes allowed in the Standard Model Examples: relations, valid in the SM, but not necessarily in general Alexey Petrov(Wayne State Univ.) 26

4. Introduction: mixing DQ=2: only at one loop in the Standard Model: possible new physics particles in the loop DQ=2 interactioncouples dynamics of D0and D0 • Time-dependence: coupled Schrödinger equations • Diagonalize: mass eigenstates flavor eigenstates Mass and lifetime differences of mass eigenstates: Alexey Petrov(Wayne State Univ.) 25

5. Introduction: mixing DQ=2: only at one loop in the Standard Model: possible new physics particles in the loop DQ=2 interactioncouples dynamics of D0and D0 • Time-dependence: coupled Schrödinger equations • Diagonalize: mass eigenstates flavor eigenstates Mass and lifetime differences of mass eigenstates: Alexey Petrov(Wayne State Univ.) 25

6. Introduction: why do we care? Falk, Grossman, Ligeti, and A.A.P. Phys.Rev. D65, 054034, 2002 2nd order effect!!! (*) up to matrix elements of 4-quark operators Alexey Petrov(Wayne State Univ.) 24

7. How would new physics affect mixing? • Look again at time development: • Expand mass matrix: Local operator, affects x, possible new phsyics Real intermediate states, affect both x and y Standard Model • : signal for New Physics? • : Standard Model? • 2. CP violation in mixing/decay With b-quark contribution neglected: only 2 generations contribute real 2x2 Cabibbo matrix new CP-violating phase f Alexey Petrov(Wayne State Univ.) 23

8. How would CP violation manifest itself in charm? • Possible sources of CP violation in charm transitions: • CPV indecay amplitudes(“direct” CPV) • CPV inmixing matrix • CPV in theinterference of decays with and without mixing Alexey Petrov(Wayne State Univ.) 22

9. Experimental constraints on mixing Idea: look for a wrong-sign final state • Time-dependent or time-integrated semileptonic analysis • Time-dependent analysis (lifetime difference) • Time-dependent analysis Quadratic in x,y: not so sensitive Sensitive to DCS/CF strong phase d Alexey Petrov(Wayne State Univ.) 21

10. Example: experimental constraints on yCP Several groups have measured yCP World average: yCP = (0.9 ± 0.4)% B. Yabsley a. What if time-dependent studies are not possible? b. What are the expectations for x and y? Alexey Petrov(Wayne State Univ.) 20

11. What if time-dependent studies are not possible I? t-charm factory (CLEO-c) Time-integrated analysis: DCSD contribution cancels out for double-tagged decays! f1 f3 f2 f4 CF DCS Quadratic in x,y: not so sensitive wanted: linear in x or y H. Yamamoto; I. Bigi, A. Sanda Alexey Petrov(Wayne State Univ.) 19

12. What if time-dependent studies are not possible II? t-charm factory (CLEO-c) • If CP violation is neglected mass eigenstates = CP eigenstates • CP eigenstates do NOT evolve with time, so can be used for “tagging” f1 KS f2 CP Eigenstate (-) p0 (-) • CLEO-c has good CP-tagging capabilities CP anti-correlatedy(3770): CP(tag) (-1)L = [CP(KS) CP(p0)] (-1) = +1 CP correlatedy(4140) Can still measure y: D. Atwood, A.A.P., hep-ph/0207165 Alexey Petrov(Wayne State Univ.) 18

13. Mixing: theoretical estimates Updated predictions A.A.P. hep-ph/0311371 • Theoretical predictions are all over the board… so: • Can x,y ~ 1% be convincingly accommodated? • What is the relationship between x and y (x ~ y, x > y, x < y?) in the Standard Model? •x from new physics y from Standard Model Δx from Standard Model (papers from SPIRES ) Alexey Petrov(Wayne State Univ.) 17

14. Theoretical estimates I mc IS large !!! A. Short distance gives a tiny contribution, consider y as an example … as can be seen form the straightforward computation… 4 unknown matrix elements with similar for x (trust me!) Alexey Petrov(Wayne State Univ.) 16

15. Theoretical estimates I A. Short distance + “subleading corrections” (in 1/mc expansion): 4 unknown matrix elements …subleading effects? 15 unknown matrix elements H. Georgi, … I. Bigi, N. Uraltsev Twenty-something unknown matrix elements Guestimate: x ~ y ~ 10-3 ? Leading contribution!!! Alexey Petrov(Wayne State Univ.) 15

16. Resume:model-independent computation with model-dependent result Alexey Petrov(Wayne State Univ.) 14

17. Theoretical estimates II mc is NOT large !!! B. Long distance physics dominates the dynamics… … with n being all states to which D0 and D0 can decay. Considerpp, pK, KKintermediate states as an example… J. Donoghue et. al. P. Colangelo et. al. cancellation expected! If every Br is known up to O(1%) the result is expected to be O(1%)! The result here is a series of large numbers with alternating signs, SU(3) forces 0 Need to “repackage” the analysis: look at the complete multiplet contribution x = ? Extremely hard… Alexey Petrov(Wayne State Univ.) 13

18. Resume:model-dependent computation with model-dependent result Alexey Petrov(Wayne State Univ.) 12

19. Theoretical expectations • Let’s compute both x and y. Consider the correlator A. Falk., Y. Grossman, Z. Ligeti, Y. Nir and A.A.P., hep-ph/0402204 • SpD(q)is an analytic function of q. To write a disp. relation, go to to HQET: Now we can interpret SpD(q)for all q Alexey Petrov(Wayne State Univ.) 11

20. Theoretical expectations Rapidly oscillates for large mc • …this implies for the correlator • HQmass dependence drops out for the second term, so forSv(q) = SpD(q)/mD mass and width difference of a heavy meson with mass E • Thus, a dispersion relation Compute DG, then find Dm! Alexey Petrov(Wayne State Univ.) 10

