,1,1,1,1 ,2,2,2,2 ,3,3,3,3 on behalf of m. bona, g. eigen, r. itoh on behalf of m. bona, g. eigen,...

,,11

,,22

,,33

On behalf of M. Bona, G. Eigen, R. ItohOn behalf of M. Bona, G. Eigen, R. Itohand E. Kouand E. Kou

G. Eigen, Vxb workshop, SLAC, October 31 2009 2

Chapter OutlineChapter OutlineSection: Introduction and goals Section: Introduction and goals 2p2pSection: MethodologySection: Methodology

Subsection: CKMfitter Subsection: CKMfitter 2p2pSubsection: UTfit Subsection: UTfit 2p2pSubsection: Scanning method Subsection: Scanning method 2p2p

Section: Experimental InputsSection: Experimental InputsSubsection: B-factories results: Subsection: B-factories results: , , (which decays to consider), (which decays to consider), , 2, 2++,,,,VVubub, , VVcbcb, , mmdd, A, Add

SLSL, B(B, B(B),radiative penguins (how to use them) ),radiative penguins (how to use them) 4p4pSubsection: Non-B-factories results (briefly on their threatment): Subsection: Non-B-factories results (briefly on their threatment): KK, , mmss, A, Ass

SLSL, , TD BTD Bss J/J/, , ss (with order calculation). (with order calculation). 2-3p2-3p

Rather than having subsubsections we indicate in the table which are inputs Rather than having subsubsections we indicate in the table which are inputs for the SM fit and inputs for the BSM fitsfor the SM fit and inputs for the BSM fits

Section Theoretical InputsSection Theoretical InputsSubsection Derivation of hadronic observables Subsection Derivation of hadronic observables 2p2pSubsection Lattice QCD inputs Subsection Lattice QCD inputs 4p4p

Benchmark models Benchmark models 5p5pSection Results from the global fits Section Results from the global fits Section Global fits beyond the Standard Model Section Global fits beyond the Standard Model 4p4p

Subsection New-physics parameterizations Subsection New-physics parameterizations 4p4pSubsection Operator analysis Subsection Operator analysis 2p2p

Section ConclusionsSection Conclusions 1-2p1-2p total: 36-38 pagestotal: 36-38 pages


MotivationMotivation

The CKM matrix is specified by 4 independent parameters, The CKM matrix is specified by 4 independent parameters, in the Wolfenstein approximation they are in the Wolfenstein approximation they are , A, , and

Unitarity of the CKM matrix specifies relations among the Unitarity of the CKM matrix specifies relations among the parametersparameters

e.g.e.g.

Combine measurements from theCombine measurements from the B and K systems to overconstrainB and K systems to overconstrain the trianglethe triangle test if phase of CKM matrixtest if phase of CKM matrix is only source of CP violationis only source of CP violation

€

VCKM =

1−122 −1

84 A3( −i)

− + A25(12−−i) 1−1

22 −1

84 −1

2A24 A2

A3(1− −i ) −A2 + A4(12−−i) 1−1

2A24

⎛

⎝

⎜ ⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟ ⎟

+O(6 )

,,11

,,22

,,33

V

udV

ub

* +VcdV

cb

* +VtdV

tb

* =0

11

Ru=

VudV

ub

*

VcdV

cb

*

Rt=

VtdV

tb

*

VcdV

cb

*

((, , ))

, φ1=arg −

VcdV

cb

*

VtdV

tb

*

⎛

⎝⎜⎜

⎞

⎠⎟⎟

, φ2=arg −

VtdV

tb

*

VudV

ub

*

⎛

⎝⎜⎜

⎞

⎠⎟⎟

, φ3=arg −

VudV

ub

*

VcdV

cb

*

⎛

⎝⎜⎜

⎞

⎠⎟⎟


MotivationMotivation

In the SM in theIn the SM in the absence of errorsabsence of errors all measurements of all measurements of UT properties exactlyUT properties exactly meet in meet in and

