Motivated by the significant experimental progress in probing semileptonic decays <math><mrow><mi>D</mi><mo>→</mo><msub><mrow><mi>P</mi></mrow><mrow><mn>1</mn></mrow></msub><msub><mrow><mi>P</mi></mrow><mrow><mn>2</mn></mrow></msub><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mo>ℓ</mo></mrow></msub></mrow></math> <math><mrow><mo>(</mo><mo>ℓ</mo><mo>=</mo><mi>μ</mi><mo>,</mo><mi>e</mi><mo>)</mo></mrow></math>, we analyze the branching ratios of the <math><mrow><mi>D</mi><mo>→</mo><msub><mrow><mi>P</mi></mrow><mrow><mn>1</mn></mrow></msub><msub><mrow><mi>P</mi></mrow><mrow><mn>2</mn></mrow></msub><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mo>ℓ</mo></mrow></msub></mrow></math> decays with the nonresonant, the light scalar meson resonant, and the vector meson resonant contributions in this work. We obtain the hadronic amplitude relations between different decay modes by the SU(3) flavor analysis, and then predict relevant branching ratios of the <math><mrow><mi>D</mi><mo>→</mo><msub><mrow><mi>P</mi></mrow><mrow><mn>1</mn></mrow></msub><msub><mrow><mi>P</mi></mrow><mrow><mn>2</mn></mrow></msub><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mo>ℓ</mo></mrow></msub></mrow></math> decays by the present experimental data with <math><mn>2</mn><mi>σ</mi></math> errors. Most of our predicted branching ratios are consistent with present experimental data within <math><mn>2</mn><mi>σ</mi></math> error bars, and others are consistent with the data within <math><mn>3</mn><mi>σ</mi></math> error bars. We find that the branching ratios of the nonresonant decays <math><mrow><mrow><msup><mrow><mi>D</mi></mrow><mrow><mn>0</mn></mrow></msup><mo>→</mo><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mover><mrow><mi>K</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mo>ℓ</mo></mrow></msub></mrow><mo>,</mo><mrow><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mi>K</mi></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mo>ℓ</mo></mrow></msub></mrow><mo>,</mo><mrow><msup><mrow><mi>D</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>→</mo><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>K</mi></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mo>ℓ</mo></mrow></msub></mrow><mo>,</mo><mrow><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mover><mrow><mi>K</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mo>ℓ</mo></mrow></msub></mrow><mo>,</mo><mrow><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mo>ℓ</mo></mrow></msub></mrow><mo>,</mo><mrow><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mo>ℓ</mo></mrow></msub></mrow></mrow></math>, and <math><mrow><mrow><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mo>→</mo><msup><mrow><mi>K</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>K</mi></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mo>ℓ</mo></mrow></msub></mrow><mo>,</mo><mspace></mspace><mrow><msup><mrow><mi>K</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mover><mrow><mi>K</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mo>ℓ</mo></mrow></msub></mrow></mrow></math> are on the order of <math><mrow><mi>O</mi><mo>(</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>3</mn></mrow></msup><mi>–</mi><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>4</mn></mrow></msup><mo>)</mo></mrow></math>. The vector meson resonant contributions are dominant in the <math><mrow><mrow><msup><mrow><mi>D</mi></mrow><mrow><mn>0</mn></mrow></msup><mo>→</mo><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mover><mrow><mi>K</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mo>ℓ</mo></mrow></msub></mrow><mo>,</mo><mrow><mrow><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mi>K</mi></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mo>ℓ</mo></mrow></msub></mrow><mo>,</mo><mrow><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mo>ℓ</mo></mrow></msub></mrow><mo>,</mo><mrow><msup><mrow><mi>D</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>→</mo><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>K</mi></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mo>ℓ</mo></mrow></msub></mrow><mo>,</mo><mrow><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mover><mrow><mi>K</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mo>ℓ</mo></mrow></msub></mrow><mo>,</mo><mrow><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mo>ℓ</mo></mrow></msub></mrow></mrow></mrow></math>, and <math><mrow><mrow><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mo>→</mo><msup><mrow><mi>K</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>K</mi></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mo>ℓ</mo></mrow></msub></mrow><mo>,</mo><mspace></mspace><mrow><msup><mrow><mi>K</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mover><mrow><mi>K</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mo>ℓ</mo></mrow></msub></mrow><mo>,</mo><mrow><msup><mrow><mi>K</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mo>ℓ</mo></mrow></msub></mrow><mo>,</mo><mrow><msup><mrow><mi>K</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mo>ℓ</mo></mrow></msub></mrow></mrow></math> decays. The nonresonant, the vector meson resonant, and the scalar resonant contributions are all important in the <math><msup><mi>D</mi><mn>0</mn></msup><mo>→</mo><mi>η</mi><msup><mi>π</mi><mo>−</mo></msup><msup><mo>ℓ</mo><mo>+</mo></msup><msub><mi>ν</mi><mo>ℓ</mo></msub></math> decays. The <math><mrow><mrow><msup><mrow><mi>D</mi></mrow><mrow><mn>0</mn></mrow></msup><mo>→</mo><msup><mrow><mi>K</mi></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mi>K</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mo>ℓ</mo></mrow></msub></mrow><mo>,</mo><mrow><msup><mrow><mi>η</mi></mrow><mrow><mo>′</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mo>ℓ</mo></mrow></msub></mrow></mrow></math> and <math><mrow><mrow><msup><mrow><mi>D</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>→</mo><msup><mrow><mover><mrow><mi>K</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mi>K</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mo>ℓ</mo></mrow></msub></mrow><mo>,</mo><mrow><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mo>ℓ</mo></mrow></msub></mrow><mo>,</mo><mrow><mi>η</mi><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mo>ℓ</mo></mrow></msub></mrow><mo>,</mo><mrow><msup><mrow><mi>η</mi></mrow><mrow><mo>′</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mo>ℓ</mo></mrow></msub></mrow></mrow></math> decays only receive both the nonresonant and the scalar resonant contributions, and both contributions are important in their branching ratios. According to our predictions, many decay modes could be observed in the experiments like BESIII, LHCb, and Belle II, and some decay modes might be measured in these experiments in the near future.

