Unitarity Triangle fits

Achille Stocchi LAL-Orsay (IN2P3/CNRS)

Recent papers:M. Bona et al. hep-ph/0509219 accepted in JHEP M . Bona et al. (hep-ph/0501199) JHEP 0507 (2005) 028

http://www.utfit.orgM. Bona, M. Ciuchini, E. Franco, V. Lubicz, G. Martinelli, F. Parodi, M. Pierini, P. Roudeau, C. Schiavi, L. Silvestrini, A. Stocchi, V.Vagnoni

Collaboration

RESULTS BASED ON THE WORK OF

bcℓ and buℓ Bd and Bs mixingK : CPV in K decaysBccs : 1 /B// : 2/BDK : 3/

How to fit the UT parameters and fit new physics

From M.H. Schuneplenary talk EPS2005

= 0.347 ± 0.021 [0.306, 0.389] @ 95% Prob.

= 0.347 ± 0.021 [0.306, 0.389] @ 95% Prob.

= 0.210 ± 0.036 [0.137, 0.279] @ 95% Prob.

= 0.210 ± 0.036 [0.137, 0.279] @ 95% Prob.

Total Fitmd,ms,Vub,Vcb,k + cos2 + + + + 2+

UT with angles only

= 0.322 ± 0.025 [0.274, 0.373] @ 95% Prob.

= 0.322 ± 0.025 [0.274, 0.373] @ 95% Prob.

= 0.187 ± 0.052 [0.090, 0.299] @ 95% Prob.

= 0.187 ± 0.052 [0.090, 0.299] @ 95% Prob.

sin(

sin(

cos

= 0.385 ± 0.028 [0.,328, 0.440] @ 95% Prob.

= 0.385 ± 0.028 [0.,328, 0.440] @ 95% Prob.

= 0.218 ± 0.043 [0.129, 0.299] @ 95% Prob.

= 0.218 ± 0.043 [0.129, 0.299] @ 95% Prob.

Sides + K

Test of SM (I)

SM solution only

The presence of New Physics might appear as a disagreement between the new measurements and what the fit predicts (given by the color code). and (for the moment) are OK. The next validation will come from ms for the bs sector.

?SM solution only

Test of SM (II)

sin2 =0.791±0.034from indirect determination sin2 =0.791±0.034

from indirect determination

sin2=0.687±0.032From direct measurementsin2=0.687±0.032

From direct measurementwe have a weak sign

of a disagreement

Tension in the fit

It can be interpreted

as a problemwith data, but it couldbe evidence

of New Physics

exclusive: BRs from HFAG;

form factor from quenched LQCD Vub=(3.80±0.27±0.47)10-3

inclusive from HFAG Vub=(4.38±0.19±0.27)10-3

incl.+excl. Vub = (4.22 ± 0.20) 10-3 from all the other inputs:

Vub = (3.48 ± 0.20) 10-3

Where do we really are on our knowledge of UT ?

Fit with NP independent variables

Fit in a NP model independent approach

± (0.18± 0.12)

± (0.41 ± 0.05)

Fit with NP independent variables

(similar plot in Botella et al. hep-ph/0502133)

It is very important to improve Vub/Vcb from s.l decays

from tree level proceses

If we use only Tree level processes -which can be assumed to be NP free-

5 new free parameters Cs,s Bs mixing

Cd,d Bd mixing

CK K mixing

Cd,d

CK Cs,s

Vub/Vcb X

md X X

K X X

ACPJ X X

X X

D X

ms X

ACPJ ~X X

DsK) X X

Today : fit possible with 6 contraints and 5 free parameters (Cd,d ,CK)

Con

stra

ints

Not yet available

Parametrizing NPphysics in F=2 processes

2 2 2

2

d

NP

q

SMi B B

SMB

CQ Q

eQ

F=2Fit in a NP model independent approach

0( / ) sin(2 2 )

| | | |

EXP SMd q d

CP d

EXP SMd

EXP SMK K

m C m

A J K

C

Vub/Vcb

D

md ACPJ

K

Using

cos2 ASL

NLO effects included

Fit in a NP model independent approach

SM-like solution 96%

NP solution 4% large NP witharbitrary phase

SM or small NP witharbitrary phase or large

NP with SM phase.

NP in B=2 and S=2 could be up to 50% wrt SM only if has the same phase of the SM

CBd = 1.27± 0.44 C = 0.95 ± 0.18

Fit in a NP model independent approach

Bd = -(4.7 ± 2.3)o

sensitive to small effects

Artificially removing the present disagreement ~20% @ 95% prob for generic NP

With present data ANP/ASM=0 @1

ANP/ASM vs NP

ANP/ASM ~1 only if NP~0 ANP/ASM ~0-40% @95% prob.

MFV New CP in bs

- - F=1 Penguins transitions F=1 Penguins transitions (just 1 transparency)(just 1 transparency)

- The B- The Bss physics (LHCb/Tevatron) physics (LHCb/Tevatron)

- Improvements existing measurements- Improvements existing measurements

- Rare decays - Rare decays (not discussed in this talk)(not discussed in this talk)

What to do ?

TWO SCENARIOS seems to be « favourite »

MFV = CKM is the only source of flavour mixing. K and md are not used (sensitive to NP).