The extraction of The extraction of , depends on QCDdepends on QCD parameters thatparameters that have large theoryhave large theory uncertaintiesuncertainties

We use 3 differentWe use 3 different fit methods: fit methods: CKMfitter, UTfit CKMfitter, UTfit and Scanning methodand Scanning method which differ in thewhich differ in the treatment of QCD parameters treatment of QCD parameters


CKMfitter MethodologyCKMfitter Methodology CKMfitter (Rfit) is a frequentist-based approach to the global fit ofCKMfitter (Rfit) is a frequentist-based approach to the global fit of

CKM matrixCKM matrix

Likelihood function:Likelihood function:

First term measures agreement between data, xFirst term measures agreement between data, xexpexp,, and prediction, xand prediction, xthth

Second term expresses our present knowledge on QCD parametersSecond term expresses our present knowledge on QCD parameters yymodmod are a set of fundamental and free parameters of theory (m are a set of fundamental and free parameters of theory (mtt, etc), etc)

Minimize Minimize

and determineand determine

where where 22min;ymin;ymodmod is the absolute minimum value of is the absolute minimum value of 2 2 functionfunction

Separate uncertainties of QCD parameters into statistical (Separate uncertainties of QCD parameters into statistical () and) and non-statistical (theory) uncertainties (non-statistical (theory) uncertainties ()) statistical uncertainties are treated like experimental errors withstatistical uncertainties are treated like experimental errors with a Gaussian likelihooda Gaussian likelihood

L[y

mod] = L

exp[x

exp−x

th(y

mod)] ×L

th[y

QCD]

2 (y

mod) ≡−2 ln(L [y

mod] )


Rfit MethodologyRfit Methodology

Treatment of theory uncertainties (Treatment of theory uncertainties ():): If fitted parameter a lies within the predicted range xIf fitted parameter a lies within the predicted range x00±±xx00 contribution to contribution to 2 2 is zerois zero If fitted parameter a lies outside the predicted range xIf fitted parameter a lies outside the predicted range x00±±xx00

the likelihood the likelihood LLthth[ y[ yQCDQCD] drops rapidly to zero, define:] drops rapidly to zero, define:

3 different analysis goals3 different analysis goals Within SM achieve best estimate of yWithin SM achieve best estimate of ythth

Within SM set CL that quantifies Within SM set CL that quantifies agreement between data and theoryagreement between data and theory

Within extended theory framework search for specific signs Within extended theory framework search for specific signs ofof

new physicsnew physics

−2 lnLth[x

0, κ, ζ] =

0, ∀x0∈ x

0±ζx

0⎡⎣

⎤⎦

x0−x

0

κx0

⎛

⎝⎜⎜

⎞

⎠⎟⎟

2

−ζ

κ

⎛

⎝⎜

⎞

⎠⎟

2

, ∀x0∉ x

0±ζx

0⎡⎣

⎤⎦


UTfit MethodologyUTfit Methodology

UTfit is a Bayesian-based approach to the global fit of CKM UTfit is a Bayesian-based approach to the global fit of CKM matrixmatrix

For M measurements cFor M measurements cjj that depend on that depend on and plus other

N parameters xi the function needs to

be evaluated by integrating over xi and cj

Using Bayes theorem one finds

where f0(, ) is the a-priory probability for and

The output pdf for and is obtained by integrating over cj and xi

f(, , x

1, . . . .x

N| c

1, . . . .c

M) ∝ f

j(c

j| , , x

1, . . . , x

N) f

i(x

i)f

0(, )

i=1,N∏

j =1,M∏


UTfit MethodologyUTfit MethodologyMeasurement inputs and all theory parameters are described by Measurement inputs and all theory parameters are described by pdfspdfs