China

Ru-Min Wang

Yi Qiao

Yi-Jie Zhang

Xiao-Dong Cheng

Yuan-Guo Xu

Four-body semileptonic charm decays <math><mi>D</mi><mo>→</mo><msub><mi>P</mi><mn>1</mn></msub><msub><mi>P</mi><mn>2</mn></msub><msup><mo>ℓ</mo><mo>+</mo></msup><msub><mi>ν</mi><mo>ℓ</mo></msub></math> based on SU(3) flavor analysis

Within the Standard Model, we investigate the <math><mi>C</mi><mi>P</mi></math> violations and the <math><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup><mo>−</mo><msubsup><mi>K</mi><mi>L</mi><mn>0</mn></msubsup></math> asymmetries in <math><msup><mi>D</mi><mo>±</mo></msup><mo>→</mo><msup><mi>K</mi><mo>*</mo></msup><mo>(</mo><mn>892</mn><msup><mo>)</mo><mn>0</mn></msup><msup><mi>π</mi><mo>±</mo></msup><mo>+</mo><msup><mover><mi>K</mi><mo>¯</mo></mover><mo>*</mo></msup><mo>(</mo><mn>892</mn><msup><mo>)</mo><mn>0</mn></msup><msup><mi>π</mi><mo>±</mo></msup><mo>→</mo><msubsup><mi>K</mi><mrow><mi>S</mi><mo>,</mo><mi>L</mi></mrow><mn>0</mn></msubsup><msup><mi>π</mi><mn>0</mn></msup><msup><mi>π</mi><mo>±</mo></msup></math> decays basing on the factorization-assisted topological-amplitude (FAT) approach and the topological amplitude (TA) approach of Cheng and Chiang [Phys. Rev. D 104, 073003 (2021).]. We find that the <math><mi>C</mi><mi>P</mi></math> violations in these decays <math><msubsup><mi>A</mi><mrow><mi>C</mi><mi>P</mi></mrow><msubsup><mi>K</mi><mrow><mi>S</mi><mo>,</mo><mi>L</mi></mrow><mn>0</mn></msubsup></msubsup></math> can exceed the order of <math><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></math> in the two approaches and consist of three parts: the indirect <math><mi>C</mi><mi>P</mi></math> violations in <math><msup><mi>K</mi><mn>0</mn></msup><mo>−</mo><msup><mover><mi>K</mi><mo>¯</mo></mover><mn>0</mn></msup></math> mixing <math><msubsup><mi>A</mi><mrow><mi>C</mi><mi>P</mi><mo>,</mo><msubsup><mi>K</mi><mrow><mi>S</mi><mo>,</mo><mi>L</mi></mrow><mn>0</mn></msubsup></mrow><mrow><mi>mix</mi></mrow></msubsup></math>, the direct <math><mi>C</mi><mi>P</mi></math> violations in charm decays <math><msubsup><mi>A</mi><mrow><mi>C</mi><mi>P</mi><mo>,</mo><msubsup><mi>K</mi><mrow><mi>S</mi><mo>,</mo><mi>L</mi></mrow><mn>0</mn></msubsup></mrow><mrow><mi>dir</mi></mrow></msubsup></math>, and the new <math><mi>C</mi><mi>P</mi></math> violation effects <math><msubsup><mi>A</mi><mrow><mi>C</mi><mi>P</mi><mo>,</mo><msubsup><mi>K</mi><mrow><mi>S</mi><mo>,</mo><mi>L</mi></mrow><mn>0</mn></msubsup></mrow><mrow><mi>int</mi></mrow></msubsup></math>, which are induced from the interference between two tree (Cabibbo-favored and doubly Cabibbo-suppressed) amplitudes with the neutral kaon mixing. The indirect <math><mi>C</mi><mi>P</mi></math> violations in <math><msup><mi>K</mi><mn>0</mn></msup><mo>−</mo><msup><mover><mi>K</mi><mo>¯</mo></mover><mn>0</mn></msup></math> mixing play a dominant role in <math><msubsup><mi>A</mi><mrow><mi>C</mi><mi>P</mi></mrow><msubsup><mi>K</mi><mrow><mi>S</mi><mo>,</mo><mi>L</mi></mrow><mn>0</mn></msubsup></msubsup></math>; the new <math><mi>C</mi><mi>P</mi></math> violation effects have a non-negligible contribution to <math><msubsup><mi>A</mi><mrow><mi>C</mi><mi>P</mi></mrow><msubsup><mi>K</mi><mrow><mi>S</mi><mo>,</mo><mi>L</mi></mrow><mn>0</mn></msubsup></msubsup></math>. We estimate the numerical results of the <math><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup><mo>−</mo><msubsup><mi>K</mi><mi>L</mi><mn>0</mn></msubsup></math> asymmetries <math><msubsup><mi>R</mi><mrow><msub><mi>K</mi><mi>S</mi></msub><mo>−</mo><msub><mi>K</mi><mi>L</mi></msub></mrow><msup><mi>D</mi><mo>±</mo></msup></msubsup></math> and find that there exists a large difference between the numerical results in the FAT approach and that of the TA approach. We present the numbers of <math><msup><mi>D</mi><mo>±</mo></msup></math> events-times-efficiency needed to observe the <math><mi>C</mi><mi>P</mi></math> violations and the <math><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup><mo>−</mo><msubsup><mi>K</mi><mi>L</mi><mn>0</mn></msubsup></math> asymmetries at the level of 3 standard deviations (<math><mrow><mn>3</mn><mi>σ</mi></mrow></math>). We also find that if one adopts the values of the decay time parameters <math><msub><mi>t</mi><mn>0</mn></msub><mo>=</mo><mn>3.0</mn><msub><mi>τ</mi><mi>S</mi></msub></math> and <math><msub><mi>t</mi><mn>1</mn></msub><mo>=</mo><mn>10.0</mn><msub><mi>τ</mi><mi>S</mi></msub></math>, the new <math><mi>C</mi><mi>P</mi></math> violation effect <math><msubsup><mi>A</mi><mrow><mi>C</mi><mi>P</mi><mo>,</mo><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup></mrow><mrow><mi>int</mi></mrow></msubsup></math> would dominate the <math><mi>C</mi><mi>P</mi></math> violation in <math><msup><mi>D</mi><mo>±</mo></msup><mo>→</mo><msup><mi>K</mi><mo>*</mo></msup><mo>(</mo><mn>892</mn><msup><mo>)</mo><mn>0</mn></msup><msup><mi>π</mi><mo>±</mo></msup><mo>+</mo><msup><mover><mi>K</mi><mo>¯</mo></mover><mo>*</mo></msup><mo>(</mo><mn>892</mn><msup><mo>)</mo><mn>0</mn></msup><msup><mi>π</mi><mo>±</mo></msup><mo>→</mo><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup><msup><mi>π</mi><mn>0</mn></msup><msup><mi>π</mi><mo>±</mo></msup></math> decays and could be observed with <math><mn>6.7</mn><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup></math> and <math><mn>6.5</mn><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup></math> <math><msup><mi>D</mi><mo>±</mo></msup></math> events-times-efficiency in the FAT approach and the TA approach, respectively. Our results could be tested by the LHCb (Large Hadron Collider beauty), Belle II, and BESIII experiments.

