1. BEACH 2004, IIT, Chicago Alexey Petrov (Wayne State Univ.) 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 Mixing and CP violation in charm

2. BEACH 2004, IIT, Chicago Alexey Petrov (Wayne State Univ.) 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. Introduction 27

3. BEACH 2004, IIT, Chicago Alexey Petrov (Wayne State Univ.) Charm transitions serve as excellent probes of New Physics 1.Processes forbidden in the Standard Model to all orders (or very rare) Examples: 2.Processes forbidden in the Standard Model at tree level Examples: 3.Processes allowed in the Standard Model Examples: relations, valid in the SM, but not necessarily in general Introduction: charm and New Physics 26

4. BEACH 2004, IIT, Chicago Alexey Petrov (Wayne State Univ.) Introduction: mixing  Q=2: only at one loop in the Standard Model: possible new physics particles in the loop  Q=2 interaction couples dynamics of D 0 and D 0  Time-dependence: coupled Schrödinger equations  Diagonalize: mass eigenstates flavor eigenstates Mass and lifetime differences of mass eigenstates: 25

5. BEACH 2004, IIT, Chicago Alexey Petrov (Wayne State Univ.) Introduction: mixing  Q=2: only at one loop in the Standard Model: possible new physics particles in the loop  Q=2 interaction couples dynamics of D 0 and D 0  Time-dependence: coupled Schrödinger equations  Diagonalize: mass eigenstates flavor eigenstates Mass and lifetime differences of mass eigenstates: 25

6. BEACH 2004, IIT, Chicago Alexey Petrov (Wayne State Univ.) Introduction: why do we care? mixing intermediate down-type quarks SM: b-quark contribution is negligible due to V cd V ub * (zero in the SU(3) limit) intermediate up-type quarks SM: t-quark contribution is dominant (expected to be large) 1. Sensitive to long distance QCD 2. Small in the SM: New Physics! (must know SM x and y) 1. Computable in QCD (*) 2. Large in the SM: CKM! (*) up to matrix elements of 4-quark operators Falk, Grossman, Ligeti, and A.A.P. Phys.Rev. D65, 054034, 2002 2 nd order effect!!! 24

7. BEACH 2004, IIT, Chicago Alexey Petrov (Wayne State Univ.) How would new physics affect mixing? Real intermediate states, affect both x and y Standard Model 1. : 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  Look again at time development :  Expand mass matrix: Local operator, affects x, possible new phsyics new CP-violating phase  23

8. BEACH 2004, IIT, Chicago Alexey Petrov (Wayne State Univ.) How would CP violation manifest itself in charm?  Possible sources of CP violation in charm transitions :  CPV in decay amplitudes (“direct” CPV)  CPV in mixing matrix  CPV in the interference of decays with and without mixing 22

9. BEACH 2004, IIT, Chicago Alexey Petrov (Wayne State Univ.) Experimental constraints on mixing 1.Time-dependent or time-integrated semileptonic analysis 2.Time-dependent analysis (lifetime difference) 3.Time-dependent analysis Quadratic in x,y: not so sensitive Sensitive to DCS/CF strong phase  Idea: look for a wrong-sign final state 21

10. BEACH 2004, IIT, Chicago Alexey Petrov (Wayne State Univ.) Example: experimental constraints on y CP Several groups have measured y CP Experiment Value, % FOCUS (2000) 3.4 ± 1.4 ± 0.7 E791(2001) 0.8 ± 2.9 ± 1.0 CLEO (2002) -1.2 ± 2.5 ± 1.4 Belle (2002) -0.5 ± 1.0 ± 0.8 BaBar (2003) 0. 2± 0.5. Belle (2003) 1.2 ± 0.7 ± 0.4 BaBar (2003, K + K - ) 1.2 ± 0.7 ± 0.4 BaBar (2003,  +  - ) 1.7 ± 1.2. World average: y CP = (0.9 ± 0.4)% a. What if time-dependent studies are not possible? b. What are the expectations for x and y? B. Yabsley 20

