In this Letter, we demonstrate that <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>T</mi></math>-odd and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>T</mi></math>-even correlations, with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>T</mi></math> representing time reversal, when satisfying specific conditions, result, respectively, in cosine and sine strong phase dependencies of the corresponding <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violation. Additionally, we identify pairs of these <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violation observables in hadron decays depend on precisely the same strong phases within the helicity amplitude scheme. This complementarity could reduce the strong phase reliance in the study of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violation while also mitigating the risk of suppressed <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violation due to exceptionally small strong phases. Moreover, our proposal holds broad application prospects in further investigating <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violation in baryon decays, which has recently been discovered in the LHCb experiment.

China

Jian-Peng Wang

Qin Qin

Fu-Sheng Yu

Complementary <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violation induced by <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>T</mi></math>-odd and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>T</mi></math>-even correlations

It is a long-standing puzzle why the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>C</mi><mi>P</mi></mrow></math> violation (CPV) in the baryon system has not yet been definitively established as in the meson one. We demonstrate that individual partial-wave CPV in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>b</mi></msub><mo stretchy="false">→</mo><mi>p</mi><msup><mi>π</mi><mo>−</mo></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi><msup><mi>K</mi><mo>−</mo></msup></math> decays can exceed 10%, but the destruction between the partial waves (the suppression by the small partial-wave weight) results in a small net direct CPV in the former (the latter) as measured currently. Our finding highlights the different dynamics responsible for CPVs in baryon and meson decays. We propose to probe the CPV observables associated with the angular distributions of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi mathvariant="normal">Λ</mi></mrow><mrow><mi>b</mi></mrow></msub><mo stretchy="false">→</mo><mi>p</mi><msub><mrow><mi>a</mi></mrow><mrow><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mn>1260</mn><mo stretchy="false">)</mo></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>p</mi><msub><mrow><mi>K</mi></mrow><mrow><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mn>1270</mn><mo stretchy="false">)</mo></mrow></math> decay products, which are large enough for being identified experimentally.

Jia-Jie Han

Ji-Xin Yu

Ya Li

Hsiang-nan Li

Zhen-Jun Xiao

Establishing <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> Violation in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>b</mi></math>-Baryon Decays

The doubly charmed baryon, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mrow><mi>c</mi><mi>c</mi></mrow><mrow><mo>+</mo><mo>+</mo></mrow></msubsup></math>, was first observed by LHCb through the nonleptonic decay modes of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi mathvariant="normal">Ξ</mi></mrow><mrow><mi>c</mi><mi>c</mi></mrow><mrow><mo>+</mo><mo>+</mo></mrow></msubsup><mo stretchy="false">→</mo><msubsup><mrow><mi mathvariant="normal">Λ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup><msup><mrow><mi>K</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> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mi>c</mi><mo>+</mo></msubsup><msup><mi>π</mi><mo>+</mo></msup></math>. Following this discovery, researchers shifted their focus to identifying other doubly charmed baryons, specifically <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>+</mo></msubsup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ω</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>+</mo></msubsup></math>. In this study, we examine the nonleptonic weak decays of doubly charmed baryons, denoted as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="script">B</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub><mo stretchy="false">→</mo><msub><mi mathvariant="script">B</mi><mi>c</mi></msub><mi>P</mi></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="script">B</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub></math> represents the doubly charmed baryons, specifically <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">(</mo><msubsup><mrow><mi mathvariant="normal">Ξ</mi></mrow><mrow><mi>c</mi><mi>c</mi></mrow><mrow><mo>+</mo><mo>+</mo></mrow></msubsup><mo>,</mo><msubsup><mrow><mi mathvariant="normal">Ξ</mi></mrow><mrow><mi>c</mi><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mo>,</mo><msubsup><mrow><mi mathvariant="normal">Ω</mi></mrow><mrow><mi>c</mi><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mo stretchy="false">)</mo></mrow></math>. The notation <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="script">B</mi><mi>c</mi></msub></math> denotes the singly charmed baryons, specifically <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><msub><mi mathvariant="script">B</mi><mover accent="true"><mn>3</mn><mo stretchy="false">¯</mo></mover></msub><mo>,</mo><msub><mi mathvariant="script">B</mi><mn>6</mn></msub><mo stretchy="false">)</mo></math>, while <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>P</mi></math> signifies the light pseudoscalar. These terms are pertinent to the nonleptonic decay modes under discussion. While the short-distance contributions can be precisely estimated through theoretical calculations, addressing the long-distance contributions for final-state-interaction effects presents a significant challenge. In order to address this issue, we utilize the rescattering mechanism of final state interaction effects to compute the long-distance contributions. We initially derive the entire hadronic loop contributions for these two-body nonleptonic decays of doubly charmed baryons. In subsequent analyses, we are able to calculate relative strong phases. As a result, we can provide predictions for their decay asymmetry parameters and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>C</mi><mi>P</mi></mrow></math> violations. Furthermore, we employ experimental data from the LHCb collaboration, specifically the ratio <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>Br</mi><mo stretchy="false">(</mo><msubsup><mrow><mi mathvariant="normal">Ξ</mi></mrow><mrow><mi>c</mi><mi>c</mi></mrow><mrow><mo>+</mo><mo>+</mo></mrow></msubsup><mo stretchy="false">→</mo><msubsup><mrow><mi mathvariant="normal">Ξ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>′</mo><mo>+</mo></mrow></msubsup><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup><mo stretchy="false">)</mo><mo>/</mo><mi>Br</mi><mo stretchy="false">(</mo><msubsup><mrow><mi mathvariant="normal">Ξ</mi></mrow><mrow><mi>c</mi><mi>c</mi></mrow><mrow><mo>+</mo><mo>+</mo></mrow></msubsup><mo stretchy="false">→</mo><msubsup><mrow><mi mathvariant="normal">Ξ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mn>1.41</mn><mo>±</mo><mn>0.17</mn><mo>±</mo><mn>0.10</mn><mo stretchy="false">)</mo></mrow></math>, to ascertain the model parameters <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>η</mi><mo>=</mo><mn>0.9</mn><mo>±</mo><mn>0.2</mn></math>. Consequently, we present the predictions of branching ratios and decay asymmetry parameters for 67 distinct decay processes and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violations for the singly Cabibbo suppressed channels. This not only strengthens the validity of our theoretical predictions, but also provides a more comprehensive theoretical framework for the future identification of other doubly charmed baryons.