Xing-Bo Yuan

Study of <math><mi>C</mi><mi>P</mi></math> violation in <math><msup><mi>D</mi><mo>±</mo></msup><mo>→</mo><msup><mi>K</mi><mo>*</mo></msup><mo>(</mo><mn>892</mn><msup><mo>)</mo><mn>0</mn></msup><msup><mi>π</mi><mo>±</mo></msup><mo>+</mo><msup><mover><mi>K</mi><mo>¯</mo></mover><mo>*</mo></msup><mo>(</mo><mn>892</mn><msup><mo>)</mo><mn>0</mn></msup><msup><mi>π</mi><mo>±</mo></msup><mo>→</mo><msubsup><mi>K</mi><mrow><mi>S</mi><mo>,</mo><mi>L</mi></mrow><mn>0</mn></msubsup><msup><mi>π</mi><mn>0</mn></msup><msup><mi>π</mi><mo>±</mo></msup></math> decays

We use the spectral lag catalog of 46 short GRBs aggregated by Xiao et al. (Astrophys J Lett 924:L29, 2022), to carry out an independent search for Lorentz invariance violation (LIV). For this purpose, we use a power-law model as a function of energy for the intrinsic astrophysical induced spectral lags. The expansion history of the universe needed for constraining LIV was obtained in a non-parametric method using cosmic chronometers. We use Bayesian model comparison to determine if the aforementioned spectral lags show evidence for LIV as compared to only astrophysically induced lags. We do not find any evidence for LIV, and obtain 95% CL lower limits on the corresponding energy scale to be  $$4 \times 10^{15}$$  <math> <mrow> <mn>4</mn> <mo>×</mo> <msup> <mn>10</mn> <mn>15</mn> </msup> </mrow> </math>   GeV and  $$6.8 \times 10^{9}$$  <math> <mrow> <mn>6.8</mn> <mo>×</mo> <msup> <mn>10</mn> <mn>9</mn> </msup> </mrow> </math>   GeV for the linear and quadratic LIV models respectively. Our results obtained by using the flat  $$\Lambda $$  <math> <mi>Λ</mi> </math>  CDM model for characterizing the cosmic expansion history are consistent with those obtained using chronometers.

India

Shantanu Desai

Rajdeep Agrawal

Germany

Haveesh Singirikonda

Search for Lorentz invariance violation using Bayesian model comparison applied to Xiao et al. GRB spectral lag catalog

Motivated by the first measured <math><msup><mrow><mi>Δ</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>→</mo><mi>p</mi><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo></mrow></msup></math> decay by the HADES Collaboration, electromagnetic Dalitz baryon decays from the spin <math><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac></math> decuplet (<math><msub><mrow><mi>T</mi></mrow><mrow><mn>10</mn></mrow></msub></math>) to the spin <math><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></math> octet (<math><msub><mrow><mi>T</mi></mrow><mrow><mn>8</mn></mrow></msub></math>) baryons are investigated by using the SU(3) flavor symmetry/breaking in this paper. All decay amplitudes of <math><msub><mrow><mi>T</mi></mrow><mrow><mn>10</mn></mrow></msub><mo>→</mo><msub><mrow><mi>T</mi></mrow><mrow><mn>8</mn></mrow></msub><msup><mrow><mi>ℓ</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>ℓ</mi></mrow><mrow><mo>−</mo></mrow></msup><mspace width="0.25em"></mspace><mo>(</mo><mi>ℓ</mi><mo>=</mo><mi>e</mi><mo>,</mo><mi>μ</mi><mo>)</mo></math> electromagnetic Dalitz decays could be related by the SU(3) flavor symmetry/breaking, so the amplitudes can be obtained by the measured branching ratio of <math><msup><mrow><mi>Δ</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>→</mo><mi>p</mi><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo></mrow></msup></math> decay from the HADES Collaboration. The branching ratios, the lepton flavor universality, and the ratios <math><mfrac><mrow><mi>B</mi><mo>(</mo><msub><mrow><mi>T</mi></mrow><mrow><mn>10</mn></mrow></msub><mo>→</mo><msub><mrow><mi>T</mi></mrow><mrow><mn>8</mn></mrow></msub><msup><mrow><mi>ℓ</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>ℓ</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>)</mo></mrow><mrow><mi>B</mi><mo>(</mo><msub><mrow><mi>T</mi></mrow><mrow><mn>10</mn></mrow></msub><mo>→</mo><msub><mrow><mi>T</mi></mrow><mrow><mn>8</mn></mrow></msub><mi>γ</mi><mo>)</mo></mrow></mfrac></math> are predicted by the relevant experimental data. <math><msub><mrow><mi>T</mi></mrow><mrow><mn>10</mn></mrow></msub><mo>→</mo><msub><mrow><mi>T</mi></mrow><mrow><mn>8</mn></mrow></msub><msup><mrow><mi>μ</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>μ</mi></mrow><mrow><mo>−</mo></mrow></msup></math> electromagnetic Dalitz decays are studied for the first time. All predicted <math><mi>B</mi><mo>(</mo><msub><mrow><mi>T</mi></mrow><mrow><mn>10</mn></mrow></msub><mo>→</mo><msub><mrow><mi>T</mi></mrow><mrow><mn>8</mn></mrow></msub><msup><mrow><mi>ℓ</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>ℓ</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>)</mo></math> except <math><mi>B</mi><mo>(</mo><msup><mrow><mi>Ξ</mi></mrow><mrow><mo>⁎</mo><mn>0</mn></mrow></msup><mo>→</mo><msup><mrow><mi>Ξ</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mi>μ</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>μ</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>)</mo></math> and <math><mi>B</mi><mo>(</mo><msup><mrow><mi>Ξ</mi></mrow><mrow><mo>⁎</mo><mo>−</mo></mrow></msup><mo>→</mo><msup><mrow><mi>Ξ</mi></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mi>μ</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>μ</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>)</mo></math> are on the order of <math><mi>O</mi><mo>(</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>5</mn></mrow></msup><mo>−</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>7</mn></mrow></msup><mo>)</mo></math>, and these decays could be observed and could be used to test the SU(3) flavor symmetry/breaking approach in the electromagnetic Dalitz decays by HADES, PANDA, BESIII, and other experiments in the near future.

Qin Chang

Electromagnetic Dalitz decays of decuplet to octet with the SU(3) flavor symmetry/breaking

