Status of the CKM matrix

Paolo Gambino Daphne-2004 7/6//2004

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Status of the CKM Status of the CKM matrixmatrix

Paolo Gambino INFN Torino


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Why CKM?

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.

Observed Flavor Violation is surprisingly close to SM prediction >>> the flavor problem

Strong interactions make CKM studies hard. Learning slowly but steadily. Theory errors dominate almost everywhere.

http://ckm-workshop.web.cern.ch/


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The CKM matrix

Wolfenstein parameterization

tbtstd

cbcscd

ubusud

CKM

VVV

VVV

VVV

V

describes Flavor Violation in the SM

3 angles and 1 phase with strong hierarchy: 0.22 sine of Cabibbo angle, A,,=O(1)

At present accuracy,Wolfenstein par must be improved_ _,


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tbtstd

cbcscd

ubusud

CKM

VVV

VVV

VVV

V 22

1

22

1

1

1

The Cabibbo angleThe Cabibbo angle

Historically, universality of

charged currents

1|||||| 222 ubusud VVV

O(10-5)

Comparison between Vud,Vus determinations oftests unitarity of the first line of VCKM

could also be measured from 2nd line, Vcd (DIS) at 10%,

W decays at LEP constrains Σij|Vij|2 at 1.3% Vcs at 1.3%


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from Vfrom Vudud

Superallowed Fermi transitions (0+->0+ β decay)

extremely precise, 9 expts, δVud~0.0005 dominated by RC

and nuclear structure

neutron β decay δVud~0.0015, will be improved at

PERKEO, Heidelberg

π+ decay to 0e th cleanest, promising in long term

but BR=10-8 PIBETA at PSI already at δVud~0.005

PDG : Vud=0.9738±0.0005 = 0.2274±0.0021


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2σ discrepancy!

Semileptonic Kl3 (K->πlν)E865 K+ disagrees 2.3σ from older exp

new KLOE (prelim) KS and KTeV KL agree with new resultK+ from KLOE, NA48 should come soon. th error?New results are con-sistent with unitarity

AG theorem:easily calculable ?

Discarding old results and using Leutwyler & Roos: |Vus|Kl3= 0.2255 ±0.0021

Next frontier: LQCD & measure slopes for Kμ3(Dalitz plot) to constrain PT

from Vus (Kl3)New lattice result: Becirevic et al

at 1% (see Lubicz talk)

E865

KLOE,KSprelim

KTeV

, K

L both

e,μ


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New ideasNew ideasτ decay (Vus) Jamin et al.

ms from sum rules or LQCD as input, may become competitive with B-factoryresults. At present

δVus~0.0045, low values

Hyperon decays (Vus)Cabibbo et al. have revisited the subject focussing on vector form fact. δVus~0.0027 (exp) but O(1%) or

more SU(3) breaking effects NOT included, lattice?

using f/fK from lattice Marciano (2004):

R.C.

Use LQCD for f/fK . Present MILC result 1.201(8)(15)Staggered fermions, partially unquenched. From there we get

= 0.2238 ± 0.0003(exp) ± 0.0004(rc) ± 0.0030(lattice)Compatible with other determinations. MILC error debated.Great potential for improvement


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EXCLUSIVE

Determination of ADetermination of A

VCKM

A can be determined using |Vcb| or |Vts|

Two roads to |Vcb|

INCLUSIVE


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The advantage of being The advantage of being inclusiveinclusive

ΛQCD«mb : inclusive decays admit systematic expansion in

ΛQCD/mb Non-pert corrections are generally small and can be controlled

Hadronization probability =1 because we sum over all statesApproximately insensitive to details of meson structure as ΛQCD«mb

(as long as one is far from perturbative singularities)

02

2

dqdqdE

d

l

can be expressed as double series in ααs s and and ΛQCD/mb

(OPE) with parton model as leading term No 1/mb

correction!


