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Theoretical comments on mixing

Theoretical comments on mixing. V.Shevchenko (ITEP). 42d Rencontres de Moriond , La Thuile, Italy, 10-24 March 2007 1. Experiment: recently reported by BaBar and Belle: Kevin Flood’s and Marco Staric’s talks at this conference.

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Theoretical comments on mixing

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

  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.. 42d Rencontres de Moriond, La Thuile, Italy, 10-24 March 2007 2

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

  4. Despite the diagrams for all four mesons (K, B, BS , 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 ALLheavy 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, 10-24 March 2007 4

  5. CKM structure of the transition matrix elements looks like But for D0 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, 10-24 March 2007 5

  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 42d Rencontres de Moriond, La Thuile, Italy, 10-24 March 2007 6

  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… 42d Rencontres de Moriond, La Thuile, Italy, 10-24 March 2007 7

  8. Standard machinery of two level systems QM… Mixing CP-violating phase φ ~ λ4 ~ 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. 42d Rencontres de Moriond, La Thuile, Italy, 10-24 March 2007 8

  9. QM continues… Long distance SM dominated Contribute to M12 only Can get NP contributions Mixing (i.e. x and y) vanishes for exact flavor SU(3) – e.g. because of GIM 42d Rencontres de Moriond, La Thuile, Italy, 10-24 March 2007 9

  10. Two main theoretical methods to compute the mixing: • “Inclusive” – goes from the short distance/high momentum • p ≥ mc 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 ms2 /mc2 ~ 0.006 and Λ2 / ms mc ~ 10 42d Rencontres de Moriond, La Thuile, Italy, 10-24 March 2007 10

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

  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 between10-4and 10-2 42d Rencontres de Moriond, La Thuile, Italy, 10-24 March 2007 12

  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. Compilation of D mixing predictions - “Nelson plot” H.Nelson, hep-ex/9909021 triangles – x in SM squares – y in SM circles– x beyond SM Mixing amplitude (|x|,|y|, etc) 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) Reference index 42d Rencontres de Moriond, La Thuile, Italy, 10-24 March 2007 14

  15. One considers time dependent rates for Cabibbo-favored “right-sign” decay, and for doubly Cabibbo-suppressed “wrong-sign” decay. RD = CFD rate/ DCSD rate ~ tan4θC x’ = x∙cos δKπ + y ∙sin δKπ y’ = -x∙sin δKπ + y ∙cos δKπ 42d Rencontres de Moriond, La Thuile, Italy, 10-24 March 2007 15

  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 RD=(0.303 ± 0.016 ± 0.010)% 3.9 σ evidence for mixing 42d Rencontres de Moriond, La Thuile, Italy, 10-24 March 2007 16

  17. Belle: based on D → K πunbinned fit to time distribution RD=(0.364 ± 0.017 ± 0.010)% based on Dalitz analysis of D → K ππ x= (0.80±0.29±0.17)% y=(0.33±0.24±0.15)% based on lifetime difference measurement for D0→ K-π+ andD0 → K- K + yCP= 1.31 ± 0.32 ± 0.25 % 3.2 σ 42d Rencontres de Moriond, La Thuile, Italy, 10-24 March 2007 17

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

  19. Conclusions • evidence for neutral D-meson mixing is presented • by BaBar and Belle • expected in the SM, dominated by complicated • nonperturbative QCD dynamics atμ ~ ms,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 42d Rencontres de Moriond, La Thuile, Italy, 10-24 March 2007 19

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