the unitarity triangle analysis and its theoretical input parameters
DESCRIPTION
Vittorio Lubicz. THE UNITARITY TRIANGLE ANALYSIS AND ITS THEORETICAL INPUT PARAMETERS. OUTLINE Flavour physics and its motivations Lattice QCD and the UTA input parameters UTA: results and perspectives. Orsay, April 14-16 2004. 1 FLAVOUR PHYSICS AND ITS MOTIVATIONS. FLAVOUR PHYSICS. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: THE UNITARITY TRIANGLE ANALYSIS AND ITS THEORETICAL INPUT PARAMETERS](https://reader036.vdocuments.site/reader036/viewer/2022062408/56813a6a550346895da26400/html5/thumbnails/1.jpg)
THE UNITARITY TRIANGLE ANALYSIS AND ITS THEORETICAL INPUT
PARAMETERS
THE UNITARITY TRIANGLE ANALYSIS AND ITS THEORETICAL INPUT
PARAMETERS
OUTLINE
1.Flavour physics and its motivations
2.Lattice QCD and the UTA input parameters
3.UTA: results and perspectives
OUTLINE
1.Flavour physics and its motivations
2.Lattice QCD and the UTA input parameters
3.UTA: results and perspectivesOrsay,
April 14-16 2004
Vittorio Lubicz
![Page 2: THE UNITARITY TRIANGLE ANALYSIS AND ITS THEORETICAL INPUT PARAMETERS](https://reader036.vdocuments.site/reader036/viewer/2022062408/56813a6a550346895da26400/html5/thumbnails/2.jpg)
2
1
FLAVOUR PHYSICS
AND ITS
MOTIVATIONS
![Page 3: THE UNITARITY TRIANGLE ANALYSIS AND ITS THEORETICAL INPUT PARAMETERS](https://reader036.vdocuments.site/reader036/viewer/2022062408/56813a6a550346895da26400/html5/thumbnails/3.jpg)
3
STANDARD MODEL AND FLAVOUR PHYSICS
STANDARD MODEL AND FLAVOUR PHYSICS
Flavour
ElectromagneticStrong
Weak
SU(2)L x U(1)Y x SU(3)
Why 3 families?
Why the hierarchy of masses?
Is the CKM mechanism and its explanation of CP violation correct?
FLAVOUR PHYSICS
Only weak interactions can change flavour [CKM]
Symmetry breaking: Higgs (?)
![Page 4: THE UNITARITY TRIANGLE ANALYSIS AND ITS THEORETICAL INPUT PARAMETERS](https://reader036.vdocuments.site/reader036/viewer/2022062408/56813a6a550346895da26400/html5/thumbnails/4.jpg)
4
THE STANDARD MODEL:
A LOW ENERGY EFFECTIVE THEORYTHE STANDARD MODEL:
A LOW ENERGY EFFECTIVE THEORY
CONCEPTUAL PROBLEMS The most obvious:
o Gravity: MPlanck = (ħc/GN)1/2 ≈ 1019 GeV
PHENOMENOLOGICAL INDICATIONS:
o Unification of couplings (MGUT ≈ 1015-1016 GeV)
o Dark matter (ΩM ≈ 0.35)
o Neutrino masses
o Matter/Anti-matter asymmetry (not enough CP in the SM)
THE “NATURAL” CUT-OFF:
Λ = O(1 TeV) NEW PHYSICS MUST BE VERY “SPECIAL”
3GF
√2πδmH = mt Λ ≈ (0.3 Λ)
222 22
![Page 5: THE UNITARITY TRIANGLE ANALYSIS AND ITS THEORETICAL INPUT PARAMETERS](https://reader036.vdocuments.site/reader036/viewer/2022062408/56813a6a550346895da26400/html5/thumbnails/5.jpg)
5
NEW PHYSICS EFFECTS IN FLAVOUR PHYSICS
NEW PHYSICS EFFECTS IN FLAVOUR PHYSICS
PRECISION ERA OF FLAVOUR PHYSICSPRECISION ERA OF FLAVOUR PHYSICS
εK = (2.271 ± 0.017) x 10-3 0.7%
Δmd = (0.503 ± 0.006) ps-1 1%
sin(2β) = 0.734 ± 0.054 7%
We need to control the theoretical input
parameters at a comparable level of
accuracy !!
