Hyperon-antihyperon pairs produced in high-energy electron-positron annihilation constitute a naturally spin-entangled system in the high-energy regime. Recently, a probabilistic amplification of entanglement, termed autodistillation, has been found in the daughter baryon-antibaryon pairs from hyperon decay and is constrained by an upper boundary. This work demonstrates that the quantum entanglement in this process may be accompanied by a decrease, constrained by a lower boundary, but it will not be completely lost. Thus, the entanglement of these systems undergoes redistribution within the phase space during the sequential decays of hyperons, highlighting the important role of hyperon polarization. By using the explicit spin density matrix of baryon pairs, it is also found that the quantumness of the system, characterized by quantum discord, always has the possibility to increase during decay processes, even when entanglement evaluated by concurrence and negativity does not increase.

China

Cong Li

Xu Cao

Ai-Qiang Guo

Chun-Xu Yu

Hong-Wei Zhang

Zhe Zhang

Entanglement redistribution of hyperon-antihyperon pair via sequential decay * Supported by the National Natural Science Foundation of China (12547111, 12447132, 12575089) and the National Key R&D Program of China (2023YFA1606703)

Motivated by the first observation of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>C</mi><mi>P</mi></mrow></math> violation in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>b</mi></math>-baryon decays, the search for baryonic decays exhibiting large <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>C</mi><mi>P</mi></mrow></math> violation will be a primary focus in the coming years. We propose that significant <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>C</mi><mi>P</mi></mrow></math>-violating effects exist in the decay <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 mathvariant="normal">Λ</mi><mi>D</mi></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi></math> denotes a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>C</mi><mi>P</mi></mrow></math> eigenstate of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>D</mi></mrow><mrow><mn>0</mn></mrow></msup><mtext>−</mtext><msup><mrow><mover accent="true"><mrow><mi>D</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mn>0</mn></mrow></msup></mrow></math> system. The predicted <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>C</mi><mi>P</mi></mrow></math> asymmetries for both the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>C</mi><mi>P</mi></mrow></math>-even and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>C</mi><mi>P</mi></mrow></math>-odd modes can reach magnitudes as large as 50%, making these decays promising targets for measurement at the LHCb experiment. Additionally, we predict for the first time several nonzero <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>C</mi><mi>P</mi></mrow></math>-violating observables associated with angular distribution parameters, providing valuable complementary information in the search for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>C</mi><mi>P</mi></mrow></math> violation in baryon decays. Furthermore, we propose a novel strategy to extract the Cabibbo-Kobayashi-Maskawa angle <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi></math> by combining data on angular distribution parameters and decay rates from the relevant channels. We emphasize that <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 mathvariant="normal">Λ</mi><mi>D</mi></math> decays are among the most promising candidates for determining <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi></math> in the baryon sector. Our findings may offer new insights for future theoretical and experimental investigations.

Zhou Rui

Zhi-Tian Zou

Ya Li

Ying Li

Large <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"><msub><mi mathvariant="normal">Λ</mi><mi>b</mi></msub><mo stretchy="false">→</mo><mi mathvariant="normal">Λ</mi><mi>D</mi></math> decays and extraction of the Cabibbo-Kobayashi-Maskawa angle <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi></math>

We extend the results of Lappi et al. [<a href="http://dx.doi.org/10.1140/epjc/s10052-023-12365-2">Eur. Phys. J. C 84, 84 (2024)</a>] to show that it is possible to obtain expressions for the longitudinal, singlet, and gluon structure functions <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>F</mi><mi>L</mi></msub></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>F</mi><mi>S</mi></msub></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>G</mi></math> in deep inelastic scattering directly in terms of the measured functions <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>F</mi><mn>2</mn></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>d</mi><msub><mi>F</mi><mn>2</mn></msub><mo>/</mo><mi>ln</mi><mo stretchy="false">(</mo><msup><mi>Q</mi><mn>2</mn></msup><mo stretchy="false">)</mo></math> modulo nonsinglet corrections expected to be small at very small <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math>. The latter can be treated at low <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math> using existing quark distributions. Our results are presented consistently to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>O</mi><mo stretchy="false">(</mo><msubsup><mi>α</mi><mi>s</mi><mn>2</mn></msubsup><mo stretchy="false">)</mo></math>, correcting and extending the mixed-order results of Lappi et al..