Errors are typically treated with a Gaussian model, only for BErrors are typically treated with a Gaussian model, only for Bkk, , and fand fBB√B√BBB a flat distribution representing the theory uncertainty is a flat distribution representing the theory uncertainty is convolved with a Gaussian representing the statistical uncertaintyconvolved with a Gaussian representing the statistical uncertainty

So if available, experimental inputs are represented by likelihoodsSo if available, experimental inputs are represented by likelihoods

The method does not make any distinction between measurement The method does not make any distinction between measurement andand

theory parameterstheory parameters

The allowed regions are well defined in terms of probabilityThe allowed regions are well defined in terms of probability allowed regions at 95% probability means that you expect theallowed regions at 95% probability means that you expect the “ “true” value in this range with 95% probabilitytrue” value in this range with 95% probability

By changing the integration variables any pdf can be extractedBy changing the integration variables any pdf can be extracted this yields an indirect determination of any interesting quantitythis yields an indirect determination of any interesting quantity


The Scanning MethodThe Scanning Method The basis is the original approach by M.H. Schune & S. Plaszczynski

used for the BABAR physics book

The fit method was extended to include over 250 single measurements

The four QCD parameters Bk, fB, BB, and Vub, Vcb, have significant theory uncertainties, thus they are scanned in the following way

We express each parameter in terms of x0 ± x±x, where is a statistical uncertainty and x is the theory uncertainty

We select a specific value x*[x0 - x, x0 + x] as a model We consider all models inside the [x0 - x, x0 + x] interval In each model the uncertainty q is treated in a statistical way

The uncertainties in the QCD parameters cc, ct, tt, and B and the quark masses mc(mc) and mb(mb) are treated like statistical uncertainties, since these uncertainties are relatively small however, if necessary, we can scan over any of these parameters


The Scanning MethodThe Scanning Method We perform maximum likelihood fits using a frequentist approach

A model is considered consistent with data if P(2M)min > 5%

For consistent models we determine the best estimate and plot a 95% CL (, ) contour we overlay contours of consistent models however, though only one of the contours is the correct one, we do not know which and thus show a representative numebr of them

For accepted fits we also study the correlations among the theoretical parameters extending their range far beyond the range specified by the theorists

We can input We can input , , 22 and and , , 33 via a likelihood function or directly via a likelihood function or directly usingusing

individual Bindividual B, , , , , a, a11, b, b11 measurements and measurements and GLW, ADS and Dalitz plot measurements in BD(*)K(*) & sin(2+), respectively

We can further determine PP, PV VV amplitudes and strong phases using Gronau and Rosner parameterizations in powers of

Work is in progress to include cos 2, s, AqSL, s and s

add contours of sin 2, and sin (2+) and improve on display


Differences among the 3 Methods Differences among the 3 Methods Fit methodologies differ: 2 frequentistFit methodologies differ: 2 frequentist

approaches vs 1 Bayesian approachapproaches vs 1 Bayesian approach

Theory uncertainties are treated Theory uncertainties are treated differently in the global fitsdifferently in the global fits

Presently, measurement input values differPresently, measurement input values differ plus some assumptions differplus some assumptions differ

For VFor Vubub and V and Vcbcb there is an issue how to there is an issue how to combine inclusive and exclusive resultscombine inclusive and exclusive results

Inclusive/exclusive averages Inclusive/exclusive averages individual results individual resultsResulting errors Resulting errors

QCD parameters inputs differ, eg fQCD parameters inputs differ, eg fBsBs, B, BBsBs, f, fBsBs/f/fBdBd, B, BBsBs/B/BBdBd ffBdBd, B, BBdBd, , f fBdBdBBBdBd, ,

We need to standardize measurement inputs, QCD parametersWe need to standardize measurement inputs, QCD parameters (at least numerical values should agree) and assumptions(at least numerical values should agree) and assumptions