Xiao-Hui Hu

Cai-Ping Jia

Ye Xing

Final-state rescattering mechanism of double-charm baryon decays: <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi mathvariant="script">B</mi></mrow><mrow><mi>c</mi><mi>c</mi></mrow></msub><mo stretchy="false">→</mo><msub><mrow><mi mathvariant="script">B</mi></mrow><mrow><mi>c</mi></mrow></msub><mi>P</mi></mrow></math>

We study the transverse momentum ( $p_T$ ) differential anisotropic flow and flow fluctuation in Pb+Pb collisions at $\sqrt{s_{_{NN}}}$ =5.02 TeV at the LHC. A (3+1)-dimensional CLVisc hydrodynamics framework with fluctuating TRENTO (or AMPT) initial conditions is utilized to simulate the space-time evolution of the quark-gluon plasma (QGP) medium. The effects of shear viscosity and the sub-nucleon structure on anisotropic flow and flow fluctuation are analyzed. Our result shows that shear viscosity tends to suppress both flow coefficients ( ${v_2\{2}\}$ , ${v_2\{4\}}$ , and ${\langle v_2\rangle}$ ) and flow fluctuation ( ${\sigma_{v_2}}$ ) owing to its smearing effect on local density fluctuation. The flow coefficients appear to be insensitive to the sub-nucleon structure, whereas the flow fluctuation ${\sigma_{v_2}}$ tends to be suppressed by the sub-nucleon structure in central collisions but enhanced in peripheral collisions. After taking into account the sub-nucleon structure effect, our numerical result can qualitatively describe the relative flow fluctuations ( ${v_2\{4\}/v_2\{2\}}$ , $F({v_2})$ ) measured by the ALICE Collaboration at the LHC. We further investigate the effects of shear viscosity, sub-nucleon structure, and initial condition model on the flow angle and flow magnitude decorrelations ( ${A_2^f}$ , ${M_2^f}$ ) using the four-particle correlation method. We find that the flow decorrelation effect is typically stronger in central collisions than in peripheral collisions. The flow angle decorrelation is found to be insensitive to the shear viscosity and sub-nucleon structure, whereas the flow magnitude decorrelation shows quite different behaviors when using the TRENTO and AMPT initial condition models. Our study sheds light on the anisotropic flow, transport properties, and initial structure of the QGP created in high-energy nuclear collisions.