K KTHE FLAVOUR
PROBLEM:
ΛK0-K
0 ≈ O(100 TeV)
QUANTUM EFFECTS
![Page 6: THE UNITARITY TRIANGLE ANALYSIS AND ITS THEORETICAL INPUT PARAMETERS](https://reader036.vdocuments.site/reader036/viewer/2022062408/56813a6a550346895da26400/html5/thumbnails/6.jpg)
6
THE CKM MATRIX
b u
l
Vub
W
3 FAMILIES:
3 angles and 1 phase
Only 1 parameter for CP VIOLATION
![Page 7: THE UNITARITY TRIANGLE ANALYSIS AND ITS THEORETICAL INPUT PARAMETERS](https://reader036.vdocuments.site/reader036/viewer/2022062408/56813a6a550346895da26400/html5/thumbnails/7.jpg)
7
THE UNITARITY TRIANGLE
![Page 8: THE UNITARITY TRIANGLE ANALYSIS AND ITS THEORETICAL INPUT PARAMETERS](https://reader036.vdocuments.site/reader036/viewer/2022062408/56813a6a550346895da26400/html5/thumbnails/8.jpg)
8
THE UNITARITY TRIANGLE ANALYSIS
Hadronic Matrix Elements from LATTICE QCD
5 CONSTRAINTS
2 PARAMETERS
sin2β(ρ, η)A(J/ψ KS)
ξ (1– )2 + 2md/ ms
fBd BBd (1– )2 + 2 md
BK [(1– ) + P]K
, λ1 ,f+ ,… 2 + 2(bu)/(bc) ρ η
η ρ
ρ η
ρ
η
Λ
2
![Page 9: THE UNITARITY TRIANGLE ANALYSIS AND ITS THEORETICAL INPUT PARAMETERS](https://reader036.vdocuments.site/reader036/viewer/2022062408/56813a6a550346895da26400/html5/thumbnails/9.jpg)
9
2
LATTICE QCD AND
THE UTA INPUT
PARAMETERS
![Page 10: THE UNITARITY TRIANGLE ANALYSIS AND ITS THEORETICAL INPUT PARAMETERS](https://reader036.vdocuments.site/reader036/viewer/2022062408/56813a6a550346895da26400/html5/thumbnails/10.jpg)
10
B π
b u
d
l
v
Vub
Vub FROM B-MESON SEMILEPTONIC DECAYS
EXPERIMENTS:
CLEO, BaBar, Belle, …
Γ(B→ πlv) = ∫dq2 λ(q2)3/2 |f+( q2)|2
192 π3
GF2|Vub|2
NON-PERTURBATIVE PHYSICS
15-20%
![Page 11: THE UNITARITY TRIANGLE ANALYSIS AND ITS THEORETICAL INPUT PARAMETERS](https://reader036.vdocuments.site/reader036/viewer/2022062408/56813a6a550346895da26400/html5/thumbnails/11.jpg)
11
APE - SPQCDR
PRECISION FLAVOUR PHYSICS ON THE LATTICEPRECISION FLAVOUR PHYSICS ON THE LATTICE
K π
s u
d
l
v
Vus = λ
B D*b c
d
l
v
Vcb = A λ2
f+(0) = 0.960 ± 0.005 ± 0.007
FNAL
FB→D*(1) = 0.913
+ 0.024- 0.017 - 0.030
+ 0.017
f+(0) = 1 - O(ms-mu)2
Ademollo-Gatto theorem
FB→D*(1) = ηA [1 - O(1/mb,1/mc)2]Luke theorem
1%
![Page 12: THE UNITARITY TRIANGLE ANALYSIS AND ITS THEORETICAL INPUT PARAMETERS](https://reader036.vdocuments.site/reader036/viewer/2022062408/56813a6a550346895da26400/html5/thumbnails/12.jpg)
12
K
K – K Mixing: εK and BK
CP Violation
K K
NON-PERTURBATIVE PHYSICS
![Page 13: THE UNITARITY TRIANGLE ANALYSIS AND ITS THEORETICAL INPUT PARAMETERS](https://reader036.vdocuments.site/reader036/viewer/2022062408/56813a6a550346895da26400/html5/thumbnails/13.jpg)
13
Lattice Results for BK
BK= 0.87 ± 0.06 ± 0.13[ D. Becirevic, Plenary talk @ LATT03]
^
High level of accuracy
Discretization effects not negligible
Estimate of quenching error from ChPT ≤ 15% (Sharpe)
LATTICE PREDICTION (!) BK = 0.90 ± 0.20 [Gavela et al., 1987]
^
L.Giusti, EPS-HEP 2003
Quench. Appr.