Iran

G.R. Boroun

United States

Loyal Durand

Phuoc Ha

Direct determination of the structure functions <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>F</mi><mi>L</mi></msub></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>F</mi><mi>S</mi></msub></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>G</mi></math> from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>F</mi><mn>2</mn></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>d</mi><msub><mi>F</mi><mn>2</mn></msub><mo>/</mo><mi>d</mi><msup><mi>Q</mi><mn>2</mn></msup></math> to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>O</mi><mo stretchy="false">(</mo><msubsup><mi>α</mi><mi>s</mi><mn>2</mn></msubsup><mo stretchy="false">)</mo></math>

In this work, we analyze the strong vertices of hadronic molecules $\textit{DK}$, $$D^*K$$ , $$DK^*$$ and their bottom analogs within the framework of three-point QCD sum rules. The contribution of interpolating currents coupling to low spin particles is considered in the phenomenological side, and the vacuum condensates $$\left\langle \bar{q}q \right\rangle ,\left\langle g_s^2GG \right\rangle ,\left\langle \bar{q}g_s\sigma Gq \right\rangle ,\left\langle g_s^3GGG \right\rangle ,{\left\langle \bar{q}q \right\rangle ^2}$$ are included in the QCD side. As an application of strong coupling constants, we also obtain the partial decay widths of these states, where $$\Gamma _{T_{DK}\rightarrow D_s\pi }=12.4_{-2.7}^{+3.2}$$ KeV, $$\Gamma _{T_{D^*K}\rightarrow D_s^*\pi }=28.5_{-4.6}^{+5.2}$$ KeV, $$\Gamma _{T_{BK}\rightarrow BK}=101_{-21}^{+36}$$ MeV and $$\Gamma _{T_{B^*K}\rightarrow B^*K}=142_{-25}^{+52}$$ MeV. It is shown that the results of $$\Gamma _{T_{DK}\rightarrow D_s\pi }$$ and $$\Gamma _{T_{D^*K}\rightarrow D_s^*\pi }$$ are compatible with the experimental data of $$D_{s0}^*(2317)$$ and $$D_{s1}(2460)$$ .

Ze Zhou

Guo-Liang Yu

Zhi-Gang Wang

Jie Lu

Analysis of the strong vertices of hadronic molecules $\textit{DK}$, $$D^*K$$ , $$DK^*$$ and their bottom analogs

We present the first lattice QCD calculation of single-channel <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mi>D</mi></math> scattering with quantum numbers <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>I</mi><mo stretchy="false">(</mo><msup><mrow><mi>J</mi></mrow><mrow><mi>P</mi></mrow></msup><mo stretchy="false">)</mo><mo>=</mo><mn>1</mn><mo stretchy="false">(</mo><msup><mrow><mn>0</mn></mrow><mrow><mo>+</mo></mrow></msup><mo stretchy="false">)</mo></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>0</mn><mo stretchy="false">(</mo><msup><mn>1</mn><mo>−</mo></msup><mo stretchy="false">)</mo></math>. The calculation is performed on the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2</mn><mo>+</mo><mn>1</mn></math> flavor Wilson-Clover ensembles with a lattice spacing <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>a</mi><mo>≃</mo><mn>0.077</mn><mtext> </mtext><mtext> </mtext><mi>fm</mi></math> and two different pion masses, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><mi>π</mi></msub><mo>≃</mo><mn>207</mn></math> and 305 MeV. The scattering parameters are determined using the Lüscher finite-volume method. Our results indicate a weak repulsive interaction in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mo stretchy="false">(</mo><msup><mn>0</mn><mo>+</mo></msup><mo stretchy="false">)</mo></math> channel and a slightly attractive interaction in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>0</mn><mo stretchy="false">(</mo><msup><mn>1</mn><mo>−</mo></msup><mo stretchy="false">)</mo></math> channel. The <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi></math>-wave isovector <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mi>D</mi></math> scattering length and effective range, extrapolated to the physical pion mass, are <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">(</mo><mo>−</mo><mn>0.25</mn><mo>±</mo><mn>0.08</mn><mo>±</mo><mn>0.12</mn><mo stretchy="false">)</mo><mtext> </mtext><mtext> </mtext><mi>fm</mi></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">(</mo><mo>−</mo><mn>5.7</mn><mo>±</mo><mn>4.5</mn><mo>±</mo><mn>1.7</mn><mo stretchy="false">)</mo><mtext> </mtext><mtext> </mtext><mi>fm</mi></mrow></math>, respectively.