21. Results: DG From each multiplet: Product is naturally O(1%) No (symmetry-enforced) cancellations A.F., Y.G., Z.L., and A.A.P. Phys.Rev. D65, 054034, 2002 Naturally implies that y ~ 1%! What about x? Alexey Petrov(Wayne State Univ.) 9

22. Results: Dm/DG=x/y: • Also: • Assume 2-parameter model for • Compute rF for 4-body and 2-body intermediate multiplets • Model dependence remains… A. Falk., Y. Grossman, Z. Ligeti, Y. Nir and A.A.P., hep-ph/0402204 Computation naturally implies that y ~ x ~ 1%! Alexey Petrov(Wayne State Univ.) 8

23. A bit more about CP violation in charm Alexey Petrov(Wayne State Univ.) 7

24. CP violation: experimental constraints 1. Standard analysis: rate asymmetries … which is of the first order in CPV parameters, but requires tagging • 2. Recall that CP of the states in are anti-correlated aty(3770): • a simple signal of CP violation: … which is of the second order in CPV parameters, i.e. tiny Alexey Petrov(Wayne State Univ.) 6

25. CP violation: new experimental possibilities 1 • Time dependent (lifetime difference analysis): • separate datasets for D0 and D0 This analysis requires 1. time-dependent studies 2. initial flavor tagging (“the D* trick”) Cuts statistics/sensitivity Alexey Petrov(Wayne State Univ.) 5

26. CP violation: new experimental possibilities 2 2. Look for CPV signals that are 1. first order in CPV 2. do not require flavor tagging Consider the final states that can be reached by both D0 and D0, but are not CP eigenstates (pr, KK*, Kp, Kr, …) where A.A.P., PRD69, 111901(R), 2004 hep-ph/0403030 Alexey Petrov(Wayne State Univ.) 4

27. CP violation: untagged asymmetries Expect time-dependent asymmetry… … and time-integrated asymmetry … whose coefficients are computed to be This is true for any final state f Alexey Petrov(Wayne State Univ.) 3

28. CP violation: untagged asymmetries(K+p-) For a particular final state Kp, the time-integrated asymmetry is simple This asymmetry is 1. non-zero due to large SU(3) breaking 2. contains no model-dependent hadronicparameters (R anddare experimental observables) 3. could be as large as 0.04% for NP Note: larger by O(100) for SCS decays (pr, …) where R ~ 1 A.A.P., PRD69, 111901(R), 2004 hep-ph/0403030 Alexey Petrov(Wayne State Univ.) 2

29. Conclusions • Charm provides great opportunities for New Physics studies • large available statistics • mixing: x, y = 0 in the SU(3) limit (as V*cbVub is very small) • mixing is a second order effect in SU(3) breaking • it is quite possible that y~ x ~ 1% in the Standard Model • Expect new data from BaBar/Belle/CLEO-c/CDF • Quantum coherence will allow CLEO-c/BES to perform new measurements of strong phases in charm mixing studies • important inputs to time-dependent studies of mixing • Quantum coherence will allow CLEO-c to perform new studies of mixing • no DCSD contamination in double-tag Kp studies • new mixing measurements unique to CLEO-c • Observation of CP-violation or FCNC transitions in the current round of experiments provide “smoking gun” signals for New Physics - untagged asymmetries are more sensitive to CPV Alexey Petrov(Wayne State Univ.) 1

30. Additional slides Alexey Petrov(Wayne State Univ.) 0

31. Questions:1. Can any model-independent statements be made for x or y ?2. Can one claim that y ~ 1% is natural? What is the order of SU(3) breaking? i.e. if what is n? Alexey Petrov(Wayne State Univ.) -1

32. Theoretical expectations At which order in SU(3)F breaking does the effect occur? Group theory? is a singlet with that belongs to 3 of SU(3)F (one light quark) The DC=1 part of HW is Introduce SU(3) breaking via the quark mass operator All nonzero matrix elements built of must be SU(3) singlets Alexey Petrov(Wayne State Univ.) -2

33. Theoretical expectations note that DiDj is symmetric belongs to 6 of SU(3)F Explicitly, 1. No in the decomposition of no SU(3) singlet can be formed D mixing is prohibited by SU(3) symmetry 2. Consider a single insertion of transforms as still no SU(3) singlet can be formed NO D mixing at first order in SU(3) breaking 3. Consider double insertion of D mixing occurs only at the second order in SU(3) breaking A.F., Y.G., Z.L., and A.A.P. Phys.Rev. D65, 054034, 2002 Alexey Petrov(Wayne State Univ.) -3

34. Example: PP intermediate states • n=PP transforms as , take 8 as an example: Numerator: Denominator: phase space function • This gives a calculable effect! • Repeat for other states • Multiply by BrFr to get y Alexey Petrov(Wayne State Univ.) -4

35. DG: SU(3) and phase space • “Repackage” the analysis: look at the complete multiplet contribution y for each SU(3) multiplet Each is 0 in SU(3) • Does it help? If only phase space is taken into account: no(mild) model dependence if CP is conserved A.F., Y.G., Z.L., and A.A.P. Phys.Rev. D65, 054034, 2002 Can consistently compute Alexey Petrov(Wayne State Univ.) -5

36. Quantum coherence: supporting measurements Time-dependent analysis where and Strong phase d is zero in the SU(3) limit and strongly model-dependent A. Falk, Y. Nir and A.A.P., JHEP 12 (1999) 019 Strong phase can be measured at CLEO-c! With 3 fb-1 of data cos d can be determined to |D cos d| < 0.05! Silva, Soffer; Gronau, Grossman, Rosner Alexey Petrov(Wayne State Univ.)