1. Zhi-zhong Xing 【 IHEP, Beijing 】 D0-D0bar Mixing and CP Violation in the Standard Model BES-Belle-CLEO-BaBar Joint Workshop on Charm Physics Beijing, November 2007

2. 2 A Fast Lesson from History Meson-Antimeson mixing has been of great interest in particle physics: K0-K0bar (1958): |x| ~ 0.47, |y| ~ 1.0;  charm quark and its mass Bd0-Bd0bar (1987): |x| ~ 0.78, |y| < 1%;  top quark mass Bs0-Bs0bar (2006): |x| ~ 27, |y| ~ 0.1;  consistent with the SM People feel excited by the preliminary observation of D0-D0bar mixing: the charming sleeping beauty ( 睡美人 ) is waking up! D0-D0bar (2007): |x| ≤ 1%, |y| ~ 1%;  no conflict with the SM

3. 3 My Life is Easier H. Li J. Napolitano N. Neri A. Schwartz M. Staric because of the excellent talks given by experimental colleagues, and the theory talk to be given tomorrow morning by A. Petrov. (1) Why is the D0-D0bar system unique and interesting? (2) SM predictions for the D0-D0bar mixing rate (x & y) (3) Phenomenology of D0-D0bar mixing and CP violation (4) Typical SM effects of CP violation in neutral-D decays Outline of my talk

4. 4 Why is the D0-D0bar system unique? ★ The only meson-antimeson system whose mixing takes place via the intermediate states with down-type quarks. d, s, b W W D0D0bar cu d, s, b W W D0 cu The mixing is very small, as the third generation (b ) plays a negligible role in FCNC box (and penguin) diagrams. ★ The only meson-antimeson system whose mixing parameters (x and y) are notoriously hard to be calculated in the SM. m_c is neither light enough ( >  _ QCD ) ---- nonperturbative regime. Measurements are the only reliable way.

5. 5 Why is the D0-D0bar system interesting? ★ It is a sensitive playground to probe CP-violating new physics, as the SM effects of CP violation in neutral-D decays are typically of O(0.1%) or smaller. ★ It is a nontrivial playground to test the CKM unitarity of quark mixing, quantum coherence, CPT symmetry,  C =  Q rule, etc. CKM unitarity + data

6. 6 D0-D0bar Mixing: Preliminaries The mixing between D0 and D0bar arises from the fact that they couple to a subset of virtual or real intermediate states. So mass and flavor states of two neutral-D mesons are different. The expansion of off-diagonal terms to 2nd order in perturbation theory is given by contributes only to M_12contributes both to M_12 & Γ_12 sensitive to new physicsdominated by the SM contribution

7. 7 D0-D0bar Mixing: Preliminaries Take care of the definition of x and y used by different collaborations! mass state flavor states CPT invariance CP state Since the effect of b quark in D0-D0bar mixing is negligibly small, it is an excellent approximation to neglect CP violation in D0-D0bar mixing.

8. 8 D0-D0bar Mixing: Preliminaries Then the mixing parameters x and y are formally given by P: principal value, Σ: over all intermediate states n with To calculate x and y, there are in general two approaches: 1)at the quark level (n = ) 2)at the hadron level (n = ) x and y could be connected by a dispersion relation in the HQET Falk, Grossman, Ligeti, Nir, Petrov, 2004

9. 9 Short-distance Estimate (Quark Level) The lowest-order short-distance calculation of the box diagram: helicity suppression Higher-order contributions to x & y in the operator product expansion have fewer powers of m_s suppression, since the chiral suppression can be lifted by quark condensates instead of mass insertion (Georgi 1992). Note: the 8-quark operator contributions to x & y are the minimal possible power of m_s and thus dominant. with very large uncertainty.

10. 10 Long-distance Estimate (Hadron Level) The OPE approach is hard to reliably describe D0-D0bar mixing, as the D meson mass is not very large. Alternatively, let’s consider n = exclusive hadronic states. This long-distance approach is reasonable because M_D lies in the middle of a region populated by excited light-quark states. In principle: sum over all possible intermediate hadronic multiplets; but In practice: that is impossible! Once the b-quark contribution is neglected, the rate of D0-D0bar mixing vanishes in the limit of flavor SU(3) symmetry. A two-body example, d, s W D0 c u d, s W D0bar u u In the SU(3) limit, the sum of these contributions is 0!

11. 11 Long-distance Estimate (Hadron Level) ★ a calculation of y in this exclusive approach is less model-dependent. ★ the estimate of x involves off-shell hadronic states, and thus is more model-dependent. One may use the dispersion relation to get x from y. Non-vanishing D0-D0bar mixing can arise as the second-order effect of SU(3) symmetry breaking (Falk, Grossman, Ligeti, Petrov 2002): However, how to estimate the size of SU(3) breaking is a big challenge! Ligeti 2007 (arXiv:0706.0919): the most important long-distance effect may be due to SU(3) symmetry breaking in phase space. For any final state F in any SU(3) representation R (e.g., PP can be in 8 or 27), one could calculate y_F_R, if D only decayed to the states in F_R.

12. 12 Long-distance Estimate (Hadron Level) Example: the contribution of the multiplet containing two pseudoscalar mesons in a SU(3) octet is given by (Falk et al 2004): If the rates of neutral-D decays to all representations were known, then y could be reconstructed from y_F_R: Those two-, three- and four-body final states account for sizable fraction of the width of neutral-D decays (Ligeti 2007).