The decays <math><mrow><msup><mrow><mi>K</mi></mrow><mrow><mo>*</mo></mrow></msup><mo>(</mo><mn>892</mn><mo>)</mo><mo>→</mo><msubsup><mrow><mi>K</mi></mrow><mrow><mi>S</mi><mo>,</mo><mi>L</mi></mrow><mrow><mn>0</mn></mrow></msubsup><mi>π</mi></mrow></math> can be used to study <math><mi>C</mi><mi>P</mi></math> violation and <math><mi>C</mi><mi>P</mi><mi>T</mi></math> violation. The <math><msup><mi>K</mi><mo>*</mo></msup><mo>(</mo><mn>892</mn><mo>)</mo></math> (hereinafter referred to as <math><msup><mi>K</mi><mo>*</mo></msup></math>) meson can be produced via <math><mi>J</mi><mo>/</mo><mi>ψ</mi></math> decays at BESIII. In this paper, we study <math><mi>C</mi><mi>P</mi></math> violation and <math><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup><mo>−</mo><msubsup><mi>K</mi><mi>L</mi><mn>0</mn></msubsup></math> asymmetry in the <math><mi>J</mi><mo>/</mo><mi>ψ</mi></math> decays involving the <math><msup><mi>K</mi><mo>*</mo></msup></math> meson in the final states and obtain the following results: <math><mrow><msub><mrow><mi>A</mi></mrow><mrow><mi>C</mi><mi>P</mi></mrow></msub><mrow><mo>(</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mo>→</mo><msup><mrow><mi>K</mi></mrow><mrow><mo>*</mo></mrow></msup><msub><mrow><mi>f</mi></mrow><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></msub><mo>→</mo><msubsup><mrow><mi>K</mi></mrow><mrow><mi>S</mi></mrow><mrow><mn>0</mn></mrow></msubsup><mi>π</mi><msub><mrow><mi>f</mi></mrow><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></msub><mo>)</mo></mrow><mo>=</mo><mrow><mo>(</mo><mn>3.64</mn><mo>±</mo><mn>0.04</mn><mo>)</mo></mrow><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow></math>, <math><mrow><msub><mrow><mi>A</mi></mrow><mrow><mi>C</mi><mi>P</mi></mrow></msub><mrow><mo>(</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mo>→</mo><msup><mrow><mi>K</mi></mrow><mrow><mo>*</mo></mrow></msup><msub><mrow><mi>f</mi></mrow><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></msub><mo>→</mo><mspace></mspace><msubsup><mrow><mi>K</mi></mrow><mrow><mi>L</mi></mrow><mrow><mn>0</mn></mrow></msubsup><mi>π</mi><msub><mrow><mi>f</mi></mrow><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></msub><mo>)</mo></mrow><mo>=</mo><mrow><mo>(</mo><mo>−</mo><mn>3.32</mn><mo>±</mo><mn>0.04</mn><mo>)</mo></mrow><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow></math>, and <math><mrow><mi>R</mi><mrow><mo>(</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mo>→</mo><msup><mrow><mi>K</mi></mrow><mrow><mo>*</mo></mrow></msup><msub><mrow><mi>f</mi></mrow><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></msub><mo>→</mo><msubsup><mrow><mi>K</mi></mrow><mrow><mi>S</mi><mo>,</mo><mi>L</mi></mrow><mrow><mn>0</mn></mrow></msubsup><mi>π</mi><msub><mrow><mi>f</mi></mrow><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></msub><mo>)</mo></mrow><mo>=</mo><mrow><mo>(</mo><mn>3.51</mn><mo>±</mo><mn>0.03</mn><mo>)</mo></mrow><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow></math>, <math><mrow><mi>R</mi><mrow><mo>(</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mo>→</mo><msup><mrow><mover><mrow><mi>K</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mo>*</mo></mrow></msup><msub><mrow><mover><mrow><mi>f</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></msub><mo>→</mo><msubsup><mrow><mi>K</mi></mrow><mrow><mi>S</mi><mo>,</mo><mi>L</mi></mrow><mrow><mn>0</mn></mrow></msubsup><mi>π</mi><msub><mrow><mover><mrow><mi>f</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></msub><mo>)</mo></mrow><mo>=</mo><mrow><mo>(</mo><mo>−</mo><mn>3.45</mn><mo>±</mo><mn>0.03</mn><mo>)</mo></mrow><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow></math>. Based on two cases, the samples of <math><msup><mn>10</mn><mn>10</mn></msup></math> and <math><msup><mn>10</mn><mn>12</mn></msup><mtext> </mtext><mtext> </mtext><mi>J</mi><mo>/</mo><mi>ψ</mi></math> events, we calculate the expected numbers of the observed signal events on the <math><mi>C</mi><mi>P</mi></math> violation and the <math><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup><mo>−</mo><msubsup><mi>K</mi><mi>L</mi><mn>0</mn></msubsup></math> asymmetry in the <math><mi>J</mi><mo>/</mo><mi>ψ</mi></math> decays with <math><msup><mi>K</mi><mo>*</mo></msup></math> meson in the final states, and we find that the BESIII experiment may be able to unambiguously observe <math><mi>C</mi><mi>P</mi></math> violation and <math><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup><mo>−</mo><msubsup><mi>K</mi><mi>L</mi><mn>0</mn></msubsup></math> asymmetry for each of these two cases. We study the possibility to constrain the <math><mi>C</mi><mi>P</mi><mi>T</mi></math> violation parameter <math><mi>z</mi></math> and discuss the sensitivity for the measurement of <math><mi>z</mi></math> in <math><mi>J</mi><mo>/</mo><mi>ψ</mi></math> decays with <math><msup><mi>K</mi><mo>*</mo></msup></math> meson in the final states at BESIII. The sensitivity of the measurement of <math><mi>z</mi></math> depends on the measured precision of the parameters <math><msub><mi>m</mi><mi>L</mi></msub><mo>−</mo><msub><mi>m</mi><mi>S</mi></msub></math>, <math><msub><mi>Γ</mi><mi>L</mi></msub></math>, <math><msub><mi>Γ</mi><mi>S</mi></msub></math>, <math><mi>p</mi></math>, and <math><mi>q</mi></math> and the consistence between the values of <math><msub><mi>t</mi><mn>0</mn></msub></math> and <math><msub><mi>t</mi><mn>1</mn></msub></math> and the event selection criteria in experiment.

Xin Zhang

Study of <math><mi>C</mi><mi>P</mi></math> violation and <math><mi>C</mi><mi>P</mi><mi>T</mi></math> violation in <math><mrow><msup><mrow><mi>K</mi></mrow><mrow><mo>*</mo></mrow></msup><mo>(</mo><mn>892</mn><mo>)</mo><mo>→</mo><msubsup><mrow><mi>K</mi></mrow><mrow><mi>S</mi><mo>,</mo><mi>L</mi></mrow><mrow><mn>0</mn></mrow></msubsup><mi>π</mi></mrow></math> decays at BESIII