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Leptonic and hadronic spectra

Total rate gives CKM elmnts; shape tells us about B structure

OPE predictions can be compared to exp only after SMEARINGand away from endpoints: they have no LOCAL meaning


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State of the artKnown corrections up to 1/mb

3: OPE/HQE predictions are only functions of possible cuts and of

Perturbative Corrections: full O(αs) and O(β0 αs2) available

For hadronic moments thanks to NEW calculations Trott,UraltsevBLM to hadr moments not yet used in fits

Recent implementation for moments of lept and hadronic spectra including a cut on the lepton energy Bauer et al.,Uraltsev & PG

Leptonic momts measured more precisely but less sensitive to higher dim parmtrs than hadr momts

1,2

3

3

43

3

32

2

22

2

10

2

3

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)()()()(1192 b

LS

b

D

b

G

bewcb

bFcl m

ram

ram

ram

rarzAVmG

Gremm,Kapustin...1,2

33 , LSD


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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(ρD

3-0.2)...]

• Need short distance masses: mbkin(μ) and mb

1S

• Exploit correlations (most moments depend on the same combination of mc,mb

as width)

• Avoid unnecessary parameters

• Define carefully 2=-1+... G2= 32+...

• Theoretical uncertainties: missing 1/mb4, missing pert and mixed

effects. Need a recipe to estimate them... More work ahead

Traditionally mQ reexpressed using

Non linear ops: T1-4

MB,D

1/mc expansion


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Babar fit to |Vcb|, BRsl, HQE

paramts

Pioneer work by CLEO & Delphi employed less precise/completedata, some external constraints, and CLEO a different scheme

Problems with 1S scheme: a cloud?

Not all points includedNo external constraint


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No sign of No sign of deteriorationdeterioration

for higher cutsfor higher cuts

Kinetic scheme:Small pert correctionsMinimal set of parmts

No 1/mc expansion Uraltsev & PG


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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+unquenching


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Testing parton-hadron Testing parton-hadron dualityduality

What is it?What is it? For all practical purposes: the OPE. No OPE, no duality Do we expect violations?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?Can we constrain them effectively? in a self-consistent way:just check the OPE predictions.

Models may give hints of how it works

Caveats?Caveats? HQE depends on many parameters and we know only a few terms of the double expansion in αs and Λ/mb.


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The photon spectrum of B->Xsγ

Motion of b quark inside B and gluon radiation smear the spike at mb/2

Belle NEW: lower cut at 1.8GeV (in the rest frame)

The photon spectrum is very insensitive to new physics, can be used to study the B meson

structure <Eγ> = mb/2 + ... var<Eγ>

=μп2/12+...

Importance of extending to Eγ(min) ~ 1.8 GeV or less for the determination of both the BR AND the B parameters (Bigi Uraltsev)

Preliminary study found Belle results compatible with Babar fit


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|Vcb| from BD*lAt 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) = 0.91+0.03-0.04

Sum rules give consistent resultsNeeds checking and unquenching

FB→D*(1) = ηA [1 - O(1/mb,1/mc)2]

BDl gives consistent but less precise results

δVcb/Vcb~ 5% and agrees with inclusive det, despite contradictory exps


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The unitarity triangleThe unitarity triangle

ikjkijVV *

tbtstd

cbcscd

ubusud

CKM

VVV

VVV

VVV

V

Unitarity determines several triangles in complex plane

0*** tbtdcbcdubud VVVVVV

01*

*

*

*

cbcd

tbtd

cbcd

ubud

VV

VV

VV

VV

|Vub/Vcb| describes a circle in the (,) plane

Vtd cannot be accessed directly:we resort to loop transitions

FCNC sensitive to new physics

O(3)

area= measure of CPV


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|Vub| (not so much) inclusive

|Vub| can be determined from total BR(bul) almost exactly like incl |Vcb| but we need kinematic cuts to avoid the ~100x larger bcl background:

mX < MD El > (MB2-MD

2)/2MB q2 > (MB-MD)2

or combined (mX,q2) cuts

The cuts destroy convergenceof the OPE, supposed to workonly away from pert singularities

Rate becomes sensitive to “local”b-quark wave function properties (like Fermi motion >>> SHAPE function)


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Each strategy has pros and cons

Luke, CKM workshop 2003


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Vub incl. and exclusive

exclusiveexclusive

Intense theoretical activity:subleading shape functionsoptimization of cuts (P+,P-

etc)weak annihilation contribs.Resum. pert. effectsrelation to bs spectrumSCET insight

A lot can be learned from exp(on WA, better constraints on s.f., subleading effects from cut dependence, bs...) REQUIRES MANY COMPLEMENTARY

MEASUREMENTS (affected by different uncert.)

