The <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>Z</mi><mn>0</mn></msup></math> bosons produced in electron-positron collisions at the potential Future Circular Collider (FCC-ee) provide unique opportunities for flavor physics. The nonzero polarization of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Λ</mi><mi>b</mi><mn>0</mn></msubsup></math> baryons produced in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>Z</mi><mn>0</mn></msup></math> decays enables access to a much larger set of observables than at the LHC, where the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Λ</mi><mi>b</mi><mn>0</mn></msubsup></math> baryons are produced unpolarized. This paper presents a toy angular analysis of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Λ</mi><mi>b</mi><mn>0</mn></msubsup><mo stretchy="false">→</mo><mrow><mi mathvariant="normal">Λ</mi><mo stretchy="false">(</mo><mo stretchy="false">→</mo><mi>p</mi><msup><mi>π</mi><mo>−</mo></msup><mo stretchy="false">)</mo><msup><mi>μ</mi><mo>+</mo></msup><msup><mi>μ</mi><mo>−</mo></msup></mrow></math> decays using simulation samples of collisions at the FCC-ee reconstructed using the IDEA detector concept and assuming a dataset of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>6</mn><mo>×</mo><msup><mn>10</mn><mn>12</mn></msup></math> <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>Z</mi><mn>0</mn></msup></math> bosons. While the statistical sensitivity achieved for individual angular observables is not expected to significantly exceed that from the LHCb Upgrade II experiment, the addition of the polarized observables leads to a significant improvement of the knowledge on the Wilson coefficients <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>C</mi><msup><mn>9</mn><mrow><mo stretchy="false">(</mo><mo>′</mo><mo stretchy="false">)</mo></mrow></msup></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>C</mi><mrow><msup><mn>10</mn><mrow><mo stretchy="false">(</mo><mo>′</mo><mo stretchy="false">)</mo></mrow></msup></mrow></msub></math>.

United States

Anja Beck

Mero Elmarassy

Asher Sabbagh

United Kingdom

Michal Kreps

Eluned Smith

Constraints on new physics from decays of polarized <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Λ</mi><mi>b</mi><mn>0</mn></msubsup></math> baryons at the FCC-ee

The process of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mrow><mi>b</mi><mi>c</mi></mrow><mo>+</mo></msubsup><mo stretchy="false">→</mo><msubsup><mi mathvariant="normal">Ξ</mi><mi>c</mi><mo>+</mo></msubsup><mi>J</mi><mo>/</mo><mi>ψ</mi></math> is among the most favored modes for searching for bottom-charm baryons. However, its branching fraction has never been studied in theory. In this work, we investigate the branching fraction of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mrow><mi>b</mi><mi>c</mi></mrow><mo>+</mo></msubsup><mo stretchy="false">→</mo><msubsup><mi mathvariant="normal">Ξ</mi><mi>c</mi><mo>+</mo></msubsup><mi>J</mi><mo>/</mo><mi>ψ</mi></math> in the final-state-interaction approach, as it is dominated by the color-suppressed nonfactorizable contributions. A similar process, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Λ</mi><mi>b</mi><mn>0</mn></msubsup><mo stretchy="false">→</mo><msup><mi mathvariant="normal">Λ</mi><mn>0</mn></msup><mi>J</mi><mo>/</mo><mi>ψ</mi></math>, is used as a control mode to fix the model parameter. Consequently, the branching fraction of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mrow><mi>b</mi><mi>c</mi></mrow><mo>+</mo></msubsup><mo stretchy="false">→</mo><msubsup><mi mathvariant="normal">Ξ</mi><mi>c</mi><mo>+</mo></msubsup><mi>J</mi><mo>/</mo><mi>ψ</mi></math> is predicted to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><mn>1.5</mn><msubsup><mn>5</mn><mrow><mo>−</mo><mn>0.42</mn></mrow><mrow><mo>+</mo><mn>0.50</mn></mrow></msubsup><mo stretchy="false">)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>4</mn></mrow></msup></math>. With the production rate of bottom-charm baryons and the detection efficiencies of the final states, it is expected for considerable signal events to observe <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mrow><mi>b</mi><mi>c</mi></mrow><mo>+</mo></msubsup></math> in the near future.

