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4. Extraction. of the. Unitarity triangle parameters. Search for New Physics. sin( b+g ). How measurements constraint UT parameters. a. g. the angles. sin( 2b). D m s. D m d. V ub /V cb. the sides. CP asymmetries in charmless. B  K * (r)g. B  tn. …. Rare decays...

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4

Extraction

of the

Unitarity triangle parameters

Search for New Physics


sin(b+g)

How measurements constraint UT parameters

a

g

the angles..

sin(2b)

Dms

Dmd

Vub/Vcb

the sides...

CP asymmetries in charmless

BK*(r)g

Btn

Rare decays...

sensitive to NP


Bccs : 1 /b

K : CPV in K decays

bcℓ and buℓ

Bd and Bs mixing

B// : 2/

BDK : 3/

An example on how to fit the UT parameters and fit new physics


From Childhood

In ~2000 the first fundamental

test of agreement between

direct and indirect sin2b

To precision era

WE HAVE TO GO ON…


Crucial Test of the SM in the quarks sector (historical..)

DONE!!

determination of CP violating parameters

measuring CP-conserving observables

CP-violating

observables

was/is the strong

motivation of the

B-Factories

sin2b = 0.726 ± 0.037

B  J/y K0

Coherent picture of CP

Violation in SM

from sides-only

We are probably beyond the era of « alternatives» to the CKM picture.

NP should appear as «corrections» to the CKM picture


TODAY SITUATION

Total Fit

Dmd,Dms,Vub,Vcb,ek+ cos2b + b +a +g + 2b+g

r = 0.164± 0.029

h = 0.340 ± 0.017



SM Fit sides”

Are there evidence of disagreement in the actual fit ?

agreement between the predicted values and the measurements at better than :

1s

3s

5s

2s

4s

6s

No disagreement for g et Dms


Some discrepencies observed between V sides”ub and sin2b

sin2b=0.675±0.026

From direct measurement

We should keep an eyes on these kinds

of disagreements. Could be NP

sin2b =0.764± 0.039

from indirect determination

(all included by sin2b)


The problem of particle physics today is : sides”

where is the NP scale L ~ 0.5, 1…1016 TeV

The quantum stabilization of the Electroweak Scale

suggest that L ~ 1 TeV

LHC will search on this range

What happens if the NP scale is at 2-3..10 TeV

…naturalness is not at loss yet…

Flavour Physics explore also this range

We want to perform flavour measurements such that :

- if NP particles are discovered at LHC we able

study the flavour structure of the NP

- we can explore NP scale beyond the LHC reach

If there is NP at scale L, it will generate new operator of

dimension D with coefficents proportional to L4-D

You could demonstrate that only operator of D=6 contribute

So that in fact you have a dependence on 1/ L2


( sides”MFV),

no new sources of flavour and CP violation

NP contributions governed by SM Yukawa couplings.

To help with a more specific example :

Example for B oscillations (FCNC-DB=2) :

dbd

prupper limit of the relative contribution of NP

dbdNP physics coupling

LeffNP scale (masses of new particles)

Minimal Flavour Violation

If couplings ~ 1

all possible intermediate

possibilities

dbq ~ 1

Leff ~ 10/pr TeV

(couplings small as CKM elements)

Leff ~ 2/pr TeV

dbs ~1

dbq ~ 0.1

Leff ~ 1/pr TeV

Leff ~ 0.08/pr TeV

Leff ~ 0.2/pr TeV

dbs ~0.1


NP physics could be always arround the corner sides”

WHAT IS REALLY STRANGE IS

THAT WE DID NOT SEE ANYTHING….

