UTA in the Standard Model With Updated Inputs after the CERN Workshop Sensitivity to New Physics
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Transcript of UTA in the Standard Model With Updated Inputs after the CERN Workshop Sensitivity to New Physics
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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
UT Fits in the Standard Model and Sensitivity to New PhysicsUT Fits in the Standard Model
and Sensitivity to New Physics
M.Ciuchini, E.Franco, VL, F.Parodi, L.Silvestrini, A.Stocchi
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1.UTA in the
Standard ModelWith updated inputs after the
CERN Workshop
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(bu)/(bc) 2 + 2 , λ1 ,f+ ,…
K [(1– ) + P] BK
md (1– )2 + 2 fB BB
md/ ms (1– )2 + 2 ξA(J/ψ KS) sin(2β)
ρ
The Unitarity Triangle Analysis
η
η ρ
ρ η
ρ η
2
Λ
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97
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Input Parameters
▲ 1.80
▼ 0.93
▼ 0.83
▼ 0.85
▲ 1.08
▲ 1.40
▼ 0.93
▲
σ(2003)
σ(2002)
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Fit Method: we use the
Bayesian Approach
f( , , x|c1,...,cm) ~ ∏ fj(c| , ,x) ∏ fi(xi) fo( , )η ρ ρ η ρ ηj=1,m
i=1,N
The Bayes Theorem:
but also frequentistic approaches have been considered: Rfit , Scanning, ...
f( , |c) ~ L (c| , ) fo( , )ρ ρ ρη η η
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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”
Bayesian
p.d.f ΔL Rfit
Example: BK = 0.86 ± 0.06 ± 0.14^
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UTA IN THE SM: FIT RESULTS
ρ = 0.162 ± 0.046 η = 0.347 + 0.029– 0.026
= 0.203 ± 0.040ρ = 0.355 ± 0.027 η F. Parodi @ ICHEP 2002
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Sin2α, Sin2β and γ Sin2α, Sin2β and γ
Sin2α = – 0.13 + 0.28– 0.23 Sin2β = 0.705 ± 0.035 γ = 64.5 + 7.5
– 6.5
Without including the χ-logs effect in ξ: γ = 60 ± 6
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INDIRECT EVIDENCE OF CP VIOLATION
Sin2βINDIR. = 0.685 ± 0.055 Sin2βDIR. = 0.734 ± 0.054
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Predictions for Δms Predictions for Δms
WITHOUT Δms
Δms = (18.6 ± 1.7) ps-1
WITH Δms
Δms = (20.9 ) ps-1 + 3.9– 4.3
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RED: WITH ALL CONSTRAINTS / BLUE: WITHOUT Δ ms
By removing the constraint from Δms: γ= 65 ± 7 → γ= 59 ± 10
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2.Sensitivity of the UT Fits to New Physics
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1) Impact of improved experimental
determinations
“To which extent improved determinations of the
experimental constraints will be able to detect New Physics?”
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MEASUREMENTS OF SIN2β
MEASUREMENTS OF SIN2β
Red lines: σ = 0.2, 0.1, 0.05, 0.02
SM prediction without A(J/ψKs)
Blue line: all errors divided by 2
SM prediction with A(J/ψKs)
B →φKs?
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MEASUREMENT OF ΔmsMEASUREMENT OF Δms
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
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MEASUREMENT OF γMEASUREMENT OF γ
Red lines: σ = 20, 15, 10, 5 degrees
Blue line: all errors divided by 2
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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?”
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1) Only 3 Families we still have the CKM Matrix and a Unitary Triangle
ASSUMPTIONS
(bu)/(bc) md, A(J/ψ KS) ms K
Tree-level Bd–Bd mixing Bs–Bs mixing K–K mixing– – –
2)
New Physics effects can only appears in one of the three mixing amplitudes.
Not true in several models: MFV,...
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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:
Im(MK) = Cε Im(MK)SM
Mq = Cq e2i (Mq)SMφq
Soares, Wolfenstein 92Grossman, Nir, Worah 97....
for Bq–Bq mixing
—
for K–K mixing—
We introduce 4 real coefficients: {Cd, φd} ,
Cs, Cε
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New Physics in K–K mixing
εK = Cε (εK)SMγ
sin(2β)
Cε
Cε = 0.86 + 0.17– 0.14
(The large error reflects the uncertainty on BK)
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New Physics in Bs–Bs mixing
Δms = Cs (Δms)SM γ
sin(2β)
Cs
In the lack of an experimental determination of Δms, Cs can be arbitrarily large…
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New Physics inBd–Bd mixing
Δmd = Cd (Δmd)SM
A(J/ψ KS) ~ sin2(β+φd)
φd
Cd
φd
CdWith φd only determined up
to a trivial twofold ambiguity: β+φd → π–β–φd
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IS THE NEW PHYSICS SOLUTION “NATURAL”?
HOW CAN WE DISCRIMINATE BETWEEN THE 2 SOLUTIONS?
Δms , γ , |Vtd|, …γ
sin(2β)ηρ
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CONCLUSIONS 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.