1. 清华大学高能物理研究中心 Center for High Energy Physics, Tsinghua University
CPV phase 𝜷 in 𝑩 𝟎 →𝑱/𝝍 𝝅 + 𝝅 − decays and limits on penguin effects
1. CP-violating phase 𝜙 𝑠
New Physics (NP) processes can modify the value of 𝜙 𝑠 if new particles contribute to box diagrams:
𝜙 𝑠 𝑚𝑒𝑎𝑠 =−2 𝛽 𝑠 + 𝛿 𝑃 + 𝛿 𝑁𝑃
𝜙 𝑠 measured value Tree Penguin New Physics
The phase −2 𝛽 𝑠 =− 37.6 − mrad is well predicted by Standard Model (SM).
In order to search for NP, penguin phase 𝛿 𝑃 should be estimated.
2. World average on 𝜙 𝑠
World average:
𝜙 𝑠 =−30±33 mrad
Combination of LHCb’s
𝐽/𝜓𝜙 & 𝐽/𝜓𝜋𝜋
𝜙 𝑠 =−10±39 mrad
NP is not a large effect ⇒ Need to control SM effects (penguins)
Tree
Penguin
3. Methodology of penguin pollution control
⇒ Using 𝐵 0 →𝐽/𝜓 𝜌 0 decay as control channel:
(a) tree diagram (b) penguin diagram
Penguin pollution can be measured using observables from a 𝑏→𝑐 𝑐 𝑑 decay, and assuming approximate SU(3) flavour symmetry it is possible to apply these results on 𝜙 𝑠 (𝑏→𝑐 𝑐 𝑠). Two possible control channels (P2VV) can be used in a separated way:
⇒ Using 𝐵 𝑠 0 →𝐽/𝜓 𝐾 ∗0 decay as control channel:
Penguin phase 𝛿 𝑃 can be calculated from measuring the mixing-induced CP-violating phase 𝛽 𝑒𝑓𝑓 and direct CP violation 𝛼 𝐶𝑃 in this channel.
Penguins suppressed to tree level by 𝜆 2 ≃ 𝑉 𝑢𝑠 2 ≃
4. Analysis strategy in 𝐵 0 →𝐽/𝜓 𝜋 + 𝜋 −
A time-dependent amplitude analysis is performed to determine the CP-violating 𝛽, by measuring simultaneously the CP-even and CP-odd decay amplitudes for each contributing resonance, without any assumption on the CP content.
Fit the entire 𝜋 + 𝜋 − mass spectrum using a six-resonance model. The most important is 𝐽/𝜓𝜌.
[PLB 742 (2015) 38-49]
(a) Tree diagram
(b) Penguin diagram
Penguins not suppressed to tree level!
5. Measurements of CP asymmetry
Polarization-independent results
𝛼 𝐶𝑃 ≡ 1−| 𝜆 𝑖 | 1+ 𝜆 𝑖
= −32± 28 −7 +9 × 10 −3
2𝛽 𝐽/𝜓 𝜌 0 = 41.7± 9.6 − ∘
rf. 2𝛽 𝑐 𝑐 𝑠 = − ∘ [HFAG]
[PLB 742 (2015) 38-49]
6. Measurement of penguin pollution phase 𝛿 𝑃
The penguin phase 𝛿 𝑃 measured in 𝐵 0 →𝐽/𝜓 𝜌 0 decay:
𝛿 𝑃 =0.9±9.8 mrad
Taking the maximum breaking in phase (𝜃≠ 𝜃 ′ ) and a range of SU(3) breaking in size [0.5, 1.5], the uncertainty on 𝛿 𝑃 becomes ±18 mrad.
Our limit ± 18 mrad is smaller than the current 𝜙 𝑠 uncertainty ±33 mrad
mostly due to S-wave modelling
𝜃− 𝜃 ′ : penguin strong phase difference between 𝑏→𝑐 𝑐 𝑑 and 𝑏→𝑐 𝑐 𝑠
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