Germany

Jie Zhu

Canada

Xiang-Yu Wu

Guang-You Qin

Anisotropic flow, flow fluctuation, and flow decorrelation in relativistic heavy-ion collisions: the roles of sub-nucleon structure and shear viscosity * Supported in part by the Natural Science Foundation of China (12225503, 11890710, 11890711, 11935007). Zhu Jie is supported in part by the China Scholarship Council (202306770009). Wu Xiang-Yu is supported in part by the National Science Foundation within the framework of the JETSCAPE collaboration (OAC-2004571) and in part by the Natural Sciences and Engineering Research Council of Canada. Some of the calculations were performed in the Nuclear Science Computing Center at Central China Normal University (NSC$^{3}$), Wuhan, Hubei, China.

In this work, we investigate the transition form factors for $$\Lambda _b\rightarrow {\Lambda (1520)}$$ within the framework of light-cone sum rules (LCSR), using the light-cone distribution amplitudes (LCDAs) of the $$\Lambda _b$$ -baryon. In the hadronic representation of the correlation function, we carefully select the appropriate Lorentz structures and isolate the contributions from both the $$\Lambda (1520)(J^P=(3/2)^-)$$ and the $$\Lambda (1890)(J^P=(3/2)^+),$$ ensuring that the form factors for $$\Lambda _b\rightarrow {\Lambda (1520)}$$ can be calculated unambiguously. We also provide predictions for various physical observables in the decay $$\Lambda _b\rightarrow {\Lambda (1520)}l^+l^-,$$ including the differential branching fraction, the lepton-side forward–backward asymmetry, the longitudinal polarization fraction, and the CP-averaged normalized angular observable. Our prediction for the differential branching fraction of $$\Lambda _b\rightarrow {\Lambda (1520)}\mu ^+\mu ^-$$ is in good agreement with the LHCb measurement within the uncertainties.

Ke-Sheng Huang

Hua-Yu Jiang

Transition form factors of the $$\Lambda _b \rightarrow \Lambda (1520)$$ in QCD light-cone sum rules

The dynamical studies on the non-leptonic weak decays of charmed baryons are always challenging, due to the large non-perturbative contributions at the charm scale. In this work, we develop the final-state rescattering mechanism to study the two-body non-leptonic decays of charmed baryons. The final-state interaction is a physical picture of long-distance effects. Instead of using the Cutkosky rule to calculate the hadronic triangle diagrams which can only provide the imaginary part of decay amplitudes, we point out that the loop integral is more appropriate, as both the real parts and the imaginary parts of amplitudes can be calculated completely. In this way, it can be obtained for the non-trivial strong phases which are essential to calculate CP violations. With the physical picture of long-distance effects and the reasonable method of calculations, it is amazingly achieved that all the nine existing experimental data of branching fractions for the <math> <msubsup> <mi>Λ</mi> <mi>c</mi> <mo>+</mo> </msubsup> </math> $$ {\Lambda}_c^{+} $$ decays into an octet light baryon and a vector meson can be explained by only one parameter of the model. Besides, the decay asymmetries and CP violations are not sensitive to the model parameter, since the dependence on the parameter is mainly cancelled in the ratios, so that the theoretical uncertainties on these observables are lowered down.

Final-state rescattering mechanism of charmed baryon decays

There is a long-standing puzzle that the CP violation (CPV) in the baryon systems has never been well established in experiments, while the CPV of mesons have been observed by decades. In this paper, we propose that the CPV of baryon decays can be generated with the rescatterings of a nucleon and a pion into some final states, i.e.   $N\pi\to N\pi$   or   $N\pi\to N\pi$  . Benefited by the fruitful data of   $N\pi\to N\pi$   scatterings, we can model-independently analyse the strong phases of   $N\pi\to N\pi$  -baryon decays using the partial wave amplitudes of   $N\pi\to N\pi$   scatterings. Avoiding the most difficult problem of non-perturbative dynamics, it makes a great advantage to predict the CPV of baryon decays with a relatively reliable understanding of the decay dynamics. We study the processes of   $N\pi\to N\pi$   and   $N\pi\to N\pi$   with   $N\pi\to N\pi$   or   $N\pi\to N\pi$  . It is found that the global CPV of the above processes in the invariant mass regions of   $N\pi\to N\pi$   scatterings are at the order of several percent. More importantly, the local CPV in some regions of the Dalitz plots can reach the order of 10%, or be even larger. Considering the predicted results and the experimental data samples, we strong suggest to measure the CPV of   $N\pi\to N\pi$  , which has a large possibility to achieve the first observation of CPV in the baryon system.