Input Measurements from B Input Measurements from B FactoriesFactories

Vub and Vcb measured in exclusive

and inclusive semileptonic B decays

md from BdBd oscillations

CP asymmetries acp(KS) from B ccKs decays angle

from B, B, & B CP measurements, add Ba1, Bb1

rruu

mmdd

sin2sin2

GLW, ADS and GGSZGGSZ analyses in BD(*)K(*)


Input Measurements from B FactoriesInput Measurements from B Factoriessin(2+) measurement from

BD(*)()

cos 2 from BJ/K* and BD00

B branching fractionsin(2sin(2+ + )) coscos

B(BB(B))


Other Input Measurements Other Input Measurements |K| from CP violation in K decays

md/ms from BdBd and BsBs oscillations

s - s from Bs measurements at the Tevatron

CKM elements Vud, Vus, Vcd, Vcs, Vtb

||KK||

mmdd//mmss


Measurement InputsMeasurement Inputs

* use * use average valuesaverage values

ObservableObservable CKMfitterCKMfitter UTfitUTfit Scanning MScanning M

|V|Vusus|| 0.2246±0.00120.2246±0.0012 0.2259±0.00090.2259±0.0009 0.2258±0.00210.2258±0.0021

|V|Vubub| [10| [10-3-3]] 3.79±0.09±0.413.79±0.09±0.41**

4.114.11+0.27+0.27-0.28-0.28 (inc) (inc)

3.38±0.36 3.38±0.36 (exc)(exc)

3.84±0.16±0.29 3.84±0.16±0.29 (ex(ex

|V|Vcbcb| [10| [10-3-3]] 40.59±0.37±0.540.59±0.37±0.58*8*

41.54±0.73 41.54±0.73 (inc)(inc)

38.6±1.1 38.6±1.1 (exc)(exc)

40.9±1.0±1.6 40.9±1.0±1.6 (exc)(exc)

B(BB(B) [10) [10-4-4]] 1.73±0.351.73±0.35 1.51±0.331.51±0.33 1.79±0.721.79±0.72

mmBBdd [ps[ps-1-1]] 0.507±0.0050.507±0.005 0.507±0.0050.507±0.005 0.508±0.0050.508±0.005

mmBBss [ps[ps-1-1]] 17.77±0.1217.77±0.12 17.77±0.1217.77±0.12 17.77±0.1217.77±0.12

||KK| [10| [10-3-3]] 2.229±0.0102.229±0.010 2.229±0.0102.229±0.010 2.232±0.0072.232±0.007

sin 2sin 2 0.671±0.0230.671±0.023 0.671±0.0230.671±0.023 0.68±0.0250.68±0.025

[ [ , , , , ]] 1-CL(1-CL()) -2-2ln(ln(LL)) B, S, C for B, S, C for & &

[GGSZ, GLW, [GGSZ, GLW, ADS]ADS]

1-CL(1-CL()) -2-2ln(ln(LL)) GGSZ, GLW, ADSGGSZ, GLW, ADS

cos 2cos 2 J/J/K*K* J/J/K*, DK*, D0000 To be doneTo be done

22++ DD(*)(*)(()) -2-2ln(ln(LL)) DD(*)(*)(())


Lattice QCD InputsLattice QCD Inputs

ParameterParameter CKMfitterCKMfitter UTfitUTfit ScanningScanning

Mean Mean statstat theotheo Mean Mean Mean Mean stat stat theotheo

ffBBss [f[fBdBd]] 228 ±3 ±17228 ±3 ±17 245 ±25245 ±25 [216 ±10 ± [216 ±10 ± 20]20]

ffBBss/f/fBBdd 1.199 ±0.008 ±0.0231.199 ±0.008 ±0.023 1.21 1.21 ±0.04±0.04

BBBBss [B[BBdBd]] 1.23 ±0.03 ±0.051.23 ±0.03 ±0.05 1.22 1.22 ±0.12±0.12

[1.29 ±.05 [1.29 ±.05 ±.08]±.08]