With masses of New Particles at few hundred GeV

effects on measurable quantities should be important

Problem known as the FLAVOUR PROBLEM

Leff <~ 1TeV + flavour-mixing

protected by additional

symmetries (as MFV)

Couplings can be still large if

Leff > 1..10..TeV


Fit in a NP model independent approach sides”

DF=2

Parametrizing NP

physics in DF=2 processes

Tree

processes

5 new free parameters

Cs,js Bs mixing

Cd,jd Bd mixing

CeK K mixing

13

family

Constraints

23

family

Today :

fit possible with 10 contraints

and 7 free parameters

(r, h, Cd,jd ,Cs,js, CeK)

12

familiy


φ sides”Bd = (-3.0 ± 2.0)o

CBd = 1.24 ± 0.43

ANP/ASM vs fNP

With present data ANP/ASM=0 @ 2s

ANP/ASM ~1 only if fNP~0

ANP/ASM ~0-40% @95% prob.


Complementarity LHC/precise measurments sides”

today

r = 20%  Leff ~ 180 GeV

tomorrow

Leff ~ 0.08/rTeV

r = 10%  Leff ~ 250 GeV

after tomorrow

electroweak scale

r = 1%  Leff ~ 800 GeV

You need to improve 20 times your precision if you want to span

the region from the EW scale to the TeV scale.

As could be

obtained at a superB ~100 times present B-factory

luminosity

NP scale ~200GeV

with MFV couplings

NP~800 GeV

This is really the most costly way of reaching high NP scale….


Adjusting the central values so sides”

that they are all compatible

Keeping the central values as measured today

with errors at the SuperB


Higgs-mediated NP in MFV at large tan sides”b

Similar formula in MSSM.

Excl. 2s

Bln

MH (TeV)

tanb

2ab-1

MH~0.4-0.8 TeV

for tanb~30-60

SuperB

MH~1.2-2.5 TeV

for tanb~30-60


W sides”-

s

b

f

t

s

B0d

s

K0

d

d

Constraints on b -> s transitions:

~

g

~

~

s

b

s

b

New Physics contribution (2-3 families)


Example on how precise measurements sides”

could allow o explore NP scale

beyond the TeV scale

~

g

MSSM

~

~

New Physics contribution

(2-3 families)

s

b

s

b

1

10-1

10-2

In the red regions the d

are measured with a

significance >3s away

from zero

1 10

ACP(bsg)

With the today precision

we do not have 3s exclusion

for any set of parameters


APPENDIX sides”

Part IV

1) More details on MFV


The previous fits sides”MFV ? j(Bd) ~0

MFV = CKM is the only source of CP violation

Fit without eKandDmd

valid in SM and MFV

eKandDmd are sensitive to NP

UniversalUTfit

Buras et al. hep-ph/0007085

Almost as good as the SM !!

Very tiny space for

see effects beyond

the SM

Starting point for studies of rare decays see for instance : Bobeth et al. hep-ph/0505110


RARE DECAYS in the framework of MFV sides”

Upper limits :

K physics

B physics

Very interesting the AFB asymmetry of BK*ll


MFV sides”

In models with one Higgs doublet or low/moderate tanb

(D’Ambrosio et al. hep-ph/0207036)

NP enters as additional contribution in top box diagram

L0 is the equivalent SM scale

dS0 = -0.03 ± 0.54

[-0.90, 1.79] @95% Prob.

To be compared with tested scale using for instance b->sg (9-12Tev)

D’Ambrosio et al. hep-ph/0207036


L sides” > 2.6 TeV @ 95% for dS0(xt) > 0

L > 3.2 TeV @ 95% for dS0(xt) > 0

L > 4.9 TeV @ 95% for dS0(xt) < 0

L > 4.9 TeV @ 95% for dS0(xt) < 0

MFV

2Higgs + large tanb also bottom Yukawa coupling must be considered

dS0B≠dS0K

dS0B

dS0K

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

Correlation coefficient =0.52


Two crucial questions : sides”

Can NP be flavour blind ?

No : NP couples to SM which violates flavour

Can we define a “worst case” scenario

Yes : the class of model with Minimal Flavour Violation (MFV),

namely : no new sources of flavour and CP violation

and so : NP contributions governed by SM Yukawa couplings.

Today

L(MFV) > 2.3L0 @95C.L.

NP masses >200GeV

SuperB

L(MFV) >~6L0 @95C.L.

NP masses >600GeV


In B sides”s sector we are not yet at the same level of precision as in Bd sector


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