Incontri di fisica del b, Parma, 19 th January 2006 on behalf of the Collaboration M. Bona, M. Ciuchini, E. Franco, V. Lubicz, G

Incontri di fisica del b, Parma, 19th January 2006

stransition 2F in search Physics New

and fitsTriangleUnitarity of Status

on behalf of the Collaborationhttp://www.utfit.org

M. Bona, M. Ciuchini, E. Franco, V. Lubicz,G. Martinelli, F. Parodi, M. Pierini, P. Roudeau,

C. Schiavi, L. Silvestrini, A. Stocchi, V. V.

BolognaBolognaVincenzo VagnoniVincenzo Vagnoni

Vincenzo Vagnoni 2Incontri di fisica del b, Parma, 19th January 2006

CKM Physics: not just a triangle...CKM Physics: not just a triangle...


1-2/2

1-2/2

u

c

d s b

A 3(1--i) -A2t

d, sbd, s b

Vtd ,Vts

B Oscillations

A 3(i)

A2

1Vtb

c,u

B decays

b

Vub,Vcb

Wolfenstein parametrization

4 parameters: ,A,

b-Physics plays a crucial role in the determination of those parameters

The CKM matrix The CKM matrix


† † 1V V V V The CKM is unitary

* * * 0ub ud cb cd tb tdV V V V V V

*22

*

1 1(1 ) ~td tb td td

cd cb cb ts

V V V VAB

V V V V

* 22 2

*

11

2ud ub ub

cd cb cb

V V VAC

V V V

*

*atan

(1 )arg td tb

cd cb

V V

V V

*

*atanarg ud ub

cd cb

V V

V V

1

The Unitarity Triangle The Unitarity Triangle

The non-diagonal elements of the matrix products correspond to 6 triangle equations


Bayes Theorem

Standard Model +OPE/HQET/Lattice QCD

to gofrom quarks

to hadrons} , mt}M. Bona et al. (UTfit Collaboration)

JHEP07 (2005) hep-ph/0501199

M. Bona et al. (UTfit Collaboration)hep-ph/0509219

M. Bona et al. (UTfit Collaboration)JHEP07 (2005) hep-ph/0501199

M. Bona et al. (UTfit Collaboration)hep-ph/0509219

The UTThe UTfitfit method and the inputs method and the inputs


StandardStandard UT UTfitfit: inputs: inputs


Standard constraints in the plane

Vub/Vcb

K sin()

levels @95% CL

md

md/ms

= 0.343 ± 0.028 [0.289, 0.396] @ 95% Prob.

= 0.343 ± 0.028 [0.289, 0.396] @ 95% Prob.

= 0.214 ± 0.047 [0.112, 0.307] @ 95% Prob.

= 0.214 ± 0.047 [0.112, 0.307] @ 95% Prob.


First crucial test of the Standard Model

Determination of CP-violating parameters measuring CP-conserving observables: results fitting with sides only vs CP-violating observables

sin 2 = 0.687 ± 0.032 experimental value from charmonium

sin 2 = 0.793 ± 0.033 expectation from side-only results


Slight inconsistence in the fit due to an increase of VSlight inconsistence in the fit due to an increase of Vubub


Tree Processes could be used to « discover » NP comparing «direct» (which are NP free) and «indirect» (where NP contributions could show up) measurements of the same quantity.

Predictions

γ = (57.9 ± 7.4)° γ = 65.0 ± 18.0γ = -115.0 ± 18.0

NEW crucial TEST« Partially » DONE


Including all the constraints…

= 0.343 ± 0.022 [0.300, 0.385] @ 95% Prob.

= 0.343 ± 0.022 [0.300, 0.385] @ 95% Prob.

= 0.215 ± 0.037 [0.141, 0.286] @ 95% Prob.

= 0.215 ± 0.037 [0.141, 0.286] @ 95% Prob.


pre-B-factoriesanalysis

UT fit with angles onlyUT fit with angles only


ms > 14.5 ps-1 at 95% CLSensitivity at 18.5 ps-1

SM prediction on SM prediction on mms s from UT fitsfrom UT fits

Despite the “heroic” efforts at LEP, SLD

and CDF Run-I(now also CDF/D0 Run-II), ms is still

unmeasured

p.d.f. for ms in SM UT fitswithout using its current

experimental limit

ms = 22.2 ± 3.1 ps-1

“Compatibility plot” for an

hypotetical future measurement

> 31 ps-1 @ 3 σ > 38 ps-1 @ 5 σ


Relevance of LQCD for exploiting Relevance of LQCD for exploiting precise precise mmd,sd,s measurements in measurements in

Unitarity Triangle fitsUnitarity Triangle fits

2

22

2

2

)1(

21

s

d

B

B

s

d

m

m

m

m

2

222622

2

02

2

2 1ˆ)1(6

ssd BB

W

tBWB

Fd BfA

m

mSmm

Gm

mmd,sd,s enter the UT fits through the constraints enter the UT fits through the constraints

where the long distance hadronic quantities are calculated in the where the long distance hadronic quantities are calculated in the framework of LQCD:framework of LQCD:

06.004.024.1ˆ

ˆ

dd

ss

BB

BB

Bf

Bf MeVBf

ss BB 38276ˆ


Fit with NP-independent constraints

using Tree-level processesassumed to be NP free*the effect of the D0-D0 mixingis negligible wrt the actual error

= ± 0.18 ± 0.11

= ± 0.41 ± 0.05

very important to improve: Vub/Vcb from semileptonic decays

from tree level processes

referencestarting point for NP modelbuilding


New Physics model independent New Physics model independent parametrization in |parametrization in |F|=2 transitionsF|=2 transitions

sdqBHB

BHBeC

qSMeffq

qfull

effqi

BqB

q,

00

002

The mixing processes being characterized by a single The mixing processes being characterized by a single amplitude, they can be parametrized in a general way by amplitude, they can be parametrized in a general way by means of two parametersmeans of two parameters