![Page 14: THE UNITARITY TRIANGLE ANALYSIS AND ITS THEORETICAL INPUT PARAMETERS](https://reader036.vdocuments.site/reader036/viewer/2022062408/56813a6a550346895da26400/html5/thumbnails/14.jpg)
14
K – K Mixing: εK and BKBBd/s – BBd/s
Mixing: fBd/s and BBd/s
THE Ds-MESON DECAY CONSTANT
A long history of lattice calculations…
fDs /fDs = 1.08 ± 0.05 (CP-PACS,MILC)Nf=0Nf=2
QU
EN
CH
ED
New results expected from
CLEO-c
fDs= 265 ± 14 ± 13 MeV LQCD Average
fDs= 285 ± 19 ± 40 MeV EXP. PDG 2002
[D.Becirevic]
![Page 15: THE UNITARITY TRIANGLE ANALYSIS AND ITS THEORETICAL INPUT PARAMETERS](https://reader036.vdocuments.site/reader036/viewer/2022062408/56813a6a550346895da26400/html5/thumbnails/15.jpg)
15
From fDs to fBd
J.Heitger, EPS-HEP 2003
JLQCD, 2003
mQ « 1/a mπ » 1/L
● Extrapolations from mQ ~ mc to mb● Effective theories:
HQET, NRQCD, “FNAL”, …
● Combine the two approaches
● Extrapolations from mq to mu,d
using ChPT as a guidance:
Orsay
, Becirevic et al.Use● Finite size approach, APE-Tov
![Page 16: THE UNITARITY TRIANGLE ANALYSIS AND ITS THEORETICAL INPUT PARAMETERS](https://reader036.vdocuments.site/reader036/viewer/2022062408/56813a6a550346895da26400/html5/thumbnails/16.jpg)
16
BBd/s – BBd/s
Mixing: fBd/s and BBd/s
QU
EN
CH
ED
fBs: the “world average” evolution
fBs /fBs = 1.12 ± 0.05 (CP-PACS,MILC)
Nf=0Nf=2 In other quantities (fBs/ fBd, BBd, BBs/ BBd) quenching effects are smaller
fBs√BBs= 254 ± 24 MeV, ξ = 1.21 ± 0.05 ± 0.01[ D. Becirevic, 2nd Workshop on the CKM Unitarity Triangle, 2003]
LATTICE AVERAGES
fBs√BBs= 276 ± 38 MeV, ξ = 1.24 ± 0.04 ± 0.06[ 1st Workshop on the CKM Unitarity Triangle, 2002 ]
![Page 17: THE UNITARITY TRIANGLE ANALYSIS AND ITS THEORETICAL INPUT PARAMETERS](https://reader036.vdocuments.site/reader036/viewer/2022062408/56813a6a550346895da26400/html5/thumbnails/17.jpg)
17
LATTICE QCD UT FIT
fB√BB 223 33 12 MeV 217 12 MeV
BK 0.86 0.06 0.14 0.71 0.11
Lattice QCD vs UT FITS
![Page 18: THE UNITARITY TRIANGLE ANALYSIS AND ITS THEORETICAL INPUT PARAMETERS](https://reader036.vdocuments.site/reader036/viewer/2022062408/56813a6a550346895da26400/html5/thumbnails/18.jpg)
18
3
THE UNITARITY
TRIANGLE ANALISYS:
RESULTS AND
PERSPECTIVES
![Page 19: THE UNITARITY TRIANGLE ANALYSIS AND ITS THEORETICAL INPUT PARAMETERS](https://reader036.vdocuments.site/reader036/viewer/2022062408/56813a6a550346895da26400/html5/thumbnails/19.jpg)
19
M.Bona, M.Ciuchini, E.Franco,
V.L., G.Martinelli, F.Parodi,
M.Pierini, P.Roudeau, C.Schiavi,
L.Silvestrini, A.Stocchi
Roma, Genova, Torino, Orsay
The Collaboration
www.utfit.org
www.utfit.org
The WEB site
THE CKM
![Page 20: THE UNITARITY TRIANGLE ANALYSIS AND ITS THEORETICAL INPUT PARAMETERS](https://reader036.vdocuments.site/reader036/viewer/2022062408/56813a6a550346895da26400/html5/thumbnails/20.jpg)
20
Sin2α = – 0.19 ± 0.25
Sin2β = 0.710 ± 0.037
γ = (61.5 ± 7.0)o
ρ = 0.178 ± 0.046
FIT RESULTS FIT RESULTS
η = 0.341 ± 0.028
![Page 21: THE UNITARITY TRIANGLE ANALYSIS AND ITS THEORETICAL INPUT PARAMETERS](https://reader036.vdocuments.site/reader036/viewer/2022062408/56813a6a550346895da26400/html5/thumbnails/21.jpg)
21
INDIRECT EVIDENCE OF CP VIOLATION
Sin2βUTA = 0.685 ± 0.052 Sin2βJ/ψ Ks = 0.734 ± 0.054
Prediction (Ciuchini et al., 2000): Sin2βUTA = 0.698 ± 0.066
3 FAMILIES - Only 1 phase - Angles from Sides
![Page 22: THE UNITARITY TRIANGLE ANALYSIS AND ITS THEORETICAL INPUT PARAMETERS](https://reader036.vdocuments.site/reader036/viewer/2022062408/56813a6a550346895da26400/html5/thumbnails/22.jpg)
22
Prediction for Δms Prediction for Δms
Δms = (18.3 ± 1.7) ps-1
WITH ALL CONSTRAINTS
A measurement is expected from Tevatron !
Δms NOT USED
Δms = (20.6 ± 3.5) ps-1
![Page 23: THE UNITARITY TRIANGLE ANALYSIS AND ITS THEORETICAL INPUT PARAMETERS](https://reader036.vdocuments.site/reader036/viewer/2022062408/56813a6a550346895da26400/html5/thumbnails/23.jpg)
23
Sin2β AND Δms:
HISTORY OF PREDICTIONS
Sin2β AND Δms:
HISTORY OF PREDICTIONS
Experiments
Other colors: Theory
![Page 24: THE UNITARITY TRIANGLE ANALYSIS AND ITS THEORETICAL INPUT PARAMETERS](https://reader036.vdocuments.site/reader036/viewer/2022062408/56813a6a550346895da26400/html5/thumbnails/24.jpg)
24
THE “COMPATIBILITY” PLOTSTHE “COMPATIBILITY” PLOTS
“To which extent improved determinations of the experimental constraints will be able to detect
New Physics?”