11. BEACH 2004, IIT, Chicago Alexey Petrov (Wayne State Univ.) What if time-dependent studies are not possible I? f3f3 f1f1 f2f2  -charm factory (CLEO-c) f4f4 Time-integrated analysis: DCSD contribution cancels out for double-tagged decays! CFDCS Quadratic in x,y: not so sensitive wanted: linear in x or y H. Yamamoto; I. Bigi, A. Sanda 19

12. BEACH 2004, IIT, Chicago Alexey Petrov (Wayne State Univ.) What if time-dependent studies are not possible II?  If CP violation is neglected mass eigenstates = CP eigenstates  CP eigenstates do NOT evolve with time, so can be used for “tagging” KSKS 00 CP Eigenstate (-) f1f1 f2f2  CLEO-c has good CP-tagging capabilities CP anti-correlated  (3770): CP(tag) (-1) L = [CP(K S ) CP(  0 )] (-1) = +1 CP correlated  (4140) (-)  -charm factory (CLEO-c) Can still measure y: D. Atwood, A.A.P., hep-ph/0207165 18

13. BEACH 2004, IIT, Chicago Alexey Petrov (Wayne State Univ.) Mixing: theoretical estimates  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 Δ x from Standard Model (papers from SPIRES ) Updated predictions A.A.P. hep-ph/0311371 17

14. BEACH 2004, IIT, Chicago Alexey Petrov (Wayne State Univ.) Theoretical estimates I A. Short distance gives a tiny contribution, consider y as an example … as can be seen form the straightforward computation… with 4 unknown matrix elements similar for x (trust me!) m c IS large !!! 16

15. BEACH 2004, IIT, Chicago Alexey Petrov (Wayne State Univ.) Theoretical estimates I A. Short distance + “subleading corrections” (in 1/m c expansion): …subleading effects? 4 unknown matrix elements 15 unknown matrix elements Twenty-something unknown matrix elements Guestimate: x ~ y ~ 10 -3 ? Leading contribution!!! H. Georgi, … I. Bigi, N. Uraltsev 15

16. BEACH 2004, IIT, Chicago Alexey Petrov (Wayne State Univ.) Resume: model-independent computation with model-dependent result 14

17. BEACH 2004, IIT, Chicago Alexey Petrov (Wayne State Univ.) Theoretical estimates II B. Long distance physics dominates the dynamics… If every Br is known up to O(1%) the result is expected to be O(1%)! m c is NOT large !!! … with n being all states to which D 0 and D 0 can decay. Consider  K, KK intermediate states as an example… cancellation expected! The result here is a series of large numbers with alternating signs, SU(3) forces 0 x = ? Extremely hard… J. Donoghue et. al. P. Colangelo et. al. Need to “repackage” the analysis: look at the complete multiplet contribution 13

18. BEACH 2004, IIT, Chicago Alexey Petrov (Wayne State Univ.) Resume: model-dependent computation with model-dependent result 12

19. BEACH 2004, IIT, Chicago Alexey Petrov (Wayne State Univ.) Theoretical expectations  Let’s compute both x and y. Consider the correlator   p D (q) is an analytic function of q. To write a disp. relation, go to to HQET: A. Falk., Y. Grossman, Z. Ligeti, Y. Nir and A.A.P., hep-ph/0402204 Now we can interpret  p D (q) for all q 11

20. BEACH 2004, IIT, Chicago Alexey Petrov (Wayne State Univ.) Theoretical expectations  …this implies for the correlator  HQ mass dependence drops out for the second term, so for  v (q) =  p D (q)/m D mass and width difference of a heavy meson with mass E Rapidly oscillates for large m c  Thus, a dispersion relation Compute , then find  m! 10

21. BEACH 2004, IIT, Chicago Alexey Petrov (Wayne State Univ.) Results:  Product is naturally O(1%) No (symmetry-enforced) cancellations Naturally implies that y ~ 1%! What about x? A.F., Y.G., Z.L., and A.A.P. Phys.Rev. D65, 054034, 2002 From each multiplet: 9

22. BEACH 2004, IIT, Chicago Alexey Petrov (Wayne State Univ.) Results:  m/  =x/y: Computation naturally implies that y ~ x ~ 1%!  Also: 1.Assume 2-parameter model for 2.Compute r F for 4-body and 2- body intermediate multiplets 3.Model dependence remains… A. Falk., Y. Grossman, Z. Ligeti, Y. Nir and A.A.P., hep-ph/0402204 8