China

Xiao-Hui Hu

Cai-Ping Jia

Ye Xing

Fu-Sheng Yu

Branching fraction of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mrow><mi>b</mi><mi>c</mi></mrow><mo>+</mo></msubsup><mo stretchy="false">→</mo><msubsup><mi mathvariant="normal">Ξ</mi><mi>c</mi><mo>+</mo></msubsup><mi>J</mi><mo>/</mo><mi>ψ</mi></math> in the final-state-interaction approach

An analysis of baryogenesis and stochastic gravitational wave production is presented for an extension of the Standard Model where the dark sector consists of dark matter particles charged under 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>x</mi></msub></math> gauge symmetry, while a subset of dark fields also carry lepton number but no <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>x</mi></msub></math> charge. We demonstrate that, with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violation induced by Yukawa couplings, equal and opposite lepton asymmetries are generated in the visible and hidden sectors. Subsequent evolution preserves the lepton number separately in each sector, and sphaleron interactions partially convert the lepton asymmetry into baryon asymmetry near the temperature of the first-order phase transition. Furthermore, we discuss stochastic gravitational wave background production for the first-order phase transition using a gauge-independent bubble nucleation dynamics which yields spectra also valid in the supercooled low-temperature regime with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mi>p</mi></msub><mo>/</mo><msub><mi>m</mi><msub><mi>A</mi><mi>x</mi></msub></msub><mo>≪</mo><mn>1</mn></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mi>p</mi></msub></math> is the percolation temperature and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><msub><mi>A</mi><mi>x</mi></msub></msub></math> is the dark photon mass. A parameter-space scan identifies regions that simultaneously account for cogenesis of baryon asymmetry and dark matter and predict stochastic gravitational wave signals within reach of current (NANOGrav, EPTA, and PPTA) and future detectors at higher frequencies, providing a unified framework for cogenesis and associated gravitational wave production.

Wan-Zhe Feng

Jinzheng Li

Pran Nath

Zong-Huan Ye

Gauge-independent gravitational waves from cogenesis in a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo>−</mo><mi>L</mi></math> conserving universe

This paper presents a detailed analysis of the three-body final state interactions in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mo>+</mo></msup><mo stretchy="false">→</mo><mi>D</mi><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><msup><mi>K</mi><mo>+</mo></msup></math> process, whose phase space is sufficient small. To precisely extract the resonance parameters, for instance the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>χ</mi><mrow><mi>c</mi><mn>0</mn><mo>/</mo><mn>2</mn></mrow></msub><mo stretchy="false">(</mo><mn>3930</mn><mo stretchy="false">)</mo></math> in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover></math> invariant mass distributions, in this process, one has to take into account final state interaction, especially the three-body final state interaction. We employ the dispersive Khuri-Treiman formalism, combined with a parametrization of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover></math> interaction based on heavy quark spin symmetry. By performing a simultaneous fit to the experimental data from LHCb, BABAR, and Belle collaborations, the scheme with three-body interaction successfully describes the invariant mass distributions of the three two-body subsystems. We precisely extract the pole structures of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>χ</mi><mrow><mi>c</mi><mn>0</mn></mrow></msub><mo stretchy="false">(</mo><mn>3930</mn><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ψ</mi><mo stretchy="false">(</mo><mn>3770</mn><mo stretchy="false">)</mo></math> as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>3.913</mn><mo>−</mo><mn>0.016</mn><mi>i</mi><mtext> </mtext><mi>GeV</mi></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>3.761</mn><mo>−</mo><mn>0.006</mn><mi>i</mi><mtext> </mtext><mi>GeV</mi></mrow></math> in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mo>+</mo></msup></math> decay. By performing the pole trajectory analysis on a uniformized complex plane, we find that both of them stem from the input bare state.