Compatibility between direct and indirect determinations as a function of the measured value and its experimental uncertainty
![Page 25: THE UNITARITY TRIANGLE ANALYSIS AND ITS THEORETICAL INPUT PARAMETERS](https://reader036.vdocuments.site/reader036/viewer/2022062408/56813a6a550346895da26400/html5/thumbnails/25.jpg)
25
IMPACT OF IMPROVED DETERMINATIONS
IMPACT OF IMPROVED DETERMINATIONS
TODAY NEXT YEARS
BK = 0.86 ± 0.06 ± 0.14
ξ = 1.24 ± 0.04 ± 0.06
fBs√BBs = 276 ± 38 MeV14
sin2β = 0.734 ± 0.05421
Δρ = 26% → 15% Δη = 7.1% → 4.6%
![Page 26: THE UNITARITY TRIANGLE ANALYSIS AND ITS THEORETICAL INPUT PARAMETERS](https://reader036.vdocuments.site/reader036/viewer/2022062408/56813a6a550346895da26400/html5/thumbnails/26.jpg)
26
Δms = (20.6 ± 3.5) ps-1 Δms = (20.6 ± 1.8) ps-1
TO
DA
Y
NEX
T Y
EA
RS
![Page 27: THE UNITARITY TRIANGLE ANALYSIS AND ITS THEORETICAL INPUT PARAMETERS](https://reader036.vdocuments.site/reader036/viewer/2022062408/56813a6a550346895da26400/html5/thumbnails/27.jpg)
27
SEARCH FOR NEW PHYSICSSEARCH FOR NEW PHYSICS
“Given the present theoretical and experimental constraints, to which extent the
UTA can still be affected by New Physics contributions?”
The New Physics mixing amplitudes can be parameterized in a simple general form:
Md = Cd e2i (Md)SMφd
Δmd = Cd (Δmd)SM
A(J/ψ KS) ~ sin2(β+φd)
New Physics in Bd–Bd mixingAn
interesting case:
![Page 28: THE UNITARITY TRIANGLE ANALYSIS AND ITS THEORETICAL INPUT PARAMETERS](https://reader036.vdocuments.site/reader036/viewer/2022062408/56813a6a550346895da26400/html5/thumbnails/28.jpg)
28
TWO SOLUTIONS: TWO SOLUTIONS:Standard Model
solution:Cd = 1 φd = 0
φd can be only determined up to a trivial twofold ambiguity:
β+φd → π–β–φd
![Page 29: THE UNITARITY TRIANGLE ANALYSIS AND ITS THEORETICAL INPUT PARAMETERS](https://reader036.vdocuments.site/reader036/viewer/2022062408/56813a6a550346895da26400/html5/thumbnails/29.jpg)
29
HOW CAN WE DISCRIMINATE BETWEEN THE TWO SOLUTIONS?
HOW CAN WE DISCRIMINATE BETWEEN THE TWO SOLUTIONS?
Δms, η [KL→πνν], γ [B→DK], |Vtd| [B→ργ], …
![Page 30: THE UNITARITY TRIANGLE ANALYSIS AND ITS THEORETICAL INPUT PARAMETERS](https://reader036.vdocuments.site/reader036/viewer/2022062408/56813a6a550346895da26400/html5/thumbnails/30.jpg)
30
Coming back to the Standard Model:
15 YEARS OF (ρ-η) DETERMINATIONS(The “commercial” plot)
15 YEARS OF (ρ-η) DETERMINATIONS(The “commercial” plot)
![Page 31: THE UNITARITY TRIANGLE ANALYSIS AND ITS THEORETICAL INPUT PARAMETERS](https://reader036.vdocuments.site/reader036/viewer/2022062408/56813a6a550346895da26400/html5/thumbnails/31.jpg)
31
CONCLUSIONS
FOR ALL THAT, WE NEEDT-FLOPS COMPUTERS!!
LATTICE QCD CALCULATIONS HAD A CRUCIAL IMPACT
ON TESTING AND CONSTRAINING THE FLAVOUR SECTOR
OF THE STANDARD MODEL
IN THE PRECISION ERA OF FLAVOUR PHYSICS, LATTICE
SYSTEMATIC UNCERTAINTIES MUST (AND CAN) BE
FURTHER REDUCED
IMPORTANT, BUT MORE DIFFICULT PROBLEMS (NON
LEPTONIC DECAYS, RARE DECAYS, ...) ARE ALSO BEING
ADDRESSED