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

42d Rencontres de Moriond, La Thuile, Italy, March 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..

42d Rencontres de Moriond, La Thuile, Italy, March The Standard Model predicts oscillations of strangeness, charm, and beauty…

42d Rencontres de Moriond, La Thuile, Italy, March 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

42d Rencontres de Moriond, La Thuile, Italy, March 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

42d Rencontres de Moriond, La Thuile, Italy, March 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

42d Rencontres de Moriond, La Thuile, Italy, March 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…

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

42d Rencontres de Moriond, La Thuile, Italy, March 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

42d Rencontres de Moriond, La Thuile, Italy, March 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 ~ and Λ 2 / m s m c ~ 10

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

42d Rencontres de Moriond, La Thuile, Italy, March 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 and 10 -2

It seems there is no problem to get x,y ~ 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, March

42d Rencontres de Moriond, La Thuile, Italy, March Compilation of D mixing predictions - “Nelson plot” H.Nelson, hep-ex/ 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/ ) gives results varying from to a few % (SUSY without R parity)

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, March

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

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 ± ± 0.010)% 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, March σ

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

42d Rencontres de Moriond, La Thuile, Italy, March 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