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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

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

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


The Standard Model predicts oscillations of strangeness,

charm, and beauty…

42d Rencontres de Moriond, La Thuile, Italy, 10-24 March 2007 3


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


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


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


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


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


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


  • 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


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


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


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


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


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


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


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


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


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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