Pushing Lattice to the Edge: Flavor Physics

1
Pushing Lattice to the Edge Flavor Physics

• Alessandro Cerri, LBNL
• Lattice 2006, Tucson, 7/26/2006

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Outline

• (Quick) Introduction
• Leptonic decays
• D???
• B???
• Semileptonic Decays
• D?Kl?
• B?Xcl?
• B?Xul?
• B Mixing
• Conclusions

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Caveat Emptor

• I will cover mostly b c related results
• Kaons experimental results not covered
• Caveats
• This is my personal selection of hot topics,
  more results are available on the market
• For many of the results I am a(n interested)
  spectator
• ICHEP06 is around the corner more results to
  come in lt1 Week

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CKM and Lattice

• Our knowledge of the unitarity triangle improved
  dramatically!
• Lattice knowledge necessary ingredient to
  complete the theoretical picture
• Experiments are becoming more and more accurate,
  lattice needs to keep the pace!

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Leptonic Decays

• Several ways of looking at
• Access to Vxy
• Cross-check of fX prediction
• In either case, this is an extremely elegant
  example of lattice?experiment interaction

l
qx
qx
?l
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Vcd D???
D?KL?
CLEO-c (PRL 95 251801, 2005) measured last year
the D mode
PDG04
D???

• Direct measurement of fD comparable to LQCD error
  bars!
• Theoretical predictions at 10 level
• Recently added
• (PRD73
  112005, 2006)
• Expect to measure the Ds decay constant soon
  (ICHEP 06?)

201?3 ?17
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Vcs Ds???
BaBar (see e.g. hep-ex/0605030) nicely provides
Ds??Ds(???)
Ds??0Ds
Ds??Ds(???)
PDG04
BR
Stat
Sys
This allows the extraction of fDs, but also of
fDs/fD
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Latest CLEO News!

• Measured B(Ds???)(0.664?0.076?0.028)
• fDs282?16?7 MeV
• (See S. Stones talk at ITEP Meeting)
• B(Ds?e?)lt3.1x10-4
• fDs/fD1.26?0.11?0.03
• ?(Ds???)/?(Ds???)9.9?1.7?0.7
• (SM9.72)
• Consistent with lepton universality!

64 events
DATA 200/pb lt0.3GeV in CC
Case (i)
24 events
DATA 200/pb gt0.3GeV in CC
Case (ii)
Xen
12 events
Electron Sample
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Vub B???
BELLE (hep-ex/060408) observes
4.2?
??
?-??-???? e-?e?? ?-?? ?-?0??
?-??-??
B?D()0?,?,a1,Ds()
Residual Energy in calorim. (GeV)
BR of B???
First direct measurement of fB Compare with
fB(216?22) MeV (HPQCD)
PDG04/HFAG
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Semileptonic Decays

• Several ways of looking at
• Access to Vxy
• Form factor embeds q2 dependence ? slightly more
  elaborate example of lattice?experiment
  interaction
• Studying will yield
  CKM-independent LQCD checks

Vxy
qx
qy
qx
qx
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Vcs, Vcd D?Kl?, D??l?
BELLE

• BaBar (ICHEP06), Belle (hep-ex/0604049), CLEO
  (PRL, hep-ex/0407035) and FOCUS (PLB607 2005
  233) measure the q2 dependence of f in

• P3(q2) strongly peaks near q20
• Extraction of Vcs requires f(0), a tough LQCD
  bullet!
• f(q2)/f(0) measured and compared to predictions
• This is an important playground to understand the
  extrapolation of

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D?Kl?, D??l? Cont.d

• Several ways of comparing to predictions

(e.g. Koerner Schuler Z Phys. C38 1988)
(Becirevic Kaidalov, PLB478 2000 417)
0.03
0.07
0.007
0.003
0.03
0.06
0.31
0.15
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Form-Factors Compared to Lattice

• Lattice predictions
• D?pen
• f(0)0.640.030.06
• a0.440.040.07
• D?Ken
• f(0)0.730.030.07
• a0.500.040.07
• C. Aubin et al., PRL 94 011601 (2005)

Assume Vcd 0.2238
D??e?
LQCD
DATA FIT (tagged)
Assume Vcs 0.9745
D?Ke?
LQCD
DATA FIT (tagged)
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Latest CLEO News!

• D?Ke? D? ?e?

0.170.100.05
0.220.050.02
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Vub B??l?

• Analogous form factors can be measured on
  semileptonic B decays
• Belle (hep-ex/0604024) ??,?
• BaBar? (ICHEP06)?
• Exp?LQCD?CKM
• Test LQCD
• Measure Vxb

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Vtd/Vts Belles b?s?

• BELLE (hep-ex/0506079)
• Measure b?s? and b?d? in exclusive processes
• B?(?,?)?
• Disentangle loop/annihilation using ?0,?,?
• Derive
• By normalizing to B(B?K?) obtain

SU(3) Breaking (10)
Ratio of form factors (0.85?0.10)
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Vtd/Vts Bs Mixing

• Vtd/Vts can also be derived from the BB mass
  difference
• QCD uncertainty is minimized resorting to the
  relative Bs/Bd mixing rate (Vtd/Vts)
• Beyond the SM physics could enter in loops!

• Measure mixing rate vs time and fit for
  oscillation frequency
• This is usually done in fourier transform
  amplitude scan

cos(?m t)
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Amplitude Scan

• Mixing amplitude fitted for each (fixed) value of
  ?m
• On average every ?m value (except the true ?m)
  will be 0
• sensitivity defined for the average experiment
  mean 0
• The actual experiment will have statistical
  fluctuations
• Actual limit for the actual experiment defined by
  the systematic band centered at the measured
  asymmetry

Just an example Not based on real data!
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Bs Mixing D0
?msgt 14.8 ps-1 _at_ 95 CL Sensitivity 14.1 ps-1
26700 lDs candidates

• signal above sensitivity threshold
• D0 decides to quote a two sided bound from
  Likelihood profile
• ?ms?17,19ps-1 _at_ 90 CL
• L dip is nice, should get deeper with more data
• Amplitude is 2.5? from 0 and 1.6? from 1

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Bs Mixing CDF
Semileptonic (50K events) hadronic (3K events)
B decays, 1 fb-1
A/?stat _at_ (?m17.3 ps-1)3.7
?msgt 16.7 ps-1 _at_ 95 CL Sensitivity 25.8 ps-1
Background has 0.2 probability to mimic this!
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Vtd/Vts from CDF

• inputs
• m(B0)/m(Bs) 0.98390 (PDG 2006)
• ? 1.21 0.047 (M. Okamoto, hep-lat/0510113)
• ? md 0.505 0.005 (PDG 2006)

-0.035
Vtd / Vts 0.208 0.001 (exp) 0.008 (theo)
-0.002
-0.006
(uncertainty is actually limited by the CKM fit
to Vtd/Vts, in particular ? and ?)
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Conclusions and Outlook

• Flavor physics relies on lattice computations
• In some cases one of the main contributions to
  syst. on VCKM determination
• New exciting measurements
• Bs Mixing
• B???
• D(s)???
• Expect more news in the next week or so!
• (Benign!) Pressure on the Lattice community for
  more precise numbers is high!