CP Violation in Decays and Tests for SU(3) Flavor Symmetry Predictions
description
Transcript of CP Violation in Decays and Tests for SU(3) Flavor Symmetry Predictions
CP Violation in Decays and Tests for SU(3) Flavor Symmetry Predictions
Xiao-Gang He , Siao-Fong Li, and Hsiu-Hsien LinJHEP08(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-LHCb
• The LHCb experiment is situated at one of the four points around LHC.
• Record the decay of particles containing b and anti-b quarks (B meson)
• B mesons formed by the colliding proton beams.
http://lhcb-public.web.cern.ch/lhcb-public/Welcome.html
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-B meson
B quark
~4200 MeV
u quark
d quark
S quark
~ 2.4 MeV
~4.9 MeV
~100 MeV
Life time(10^-12 s)
1.64
1.53
1.47
𝐵+¿ ¿
𝐵0
𝐵𝑠0
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
++
PP
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
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