LATTICE QCD AND FLAVOR PHYSICS Vittorio Lubicz OUTLINE OUTLINE 1. - - PowerPoint PPT Presentation
LATTICE QCD AND FLAVOR PHYSICS Vittorio Lubicz OUTLINE OUTLINE 1. Motivations for flavor physics 1. Motivations for flavor physics 2. Lattice QCD and quark masses 2. Lattice QCD and quark masses 3. CKM matrix 3. CKM matrix a) The Cabibbo angle
INAUGURAL CONFERENCE September 19 - 21, 2005
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K K K K
x x sL
˜
dR
˜
g
˜
sL
˜
dR
˜
g
˜
E.g.:
(5) (6 2 )
+
NP N i P i i i i i
SM eff
c c O O = + + Λ Λ
…
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QUARK MASSES CAN BE DETERMINED BY COMBINING TOGETHER A THEORETICAL AND AN EXPERIMENTAL INPUT. E.G.: ♦ BEING FUNDAMENTAL PARAMETERS OF THE STANDARD MODEL, QUARK MASSES CANNOT BE DETERMINED BY THEORETICAL CONSIDERATIONS ONLY. ♦ QUARK MASSES CANNOT BE DIRECTLY MEASURED IN
THE EXPERIMENTS, BECAUSE QUARKS ARE CONFINED INSIDE HADRONS
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ADJUSTED UNTIL
LATT = MH EXP
PERTURBATION THEORY OR NON-PERTURBATIVE METHODS
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PERTURBATION THEORY
ADJUSTED UNTIL MH
LATT = MH EXP
SLATT = SQCD+ a S1 + a2 S2 + …
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p p p p p p
Several NPR techniques have been developed: Ward Identities, Schrodinger functional, X-space
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V.Lubicz, plenary at Lattice 2000 T.Izubuchi, plenary at Lattice 2005
UNQUENCHED
2004
The highest values
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From S. Hashimoto ICHEP 2004 RATIOS OF LIGHT QUARK MASSES ARE PREDICTED ALSO BY CHIRAL PERTURBATION THEORY:
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SFT and neutron β-decay
(BNL-E865 + old exps)
b→u incl. and excl. ( |Vub|2 ≈ 10-5 )
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BNL-E865
PRL 91, (2003) 261802
NA48
PLB 602, (2004) 41
KTeV
PRL 93, (2004) 181802
Summer 2004
us f+
⋅
F.Mescia ICHEP ‘04 KLOE
hep-ex/0508027
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2 5 3 2 2 2 2
192 ) ) ( (1
| | V | (0)
F K ew K l K l
us
G M C I S
f
π
π δ
−
+
⋅ ⋅ +
K π
s u d l v
Vus = λ
Vector Current Conservation
f2 = − 0.023
Independent of Li (Ademollo-Gatto) THE LARGEST UNCERTAINTY
“Standard” estimate:
Leutwyler, Roos (1984) (QUARK MODEL)
f4 = −0.016 ± 0.008
f+(0) = 1 - O(ms-mu)2 Ademollo- Gatto: O(1%). But represents the largest theoret. uncertainty
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C12 (µ) and C34 (µ) can be determined from the slope and the curvature
f4 = ∆loops(µ) − [C12 (µ) + C34 (µ)] ( MK − Mπ ) 8 Fπ
4 2 2 2
Jamin et al., f4 = -0.018 ± 0.009 [Dispersive analysis]
LOC
Cirigliano et al., f4 = -0.002 ± 0.008 [1/Nc+Low resonance]
LOC
Leutwyler and Roos, f4 = -0.016 ± 0.008 [Quark model ]
LOC
A PRECISION OF O(1%) MUST BE REACHED ON THE LATTICE !!
Post and Schilcher, Bijnens and Talavera
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2
D.Becirevic, G.Isidori, V.L., G.Martinelli, F.Mescia, S.Simula, C.Tarantino, G.Villadoro. [NPB 705,339,2005] 1%
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LQCD: λ+ = ( 25 ± 2 ) 10-3 λ0= ( 12 ± 2 ) 10-3 KTeV: λ+= ( 24.11 ± 0.36 ) 10-3 λ0= ( 13.62 ± 0.73 ) 10-3 Comparison of polar fits:
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f+ (0) = 0.960 ± 0.005 ± 0.007
K0π-
( In agreement with LR !! )
C.Dawson, plenary at Lattice 2005
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Summer 2004
V
us f+
⋅
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1-λ2 λ A λ3(ρ-iη)
1- λ2/2 A λ2 Aλ3(1- ρ-iη) -A λ2 1
CP violation
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1-λ2 λ A λ3(ρ-iη)
1- λ2/2 A λ2 Aλ3(1- ρ-iη) -A λ2 1
CP violation
Hadronic matrix elements from LATTICE QCD
2 + 2
(b→u)/(b→c) ρ η
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1-λ2 λ A λ3(ρ-iη)
1- λ2/2 A λ2 Aλ3(1- ρ-iη) -A λ2 1
CP violation
Hadronic matrix elements from LATTICE QCD
2 + 2
(b→u)/(b→c) ρ η
(1– )2 +
2
∆md/ ∆ms ρ η
(1– )2 +
2
∆md ρ η
2
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1-λ2 λ A λ3(ρ-iη)
1- λ2/2 A λ2 Aλ3(1- ρ-iη) -A λ2 1
CP violation
Hadronic matrix elements from LATTICE QCD
2 + 2
(b→u)/(b→c) ρ η
(1– )2 +
2
∆md/ ∆ms ρ η
(1– )2 +
2
∆md ρ η
2
) + P]
η ρ
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1-λ2 λ A λ3(ρ-iη)
1- λ2/2 A λ2 Aλ3(1- ρ-iη) -A λ2 1
CP violation
Hadronic matrix elements from LATTICE QCD
2 + 2
(b→u)/(b→c) ρ η
(1– )2 +
2
∆md/ ∆ms ρ η
(1– )2 +
2
∆md ρ η
2
) + P]
η ρ A(J/ψ KS)
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UNQUENCHED QUENCHED
B π
b u d l v
Vub
Γ(B→ πlv) = ∫dq2 λ(q2)3/2 |f+( q2)|2
192 π3 GF
2|Vub|2
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K K
From S. Hashimoto ICHEP 2004
QUENCHED
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LATTICE PREDICTION (!)
BK = 0.90 ± 0.20 [Gavela et al., 1987]
^
K K
From S. Hashimoto ICHEP 2004
QUENCHED
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From S. Hashimoto
ICHEP 2004
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Sin2β = 0.734 ± 0.024
[JHEP 0507 (2005) 028]
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Prediction (Ciuchini et al., 2000):
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∆ms = (22.2 ± 3.1) ps-1
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