Spain

Pan-Pan Shi

Feng-Kun Guo

Chuan Liu

Liuming Liu

Peng Sun

Jia-Jun Wu

Hanyang Xing

Low-energy <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mi>D</mi></math> scattering in lattice QCD

We investigate the modification of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi></math> meson mass in asymmetric nuclear matter at zero and finite temperatures employing an effective Lagrangian approach that considers the contributions of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mi>D</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><msup><mi>D</mi><mo>*</mo></msup></math> meson loops. The medium dependence of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi></math> meson masses is determined using the hadronic chiral SU(3) model, where scalar condensates are calculated and subsequently utilized in the QCD sum rules approach. Our findings indicate that an increase in baryonic density results in a negative mass shift of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi></math> meson. This suggests that the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi></math> meson is attracted to nuclear mean fields indicating the possibility of the formation of meson-nucleus bound states. Moreover, we have also determined the binding energy and absorption decay width of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi></math> meson for both the ground and excited states of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi mathvariant="normal">O</mi><mn>16</mn></msup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>Ca</mi><mn>40</mn></msup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>Zr</mi><mn>90</mn></msup></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>Pb</mi><mn>208</mn></msup></math> nuclei. These results are expected to contribute to the understanding of experimental data from upcoming studies at Jefferson lab and the facility for antiproton and ion research, where low-momentum charmed mesons can be produced and examined within nuclei.

India

Manpreet Kaur

Arvind Kumar

Study of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi></math> mass shift and bound states: Impact of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mi>D</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><msup><mi>D</mi><mo>*</mo></msup></math> meson loops

We present results for the inclusive semileptonic <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>D</mi><mi>s</mi></msub><mo stretchy="false">→</mo><msub><mi>X</mi><mi>s</mi></msub><mo>ℓ</mo><mover accent="true"><mi>ν</mi><mo stretchy="false">¯</mo></mover></math> decay rate from lattice QCD. Chiral and continuum extrapolations are performed using gauge ensembles generated with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math> flavors of Möbius domain-wall fermions. Systematic errors are fully addressed including those from the integral over all possible final states. Our results are in agreement with currently available experimental data, with an error at the few-percent level.

Japan

Ryan Kellermann

Germany

Alessandro Barone

United Kingdom

Ahmed Elgaziari

Shoji Hashimoto

Takashi Kaneko

Zhi Hu

CERN

Andreas Jüttner

Inclusive semileptonic <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>D</mi><mi>s</mi></msub><mo stretchy="false">→</mo><msub><mi>X</mi><mi>s</mi></msub><mo>ℓ</mo><mover accent="true"><mi>ν</mi><mo stretchy="false">¯</mo></mover></math> decays from lattice QCD: Continuum and chiral extrapolation