23. BEACH 2004, IIT, Chicago Alexey Petrov (Wayne State Univ.) A bit more about CP violation in charm 7

24. BEACH 2004, IIT, Chicago Alexey Petrov (Wayne State Univ.) CP violation: experimental constraints 1. Standard analysis: rate asymmetries ModeE791, %FOCUS, %CLEO, % D 0 → K + K - -1.0±4.9±1.2-0.1±2.2±1.50.0±2.2±0.8 D0 → +-D0 → +- -4.9±7.8±3.04.8±3.9±2.51.9±3.2±0.8 D 0 → K S  0 0.1±1.3 D0 → 0+K-D0 → 0+K- -3.1±8.6 … which is of the first order in CPV parameters, but requires tagging 2. Recall that CP of the states in are anti-correlated at  (3770):  a simple signal of CP violation: … which is of the second order in CPV parameters, i.e. tiny 6

25. BEACH 2004, IIT, Chicago Alexey Petrov (Wayne State Univ.) CP violation: new experimental possibilities 1 1.Time dependent (lifetime difference analysis): separate datasets for D 0 and D 0 This analysis requires 1. time-dependent studies 2. initial flavor tagging (“the D * trick”) Cuts statistics/sensitivity 5

26. BEACH 2004, IIT, Chicago Alexey Petrov (Wayne State Univ.) 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 D 0 and D 0, but are not CP eigenstates ( , KK *, K , K , …) where A.A.P., PRD69, 111901(R), 2004 hep-ph/0403030 4

27. BEACH 2004, IIT, Chicago Alexey Petrov (Wayne State Univ.) CP violation: untagged asymmetries Expect time-dependent asymmetry… … whose coefficients are computed to be This is true for any final state f … and time-integrated asymmetry 3

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

29. BEACH 2004, IIT, Chicago Alexey Petrov (Wayne State Univ.) Conclusions  Charm provides great opportunities for New Physics studies –large available statistics –mixing: x, y = 0 in the SU(3) limit (as V * cb V ub 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 K  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 1

30. BEACH 2004, IIT, Chicago Alexey Petrov (Wayne State Univ.) Additional slides 0

31. BEACH 2004, IIT, Chicago Alexey Petrov (Wayne State Univ.) 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?

32. BEACH 2004, IIT, Chicago Alexey Petrov (Wayne State Univ.) 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) Introduce SU(3) breaking via the quark mass operator All nonzero matrix elements built of must be SU(3) singlets The  C=1 part of H W is -2

33. BEACH 2004, IIT, Chicago Alexey Petrov (Wayne State Univ.) Theoretical expectations note that D i D j is symmetric belongs to 6 of SU(3) F D mixing is prohibited by SU(3) symmetry Explicitly, 1. No in the decomposition of no SU(3) singlet can be formed 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 -3

34. BEACH 2004, IIT, Chicago Alexey Petrov (Wayne State Univ.) Example: PP intermediate states n=PP transforms as, take 8 as an example: This gives a calculable effect! Numerator: 1.Repeat for other states 2.Multiply by Br Fr to get y Denominator: phase space function -4

35. BEACH 2004, IIT, Chicago Alexey Petrov (Wayne State Univ.)  : SU(3) and phase space “Repackage” the analysis: look at the complete multiplet contribution Does it help? If only phase space is taken into account: no (mild) model dependence Each is 0 in SU(3) y for each SU(3) multiplet if CP is conserved Can consistently compute A.F., Y.G., Z.L., and A.A.P. Phys.Rev. D65, 054034, 2002 -5

36. BEACH 2004, IIT, Chicago Alexey Petrov (Wayne State Univ.) Quantum coherence: supporting measurements Time-dependent analysis A. Falk, Y. Nir and A.A.P., JHEP 12 (1999) 019 Strong phase can be measured at CLEO-c! where and Strong phase  is zero in the SU(3) limit and strongly model-dependent With 3 fb -1 of data cos  can be determined to |  cos  | < 0.05! Silva, Soffer; Gronau, Grossman, Rosner