13. 13 Long-distance Estimate (Hadron Level) Example for illustration (Ligeti 2007): Large SU(3) violation when some states are not allowed at all in those heavy multiplets (e.g., 4 M_K > M_D): y_4P ~ sin^2  _C. There do exist some final states which can contribute to y near the 1% level. The dispersion relation implies the order of x similar to that of y. Unlike the case of y, the hadronic matrix elements do not cancel in x. The most important contributions to x come again from four-body final states, so x & y could be comparable in magnitude. Conclusion: the SM predictions for x and y remain quite uncertain, but the above order-of-magnitude estimates seem reasonable. Typically,(with plausible assumptions)

14. 14 Phenomenology of Neutral-D Decays Phenomenology of neutral-D decays [Xing, Phys. Rev. D 55, 196 (1997)] ★ Time-dependent incoherent D0 and D0bar decays: D0-D0bar Mixing is entangled with CP violation for a specific final state f.

15. 15 ★ Time-independent coherent D0 and D0bar decays: Phenomenology of Neutral-D Decays Maybe, only the time- integrated decay rate is of realistic interest: C = -1 [Ψ(3770)]: the 2nd and 4th terms vanish. It is desirable to measure the joint (coherent) D0-D0bar decays for the C = +1 case at the Ψ(4140) resonance.

16. 16 Phenomenology of Neutral-D Decays Analytical approximations up to the second order of small x and y can also be found in Xing, Phys. Rev. D 55, 196 (1997). In particular, ◆ Semi-leptonic D decays (wrong-sign and right-sign dilepton events): measurement of D0-D0bar mixing and test of CPT and ΔQ = ΔC rules. ◆ Neutral-D decays into CP eigenstates (K^+K^-, K_S  ^0, etc): study of D0-D0bar mixing, CP violation and final-state interactions. ◆ Neutral-D decays into non-CP eigenstates (K^+  ^-, K^-  ^+, etc): study of D0-D0bar mixing, CP violation and final-state interactions. ◆ Coherent CP-forbidden D0-D0bar decays on the C = ± 1 resonance. Experimental evidence for D0-D0bar mixing obtained by BaBar & Belle: ⊙ from a measurement of the time dependence of the doubly-Cabibbo- suppressed decay (DCSD) D^0 → K^+  ^- and its CP-conjugate mode. ⊙ from lifetime measurements of D^0 → K^-  ^+, K^+K^- channels. I skip this part, since it has been nicely covered by previous speakers.

17. 17 Mixing Effects on the Resonances Three examples (Xing, talk given in the 2nd BPCP meeting, Hawaii 1997, hep-ph/9703459): BESIII

18. 18 Three Types of CP Violation Type 1: CP violation in D0-D0bar mixing (SM prediction: < 10^-4 with large uncertainties) Type 2: CP violation in direct decay [direct CP violation] (SM: ≤ 10^-3) (  : strong,  : weak) Type 3: CP violation from the interplay of decay and mixing [indirect CP violation] (SM: ≤ 10^-3)

19. 19 Why is CP Violation so Small? Naive reason: the charm unitarity triangle is too sharp in the SM. Imaginary Magnitudes of CP-violating asymmetries in D-meson decays are at most of order 10^-3 in the SM, even if there are large final-state interactions. In general, the singly Cabibbo-suppressed D-meson decays have larger CP-violating effects than the Cabibbo-flavored decays and DCSDs.

20. 20 Model-dependent Estimate For example: Buccella, Lusignoli, Mangano, Miele, Santorelli, 1993, 1995

21. 21 Experimental Data For example: Schwartz, talk given today; Mancinelli, arXiv:0711.1571.

22. 22 Strange CP violation in D decays Semi-leptonic, two-body and multi-body non-leptonic D decays with K_S or K_L: a CP asymmetry of 3.3×10^-3 shows up as “a calibration for the experimental systematics of asymmetries at the 0.1% level” (Kaplan 95) For charged- and neutral-D decays with K_S or K_L in the final states, a known CP-violating effect (induced by K0-K0bar mixing) must appear. [Xing, Phys. Lett. B 353, 313 (1995)]

23. 23 CP-forbidden Decays On the Ψ(3770) & Ψ(4140) resonances, the coherent neutral-D decays initial CP final CP can occur due to CP violation, if f_1 and f_2 are proper CP eigenstates. BES-III should be able to search for this type of CP-violating effects. Finally, let me just list some recent phenomenological articles and talks on D0-D0bar mixing and (or) CP violation in the SM: Asner, Sun, hep-ph/0507238; Du, hep-ph/0608313; Grossman, Kagan, Nir, hep-ph/0609178; Li, Yang, hep-ph/0610073; Cheng, He, Li, Wang, Yang, arXiv:0704.0120 [hep-ph]; Xing, Zhou, arXiv:0704.0971 [hep-ph]; Ligeti, arXiv:0706.0919 [hep-ph]; Sinha, Sinha, Browder, Deshpande, Pakvasa, arXiv:0708.0454 [hep-ph]; Petrov, arXiv:0711.1564 [hep-ph].

24. 24 The SM predictions for D0-D0bar mixing and CP violation involve very large uncertainties, and they are very hard to get improved. Concluding Remarks However, D0-D0bar mixing up to the 1% level is very possible in the SM, consistent with current experimental evidence. It might not be very sensitive to new physics. CP violation up to the 0.1% level is expected in the SM, and thus a signal of CP violation at the 1% would serve as a robust signal of new physics in the charm sector. But I personally believe that new physics might be decoupled to standard flavor physics at low energy scales, just like physics of massive neutrinos. I hope that I will be wrong. No matter whether there is new physics or not, it is interesting & important to study D0-D0bar mixing & charming CP violation.

25. 25 Many people in the audience believe: CP symmetry is beautiful. Concluding Remarks Peter Minkowski believes: asymmetry is a sister of symmetry. So, I have a good reason to believe: asymmetry is also beautiful. Let us look for this sleeping beauty together in the charm sector!