The large data sample of the <math><mrow><msub><mrow><mi>B</mi></mrow><mrow><mi>c</mi></mrow></msub></mrow></math> meson collected at the LHC experiment and the HL-LHC experiment provides us the opportunity to study the <math><mrow><msub><mrow><mi>B</mi></mrow><mrow><mi>c</mi></mrow></msub></mrow></math> decays and the related physics. In this paper, we investigate the effect of <math><mrow><msup><mrow><mi>K</mi></mrow><mrow><mn>0</mn></mrow></msup><mo>−</mo><msup><mrow><mover><mrow><mi>K</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mn>0</mn></mrow></msup></mrow></math> mixing on the branching ratios, <math><mi>C</mi><mi>P</mi></math> violations and <math><mi>C</mi><mi>P</mi><mi>T</mi></math> violations in the <math><mrow><msubsup><mrow><mi>B</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>±</mo></mrow></msubsup><mo>→</mo><msup><mrow><mi>B</mi></mrow><mrow><mo>±</mo></mrow></msup><msubsup><mrow><mi>K</mi></mrow><mrow><mi>S</mi><mo>,</mo><mi>L</mi></mrow><mrow><mn>0</mn></mrow></msubsup></mrow></math> decays. We find that some of the <math><mrow><msubsup><mrow><mi>B</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>±</mo></mrow></msubsup><mo>→</mo><msup><mrow><mi>B</mi></mrow><mrow><mo>±</mo></mrow></msup><msubsup><mrow><mi>K</mi></mrow><mrow><mi>S</mi><mo>,</mo><mi>L</mi></mrow><mrow><mn>0</mn></mrow></msubsup><mo>→</mo><msub><mrow><mi>f</mi></mrow><mrow><msup><mrow><mi>B</mi></mrow><mrow><mo>±</mo></mrow></msup></mrow></msub><msub><mrow><mi>f</mi></mrow><mrow><msubsup><mrow><mi>K</mi></mrow><mrow><mi>S</mi><mo>,</mo><mi>L</mi></mrow><mrow><mn>0</mn></mrow></msubsup></mrow></msub></mrow></math> decay chains have large branching ratios, whose maximum value can exceed the order of <math><msup><mn>10</mn><mrow><mo>−</mo><mn>6</mn></mrow></msup></math>, the minimum number of <math><msubsup><mi>B</mi><mi>c</mi><mo>±</mo></msubsup></math> events times efficiency for observing the decays at three standard deviations (<math><mrow><mn>3</mn><mi>σ</mi></mrow></math>) level is about <math><msup><mn>10</mn><mn>6</mn></msup></math>. We study the <math><mrow><mi>C</mi><mi>P</mi></mrow></math> asymmetries in the <math><mrow><msubsup><mrow><mi>B</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>±</mo></mrow></msubsup><mo>→</mo><msup><mrow><mi>B</mi></mrow><mrow><mo>±</mo></mrow></msup><msubsup><mrow><mi>K</mi></mrow><mrow><mi>S</mi><mo>,</mo><mi>L</mi></mrow><mrow><mn>0</mn></mrow></msubsup></mrow></math> decays and find that the <math><mi>C</mi><mi>P</mi></math> asymmetries can exceed the order of <math><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></math>, which are dominated by <math><mrow><msup><mrow><mi>K</mi></mrow><mrow><mn>0</mn></mrow></msup><mo>−</mo><msup><mrow><mover><mrow><mi>K</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mn>0</mn></mrow></msup></mrow></math> mixing. We give the most promising processes to observe the <math><mi>C</mi><mi>P</mi></math> violations and the ranges of the numbers of <math><msubsup><mi>B</mi><mi>c</mi><mo>±</mo></msubsup></math> events-times-efficiency needed to observe the <math><mi>C</mi><mi>P</mi></math> asymmetries at a significance of <math><mrow><mn>3</mn><mi>σ</mi></mrow></math> in these decays. We investigate the possibility to constraint the <math><mi>C</mi><mi>P</mi><mi>T</mi></math> violation parameter <math><mi>z</mi></math> in the <math><mrow><msubsup><mrow><mi>B</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>±</mo></mrow></msubsup><mo>→</mo><msup><mrow><mi>B</mi></mrow><mrow><mo>±</mo></mrow></msup><msubsup><mrow><mi>K</mi></mrow><mrow><mi>S</mi><mo>,</mo><mi>L</mi></mrow><mrow><mn>0</mn></mrow></msubsup><mo>→</mo><msub><mrow><mi>f</mi></mrow><mrow><msup><mrow><mi>B</mi></mrow><mrow><mo>±</mo></mrow></msup></mrow></msub><msub><mrow><mi>f</mi></mrow><mrow><msubsup><mrow><mi>K</mi></mrow><mrow><mi>S</mi><mo>,</mo><mi>L</mi></mrow><mrow><mn>0</mn></mrow></msubsup></mrow></msub></mrow></math> decays and give the most promising processes to constraint the parameter <math><mi>z</mi></math>.

Effect of <math><mrow><msup><mrow><mi>K</mi></mrow><mrow><mn>0</mn></mrow></msup><mo>−</mo><msup><mrow><mover><mrow><mi>K</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mn>0</mn></mrow></msup></mrow></math> mixing on <math><mi>C</mi><mi>P</mi></math> and <math><mi>C</mi><mi>P</mi><mi>T</mi></math> violations in <math><mrow><msubsup><mrow><mi>B</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>±</mo></mrow></msubsup><mo>→</mo><msup><mrow><mi>B</mi></mrow><mrow><mo>±</mo></mrow></msup><msubsup><mrow><mi>K</mi></mrow><mrow><mi>S</mi><mo>,</mo><mi>L</mi></mrow><mrow><mn>0</mn></mrow></msubsup></mrow></math> decays

