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

Theoretical comments on

mixing

V.Shevchenko (ITEP)

42d Rencontres de Moriond, La Thuile, Italy, 10-24 March 2007 1

00 DD


Experiment: recently reported by BaBar and Belle: Kevin Flood’s and Marco Staric’s talks at thisconference

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..


The Standard Model predicts oscillations of strangeness,charm, and beauty…

d

d

s

s

b

b

sd ,

sd ,

c

c

u

u

00 KK

ss BBBB ,, 00

00 DD

tcu ,,

tcu ,,tcu ,,

tcu ,,bsd ,,

bsd ,,


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 ALL heavy degree of freedom, however. We have much better access to c-quark than to t-quark parameters from oscillations because of GIM00 KK


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 quarkbelongs to another generation. Quantitatively


In other words D is “inverse analog” of K oscillations

c-quark dominating K oscillations is heavy d.o.f. for K whiles-quark dominating D oscillations is light d.o.f. for D

Very different physics

In the SM about 80% of massdifference comes from the real part of the box diagramsand 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

)()( SLK KMKMM

KK M 2


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.

LHB MMM

BB M

For D oscillations the situation is reversed and we have all reasons to believe that they are dominated by long-distance physics…


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.


QM continues…

Contribute to M12 only Can get NP contributions

Long distanceSM dominated

Mixing (i.e. x and y) vanishes for exact flavor SU(3) – e.g. because of GIM


Two main theoretical methods to compute the mixing:

1. “Inclusive” – goes from the short distance/high momentump ≥ 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 /mc

2 ~ 0.006and Λ2 / ms mc ~ 10


Very strong suppression: x~10-5, y~ 10-7 But higher orders!

(from hep-ph/0110317 by A.Falk et al)


In exclusive approach one instead sums over a set oflowest 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 bothby the matrix elements and the phase space. Estimatesfor y range between 10-4 and 10-2

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



Compilation of D mixing predictions - “Nelson plot”

H.Nelson, hep-ex/9909021

Mix

ing

am

pli

tud

e (|

x|,|

y|,

etc)

Reference index

triangles – x in SMsquares – y in SMcircles – 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)

One considers time dependent rates

for Cabibbo-favored “right-sign” decay, and

for doubly Cabibbo-suppressed

RD = CFD rate/ DCSD rate ~ tan4 θC

x’ = x∙cos δKπ + y ∙sin δKπ y’ = -x∙sin δKπ + y ∙cos δKπ

“wrong-sign” decay.



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

Belle:

based on lifetime difference measurement for D0 → K- π+

and D0 → K- K +

based on D → K π unbinned fit to time distribution

RD=(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)%

yCP= 1.31 ± 0.32 ± 0.25 %


3.2 σ


Mix

ing

am

pli

tud

e (|

x|,|

y|,

etc)

Reference index

yBaBar

It seems that no miracle has happened

At least this time…


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 ~ 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

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