Motivated by the latest CDF W-mass measurement as well as the muon <math><mi>g</mi><mo>−</mo><mn>2</mn></math> anomaly and the discrepancies observed in <math><mi>b</mi><mo>→</mo><mi>s</mi><msup><mrow><mi>ℓ</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>ℓ</mi></mrow><mrow><mo>−</mo></mrow></msup></math> transitions, we propose an extension of the Standard Model (SM) with the <math><mi>S</mi><mi>U</mi><msub><mrow><mo>(</mo><mn>2</mn><mo>)</mo></mrow><mrow><mi>L</mi></mrow></msub></math>-singlet vector-like fermion partners that are featured by additional <math><mi>U</mi><msup><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow><mrow><mo>′</mo></mrow></msup></math> gauge symmetry. The fermion partners have the same SM quantum numbers as of the right-handed SM fermions, and can therefore mix with the latter after the electroweak and the <math><mi>U</mi><msup><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow><mrow><mo>′</mo></mrow></msup></math> symmetry breaking. As a result, desirable loop-level corrections to the <math><msub><mrow><mo>(</mo><mi>g</mi><mo>−</mo><mn>2</mn><mo>)</mo></mrow><mrow><mi>μ</mi></mrow></msub></math>, the W-boson mass <math><msub><mrow><mi>m</mi></mrow><mrow><mi>W</mi></mrow></msub></math> and the Wilson coefficient <math><msub><mrow><mi>C</mi></mrow><mrow><mn>9</mn></mrow></msub></math> in <math><mi>b</mi><mo>→</mo><mi>s</mi><msup><mrow><mi>μ</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>μ</mi></mrow><mrow><mo>−</mo></mrow></msup></math> transitions can be obtained. The final allowed parameter space is also consistent with the constraints from the <math><mi>Z</mi><mo>→</mo><msup><mrow><mi>μ</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>μ</mi></mrow><mrow><mo>−</mo></mrow></msup></math> decay, the neutrino trident production and the LHC direct searches for the vector-like quarks and leptons.

China

Xin-Qiang Li

Ze-Jun Xie

Ya-Dong Yang

Xing-Bo Yuan

Correlating the CDF -mass Shift With the Muon − 2 and the → Transitions

Recently, the Belle II collaboration announced the first measurement of the branching ratio   <math> <mi>B</mi> <mfenced> <mrow> <msup> <mi>B</mi> <mo>+</mo> </msup> <mo>→</mo> <msup> <mi>K</mi> <mo>+</mo> </msup> <mi>ν</mi> <mover> <mi>ν</mi> <mo>¯</mo> </mover> </mrow> </mfenced> </math>  $$ \mathcal{B}\left({B}^{+}\to {K}^{+}\nu \overline{\nu}\right) $$ , which is found to be about 2.7σ higher than the Standard Model (SM) prediction. We decipher the data with two new physics scenarios: the underlying quark-level   <math> <mi>b</mi> <mo>→</mo> <mi>sν</mi> <mover> <mi>ν</mi> <mo>¯</mo> </mover> </math>  $$ b\to s\nu \overline{\nu} $$  transition is, besides the SM contribution, further affected by heavy new mediators that are much heavier than the electroweak scale, or amended by an additional decay channel with undetected light final states like dark matter or axion-like particles. These two scenarios can be most conveniently analyzed in the SM effective field theory (SMEFT) and the dark SMEFT (DSMEFT) framework, respectively. We consider the flavour structures of the resulting effective operators to be either generic or satisfy the minimal flavour violation (MFV) hypothesis, both for the quark and lepton sectors. In the first scenario, once the MFV assumption is made, only one SM-like low-energy effective operator induced by the SMEFT dimension-six operators can account for the Belle II excess, whose parameter space is, however, excluded by the Belle upper bound of the branching ratio   <math> <mi>B</mi> <mfenced> <mrow> <msup> <mi>B</mi> <mn>0</mn> </msup> <mo>→</mo> <msup> <mi>K</mi> <mrow> <mo>∗</mo> <mn>0</mn> </mrow> </msup> <mi>ν</mi> <mover> <mi>ν</mi> <mo>¯</mo> </mover> </mrow> </mfenced> </math>  $$ \mathcal{B}\left({B}^0\to {K}^{\ast 0}\nu \overline{\nu}\right) $$ . In the second scenario, it is found that the Belle II excess can be accommodated by 22 of the DSMEFT operators involving one or two scalar, fermionic, or vector dark matters as well as axion-like particles. These operators also receive dominant constraints from the B 0 → K *0 + inv and B  s  → inv decays. Once the MFV hypothesis is assumed, the number of viable operators is reduced to 14, and the B + → π + + inv and K + → π + + inv decays start to put further constraints on them. Within the parameter space allowed by all the current experimental data, the q 2 distributions of the B → K (*) + inv decays are then studied for each viable operator. We find that the resulting prediction of the operator   <math> <msub> <mi>Q</mi> <mi>qχ</mi> </msub> <mo>=</mo> <mfenced> <mrow> <msub> <mover> <mi>q</mi> <mo>¯</mo> </mover> <mi>p</mi> </msub> <msub> <mi>γ</mi> <mi>μ</mi> </msub> <msub> <mi>q</mi> <mi>r</mi> </msub> </mrow> </mfenced> <mfenced> <mrow> <mover> <mi>χ</mi> <mo>¯</mo> </mover> <msup> <mi>γ</mi> <mi>μ</mi> </msup> <mi>χ</mi> </mrow> </mfenced> </math>  $$ {\mathcal{Q}}_{q\chi}=\left({\overline{q}}_p{\gamma}_{\mu }{q}_r\right)\left(\overline{\chi}{\gamma}^{\mu}\chi \right) $$  with a fermionic dark matter mass m  χ  ≈ 700 MeV can closely match the Belle II event distribution in the bins 2 ≤ q 2 ≤ 7 GeV2. In addition, we, for the first time, calculate systematically the longitudinal polarization fraction F  L  of K * in the B → K * + inv decays within the DLEFT. By combining the decay spectra and F  L , almost all the DSMEFT operators are found to be distinguishable from each other. Finally, the future prospects at Belle II, CEPC and FCC-ee are also discussed for some of these FCNC processes.

