Post on 23-Feb-2016
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CP Violation in Decays and Tests for SU(3) Flavor Symmetry Predictions
Xiao-Gang He , Siao-Fong Li, and Hsiu-Hsien LinNTU
JHEP08(2013)065
Outline• Motivation• Introduction• • Breaking effect• Other Decays• Summary
Motivation• The LHCb has measured the first direct CP violation in arXiv 1304.6173v2
𝐴𝐶𝑃 (𝑋→𝑌 )= Γ(𝑋→𝑌 )−Γ (𝑋→𝑌 )Γ (𝑋→𝑌 )+Γ (𝑋→𝑌 )
Motivation• Relation between
Δ (𝑋→𝑌 )=Γ (𝑋→𝑌 )−Γ (𝑋→𝑌 )
𝐴𝐶𝑃 ¿¿¿0𝐶𝐾𝑀 ,𝑆𝑈 (3)
Δ ¿
𝐴𝐶𝑃
Introduction-CP Violation and KM mechanism
• P parity and C parity
Introduction-CP Violation and KM mechanism
• KM Matrix
• Important properties
Unitary triangle ex. ++Jarlskog Invariant ex.
𝐽=𝑠12𝑠2𝑠3𝑐1𝑐2𝑐3𝑠𝑖𝑛𝛿
Introduction-Three types of CP Violation
• Indirect CP violation- CP Violation in mixing
- CP Violation in interference of decays with and without mixing
• Direct CP violation
𝑃 (𝐵→𝐵 )≠ 𝑃 (𝐵→𝐵)
𝑃 (𝐵(𝑡)→ 𝑓 𝐶𝑃)≠ 𝑃 (𝐵(𝑡 )→ 𝑓 𝐶𝑃 )
𝑃 (𝐵→ 𝑓 )≠𝑃 (𝐵→ 𝑓 ) ! We do.
Introduction-Decay amplitude
• In hadrons……
• Operator Product Expansion(Wilson and Zimermann,1972)
Introduction-Decay amplitude
𝑂1=(𝑞𝑖𝑢 𝑗)𝑉 − 𝐴(𝑢𝑖𝑏 𝑗)𝑉 −𝐴
O2=(𝑞𝑢)𝑉 − 𝐴(𝑢𝑏)𝑉 − 𝐴
𝑂3,5=(𝑞𝑏)𝑉 −𝐴 Σ𝑞 ′ (𝑞 ′𝑞 ′)𝑉 ∓𝐴
𝑂4 ,6=(𝑞𝑖𝑏 𝑗)𝑉 −𝐴 Σ𝑞 ′ (𝑞 ′ 𝑗𝑞 ′ 𝑖)𝑉∓𝐴
𝑂7,9=32 (𝑞𝑏)𝑉 − 𝐴Σ𝑞 ′ 𝑒𝑞 ′ (𝑞′𝑞 ′ )𝑉∓𝐴
𝑂8 , 10=32 (𝑞𝑖𝑏 𝑗)𝑉 − 𝐴Σ𝑞 ′ 𝑒𝑞 ′ (𝑞 ′ 𝑗𝑞 ′𝑖)𝑉∓ 𝐴
𝑂11=𝑔𝑠16 𝜋 2
𝑞𝜎𝜇𝜐𝐺𝜇𝜈 (1+𝛾 5 )𝑏
𝑂12=𝑄𝑏𝑒16𝜋 2
𝑞𝜎 𝜇𝜐𝐹𝜇𝜈 (1+𝛾5 )𝑏
Buras et al., Phys. Mod. Vol.68 No.4
Introduction-SU(3) Flavor Symmetry
• SU(3) flavor symmetry Lagrangian isn’t affected by flavor transformation.
3⨂3⨂ 3=15⨁6⨁3⨁ 3 ==
𝑚𝑏≅ 4.2𝐺𝑒𝑉 >Λ𝑄𝑐𝐷≅ 1𝐺𝑒𝑉≫𝑚𝑢 ,𝑑 , 𝑠
Introduction-SU(3) Flavor Symmetry
• Effective Hamilton
SU(3) Prediction For CP Asymmetry In
&
q=d
q=s
M Savage et al. , Phys. Rev. D 39, 3346
SU(3) Prediction For CP Asymmetry In
&
SU(3) Prediction For CP Asymmetry In
& d b u d u sb su u
T++
PPP
SU(3) Prediction For CP Asymmetry In
& d b u d u sb su u
A ¿
A ¿
A ¿
A ¿
𝑚𝑏≅ 4.2𝐺𝑒𝑉 >Λ𝑄𝑐𝐷≅ 1𝐺𝑒𝑉≫𝑚𝑢 ,𝑑 , 𝑠SU(3) Symmetry
SU(3) Prediction For CP Asymmetry In
&
Δ ¿
− 𝐼𝑚 (𝑉 𝑢𝑏𝑉 𝑢𝑑∗ 𝑉 𝑡𝑏
∗ 𝑉 𝑡𝑑 )=𝐼𝑚 (𝑉 𝑢𝑏𝑉 𝑢𝑠∗ 𝑉 𝑡𝑏
∗ 𝑉 𝑡𝑠 )
A ¿
A ¿
A ¿A ¿
Breaking Effects
• Deviation from experiment and theory
• We can’t conclude that large SU(3) breaking in the relation.
0
LHCb
LHCb+PDG+CDF
QCD Factorization
pQCD
Experiment
Theory
CP Asymmetry In Decays
𝑓 𝐵𝑚𝐵
200𝑀𝑒𝑉5.3𝐺𝑒𝑉
CP Asymmetry In Decays
CP Asymmetry In Decays
−0.21±0.14 ±0.01 0.013±0.0027 −0.022±0.025 ±0.010 0.344 ±0.424
arXiv:1308.1277v1
0.38±0.15 ±0.02 −0.079±0.032 −0.14±0.11±0.02 0.677 ±0.544
arXiv:1308.1428v1
Sign Size
O X
X X
O O
O X
XX
XO
CP Asymmetry In DecaysSign Size
O X
X X
Generally different
Summary
• The relation between and we have studied may well hold in SM with SU(3) symmetry.
• The other relations can be tested in the SM with SU(3) symmetry when more data become available.
• Large SU(3) breaking effects and CP violation in B+ decaysinto three charged octet pseudoscalar mesons arXiv:1307.7186v3
Thank for your attention