Exclusive modes: Exclusive modes: LCSR and LQCDLCSR and LQCDcomplement each other, but complement each other, but ~20% ~20% error. Waiting for unquenching… error. Waiting for unquenching…

New Babar MX 4.62(38)(49)New Belle (q2,MX) 4.66(28)(40)(58)

But th error probably overestimatedWE ARE ALREADY AT 10%


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εεKK, , ΔΔMMdd,,ΔΔMMss: hoping for new physics : hoping for new physics at the mercy of lattice QCD at the mercy of lattice QCD

To use εK and ΔmBd,s to extract CKM parameters, we need 3 quantities from lattice: BK , BBqf2

Bq andTypical errors for quenched results: 10-17%, less for

ξ


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Progress in LQCD 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: ξ 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

ξ=1.18(4)(+12-0) Lellouch ξ=1.21(5)(1) Becirevic

quenched

Quench. Appr.


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Two alternative routes to |Vtd|

• A good measurement of BR(K++), O(10-10), will provide an excellent clean determination 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/BK* can give a determination of Vtd.

New Belle result (first observation of b d) :

BR(B (,ω) )=(1.8±0.6±0.1)x10-6

R(B/BK*)=(4.2±1.3)% Ali et al. extract from this 0.16<|Vtd/Vts|<0.29 at 1σ, 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 resultsGlobal fit results

ρ = 0.204 ± 0.045 η = 0.341 ± 0.027

http://www.utfit.org


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Global fit results (II)Global fit results (II)

http://ckmfitter.in2p3.fr

= = 0.1890.189±0.078±0.078

=0.358±0.044

slightly different inputs


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Fitting methods: a matter of tasteFitting methods: a matter of tasteDiffer 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 Δms.

Con: does not provide a 2 test

Rfit (CKMfitter)Non gaussian parameters haveflat likelihood, not pdfPro: 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 1σ RANGES TOO SERIOUSLY


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CP violation in the B and K sectorsCP violation in the B and K sectors

Using only the sides of the UT (CP conserving)

Sin2βJ/ψ Ks = 0.734 ± 0.054 Sin2βUT = 0.706 ± 0.048 (without direct meas.)


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Prediction of Prediction of ΔΔmmss

DIRECT MEASUREMENT: Δms > 14.5 @ 95 % C.L.

Δms = 21.0 ± 3.3 ps-1

(Δms not used)

Δms = 18.5 ± 1.7 ps-1

(with all constraints)

In the absence of new physics Tevatron should measure it soon

http://www.slac.stanford.edu/%7Epierini/triangolo/ckm-dms/ckm-dms.html




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25.022.027.02sin

)2.59( 2.72.6

At 95%CL [42-78.5]

Prediction of Prediction of andand

46.056.029.02sin

)62( 1012

new Belle Bnew Belle BDKDK

sin2


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Fitting non-pert parametersFitting non-pert parameters

LATTICE QCD UT FIT

fB√BB223 33 12

MeV217 12 MeV

BK 0.86 0.06 0.14 0.71 0.11

UTfit


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BK = 0.86 ± 0.06 ± 0.14

ξ = 1.24 ± 0.04 ± 0.06

fBs√BBs = 276 ± 38 MeV14

sin2β = 0.734 ± 0.05421

The near (?) future?

Δρ = 24% → 15% Δη = 7% → 4.6%

A direct measurement of Δms will also have a significant effect


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SummarySummary 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 BKS)

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


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comparison

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Status of the CKM matrix

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