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