1. Theoretical comments on mixing V.Shevchenko (ITEP) 42d Rencontres de Moriond, La Thuile, Italy, 10-24 March 2007 1

2. 42d Rencontres de Moriond, La Thuile, Italy, 10-24 March 2007 2 Experiment: recently reported by BaBar and Belle: Kevin Flood’s and Marco Staric’s talks at this conference Theory: long story, see papers and talks by H.Georgi, H.Nelson, Z.Ligeti, A.Petrov, Y.Grossman, I.Bigi and others… The most recent update: illuminating Patricia Ball’s talk at Electroweak session here last week..

3. 42d Rencontres de Moriond, La Thuile, Italy, 10-24 March 2007 3 The Standard Model predicts oscillations of strangeness, charm, and beauty…

4. 42d Rencontres de Moriond, La Thuile, Italy, 10-24 March 2007 4 Despite the diagrams for all four mesons (K, B, B S, D) look similar, the physical picture of mixing is different… For K and B mesons the dominant contribution comes from the heaviest up-type quark corresponding to the down-quarks propagating in the loop. Oscillation frequency provides information about “the nearest” heavy degree of freedom Not to ALL heavy degree of freedom, however. We have much better access to c-quark than to t-quark parameters from oscillations because of GIM

5. 42d Rencontres de Moriond, La Thuile, Italy, 10-24 March 2007 5 CKM structure of the transition matrix elements looks like But for D 0 mesons there is no such thing as “the nearest heaviest” down-type quark, since b quark belongs to another generation. Quantitatively

6. 42d Rencontres de Moriond, La Thuile, Italy, 10-24 March 2007 6 In other words D is “inverse analog” of K oscillations c-quark dominating K oscillations is heavy d.o.f. for K while s-quark dominating D oscillations is light d.o.f. for D Very different physics In the SM about 80% of mass difference comes from the real part of the box diagrams and c-quark is dominant over t-quark there. The rest 20% is due to long distance contributions. As for it entirely comes from long distance effects

7. 42d Rencontres de Moriond, La Thuile, Italy, 10-24 March 2007 7 In case of B oscillations the long distance contributions to are estimated to be very small and physics is essentially described by local effective Hamiltonian. Also and usually is neglected. For D oscillations the situation is reversed and we have all reasons to believe that they are dominated by long-distance physics…

8. 42d Rencontres de Moriond, La Thuile, Italy, 10-24 March 2007 8 Standard machinery of two level systems QM… Mixing CP-violating phase φ ~ λ 4 ~ 0.002 in the SM – interesting place for possible NP beyond MFV. But if it would be x<<y the sensitivity to NP is low.

9. 42d Rencontres de Moriond, La Thuile, Italy, 10-24 March 2007 9 QM continues… Contribute to M 12 only Can get NP contributions Long distance SM dominated Mixing (i.e. x and y) vanishes for exact flavor SU(3) – e.g. because of GIM

10. 42d Rencontres de Moriond, La Thuile, Italy, 10-24 March 2007 10 Two main theoretical methods to compute the mixing: 1.“Inclusive” – goes from the short distance/high momentum p ≥ m c region, essentially in the spirit of the standard operator product expansion. H.Georgi, ’92; I.Bigi, N.Uraltsev, ’00 Interplay of two relevant parameters: 2. “Exclusive” – large distance view – assume a few intermediate/final states dominance and treat these physical channels exclusively. A.Falk, Y.Grossman, Z.Ligeti, A.Petrov, Y.Nir, ’01, ’04 m s 2 /m c 2 ~ 0.006 and Λ 2 / m s m c ~ 10

11. 42d Rencontres de Moriond, La Thuile, Italy, 10-24 March 2007 11 Very strong suppression: x~10 -5, y~ 10 -7 But higher orders! (from hep-ph/0110317 by A.Falk et al)

12. 42d Rencontres de Moriond, La Thuile, Italy, 10-24 March 2007 12 In exclusive approach one instead sums over a set of lowest resonances, belonging to the class F (PP, PV, VV etc) and SU(3) representation R. y=0 in the exact SU(3) limit. However SU(3) is broken both by the matrix elements and the phase space. Estimates for y range between 10 -4 and 10 -2

13. It seems there is no problem to get x,y ~ 10 -3 in this or in that way in the SM and both inclusive and exclusive analysis support each other from different prospectives. However quantitative status of theory predictions is not good from both sides 42d Rencontres de Moriond, La Thuile, Italy, 10-24 March 2007 13

14. 42d Rencontres de Moriond, La Thuile, Italy, 10-24 March 2007 14 Compilation of D mixing predictions - “Nelson plot” H.Nelson, hep-ex/9909021 Mixing amplitude (|x|,|y|, etc) Reference index triangles – x in SM squares – y in SM circles – x beyond SM Recent analysis of NP contributions to y ( E.Golowich, S.Pakvasa, A.Petrov, hep-ph/0610039 ) gives results varying from 10 -10 to a few % (SUSY without R parity)

15. One considers time dependent rates for Cabibbo-favored “right-sign” decay, and for doubly Cabibbo-suppressed R D = CFD rate/ DCSD rate ~ tan 4 θ C x’ = x∙cos δ Kπ + y ∙sin δ Kπ y’ = -x∙sin δ Kπ + y ∙cos δ Kπ “wrong-sign” decay. 42d Rencontres de Moriond, La Thuile, Italy, 10-24 March 2007 15

16. 42d Rencontres de Moriond, La Thuile, Italy, 10-24 March 2007 16 Let us come now to the experimental results… BaBar, hep-ex/0703020 y’=(9.7±4.4±3.1)∙10 -3 x’ 2 =(-0.22±0.30±0.20)∙10 -3 R D =(0.303 ± 0.016 ± 0.010)% 3.9 σ evidence for mixing

17. Belle: based on lifetime difference measurement for D 0 → K - π + and D 0 → K - K + based on D → K π unbinned fit to time distribution R D =(0.364 ± 0.017 ± 0.010)% based on Dalitz analysis of D → K π π y=(0.33±0.24±0.15)% x = (0.80±0.29±0.17)% y CP = 1.31 ± 0.32 ± 0.25 % 42d Rencontres de Moriond, La Thuile, Italy, 10-24 March 2007 17 3.2 σ

18. 42d Rencontres de Moriond, La Thuile, Italy, 10-24 March 2007 18 Mixing amplitude (|x|,|y|, etc) Reference index y BaBar It seems that no miracle has happened At least this time…

19. 42d Rencontres de Moriond, La Thuile, Italy, 10-24 March 2007 19 Conclusions evidence for neutral D-meson mixing is presented by BaBar and Belle expected in the SM, dominated by complicated nonperturbative QCD dynamics at μ ~ m s,c If averages will stay where they are not much hope to see NP in D-mixing (except perhaps for CP violating phase, which is a typical null test), since y ~ x and they are just quite large to screen possible NP effects, but not too large to exceed the SM compatible values range