Xin-Yue Hu

Jiahao He

Pengyu Niu

Japan

Qian Wang

Thailand

Yupeng Yan

Three-body final state interactions in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mo>+</mo></msup><mo stretchy="false">→</mo><mi>D</mi><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><msup><mi>K</mi><mo>+</mo></msup></math> decays

Higgs self-coupling is crucial to understand the structure of the scalar potential and the mechanism of electroweak symmetry breaking. In this study, we utilize a deep neural network based on a particle Transformer model that relies on an attention mechanism to comprehensively analyze the measured trilinear Higgs self-coupling through Higgs pair production with subsequent decay into four $\textit{b}$-quarks ( $ HH\to b\bar{b}b\bar{b} $ ) at the LHC. The model processes the full event-level information as input and bypasses explicit jet pairing. It also serves as an event classifier. At HL-LHC, our approach constrains $ \kappa_\lambda $ to $ (-0.25,\,5.41) $ at 68% CL, and thus achieved an improvement of ~44% in precision over conventional cut-based analyses. The results of a comparison against alternative machine learning architectures demonstrate the outstanding performance of the Transformer-based model owing to its ability to capture correlations in high-dimensional collision data with the help of the attention mechanism. These findings highlight the potential of attention-based networks and end-to-end event classifiers in collider phenomenology.

Yongcheng Wu

Liang Xiao

Yan Zhang

Deep learning to improve the sensitivity of Higgs pair searches in the 4$\textit{b}$ channel at the LHC * Supported by the National Natural Science Foundation of China (NNSFC) (12305112)

Recently, many new excited states of heavy mesons have been discovered in recent experiments, including radially excited states. The production processes of these states from the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mrow><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo></mrow></msub></math> meson have drawn significant interest. In this paper, we use the covariant light-front approach to study the nonleptonic <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mrow><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo></mrow></msub></math> meson decays to the first radially excited states <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>D</mi><mrow><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo></mrow></msub><mo stretchy="false">(</mo><mn>2</mn><mi>S</mi><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mrow><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo></mrow><mo>*</mo></msubsup><mo stretchy="false">(</mo><mn>2</mn><mi>S</mi><mo stretchy="false">)</mo></math>. Our results reveal that many channels exhibit large branching ratios in the range <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>10</mn><mrow><mo>−</mo><mn>5</mn></mrow></msup><mi>–</mi><msup><mn>10</mn><mrow><mo>−</mo><mn>4</mn></mrow></msup></math>, even up to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></math> for individual channels, which are detectable by current experiments. Our predictions for the decays <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mrow><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo></mrow></msub><mo stretchy="false">→</mo><msubsup><mi>D</mi><mrow><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup><mo stretchy="false">(</mo><mn>2</mn><mi>S</mi><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mi>π</mi><mo>,</mo><mi>ρ</mi><mo>,</mo><msup><mi>K</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup><mo stretchy="false">)</mo></math> are larger than those given by the Bethe-Salpeter (BS) equation method, but agree well with the relativistic quark mode (RQM) and the relativistic independent quark model (RIQM) calculations. For comparison, we also present the branching ratios of the decays <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mrow><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo></mrow></msub><mo stretchy="false">→</mo><msubsup><mi>D</mi><mrow><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup><mo stretchy="false">(</mo><mn>1</mn><mi>S</mi><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mi>π</mi><mo>,</mo><mi>ρ</mi><mo>,</mo><msup><mi>K</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup><mo stretchy="false">)</mo></math>, which are comparable with other theoretical results and the data. Although the branching ratios of the decays <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mrow><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo></mrow></msub><mo stretchy="false">→</mo><msubsup><mi>D</mi><mrow><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo></mrow><mo>*</mo></msubsup><mo stretchy="false">(</mo><mn>1</mn><mi>S</mi><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mi>ρ</mi><mo>,</mo><msup><mi>K</mi><mo>*</mo></msup><mo stretchy="false">)</mo></math> are much larger than those of the decays <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mrow><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo></mrow></msub><mo stretchy="false">→</mo><msubsup><mi>D</mi><mrow><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo></mrow><mo>*</mo></msubsup><mo stretchy="false">(</mo><mn>2</mn><mi>S</mi><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mi>ρ</mi><mo>,</mo><msup><mi>K</mi><mo>*</mo></msup><mo stretchy="false">)</mo></math>, the polarization properties between them are similar, that is, the longitudinal polarization fractions are dominant and can amount roughly to 90%.