BBBBss/B/BBBdd [[]] 1.05 ±0.02 ±0.051.05 ±0.02 ±0.05 1.00 1.00 ±0.03±0.03

[1.2 ±.028 [1.2 ±.028 ±.05]±.05]

BBK K [2 GeV][2 GeV] 0.525 ±0.0036 ±0.0520.525 ±0.0036 ±0.052

BBKK 0.721 ±0.005 ±0.0400.721 ±0.005 ±0.040 0.75 0.75 ±0.07±0.07

0.79 ±0.04 0.79 ±0.04 ±0.09±0.09

mmcc(m(mcc) ) [GeV][GeV]

1.286 ±0.013 ±0.0401.286 ±0.013 ±0.040 1.3 ±0.11.3 ±0.1 1.27±0.111.27±0.11

mmtt(m(mtt) [GeV]) [GeV] 165.02 ±1.16 ±0.11165.02 ±1.16 ±0.11 161.2 161.2 ±1.7±1.7

163.3 ±2.1163.3 ±2.1

cccc Calculated from mCalculated from mcc(m(mcc) & ) & ss

1.38 1.38 ±0.53±0.53

1.46±0.221.46±0.22

ctct 0.47±0.040.47±0.04 0.47 0.47 ±0.04±0.04

0.47±0.040.47±0.04

tttt 0.5765±0.00650.5765±0.0065 0.574 0.574 ±0.004±0.004

0.5765±0.00650.5765±0.0065

BB(MS)(MS) 0.551±0.0070.551±0.007 0.55 0.55 ±0.01±0.01

0.551±0.0070.551±0.007

ss 0.1176±0.00200.1176±0.0020 0.119 0.119 ±0.03±0.03

0.1180.118


Global Fit ResultsGlobal Fit ResultsInputs: |VInputs: |Vudud|, |V|, |Vusus| |

|V|Vcbcb|, |V|, |Vubub|| BB(B(B)) ||KK|| mmBBdd, , mmBBss

sin 2sin 2, 1-CL(, 1-CL(), 1-CL(), 1-CL())

Note scales are not the same! Note scales are not the same!

20082008inputsinputs


Tension from Tension from BB(B(B))

BB(B(B) is proportional to ) is proportional to |V|Vubub||22 and f and f22

BBdd

from global fitfrom global fit BB(B(B)=(0.79)=(0.79+0.016+0.016))1010-4-4

WA: WA: BB(B(B)=(1.73±0.35))=(1.73±0.35)1010-4-4

2.42.4 discrepancy discrepancy

If If BB(B(B) or sin 2) or sin 2 are removed are removed 22

minmin in global fit drops by 2.4 in global fit drops by 2.4

|V|Vubub|, |V|, |Vcbcb| remain unaffected| remain unaffected

direct measurementdirect measurement

allowed region by fitallowed region by fit

-0.010-0.010


Constraints in the mConstraints in the mHH-tan-tan Plane Plane

From BABAR/Belle average From BABAR/Belle average we extractwe extract

We can use the 95% CLWe can use the 95% CL to present exclusions atto present exclusions at 95% CL in the m95% CL in the mH+H+-tan-tan plane plane

BB

1.2< 101.2< 1099 aa <4.6<4.6

BBXXss

Dark matterDark matter

mmHH

95% C.L. exclusions95% C.L. exclusions

TevatronTevatron

KK

tan tan

LEPLEP

rrHH

tan tan /m/mHH

95%CL95%CL

HH++

rH=1. 67 ±0. 34

exp±0. 36

fB,V

ub

rH= 1 −

mB

2

mH+

2 (1 + 0⋅tan)

tan2 ⎛

⎝⎜⎜

⎞

⎠⎟⎟

2

ATLAS 5ATLAS 5 discovery curve discovery curve


Model-Independent Analysis of UTModel-Independent Analysis of UT

Assume that new physics only affects short-distance part of B=2

We use model-independent parameterization for BWe use model-independent parameterization for Bdd and B and Bss

where Hwhere Hfull full = H= HSM SM + H+ HNPNP

Several observables are Several observables are modified by the magnitude modified by the magnitude or phase of or phase of qq