HSMeff includes only SM box diagrams while Hfull

eff includes New Physics contributions as well

00

00

Im

Im

KHK

KHKC

SMeff

fulleff

K

For the neutral kaon mixing case, it is convenient to For the neutral kaon mixing case, it is convenient to introduce only one parameterintroduce only one parameter

mK is not considered since the long distance effects are not well controlled

Four “independent” observables (C=1, Four “independent” observables (C=1, =0 in SM)=0 in SM) CBd, Bd, CBs, Bs

5 additional parameters 5 additional parameters


not yet available

6 available constraints

Allowing for NP in |Allowing for NP in |F|=2 transitions the F|=2 transitions the additional parameters are left free in the fitadditional parameters are left free in the fit

SMKK

BSM

BSM

BSM

SMsBs

SMdBd

K

s

d

d

s

d

C

mCm

mCm

exp

exp

exp

exp

exp

exp


|Vub/Vcb| md

K

ACP(J/K0) (DK)

|Vub/Vcb| md

K

ACP(J/K0) (DK)

+ cos2 ASL

cos2 ASL

Using the NP model independentapproach in the fit

SM-like solution

The inclusion of ASL has an impact for suppressing the satellite NP

solution

(very suppressed) « NP » solution


CBd = 1.27 ± 0.44

Bd = -4.7 ± 2.3

CK = 0.95 ± 0.18

Still 50% room for New Physics in md amplitude

But the New Physics mixing phase is already

very constrained,must be close to zero!

Using the NP model independentapproach in the fit (II)


New Physics in the bd sector starts to be quite constrained andmost probably will not come as an alternative to

the CKM picture, but rather as a «correction»

What to say/hope then?What to say/hope then?

Basically two scenarios

Minimal Flavour Violation:the only source of flavour

violation is in the SM Yukawa couplings (implies =0)

New Physics couplings between third and second families

(bs sector) are stronger with respect to the bd ones

Flavour physics needs to improve existing measurements in the Bd sector and perform precise measurement in the Bs sector:

Physics case for SuperB and LHCbPhysics case for SuperB and LHCb


Universal Unitarity Triangle:generalized SM analysis and MFV

MFV = no additional flavour mixingonly mixing processes are sensitive to NP

For UUT we do not use K and md in the fit

= 0.258 ± 0.066 from UUT fit = 0.258 ± 0.066 from UUT fit

= 0.319 ± 0.039 from UUT fit= 0.319 ± 0.039 from UUT fit

Buras et al. hep-ph/0007085


NP bounds in MFV scenario with small tan

NP enters as additional contributionto the top box diagram(D'Ambrosio et al. hep-ph/0207036)

0 = 2.4 TeV0 is the equivalent SM scale

> 3.6 TeV @ 95% for S0(xt) > 0 > 5.1 TeV @ 95% for S0(xt) < 0

S0 = -0.03 ± 0.54 [-0.90, 1.79] @95% Prob.

S0 = -0.03 ± 0.54 [-0.90, 1.79] @95% Prob.

a = 1 (as a reference)


S0B ≠ S0

K S0B ≠ S0

K



S0B S0

K

NP bounds in MFV scenario with large tan


2010: where will we stand?2010: where will we stand?

ObservableObservable Sensitivity in 2010Sensitivity in 2010

sin2sin2 0.0100.010

55oo

55oo

|V|Vcbcb|| 1%1%

|V|Vubub|| 4%4%

BBKK5%5%

5%5%

3%3%

mmss0.3 ps0.3 ps-1-1 (syst.) (syst.)

sin2sin2 0.0450.045

ss BB B̂f

Assumptions B Factories will collect L=2 ab-1

two good years of data taking at LHCb (L=4 fb-1) improvements in LQCD quantities


2010 sensitivity to New Physics observables 2010 sensitivity to New Physics observables in |in |F|=2 transitions from UT fitsF|=2 transitions from UT fits

(assuming Standard Model validity)(assuming Standard Model validity)

0.1(now ~0.2)

K0 sector

1.3°

(now ~3°)

Bd sector

0.14(now ~0.5)

1.3o

Bs sector

0.12

Only using the measurements from a few key LHCb BOnly using the measurements from a few key LHCb Bss

channels channels (in particular (in particular mmss and sin2 and sin2)), the precision on NP , the precision on NP

observables for bobservables for bs FCNC transitions in 2010 will be at the s FCNC transitions in 2010 will be at the same level as the bsame level as the bd transitions!d transitions!


Concluding remarksConcluding remarks A large set of new bounds from B-factories allows over-constraining the

Unitarity Triangle Standard Model is “sadly” showing an impressive consistency in the CKM sector If NP will show up, it will appear as a correction to the SM rather than as a revolution The only tension in the fit comes from a slight disagreement between sin2 and Vub

By using only the constraints from |Vub|/|Vcb| and , we have a (“NP free”) tree level determination of and

This is a starting reference point for NP model building, since all the NP models have to agree with it

Adopting a NP model independent parametrization, we fit SM ( and ) and NP (corrections to SM in mixing amplitudes and phases) together

Constributions of NP to the Bd mixing phase are already very constrained same phase of SM MFV scenarios seem preferred by data

UUT fits are then the starting point of a MFV analysis We can translate the measurement of MFV NP sensitive quantities (mixing) into

bounds on the tested scale

More data are needed for NP hunting at low energies!More data are needed for NP hunting at low energies!

Documents

Incontri di fisica del b, Parma, 19 th January 2006 on behalf of the Collaboration M. Bona, M. Ciuchini, E. Franco, V. Lubicz, G