Motivated by recent anomalies in flavor changing neutral current <math><mi>b</mi><mo>→</mo><mi>s</mi><msup><mo>ℓ</mo><mo>+</mo></msup><msup><mo>ℓ</mo><mo>−</mo></msup></math> transitions, we study <math><msub><mi>B</mi><mn>1</mn></msub><mo>→</mo><msub><mi>B</mi><mn>2</mn></msub><msup><mo>ℓ</mo><mo>+</mo></msup><msup><mo>ℓ</mo><mo>−</mo></msup><mo>(</mo><mo>ℓ</mo><mo>=</mo><mi>e</mi><mo>,</mo><mi>μ</mi><mo>,</mo><mi>τ</mi><mo>)</mo></math> semileptonic weak decays with the SU(3) flavor symmetry, where <math><msub><mi>B</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></math> are the spin-<math><mfrac><mn>1</mn><mn>2</mn></mfrac></math> baryons of single bottomed antitriplet <math><msub><mi>T</mi><mrow><mi>b</mi><mn>3</mn></mrow></msub></math>, single charmed antitriplet <math><msub><mi>T</mi><mrow><mi>c</mi><mn>3</mn></mrow></msub></math>, or light baryons octet <math><msub><mi>T</mi><mn>8</mn></msub></math>. Using the SU(3) irreducible representation approach, we first obtain the amplitude relations among different decay modes and then predict the relevant not-yet measured observables of <math><msub><mi>T</mi><mrow><mi>b</mi><mn>3</mn></mrow></msub><mo>→</mo><msub><mi>T</mi><mn>8</mn></msub><msup><mo>ℓ</mo><mo>+</mo></msup><msup><mo>ℓ</mo><mo>−</mo></msup></math>, <math><msub><mi>T</mi><mrow><mi>c</mi><mn>3</mn></mrow></msub><mo>→</mo><msub><mi>T</mi><mn>8</mn></msub><msup><mo>ℓ</mo><mo>+</mo></msup><msup><mo>ℓ</mo><mo>−</mo></msup></math>, and <math><msub><mi>T</mi><mn>8</mn></msub><mo>→</mo><msubsup><mi>T</mi><mn>8</mn><mo>′</mo></msubsup><msup><mo>ℓ</mo><mo>+</mo></msup><msup><mo>ℓ</mo><mo>−</mo></msup></math> decays. (a) We calculate the branching ratios of the <math><msub><mi>T</mi><mrow><mi>b</mi><mn>3</mn></mrow></msub><mo>→</mo><msub><mi>T</mi><mn>8</mn></msub><msup><mi>μ</mi><mo>+</mo></msup><msup><mi>μ</mi><mo>−</mo></msup></math> and <math><msub><mi>T</mi><mrow><mi>b</mi><mn>3</mn></mrow></msub><mo>→</mo><msub><mi>T</mi><mn>8</mn></msub><msup><mi>τ</mi><mo>+</mo></msup><msup><mi>τ</mi><mo>−</mo></msup></math> decay modes in the whole <math><msup><mi>q</mi><mn>2</mn></msup></math> region and in the different <math><msup><mi>q</mi><mn>2</mn></msup></math> bins by the measurement of <math><msubsup><mi>Λ</mi><mi>b</mi><mn>0</mn></msubsup><mo>→</mo><msup><mi>Λ</mi><mn>0</mn></msup><msup><mi>μ</mi><mo>+</mo></msup><msup><mi>μ</mi><mo>−</mo></msup></math>. Many of them are obtained for the first time. In addition, the longitudinal polarization fractions and the leptonic forward-backward asymmetries of all <math><msub><mi>T</mi><mrow><mi>b</mi><mn>3</mn></mrow></msub><mo>→</mo><msub><mi>T</mi><mn>8</mn></msub><msup><mo>ℓ</mo><mo>+</mo></msup><msup><mo>ℓ</mo><mo>−</mo></msup></math> decays are very similar to each other in certain <math><msup><mi>q</mi><mn>2</mn></msup></math> bins due to the SU(3) flavor symmetry. (b) We analyze the upper limits of <math><mi>B</mi><mo>(</mo><msub><mi>T</mi><mrow><mi>c</mi><mn>3</mn></mrow></msub><mo>→</mo><msub><mi>T</mi><mn>8</mn></msub><msup><mo>ℓ</mo><mo>+</mo></msup><msup><mo>ℓ</mo><mo>−</mo></msup><mo>)</mo></math> by using the experimental upper limits of <math><mi>B</mi><mo>(</mo><msubsup><mi>Λ</mi><mi>c</mi><mo>+</mo></msubsup><mo>→</mo><mi>p</mi><msup><mi>μ</mi><mo>+</mo></msup><msup><mi>μ</mi><mo>−</mo></msup><mo>)</mo></math> and <math><mi>B</mi><mo>(</mo><msubsup><mi>Λ</mi><mi>c</mi><mo>+</mo></msubsup><mo>→</mo><mi>p</mi><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup><mo>)</mo></math>, and find the experimental upper limit of <math><mi>B</mi><mo>(</mo><msubsup><mi>Λ</mi><mi>c</mi><mo>+</mo></msubsup><mo>→</mo><mi>p</mi><msup><mi>μ</mi><mo>+</mo></msup><msup><mi>μ</mi><mo>−</mo></msup><mo>)</mo></math> giving the effective bounds on the relevant SU(3) flavor symmetry parameters. The predictions of <math><mi>B</mi><mo>(</mo><msubsup><mi>Ξ</mi><mi>c</mi><mn>0</mn></msubsup><mo>→</mo><msup><mi>Ξ</mi><mn>0</mn></msup><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup><mo>)</mo></math> and <math><mi>B</mi><mo>(</mo><msubsup><mi>Ξ</mi><mi>c</mi><mn>0</mn></msubsup><mo>→</mo><msup><mi>Ξ</mi><mn>0</mn></msup><msup><mi>μ</mi><mo>+</mo></msup><msup><mi>μ</mi><mo>−</mo></msup><mo>)</mo></math> will be different between the single-quark transition dominant contributions and the <math><mi>W</mi></math>-exchange dominant ones. (c) As for <math><msub><mi>T</mi><mn>8</mn></msub><mo>→</mo><msubsup><mi>T</mi><mn>8</mn><mo>′</mo></msubsup><msup><mo>ℓ</mo><mo>+</mo></msup><msup><mo>ℓ</mo><mo>−</mo></msup></math> decays, we analyze the single-quark transition contributions and the <math><mi>W</mi></math>-exchange contributions by using the two experimental measurements of <math><mi>B</mi><mo>(</mo><msup><mi>Ξ</mi><mn>0</mn></msup><mo>→</mo><msup><mi>Λ</mi><mn>0</mn></msup><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup><mo>)</mo></math> and <math><mi>B</mi><mo>(</mo><msup><mi>Σ</mi><mo>+</mo></msup><mo>→</mo><mi>p</mi><msup><mi>μ</mi><mo>+</mo></msup><msup><mi>μ</mi><mo>−</mo></msup><mo>)</mo></math>, and give the branching ratio predictions by assuming either single-quark transition dominant contributions or the <math><mi>W</mi></math>-exchange dominant contributions. According to our predictions, some observables are accessible to the experiments at BESIII, LHCb and Belle-II.

Chong Hua

Studying <math><msub><mi>B</mi><mn>1</mn></msub><mo>(</mo><msup><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>+</mo></msup><mo>)</mo><mo>→</mo><msub><mi>B</mi><mn>2</mn></msub><mo>(</mo><msup><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>+</mo></msup><mo>)</mo><msup><mo>ℓ</mo><mo>+</mo></msup><msup><mo>ℓ</mo><mo>−</mo></msup></math> semileptonic weak baryon decays with the SU(3) flavor symmetry