We present a precise and systematic analysis of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mo stretchy="false">→</mo><mi>V</mi><mi>V</mi></math> decays within the factorization-assisted topological-amplitude approach, where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi></math> denotes the set <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">{</mo><msup><mi>D</mi><mn>0</mn></msup><mo>,</mo><msup><mi>D</mi><mo>+</mo></msup><mo>,</mo><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup><mo stretchy="false">}</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>V</mi></math> represents the vector mesons <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ρ</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>*</mo></msup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ω</mi></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ϕ</mi></math>. Given the limited current experimental data, the factorization-assisted topological-amplitude approach serves as a available phenomenological framework for predicting charmed meson decays to both vector mesons. In this framework, incorporating flavor SU(3) symmetry-breaking effects, we can express nonfactorizable contributions of different modes as a minimal set of universal parameters globally fitted to experimental data. Utilizing 36 experimental data points for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mo stretchy="false">→</mo><mi>V</mi><mi>V</mi></math> decays, we precisely extract ten nonfactorizable parameters associated with the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>E</mi></math> topological diagrams with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>χ</mi><mn>2</mn></msup><mo>/</mo><mrow><mi mathvariant="normal">d</mi><mo>.</mo><mi mathvariant="normal">o</mi><mo>.</mo><mi mathvariant="normal">f</mi><mo>.</mo></mrow><mo>=</mo><mn>8.43</mn></math>. We find that a large strong phase in the longitude <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>E</mi></math> amplitude causes strong destructive interference with the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi></math> longitudinal component, yielding <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mo stretchy="false">∥</mo></msub><mo>&gt;</mo><msub><mi>f</mi><mi>L</mi></msub></math>, contrary to the naive factorization predictions. Additionally, for modes processing exclusively by the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>E</mi></math> diagram, the amplitude hierarchy <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">|</mo><mi>S</mi><mo stretchy="false">|</mo><mo>&lt;</mo><mo stretchy="false">|</mo><mi>D</mi><mo stretchy="false">|</mo></math> leads to a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi></math>-wave branching fraction larger than that of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi></math> wave. This explains recent observations that contradict <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi></math>-wave dominance predictions. The predicted branching fractions and polarizations for 28 decay modes are consistent with existing experimental data. Unobserved modes, especially those with branching fractions of the order of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><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>2</mn></mrow></msup></mrow></math>, the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi></math>-wave-dominated modes, and modes exhibiting <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mo stretchy="false">∥</mo></msub><mo>&gt;</mo><msub><mi>f</mi><mi>L</mi></msub></math>, await measurement by BESIII, STCF, Belle II, and LHCb.

Jing Ou-Yang

Hui Zheng

Run-Hui Li

Si-Hong Zhou

Precise theoretical prediction on branching fractions and polarizations of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mo stretchy="false">→</mo><mi>V</mi><mi>V</mi></math> decays

We investigate the possibility of realizing strong first-order electroweak phase transition (SFOEWPT) in an effective field theory framework where the Standard Model is extended with a complex scalar singlet (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ϕ</mi></math>) charged under a local <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><msub><mo stretchy="false">)</mo><mi>D</mi></msub></math> gauge group. The tree-level scalar potential contains a dimension-six term of the form <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">|</mo><mi>H</mi><msup><mo stretchy="false">|</mo><mn>2</mn></msup><mo stretchy="false">|</mo><mi>ϕ</mi><msup><mo stretchy="false">|</mo><mn>4</mn></msup></math>. We show that this higher-dimensional operator plays a crucial role in the phase transition dynamics by weakening the correlation between the Higgs-singlet portal coupling and the scalar mixing angle that typically constrains singlet-extended models. Consequently, SFOEWPT can be achieved over a significantly extended region of parameter space. The strength of the phase transition is primarily driven by the vacuum expectation value of the singlet scalar, which plays a central role in this analysis. We analyze the phase transition in this model and identify regions of parameter space consistent with SFOEWPT. The resulting phase transition can generate stochastic gravitational-wave signals potentially observable at future interferometers. The extended scalar sector in presence of the dimension-six operator also leads to distinctive multiscalar production signatures at the LHC, intimately correlated with the singlet scalar VEV.

Arka Bhattacharyya

Sanjoy Biswas

Saurabh Niyogi

Electroweak phase transitions in a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><msub><mo stretchy="false">)</mo><mi>D</mi></msub></math> extension of the standard model with dimension-six operators: Gravitational waves and LHC signatures

We apply the intertwiner operator method of arXiv:2411.08865 to topological field theories, including BF theories, Chern-Simons theory, and three-dimensional gravity. We construct the operator on foliated manifolds while preserving covariance on the Cauchy surface, and compare canonical and holomorphic quantization, providing the intertwiner in both frameworks. For three-dimensional gravity, we present both covariant and time-gauge formulations, analyze the constraints, and construct the corresponding intertwiner. As an application, we derive the path ordering of Wilson loops in Chern-Simons theory. The study of observables is left for future work. (The intertwiner discussed here establishes a morphism between the respective Hilbert spaces on which the two BRST charges, <italic>Q</italic> <inf>0</inf> and <italic>Q</italic>, act. This should be distinguished from the unrelated intertwiner operator used in loop quantum gravity.)

Italy

P.A. Grassi

E.M.G. Landò

Intertwiners for D=3 gauge theories