Status of the CKM matrix

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Status of the CKM matrix
Paolo Gambino INFN Torino
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Why CKM?
Observed Flavor Violation is surprisingly close
to SM prediction gtgtgt the flavor
problem Strong interactions make CKM studies
hard. Learning slowly but steadily. Theory errors
dominate almost everywhere.

• For a complete overview, see the Proceedings of
  the 2002 and 2003 CKM workshops
• CKM1 Yellow Book Cern-2003-002-corr
  (hep-ph/0304132)
• CKM2 eConf C0304052 (2003)
• http//ckm-workshop.web.cern.ch
• CKM3 will take place in San Diego, march 2005
• Many thanks to M. Bona, G.Isidori, V.Lubicz, M.
  Pierini,N.Uraltsev and to all UTfitters.

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The CKM matrix
describes Flavor Violation in the SM

• Wolfenstein parameterization

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The Cabibbo angle
Historically, universality of charged currents
Comparison between Vud,Vus determinations
of tests unitarity of the first line of VCKM
? could also be measured from 2nd line, Vcd
(DIS) at 10, W decays at LEP constrains
SijVij2 at 1.3 ? Vcs at 1.3
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? from Vud
Superallowed Fermi transitions (0-gt0 ß
decay) extremely precise, 9 expts, dVud0.0005
dominated by RC and nuclear structure neutron ß
decay dVud0.0015, will be improved at PERKEO,
Heidelberg p decay to ?0e? th cleanest,
promising in long term but BR10-8 PIBETA at PSI
already at dVud0.005
PDG Vud0.97380.0005 ? 0.22740.0021
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? from Vus (Kl3)
2s discrepancy!
Discarding old results and using Leutwyler
Roos VusKl3 0.2255 0.0021 Next frontier
LQCD measure slopes for Kµ3(Dalitz plot) to
constrain ?PT
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New ideas
Hyperon decays (Vus) Cabibbo et al. have
revisited the subject focussing on vector form
fact. dVus0.0027 (exp) but O(1) or more SU(3)
breaking effects NOT included, lattice?
t decay (Vus) Jamin et al. ms from sum rules or
LQCD as input, may become competitive with
B-factory results. At present dVus0.0045, low
values
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Determination of A
A can be determined using Vcb or Vts Two
roads to Vcb
EXCLUSIVE
INCLUSIVE
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The advantage of being inclusive
?QCDmb inclusive decays admit systematic
expansion in ?QCD/mb Non-pert corrections are
generally small and can be controlled Hadronizati
on probability 1 because we sum over all
states Approximately insensitive to details of
meson structure as ?QCDmb (as long as one is far
from perturbative singularities)
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Leptonic and hadronic spectra
OPE predictions can be compared to exp only after
SMEARING and away from endpoints they have no
LOCAL meaning
Total rate gives CKM elmnts shape tells us about
B structure
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State of the art

• Known corrections up to 1/mb3 OPE/HQE
  predictions are only functions of possible cuts
  and of

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Which masses? Which scheme?

• mq(pole) is ill-defined, cannot be determined
  better than 100MeV, and induces large
  uncontrolled higher orders
• Vcb k0 1-0.66 (mb-4.6) 0.39 (mc-1.15)
• 0.01 (??2 -0.4)
  0.05(?G2-0.35)0.09(?D3-0.2)...
• Need short distance masses mbkin(µ) and mb1S
• Exploit correlations (most moments depend on the
  same combination of mc,mb as width)
• Avoid unnecessary parameters
• Define carefully ??2-?1...
  ?G2 3?2...
• Theoretical uncertainties missing 1/mb4, missing
  pert and mixed effects. Need a recipe to estimate
  them... More work ahead
• Traditionally mQ reexpressed using

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Babar fit to Vcb, BRsl, HQE paramts
Pioneer work by CLEO Delphi employed less
precise/complete data, some external constraints,
and CLEO a different scheme Problems with 1S
scheme a cloud?
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Kinetic scheme Small pert corrections Minimal
set of parmts No 1/mc expansion
Uraltsev PG
No sign of deterioration for higher cuts
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Comparison with other determinations
A real step forward non-pert parameters are
everywhere in B physics
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?unquenching
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Testing parton-hadron duality

• What is it? For all practical purposes the OPE.
  No OPE, no duality
• Do we expect violations? Yes, Problems
  prevalently arise because OPE must be continued
  analytically. there are effects that cannot be
  described by the OPE, like hadronic thresholds.
• Can we constrain them effectively?
• in a self-consistent wayjust check the OPE
  predictions. Models may give hints of how it
  works
• Caveats? HQE depends on many parameters and we
  know only a few terms of the double expansion in
  as and ?/mb.

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The photon spectrum of B-gtXs?
Motion of b quark inside B and gluon radiation
smear the spike at mb/2
The photon spectrum is very insensitive to new
physics, can be used to study the B meson
structure ltE?gt mb/2 ... varltE?gt µ?2/12...
Importance of extending to E?(min) 1.8
GeV or less for the determination of both the
BR AND the B parameters (Bigi Uraltsev) Prelimina
ry study found Belle results compatible with
Babar fit
Belle NEW lower cut at 1.8GeV (in the ? rest
frame)
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Vcb from B?Dl?
At zero recoil, where rate vanishes. Despite
extrapolation, exp error 2 Main problem is
form factor F(1) The non-pert quantities
relevant for excl decays cannot be
experimentally determined Must be calculated but
HQET helps.
No new calculation since CKM1 F(1)
0.910.03-0.04 Sum rules give consistent
results Needs checking and unquenching
dVcb/Vcb 5 and agrees with inclusive det,
despite contradictory exps
B?Dl? gives consistent but less precise results
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The unitarity triangle
Unitarity determines several triangles in
complex plane
O(?3)
area measure of CPV
Vtd cannot be accessed directly we resort to
loop transitions FCNC sensitive to new physics
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Vub (not so much) inclusive