NPNP

In BIn Bdd system we compare system we compare RRu u & & with sin 2 with sin 2, sin2, sin2 and and mmd d that may be modified that may be modified by NP parameters (by NP parameters (dd, , dd) )

In BIn Bss system we compare R system we compare Ru u & & with with mmss, , ss, and , and ss that may be that may be modified by NP parameters (modified by NP parameters (dd, , dd))

Bq

0 HB=2

f ull Bq

0

Bq

0 HB=2

SM Bq

0=

q

NP = q

NP exp 2iφq

NP{ }


Model-Independent Analysis of UT for |Model-Independent Analysis of UT for |dd|- |- dd

Inputs: Inputs: mmdd, , mmss, sin 2, sin 2, , , , dd, A, ASLSLBdBd, A, ASLSL

BsBs , w/o , w/o BB(B(B))

Dominant constraints come from Dominant constraints come from and and mmdd

Semileptonic asymmetries ASemileptonic asymmetries ASLSL exclude symmetric solution with exclude symmetric solution with <0<0

dd=1 (SM) is disfavored by 2.1=1 (SM) is disfavored by 2.1 (discrepancy (discrepancy BB(B(B) and sin 2) and sin 2))

ddNPNP=(-12=(-12+9+9

-6-6))0 0 @ 95% CL (@ 95% CL (discrepancy is 0.6discrepancy is 0.6 w/o w/o BB(B(B) )) )

||dd||


Model-Independent Analysis of UT for |Model-Independent Analysis of UT for |ss|- |- ss

Inputs: Inputs: ss, , mmdd, , mmss, A, ASLSLBdBd, A, ASLSL

BsBs, , ss, , ss, , BB(B(B))

Dominant constraints come from direct measurements of Dominant constraints come from direct measurements of ss, , ss in Bin BJ/J/ and and mms s from the Tevatronfrom the Tevatron

ss is 2.2 is 2.2 away from the SM prediction away from the SM prediction

ss =1 is disfavored at 1.9 =1 is disfavored at 1.9 level independent of level independent of BB(B(B))

||ss||


Final RemarksFinal RemarksAmong the 3 global CKM fitting methods we need to standardize

All measurement inputsWhat QCD parameters to use, their central values, their statistical

errors and their theory errorsThe notation for quantities in the text, on plots and in equations

We need to specify which input parameters are used in the fits and

standardize on the assumptions This is important for comparing results

We will present results in form of plots with values listed in tables we accompany the results with a few remarks in particular in cases of discrepancies we need to discuss them

Most of the writing probably has to be done by the co-conveners


More Recent PublicationsMore Recent PublicationsCKMfitter publications

J. Charles et al., Eur. Phys. J. C41, 1-135, 2005.

UTfit publications:M. Bona et al., JHEP 0610:081, 2006.M. Bona et al., JHEP 0610:081, 2006.M. Bona et al., Phys.Rev.D76:014015, 2007.M. Bona et al., Phys.Rev.D76:014015, 2007.M. Bona et al., Phys.Rev.Lett.97:151803, 2006. M. Bona et al., Phys.Rev.Lett.97:151803, 2006. M Bona et al., Phys.Lett.B687:61-69, 2010.M Bona et al., Phys.Lett.B687:61-69, 2010.

Scanning methodScanning methodG. Eigen et al., Eur.Phys.J.C33:S644-S646,2004.G. Eigen et al., Eur.Phys.J.C33:S644-S646,2004.G.P. Dubois-Felsmann et al., hep-ph/0308262.G.P. Dubois-Felsmann et al., hep-ph/0308262.

,1,1,1,1 ,2,2,2,2 ,3,3,3,3 on behalf of m. bona, g. eigen, r. itoh on behalf of m. bona, g. eigen,...

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