= 0.258 ± 0.066 UUTfit = 0.258 ± 0.066 UUTfit

Buras et al. hep-ph/0007085Universal UTfit

= 0.319 ± 0.039 UUTfit

Almost as good as the SM !! Starting point for studies of rare decays see for instance : Bobeth et al. hep-ph/0505110

In models with one Higgs doublet or low/moderate tan (D’Ambrosio et al. hep-ph/0207036)NP enters as additional contribution in top box diagram

0 0 0

2

00 0

( ) ( ) ( )

( ) 4 2.4

t t t

t

S x S x S x

S x a TeV

0 is the equivalent SM scale

0

0

5.1 @95% ( )

3.6 @95% ( )t

t

TeV for positive S x

TeV for negative S x

MFV

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

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

To be compared with tested scale using for instance b->s (9-12Tev)D’Ambrosio et al. hep-ph/0207036

0/ ~ 2

2Higgs + large tan also bottom Yukawa coupling must be considered MFV

S0B ≠ S0

K S0B ≠ S0

K

> 2.6 TeV @ 95% for S0(xt) > 0

> 4.9 TeV @ 95% for S0(xt) < 0

> 3.2 TeV @ 95% for S0(xt) > 0

> 4.9 TeV @ 95% for S0(xt) < 0

S0B S0

K

Could give infomation on the tan regime …not yet at the present

Correlation coefficient =0.52

New physics in bs transitions

The SUSY option

F=1 F=2

if ms>31(38)ps-1

new physcis at 3(5)

d d

sb

W

B0d

t ss

K0

g

sb b s

~

~ ~

LRd

23

4

6

( ) (3.29 0.34) 10

( ) ( 0.02 0.04)

( ) (6.1 1.4 1.3) 10

limit ( )

S

CP S

S

S

BR B X

A B X

BR B X l l

M BR B K

other information

CKM Matrix in ≤2010-where we will beWe have supposed that - B Factories will collect 2ab-1

- two years data taking at LHCb (4fb-1)

< 1° from charmonium ~ 7 ° ~ 5° (half B-factories/half LHCb)

Vub ~ 5%Vcb ~ 1%

ms at 0.3ps-1

(Tevatron or/and LHCb)

Inputs

sin(2) 0.694 ± 0.012

sin(2) -0.543 ± 0.093

51.7 ± 3.0

0.240 ± 0.017

0.307 ± 0.010

Outputs

sin2± 0.045

CKM2010

fBBB ~ 5% ~ 3%BK ~ 5%

Lattice

Bands are 95% regionsfrom angle measurements

Contours are 68%/95% regionsfrom sides measurements

Bands are 95% regionsfrom sides measurements

Contours are 68%/95% regionsfrom angle measurements

An important point is that the relative precisions on CP-violating quantities are on phase with CP-conserving quantities IF

fBBB ~ 5% ~ 3%BK ~ 5%

Lattice calculations at few % level

Parenthesis for Lattice people

φBd = (-0.1 ± 1.3)o CBd = 0.98 ± 0.14 φBs = (0.0 ± 1.3)o CBs = 0.99 ± 0.12

in ≤ 2010 : same and impressive precision on b d and b s transitions

In the « sad » hypotesis the SM still work in 2010…. CKM2010

VERY IMPORTANT

B →

BR(B → τ ν) = (1.03 ± 0.32)10-4 ([0.47,1.74] @ 95% prob.)

fB = 0.178 ± 0.062 GeV from the exp+UTfit

fB = 0.192 ± 0.026 ± 0.009 GeV Lattice QCD

< 1.8 10-4 @ 90% CL

New comers soon.. ?exp. limit

Exp. likelkihoodBR(B → τ ν) = (0.98 ± 0.49)10-4 [0.17,2.08] @ 95% prob.)

SM expectation

UTfits are in a mature age with recent precise measurement of UT sides and angles

The SM CKM picture of CP violation and FCNC is strongly supported by data

At least in this sector, we are beyond the alternativeto CKM picture, and we should look at « corrections ».

Generic NP in the b d start to be quite constrained

Bd ~ 0

Conclusions

Studied presented in MFV.We start to test interesting NP scales.

What about the bs B=2 sector ? Still large room for NP. LHCb plays the central role on it.

CKM2010

Bs sector

We need precision measurements to test NP and to push the NP scale in interesting ranges and to play the complementarity at LHC

CKM2010

Bd sector

and if SuperB…..

See Report INFN-AE 05-08and related talks at this conference

BACKUP SLIDES

BR(B →) BR(B →K*)

caveat: * SU(3) breaking effect* QCD/mb corrections B(~cos) to / ( smaller for B0 than B+)

using onlyB →0

|Vtd/Vts| = 0.10 ± 0.45[0.02,0.18] @ 95% Prob.

Using the |Vtd/Vts| value from the SM, we can extract R.

R = -0.67 ± 0.24[-0.99, 0.10] @ 95%

K± ± with 3 signal events

latest result from E949:BR(K± ±) = 1.47 10-10 +1.30

- 0.89

}

ellipse centered in (0, 0)

D'Ambrosio, Isidorihep-ph/0112135

10% error withUTfit central value(BR = 0.83 10-10)

10% errorwith currentcentral value

Fit in a NP model independent approach

SM-like

Cd cos2() sin2() sin(2) ASL

SM-LIKE 60o 1 0.68 -0.23 0.96 OK

NP1 60o 1 -0.68 0.96 -0.23 OK

NP2 120o 0.4 0.68 -0.23 -0.96 10-2

NP3 120o 0.4 -0.68 0.96 0.23 0K

Vub/Vcb

D

md ACPJ

K

Using

0.26

In MFV CKM2010

0.54

Now

2010