• Vub can be determined from total BR(b?ul?)
  almost exactly like incl Vcb but we need
  kinematic cuts to avoid the 100x larger b?cl?
  background
• mX lt MD El gt (MB2-MD2)/2MB
  q2 gt (MB-MD)2
• or combined (mX,q2) cuts
• The cuts destroy convergence
• of the OPE, supposed to work
• only away from pert singularities
• Rate becomes sensitive to local
• b-quark wave function properties
• (like Fermi motion
• gtgtgt SHAPE function)

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Each strategy has pros and cons
Luke, CKM workshop 2003
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Vub incl. and exclusive

• Intense theoretical activity
• subleading shape functions
• optimization of cuts (P,P- etc)
• weak annihilation contribs.
• Resum. pert. effects
• relation to b?s? spectrum
• SCET insight
• A lot can be learned from exp
• (on WA, better constraints on s.f., subleading
  effects from cut dependence, b?s?...)

REQUIRES MANY COMPLEMENTARY MEASUREMENTS
(affected by different uncert.)
Exclusive modes LCSR and LQCD complement each
other, but 20 error. Waiting for unquenching
New Babar MX 4.62(38)(49) New Belle (q2,MX)
4.66(28)(40)(58) But th error probably
overestimated WE ARE ALREADY AT 10
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eK, ?Md,?Ms hoping for new physics at the mercy
of lattice QCD
To use eK and ?mBd,s to extract CKM parameters,
we need 3 quantities from lattice BK , BBqf2Bq
and Typical errors for quenched results 10-17,
less for ?
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Progress in LQCD

• Despite folklore, there has been progress
• B physics simulations are multiscale present
• lattices can resolve neither b (too heavy)
• nor light q (too light)
• 3 main sources of systematics
• Discretization (different complementary approach)
• Chiral extrapolation (needs lighter quarks)
• Quenching (getting there many new unquenched
  results)

Example of difficulties ? parameter Chiral
extrapolation done using ChPT but at NLO large
logs appear (10-20) can we trust ChPT in regime
of simulations? (chiral logs are not observed in
that range) Waiting for lower mq, a 10 effect
maybe safe ?1.18(4)(12-0) Lellouch
?1.21(5)(1) Becirevic
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Two alternative routes to Vtd

• A good measurement of BR(K????),
• O(10-10), will provide an excellent clean deter
• mination of Vtd.
• BR(KL ??0??)3x10-11, determines ?
• Both very useful, but theory must be
• improved,exp is still far and prospects
• at NA48, CKM,JHF,KOPIO unclear

B???/B?K? can give a determination of Vtd. New
Belle result (first observation of b ?d) BR(B
?(?,?) ?)(1.80.60.1)x10-6
R(B???/B?K?)(4.21.3) Ali et al. extract from
this 0.16ltVtd/Vtslt0.29 at 1s, in agreement with
fits, but less precise. Form factors from LC
sum-rules. Exploratory calculations on the
lattice confirm LCSR their improvement is
essential
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Global fit results
http//www.utfit.org
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Global fit results (II)
http//ckmfitter.in2p3.fr
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Fitting methods a matter of taste
Differ in treatment of theory error. Two main
groups
Bayesian (UTfit) Non gaussian errors (th exp)
are assigned a flat pdf, to be convoluted with
gaussian pdfs Pro conceptually clean, easy for
?ms. Con does not provide a ?2 test
Rfit (CKMfitter) Non gaussian parameters
have flat likelihood, not pdf Pro more
conservative (beware of theorists guessing
errors!) Con CL is at least x
Difference important especially when theory
(non-gaussian) error dominates. The 99 CL
ranges of global fit are quite similar with SAME
INPUTS. see CKM Yellow book
DO NOT TAKE 1s RANGES TOO SERIOUSLY
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CP violation in the B and K sectors
Using only the sides of the UT (CP conserving)
Sin2ßUT 0.706 0.048 (without direct meas.)
Sin2ßJ/? Ks 0.734 0.054
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Prediction of ?ms
?ms 18.5 1.7 ps-1 (with all constraints)
?ms 21.0 3.3 ps-1 (?ms not used)
DIRECT MEASUREMENT ?ms gt 14.5 _at_ 95 C.L.
In the absence of new physics Tevatron should
measure it soon
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Prediction of ? and ?
At 95CL 42-78.5
sin2?
new Belle B?DK
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Fitting non-pert parameters
UTfit
LATTICE QCD UT FIT
fBvBB 223 ? 33 ? 12 MeV 217 ? 12 MeV
BK 0.86 ? 0.06 ? 0.14 0.71 ? 0.11
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The near (?) future?
A direct measurement of ?ms will also have a
significant effect
?? 24 ? 15 ?? 7 ? 4.6
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Summary

• CKM describes well a host of data. Present errors
  are dominantly theoretical LQCD best hope, but
  theory control can be improved by new data at
  B-Factories,Cleo-c,Tevatron...
• New Vcb inclusive/momnts analysis by Babar
  duality verified at level, better determination
  of non-pert B parameters
• First row universality problem seems resolved by
  new Kl3 data
• Progress in LQCD learning to unquench etc
• Excellent agreement so far with direct angle
  measurmnt
• 
  (pending scrutiny of B??KS)

...nevertheless, still room for new physics
(we have tested only a few FCNC)
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comparison