Zhi-Jie Sun

Yong-Jin Sun

Zhi-Qing Zhang

You-Ya Yang

Si-Yang Wang

<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>D</mi><mrow><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo></mrow></msub><mo stretchy="false">(</mo><mn>2</mn><mi>S</mi><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mrow><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo></mrow><mo>*</mo></msubsup><mo stretchy="false">(</mo><mn>2</mn><mi>S</mi><mo stretchy="false">)</mo></math> production in nonleptonic <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mrow><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo></mrow></msub></math> weak decays

India

Rimi Debnath

Sanjeeda Sultana

Khandro K. Chokyi

Surajit Chattopadhyay

Corrigendum to “Phenomenological insights into holographically reconstructed fractional action cosmology: Cosmic dynamics, thermodynamics, and statefinder diagnostics” [Nuclear Physics B Volume: 1018 (September 2025) 117074]

Motivated by the stringent experimental bounds on proton lifetime and the need for precise low-energy predictions, there has been renewed interest in the renormalization group (RG) evolution of Wilson coefficients for baryon number violating (BNV) operators and their characteristic new-physics scales. In this work, we analyze the RG running of dimension-6 four-fermion operators in the $$ \overline{\textrm{MS}} $$ scheme that mediate nucleon decay channels such as $\textit{p}$ → $\textit{e}$ $\textit{π}$ , while systematically accounting for the impact of baryon number conserving (BNC) new-physics that can enter the theory at an intermediate scale as higher-dimensional effective field theory operators. These BNC operators mix with BNV ones at 1-loop and alter the RG flow. The running is performed from the electroweak scale up to representative intermediate scales of 10 GeV, 10 GeV, and 10 GeV, corresponding to possible thresholds for new BNC degrees of freedom. Comparing the RG evolved coefficients with current experimental bounds on nucleon decay lifetimes, we find that the inclusion of BNC-BNV mixing, dominated by top quark loops, can significantly lower the effective proton decay scale to ∼ 10 GeV, thus mitigating the need of a large desert. A Python package (Available at: ) is provided to facilitate the RG evolution of nucleon-decay Wilson coefficients, allowing for the inclusion of generic BNC effects.

Mathew Arun

M Shyam

Ritik Pal

RG evolution and effect of intermediate new-physics on ∆$\textit{B}$ = 1 four-fermion operators

