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UTA in the Standard Model With Updated Inputs after the CERN Workshop Sensitivity to New Physics

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UT Fits in the Standard Model and Sensitivity to New Physics

M.Ciuchini, E.Franco, VL, F.Parodi, L.Silvestrini, A.Stocchi

UTA in the Standard Model

With Updated Inputs after the CERN Workshop

Sensitivity to New Physics

1.Impact of Improved Determinations

2. UTA with New Physics Contributions

ρ

ρ

η

η

η

ρ

η

ρ

ρ

η

ρ

f( , , x|c1,...,cm) ~ ∏ fj(c|,,x) ∏ fi(xi) fo(,)

j=1,m

i=1,N

f( , |c) ~ L(c|,) fo(,)

Fit Method: we use the

Bayesian Approach

The Bayes Theorem:

but also frequentistic approaches have been considered: Rfit , Scanning, ...

^

Example: BK = 0.86 ± 0.06 ± 0.14

ΔL

p.d.f

Rfit

Conclusion of the CERN Workshop:

“The main origin of the difference on the output quantities between the Bayesian and the Rfit method comes from the likelihood associated to the input quantities”

“If same (and any) likelihood are used the output results are very similar”

ρ

+ 0.029

= 0.347

– 0.026

= 0.162 ± 0.046

η

ρ

F. Parodi @ ICHEP 2002

= 0.355 ± 0.027

= 0.203 ± 0.040

UTA IN THE SM: FIT RESULTS

γ= 64.5

+ 0.28

+ 7.5

– 0.23

– 6.5

Sin2α, Sin2βandγ

Sin2β= 0.705 ± 0.035

Without including the χ-logs effect inξ:

γ= 60 ± 6

RED: WITH ALL CONSTRAINTS / BLUE: WITHOUT Δms

By removing the constraint from Δms: γ= 65 ± 7 → γ= 59 ± 10

1) Impact of improved experimental determinations

“To which extent improved determinations of the experimental constraints will be able to detect New Physics?”

B →φKs?

MEASUREMENTS OF SIN2β

SM prediction without A(J/ψKs)

Red lines: σ= 0.2, 0.1, 0.05, 0.02

Blue line: all errors divided by 2

Red lines: σ= 1.0, 0.5, 0.2, 0.1 ps-1

Blue line: all errors divided by 2

Blue line: error on ξ divided by 2

2) UTA with New Physics contributions

“Given the present theoretical and experimental constraints, to which extent the UTA can still be affected by New Physics contributions?”

–

–

ASSUMPTIONS

1) Only 3 Families we still have the CKM Matrix and a Unitary Triangle

2)

New Physics effects can only appears in one of the three mixing amplitudes.

Not true in several models: MFV,...

—

φq

for Bq–Bq mixing

Im(MK) = Cε Im(MK)SM

—

for K–K mixing

PARAMETERIZATION

The New Physics Hamiltonian contains in general new FC parameters, new short-distance coefficients and matrix elements of new local operators.

We parameterize the New Physics mixing amplitudes in a simple general form:

Soares, Wolfenstein 92

Grossman, Nir, Worah 97

....

We introduce 4 real coefficients: {Cd, φd},Cs, Cε

γ

εK = Cε(εK)SM

Cε

sin(2β)

+ 0.17

Cε = 0.86

– 0.14

(The large error reflects the uncertainty on BK)

γ

Δms = Cs(Δms)SM

Cs

sin(2β)

In the lack of an experimental determination of Δms, Cs can be arbitrarily large…

Bd–Bd mixing

Cd

Δmd = Cd(Δmd)SM

A(J/ψ KS)~ sin2(β+φd)

Cd

φd

φd

With φd only determined up to a trivial twofold ambiguity: β+φd → π–β–φd

HOW CAN WE DISCRIMINATE BETWEEN THE 2 SOLUTIONS?

Δms ,γ , |Vtd|, …

η

ρ

sin(2β)

γ

IS THE NEW PHYSICS SOLUTION “NATURAL”?

- A LOT OF IMPORTANT WORK HAS BEEN DONE SINCE THE LAST CKM WORKSHOP IN ORDER TO IMPROVE THE DETERMINATION OF BOTH EXPERIMENTAL AND THEORETICAL INPUTS IN THE UTA
- THE RESULTS OF THE UTA ARE IN EXCELLENT AGREEMENT WITH THE STANDARD MODEL PREDICTIONS, BUT (LUCKILY) WE STILL HAVE ROOM FOR NEW PHYSICS.

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