CP violation of baryon decays with  Rescatterings  

The similar densities of dark matter and baryons in the universe imply that they may arise from the same ultraviolet model. B-Mesogenesis, which assumes dark matter is charged under the baryon number, attempts to simultaneously explain the origin of baryon asymmetry and dark matter in the universe. In particular, B-Mesogenesis may induce bottom-baryon decays into invisible or semi-invisible final states, which provide a distinctive signal for probing this scenario. In this work, we systematically study the invisible decays of bottom baryons into dark matter and the semi-invisible decays of bottom baryons into a meson or a photon together with a dark matter particle. In particular, the fully invisible decay can reveal the stable particles in B-Mesogenesis. Some QCD-based frameworks are used to calculate the hadronic matrix elements under the B-Mesogenesis model. We estimate the constraints on the Wilson coefficients or the product of some new physics couplings with the Wilson coefficients according to the semi-invisible and invisible decays of bottom baryons detectable at future colliders.

Yong Zheng

Jian-Nan Ding

Dong-Hao Li

Lei-Yi Li

Cai-Dian Lü

Invisible and semi-invisible decays of bottom baryons  

CP violation (CPV) in the baryon sectors has not yet been established experimentally. In this work, we propose to search for the hyperon CPV through the Cabibbo-favored charm-baryon decaying processes involving a hyperon in the final states, such as <math><msubsup><mrow><mi>Λ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mo>→</mo><msup><mrow><mi>Λ</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup></math> with <math><msup><mrow><mi>Λ</mi></mrow><mrow><mn>0</mn></mrow></msup><mo>→</mo><mi>p</mi><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup></math>. The CPV of the hyperon decays is accessed exclusively in these chain processes, since the CPV in the Cabibbo-favored charm decays is vanishing in the Standard Model (SM). The hyperons are polarized in the weak charm decays, so that we can measure the Lee-Yang asymmetric parameter α by analyzing the angular distributions, and then measure the α-induced CPV. We expect that it is accessible for Belle II and LHCb to reach the SM prediction of the hyperon CPV in the near future.

Probing hyperon CP violation with charmed baryon decays

The electric dipole moment (EDM) of elementary particles, arising from flavor-diagonal <math><mi>C</mi><mi>P</mi></math> violation, serves as a powerful probe for new physics beyond the Standard Model and holds the potential to provide novel insights in unraveling the puzzle of the matter-dominated Universe. Hyperon EDM is a largely unexplored territory. In this paper, we present a comprehensive angular analysis that focuses on entangled hyperon-antihyperon pairs in <math><mi>J</mi><mo>/</mo><mi>ψ</mi></math> decays for the indirect extraction of hyperon EDM. The statistical sensitivities are investigated for BESIII and the proposed Super Tau-Charm Facility (STCF). Leveraging the statistics from the BESIII experiment, the estimated sensitivity for <math><mi>Λ</mi></math> EDM can reach an impressive level of <math><mrow><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>19</mn></mrow></msup><mtext> </mtext><mtext> </mtext><mi>e</mi><mtext> </mtext><mi>cm</mi></mrow></math>, achieving a 3-orders-of-magnitude improvement over the only existing measurement in a fixed-target experiment at Fermilab with similar statistics. The estimated sensitivities for the <math><msup><mi>Σ</mi><mo>+</mo></msup></math>, <math><msup><mi>Ξ</mi><mo>−</mo></msup></math>, and <math><msup><mi>Ξ</mi><mn>0</mn></msup></math> hyperons at the same level of <math><mrow><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>19</mn></mrow></msup><mtext> </mtext><mtext> </mtext><mi>e</mi><mtext> </mtext><mi>cm</mi></mrow></math> will mark the first-ever achievement and the latter two will be the first exploration of hyperons with two strange valence quarks. The EDM measurements for hyperons conducted at the BESIII experiment will be a significant milestone and serve as a litmus test for new physics such as supersymmetry and the left-right symmetrical model. Furthermore, at the STCF experiment, the sensitivity of hyperon EDM measurements can be further enhanced by 2 orders of magnitude. Additionally, this angular analysis enables the determination of <math><mi>C</mi><mi>P</mi></math> violation in hyperon decays, the effective weak mixing angle, and beam polarization.