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Vus from Kl3 decays
Federico Mescia INFN-Frascati and University of
Rome, Roma Tre

• OUTLINE
• Motivations Vus and the CKM Unitarity
• The Lattice calculation of f(0) SU(3)
  breaking
• Physical Results and Discussion
• f(0) 0.960(9) ? Vus2 Vud2
  Vub20.9992(13)

Euridice, February 8-12, LNF
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Unitarity
The most accurate test of CKM unitarity- Vus
Vus ? possibly responsible!! Relies on old
experimental and theoretical results of Kl3
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Rate

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(No Transcript)
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F(0) chiral th
f(0) and The Ademollo-Gatto Theorem
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MODEL ESTIMATES OF f4
A lattice estimate of f4 is clearly needed! !!No
Scale Ambiguity!!
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F4-strategy
f4-Lattice QCD Challenge Our Strategy

VERY CHALLENGING A PRECISION OF O(1) MUST BE
REACHED ON THE LATTICE !!

• 1. Evaluation of f0q2 (MK - Mp)2 with very
  high precision (lt1).
• 2. Extrapolation of f0(q2max) to f0(0)f(0)
  estimating the slope ?0
• 3. We consider ?f f(0)-1-f2Q (subtraction of
  the unphysical chiral logs)
• and extrapolate (ms/2 mq ms) to the
  physical meson masses
• Finally, ?f will be our estimate of f4.

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F0(q2max)-FNAL
1) f0(q2max)- High precision measure (FNAL)

• For MK?Mp , R?1 O(M2K-M2p)2
• Stat. and Syst. errors scale as (M2K-M2p)2,
  like the physical SU(3) breaking effects.
• Independent of Zv and bv

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Q2 dependence
2) Extrapolation of f0(qMAX) to f(0)
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Check of the theory form factor vs experiment
Chiral-QCD also predicts similar values.

High precision measurements ISTRA
(hep-ex/0404030-Kl3) Polar fit not available
but curvature visible for f(q2).
.
? and ?0 from a linear fit consistent with
KTeV.
NA48 (hep-ex/0410065-KLe3) ?
from a linear and a polar fit consistent with
KTeV.
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F2-sub
3) Df and subtraction of the chiral logs

• Scale independent and no leading quenched
  artefacts
• Hopefully suited for a smoth chiral behaviour

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F2-Extr.
3) Chiral extrapolation
Having subtracted the leading log. correction,
several extrapolations are tried
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Results Ext.
D. Becirevic et al,Nucl.Phys.B705339-362,
2005
Systematic error The dominant contributions come
from the uncertainties on the q2 and mass
dependencies of the form factor
A preliminary unquenched (Nf3) estimate has been
recently presented MILC-hep/lat-0412044
?f - 0.015 0.006stat 0.009syst They applied
our strategy (good!) but staggered fermions (less
good!!)
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• CKM-Unitarity recovered

Vus2 Vud2 Vub20.9993(14)

• Vud0.9740(5)
• (Updated average hep-ph/0406324)

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FUTURE IMPROVEMENTS Twisted boundary
conditions (Bedaque, De Divitiis et al)
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F(0)-talavera
2) f0(0), ?0, c0 and Chiral Theory at O(p6)

• From NNLO ChPT (Post, Schilcher (2001), Bijnens,
  Talavera (2003)),
• C12 (µ) and C34 (µ) from the slope and curvature
  of the scalar form factor
• For the time being, (Lat. and Exp.) l0 and c0 not
  accurate enough
• Our values for the slopes agree well with the
  exp. measurements

Mind f(0), ?0 and c0 related to the same LECs
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The end
CONCLUSIONS
? In order to estimate Vus and test the CKM
relation, Kl3 decays offer a good opportunity,
thanks to Ademollo-Gatto Theorem.
? Over the years, a great deal of activity has
been devoted to reach higher precision and to
reduce model-assumptions.
? We have presented a methodology to reach 1
accuracy for f (0)
? Our calculation of f (0) is the first one
obtained by using a non-perturbative method based
only on QCD, albeit in the quenched approximation
(which can be in principle removed)
? Our final result, f (0) 0.960 0.005stat
0.007syst is in good agreement with the estimate
made by Leutwyler and Roos (PDG)
? The most important step is to remove the
quenched approximation
?Further steps using lower masses(considering
finite volume effects)
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The end
Comments on other routes to Vus
VusUni (0.22650.0020) VusKl3
(0.22590.0021)
The dominant source of systematic error comes
from the lattice calculation. VERY
DIFFICULT TO REDUCE !!
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The end
Comments on other routes to Vus
VusUni (0.22650.0020) VusKl3
(0.22590.0021)