The <math><msubsup><mi>a</mi><mn>0</mn><mn>0</mn></msubsup><mo>(</mo><mn>980</mn><mo>)</mo><mo>−</mo><msub><mi>f</mi><mn>0</mn></msub><mo>(</mo><mn>980</mn><mo>)</mo></math> mixing is one of the most promising potential tools to learn about the nature of <math><msubsup><mi>a</mi><mn>0</mn><mn>0</mn></msubsup><mo>(</mo><mn>980</mn><mo>)</mo></math> and <math><msub><mi>f</mi><mn>0</mn></msub><mo>(</mo><mn>980</mn><mo>)</mo></math>. Using the <math><msub><mi>f</mi><mn>0</mn></msub><mo>(</mo><mn>980</mn><mo>)</mo><mo>−</mo><msubsup><mi>a</mi><mn>0</mn><mn>0</mn></msubsup><mo>(</mo><mn>980</mn><mo>)</mo></math> mixing intensity <math><msub><mi>ξ</mi><mrow><mi>a</mi><mi>f</mi></mrow></msub></math> measured recently at the BESIII experiment, we calculate the branching ratio of the isospin violation decay <math><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi><mo>→</mo><mi>γ</mi><msub><mrow><mi>η</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>→</mo><mspace></mspace><mi>γ</mi><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup><msubsup><mrow><mi>a</mi></mrow><mrow><mn>0</mn></mrow><mrow><mn>0</mn></mrow></msubsup><mo>(</mo><mn>1450</mn><mo>)</mo><mo>→</mo><mi>γ</mi><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup><msubsup><mrow><mi>a</mi></mrow><mrow><mn>0</mn></mrow><mrow><mn>0</mn></mrow></msubsup><mo>(</mo><mn>980</mn><mo>)</mo><msub><mrow><mi>f</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mn>500</mn><mo>)</mo><mo>→</mo><mi>γ</mi><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup><msub><mrow><mi>f</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mn>980</mn><mo>)</mo><msub><mrow><mi>f</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mn>500</mn><mo>)</mo><mo>→</mo><mi>γ</mi><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup></mrow></math>. The value of the branching ratio is found to be <math><mi>O</mi><mo>(</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>6</mn></mrow></msup><mo>)</mo></math>, which can be observed with <math><mrow><msup><mrow><mn>10</mn></mrow><mrow><mn>10</mn></mrow></msup><mtext> </mtext><mtext> </mtext><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></math> events collected at the BESIII experiment. The narrow peak from the <math><msub><mi>f</mi><mn>0</mn></msub><mo>(</mo><mn>980</mn><mo>)</mo><mo>−</mo><msubsup><mi>a</mi><mn>0</mn><mn>0</mn></msubsup><mo>(</mo><mn>980</mn><mo>)</mo></math> mixing in the <math><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math> mass square spectrum can also be observed. In addition, we study the nonresonant decay <math><mrow><msubsup><mrow><mi>a</mi></mrow><mrow><mn>0</mn></mrow><mrow><mn>0</mn></mrow></msubsup><mo>(</mo><mn>1450</mn><mo>)</mo><mo>→</mo><msub><mrow><mi>f</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mn>980</mn><mo>)</mo><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>(</mo><mtext>nonresonant</mtext><mo>)</mo></mrow></math>, which is dominated by the <math><msubsup><mi>a</mi><mn>0</mn><mn>0</mn></msubsup><mo>(</mo><mn>980</mn><mo>)</mo><mo>−</mo><msub><mi>f</mi><mn>0</mn></msub><mo>(</mo><mn>980</mn><mo>)</mo></math> mixing. We find that the nonresonant decay <math><msubsup><mi>a</mi><mn>0</mn><mn>0</mn></msubsup><mo>(</mo><mn>1450</mn><mo>)</mo><mo>→</mo><msub><mi>f</mi><mn>0</mn></msub><mo>(</mo><mn>980</mn><mo>)</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math> and the decay <math><msubsup><mi>a</mi><mn>0</mn><mn>0</mn></msubsup><mo>(</mo><mn>1450</mn><mo>)</mo><mo>→</mo><msub><mi>f</mi><mn>0</mn></msub><mo>(</mo><mn>980</mn><mo>)</mo><msub><mi>f</mi><mn>0</mn></msub><mo>(</mo><mn>500</mn><mo>)</mo></math> can be combined to measure the mixing intensity <math><msub><mi>ξ</mi><mrow><mi>a</mi><mi>f</mi></mrow></msub></math> in experiment. These decays are the perfect complement to the decay <math><msub><mi>χ</mi><mrow><mi>c</mi><mn>1</mn></mrow></msub><mo>→</mo><msub><mi>f</mi><mn>0</mn></msub><mo>(</mo><mn>980</mn><mo>)</mo><msup><mi>π</mi><mn>0</mn></msup><mo>→</mo><mspace></mspace><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><msup><mi>π</mi><mn>0</mn></msup></math>, which had been observed at the BESIII experiment, the observations of which will make the measurement of the mixing intensity <math><msub><mi>ξ</mi><mrow><mi>a</mi><mi>f</mi></mrow></msub></math> more precisely.

Study of <math><mrow><msubsup><mrow><mi>a</mi></mrow><mrow><mn>0</mn></mrow><mrow><mn>0</mn></mrow></msubsup><mo>(</mo><mn>980</mn><mo>)</mo><mo>−</mo><msub><mrow><mi>f</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mn>980</mn><mo>)</mo></mrow></math> mixing from <math><msub><mi>a</mi><mn>0</mn></msub><mo>(</mo><mn>1450</mn><mo>)</mo><mo>→</mo><msubsup><mi>a</mi><mn>0</mn><mn>0</mn></msubsup><mo>(</mo><mn>980</mn><mo>)</mo><msub><mi>f</mi><mn>0</mn></msub><mo>(</mo><mn>500</mn><mo>)</mo><mo>→</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><msub><mi>f</mi><mn>0</mn></msub><mo>(</mo><mn>500</mn><mo>)</mo></math>

The semileptonic decays and two-body nonleptonic decays of a light baryon octet (<math><msub><mi>T</mi><mn>8</mn></msub></math>) and a decuplet (<math><msub><mi>T</mi><mn>10</mn></msub></math>) consisting of light <math><mrow><mi>u</mi></mrow></math>, <math><mrow><mi>d</mi></mrow></math>, <math><mrow><mi>s</mi></mrow></math> quarks are studied with the SU(3) flavor symmetry. We obtain the amplitude relations between different decay modes by the SU(3) irreducible representation approach, and we then predict relevant branching ratios by presenting experimental data within <math><mn>1</mn><mi>σ</mi></math> error. We find that the predictions for all branching ratios except <math><mi>B</mi><mo>(</mo><mi>Ξ</mi><mo>→</mo><msup><mi>Λ</mi><mn>0</mn></msup><mi>π</mi><mo>)</mo></math> and <math><mi>B</mi><mo>(</mo><msup><mi>Ξ</mi><mo>*</mo></msup><mo>→</mo><mi>Ξ</mi><mi>π</mi><mo>)</mo></math> are in good agreement with present experimental data, which implies that the neglected <math><msub><mi>C</mi><mo>+</mo></msub></math> terms or SU(3) breaking effects might contribute on the order of a few percent in <math><mi>Ξ</mi><mo>→</mo><msup><mi>Λ</mi><mn>0</mn></msup><mi>π</mi></math> and <math><msup><mi>Ξ</mi><mo>*</mo></msup><mo>→</mo><mi>Ξ</mi><mi>π</mi></math> weak decays. We predict that <math><mrow><mi>B</mi><mo>(</mo><msup><mrow><mi>Ξ</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>→</mo><msup><mrow><mi>Σ</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mi>μ</mi></mrow><mrow><mo>−</mo></mrow></msup><msub><mrow><mover><mrow><mi>ν</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mi>μ</mi></mrow></msub><mo>)</mo><mo>=</mo><mo>(</mo><mn>1.13</mn><mo>±</mo><mn>0.08</mn><mo>)</mo><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>6</mn></mrow></msup></mrow></math>, <math><mi>B</mi><mo>(</mo><msup><mi>Ξ</mi><mo>−</mo></msup><mo>→</mo><msup><mi>Λ</mi><mn>0</mn></msup><msup><mi>μ</mi><mo>−</mo></msup><msub><mover><mi>ν</mi><mo>¯</mo></mover><mi>μ</mi></msub><mo>)</mo><mo>=</mo><mo>(</mo><mn>1.58</mn><mo>±</mo><mn>0.04</mn><mo>)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>4</mn></mrow></msup></math>, <math><mrow><mi>B</mi><mo>(</mo><msup><mrow><mi>Ω</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>→</mo><msup><mrow><mi>Ξ</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mi>μ</mi></mrow><mrow><mo>−</mo></mrow></msup><msub><mrow><mover><mrow><mi>ν</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mi>μ</mi></mrow></msub><mo>)</mo><mo>=</mo><mo>(</mo><mn>3.7</mn><mo>±</mo><mn>1.8</mn><mo>)</mo><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow></math>, <math><mi>B</mi><mo>(</mo><msup><mi>Σ</mi><mo>−</mo></msup><mo>→</mo><msup><mi>Σ</mi><mn>0</mn></msup><msup><mi>e</mi><mo>−</mo></msup><msub><mover><mi>ν</mi><mo>¯</mo></mover><mi>e</mi></msub><mo>)</mo><mo>=</mo><mspace></mspace><mo>(</mo><mn>1.35</mn><mo>±</mo><mn>0.28</mn><mo>)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>10</mn></mrow></msup></math>, and <math><mi>B</mi><mo>(</mo><msup><mi>Ξ</mi><mo>−</mo></msup><mo>→</mo><msup><mi>Ξ</mi><mn>0</mn></msup><msup><mi>e</mi><mo>−</mo></msup><msub><mover><mi>ν</mi><mo>¯</mo></mover><mi>e</mi></msub><mo>)</mo><mo>=</mo><mo>(</mo><mn>4.2</mn><mo>±</mo><mn>2.4</mn><mo>)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>10</mn></mrow></msup></math>. We also study <math><msub><mi>T</mi><mn>10</mn></msub><mo>→</mo><msub><mi>T</mi><mn>8</mn></msub><msub><mi>P</mi><mn>8</mn></msub></math> weak, electromagnetic, or strong decays. Some of these decay modes could be observed by BESIII, LHCb, and other experiments in the near future. Because of the very small lifetimes of <math><msup><mi>Σ</mi><mn>0</mn></msup></math>, <math><msup><mi>Ξ</mi><mrow><mo>*</mo><mn>0</mn><mo>,</mo><mo>−</mo></mrow></msup></math>, <math><msup><mi>Σ</mi><mrow><mo>*</mo><mn>0</mn><mo>,</mo><mo>−</mo></mrow></msup></math>, and <math><msup><mi>Δ</mi><mrow><mn>0</mn><mo>,</mo><mo>−</mo></mrow></msup></math>, the branching ratios of these baryon weak decays are only on the order of <math><mi>O</mi><mo>(</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>20</mn></mrow></msup><mo>−</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>13</mn></mrow></msup></math>), which is too small to be reached in current experiments. The longitudinal branching ratios of <math><mrow><msub><mrow><mi>T</mi></mrow><mrow><mn>8</mn><mi>A</mi></mrow></msub><mo>→</mo><msub><mrow><mi>T</mi></mrow><mrow><mn>8</mn><mi>B</mi></mrow></msub><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>−</mo></mrow></msup><msub><mrow><mover><mrow><mi>ν</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mo>ℓ</mo></mrow></msub><mo>(</mo><mo>ℓ</mo><mo>=</mo><mi>μ</mi><mo>,</mo><mi>e</mi><mo>)</mo></mrow></math> decays are also given.