Biao-Feng Hou

Meng Shen

Deciphering the Belle II data on   <math> <mi>B</mi> <mo>→</mo> <mi>Kν</mi> <mover> <mi>ν</mi> <mo>¯</mo> </mover> </math>  $$ B\to K\nu \overline{\nu} $$  decay in the (dark) SMEFT with minimal flavour violation

The recently updated measurement of the W-boson mass by the CDF collaboration exhibits a 7σ deviation from the SM expectation, which may imply a sign of new physics beyond the SM. The observed discrepancy could be explained by new fermions that carry the electroweak gauge charges and affect the vacuum polarization of gauge bosons. Notably, if the new fermions also have the same quantum numbers as of the SM quarks, they can mix with the latter and thus modify the penguin diagrams governing the <math><mi>b</mi><mo>→</mo><mi>s</mi><msup><mrow><mi>ℓ</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>ℓ</mi></mrow><mrow><mo>−</mo></mrow></msup></math> transitions. Therefore, the W-boson mass shift could be related to the <math><mi>b</mi><mo>→</mo><mi>s</mi><msup><mrow><mi>ℓ</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>ℓ</mi></mrow><mrow><mo>−</mo></mrow></msup></math> anomalies observed by the LHCb collaboration during the past few years. To investigate this possibility, we consider in this letter a model containing a vector-like top partner gauged under a new <math><mi>U</mi><msup><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow><mrow><mo>′</mo></mrow></msup></math> symmetry. It is found that the latest CDF <math><msub><mrow><mi>m</mi></mrow><mrow><mi>W</mi></mrow></msub></math> measurement and the <math><mi>b</mi><mo>→</mo><mi>s</mi><msup><mrow><mi>ℓ</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>ℓ</mi></mrow><mrow><mo>−</mo></mrow></msup></math> anomalies can be simultaneously accommodated at 2σ level.

Correlating the CDF -boson Mass Shift With the → Anomalies

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.