Mao-Zhi Yang

Hai-Bo Li

Testing SU(3) flavor symmetry in semileptonic and two-body nonleptonic decays of hyperons

Using the measured branching fraction of the decay <math><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi><mo>→</mo><mi>η</mi><mi>Y</mi><mo>(</mo><mn>2175</mn><mo>)</mo><mo>→</mo><mi>η</mi><mi>ϕ</mi><msub><mrow><mi>f</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mn>980</mn><mo>)</mo><mo>→</mo><mi>η</mi><mi>ϕ</mi><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup></mrow></math> from the BESIII experiment, we estimate branching fraction of <math><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi><mo>→</mo><mi>η</mi><mi>Y</mi><mo>(</mo><mn>2175</mn><mo>)</mo><mo>→</mo><mi>η</mi><mi>ϕ</mi><msub><mrow><mi>f</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mn>980</mn><mo>)</mo><mo>→</mo><mi>η</mi><mi>ϕ</mi><mi>η</mi><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup></mrow></math> decay, which proceeds via the <math><mrow><msub><mrow><mi>f</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mn>980</mn><mo>)</mo><mtext>−</mtext><msubsup><mrow><mi>a</mi></mrow><mrow><mn>0</mn></mrow><mrow><mn>0</mn></mrow></msubsup><mo>(</mo><mn>980</mn><mo>)</mo></mrow></math> mixing and the <math><mrow><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup><mtext>−</mtext><mi>η</mi></mrow></math> mixing. The branching fraction is predicted to be about <math><mi>O</mi><mo>(</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>6</mn></mrow></msup><mo>)</mo></math>, which can be accessed with <math><mn>1</mn><msup><mn>0</mn><mn>10</mn></msup><mtext> </mtext><mtext> </mtext><mi>J</mi><mo>/</mo><mi>ψ</mi></math> events collected at BESIII. The decay is dominated by the contribution from <math><mrow><msub><mrow><mi>f</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mn>980</mn><mo>)</mo><mtext>−</mtext><msubsup><mrow><mi>a</mi></mrow><mrow><mn>0</mn></mrow><mrow><mn>0</mn></mrow></msubsup><mo>(</mo><mn>980</mn><mo>)</mo></mrow></math> mixing. We find that the interference between the amplitudes due to <math><mrow><msub><mrow><mi>f</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mn>980</mn><mo>)</mo><mtext>−</mtext><msubsup><mrow><mi>a</mi></mrow><mrow><mn>0</mn></mrow><mrow><mn>0</mn></mrow></msubsup><mo>(</mo><mn>980</mn><mo>)</mo></mrow></math> mixing and that due to <math><mrow><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup><mtext>−</mtext><mi>η</mi></mrow></math> mixing is constructive. The branching fraction can be increased by about 10%, owing to the interference effect. We also study the <math><mi>η</mi><msup><mi>π</mi><mn>0</mn></msup></math> mass squared spectrum and find that a narrow peak due to the <math><mrow><msub><mrow><mi>f</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mn>980</mn><mo>)</mo><mtext>−</mtext><msubsup><mrow><mi>a</mi></mrow><mrow><mn>0</mn></mrow><mrow><mn>0</mn></mrow></msubsup><mo>(</mo><mn>980</mn><mo>)</mo></mrow></math> mixing in the <math><mi>η</mi><msup><mi>π</mi><mn>0</mn></msup></math> mass squared spectrum should be observed. The observation of this decay in experiment will be helpful to determine the <math><mrow><msub><mrow><mi>f</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mn>980</mn><mo>)</mo><mtext>−</mtext><msubsup><mrow><mi>a</mi></mrow><mrow><mn>0</mn></mrow><mrow><mn>0</mn></mrow></msubsup><mo>(</mo><mn>980</mn><mo>)</mo></mrow></math> mixing intensity and get information about the structures of the light scalar mesons.

Study of the isospin breaking decay <math><mrow><mi>Y</mi><mo>(</mo><mn>2175</mn><mo>)</mo><mo>→</mo><mi>ϕ</mi><msub><mi>f</mi><mn>0</mn></msub><mo>(</mo><mn>980</mn><mo>)</mo><mo>→</mo><mi>ϕ</mi><mi>η</mi><msup><mi>π</mi><mn>0</mn></msup></mrow></math> at BESIII