Ru-Min Wang

Xiao-Dong Cheng

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

Motivated by the recent anomalies in <math><mi>b</mi><mo>→</mo><mi>s</mi><msup><mrow><mi>ℓ</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>ℓ</mi></mrow><mrow><mo>−</mo></mrow></msup></math> transitions, we explore a minimal <math><msup><mrow><mi>Z</mi></mrow><mrow><mo>′</mo></mrow></msup></math> scenario, in which the <math><msup><mrow><mi>Z</mi></mrow><mrow><mo>′</mo></mrow></msup></math> boson has a flavour-changing coupling to charm and top quarks and a flavour-conserving coupling to muons. It is found that such a <math><msup><mrow><mi>Z</mi></mrow><mrow><mo>′</mo></mrow></msup></math> boson can explain the current <math><mi>b</mi><mo>→</mo><mi>s</mi><msup><mrow><mi>ℓ</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>ℓ</mi></mrow><mrow><mo>−</mo></mrow></msup></math> anomalies, while satisfying other flavour and collider constraints simultaneously. The <math><msup><mrow><mi>Z</mi></mrow><mrow><mo>′</mo></mrow></msup></math> boson can be as light as few hundreds GeV. In this case, the <math><mi>t</mi><mo>→</mo><mi>c</mi><msup><mrow><mi>μ</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>μ</mi></mrow><mrow><mo>−</mo></mrow></msup></math> decay and the <math><mi>t</mi><msup><mrow><mi>Z</mi></mrow><mrow><mo>′</mo></mrow></msup></math> associated production at the LHC could provide sensitive probes of such a <math><msup><mrow><mi>Z</mi></mrow><mrow><mo>′</mo></mrow></msup></math> boson. As a special feature, the <math><msup><mrow><mi>Z</mi></mrow><mrow><mo>′</mo></mrow></msup></math> contributions to all rare B- and K-meson processes are controlled by one parameter. This results in interesting correlations among these processes, which could provide further insights into this scenario. In addition, an extended scenario, in which the <math><msup><mrow><mi>Z</mi></mrow><mrow><mo>′</mo></mrow></msup></math> boson interacts with the <math><mi>S</mi><mi>U</mi><msub><mrow><mo>(</mo><mn>2</mn><mo>)</mo></mrow><mrow><mi>L</mi></mrow></msub></math> fermion doublets with analogous couplings as in the minimal scenario, is also investigated.

Dong-Yang Wang

Explaining the Anomalies in ′ scenarios with top-FCNC couplings

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

We extend on-shell bootstrap methods from spacetime amplitudes to the world sheet objects of the Cachazo-He-Yuan formalism. We observe that the integrands corresponding to tree-level nonlinear sigma model, Yang-Mills and <math><mo>(</mo><mi>D</mi><mi>F</mi><msup><mo>)</mo><mn>2</mn></msup></math> theory are determined by demanding enhanced UV scaling under Britto-Cachazo-Feng-Witten shifts. Back in spacetime, we also find that <math><mo>(</mo><mi>D</mi><mi>F</mi><msup><mo>)</mo><mn>2</mn></msup></math> theory is fixed by gauge invariance/UV scaling and simple locality assumptions.

France

Laurentiu Rodina

UV consistency conditions for Cachazo-He-Yuan integrands

The Cachazo-He-Yuan formula was originally proposed to describe on-shell scattering of particles from a single massless field. We present a method to modify it to include several interacting scalar fields, all possessing different masses and possibly off-shell momenta. The method is applied to Yukawa interactions between a number of scalar nucleons and pions, and to the <math><msub><mi>ϕ</mi><mn>1</mn></msub><msub><mi>ϕ</mi><mn>2</mn></msub><msub><mi>ϕ</mi><mn>3</mn></msub></math> coupling of three different scalar fields. Composite models constructed from existing theories can be used to broaden the scope of the method. The modification is applied to describe Compton scattering from a massive particle and to photon bremsstrahlung. It is also employed to generalize the disk function <math><mi>Z</mi></math> and the sphere function <math><mi>J</mi></math>.

Canada

C. S. Lam

Cachazo-He-Yuan theory for several fields

Möbius invariance is used to construct gluon tree amplitudes in the Cachazo, He, and Yuan (CHY) formalism. If it is equally effective in steering the construction of off-shell tree amplitudes, then the S-matrix CHY theory can be used to replace the Lagrangian Yang-Mills theory. Unfortunately that is not possible. We find that the CHY formula can indeed be modified to obtain a Möbius-invariant off-shell amplitude <math><msub><mi>M</mi><mi>P</mi></msub></math>, but this modified amplitude lacks local gauge invariance, which can be restored to give the correct Yang-Mills amplitude only by the addition of a complementary amplitude <math><msub><mi>M</mi><mi>Q</mi></msub></math>. Although neither <math><msub><mi>M</mi><mi>P</mi></msub></math> nor <math><msub><mi>M</mi><mi>Q</mi></msub></math> is fully gauge invariant, both are partially gauge invariant in a sense to be explained.