Inspired by the observation of the doubly charmed tetraquark state <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub></math> at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi><mi>p</mi></math> collisions in the inclusive processes, we systematically investigate the production of doubly charmed tetraquark states in exclusive <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mi>c</mi></msub></math> decays. In this work, we assume the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub></math> as a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><msup><mi>D</mi><mo>*</mo></msup></math> bound state, and then predict the masses of its heavy quark spin symmetry partner <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mo>*</mo></msup><msup><mi>D</mi><mo>*</mo></msup></math> (denoted by <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>*</mo></msubsup></math>) as well as their SU(3)-flavor symmetry partners, i.e., <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>D</mi><mi>s</mi></msub><msup><mi>D</mi><mo>*</mo></msup><mo>/</mo><msubsup><mi>D</mi><mi>s</mi><mo>*</mo></msubsup><mi>D</mi></math> (denoted by <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi><mi>s</mi></mrow><mo>+</mo></msubsup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi><mi>s</mi></mrow><mrow><mo>+</mo><mo>+</mo></mrow></msubsup></math>) and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mo>*</mo></msup><msubsup><mi>D</mi><mi>s</mi><mo>*</mo></msubsup></math> (denoted by <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi><mi>s</mi></mrow><mrow><mo>*</mo><mo>+</mo></mrow></msubsup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi><mi>s</mi></mrow><mrow><mo>*</mo><mo>+</mo><mo>+</mo></mrow></msubsup></math>), using the contact range effective field theory. Within the molecular picture, we compute their partial decay widths and production rates in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mi>c</mi></msub></math> meson decays. We identify the decays <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mi>c</mi></msub><mo stretchy="false">→</mo><msup><mi>D</mi><mn>0</mn></msup><msup><mi>D</mi><mn>0</mn></msup><msup><mi>π</mi><mo>+</mo></msup><msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mi>c</mi></msub><mo stretchy="false">→</mo><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup><msup><mi>D</mi><mn>0</mn></msup><msup><mi>π</mi><mo>+</mo></msup><msup><mi>D</mi><mo>−</mo></msup></math> as promising channels to observe the tetraquark states <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi><mi>s</mi></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo><mo>+</mo><mo>+</mo></mrow></msubsup></math>, respectively. Finally, by combining these results with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mi>c</mi></msub></math> production cross sections, we estimate the expected event yields for these states in the upcoming LHC Runs 3 and 4. Our results indicate that the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi><mi>s</mi></mrow><mo>+</mo></msubsup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi><mi>s</mi></mrow><mrow><mo>*</mo><mo>+</mo><mo>+</mo></mrow></msubsup></math> states are likely to be observed in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mi>c</mi></msub></math> decays, while it is quite difficult for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>*</mo></msubsup></math> states.

Yi Zhang

Ming-Zhu Liu

Li-Sheng Geng

Productions of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub></math> and its SU(3)-flavor symmetry and heavy quark spin symmetry partners in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mi>c</mi></msub></math> decays

We develop a strategy for computing the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><mi>K</mi><msup><mo>ℓ</mo><mo>+</mo></msup><msup><mo>ℓ</mo><mo>−</mo></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mi>s</mi></msub><mo stretchy="false">→</mo><mi>γ</mi><msup><mo>ℓ</mo><mo>+</mo></msup><msup><mo>ℓ</mo><mo>−</mo></msup></math> decay amplitudes using lattice QCD (where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mo>ℓ</mo><mo>±</mo></msup></math> are charged leptons). We focus on those terms which contain complex contributions to the amplitude, due to on-shell intermediate states propagating between the weak operator and electromagnetic current(s). Such terms, which are generally estimated using model calculations and represent significant uncertainties in the phenomenological predictions for these decays, cannot be computed using standard lattice QCD techniques. It has recently been shown that such contributions can be computed using spectral density methods and our proposed strategy, which we discuss in detail, is built on this approach. The complex contributions include the “charming penguins” [matrix elements of the current-current operators <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>O</mi><mn>1</mn><mrow><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo></mrow></msubsup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>O</mi><mn>2</mn><mrow><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo></mrow></msubsup></math> defined in Eq. (6) below], in which the charm-quark loop can propagate long distances, particularly close to the region of charmonium resonances. They also include the contributions from the chromomagnetic operator [<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>O</mi><mn>8</mn></msub></math> in standard notation, defined in Eq. (8) below]. We discuss the renormalization of the ultraviolet divergences, and in particular those which arise due to “contact” terms, and explain how those which appear as inverse powers of the lattice spacing can be subtracted nonperturbatively. We apply the spectral density methods in an instructive exploratory computation of the charming penguin diagram in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><mi>K</mi><msup><mo>ℓ</mo><mo>+</mo></msup><msup><mo>ℓ</mo><mo>−</mo></msup></math> decays in which the virtual photon is emitted from the charm-quark loop [the diagram in Fig. 1(a) below] and discuss the prospects and strategies for the reliable determination of the amplitudes in future dedicated computations; computations which are, however, beyond the scope of the present paper.

Italy

Roberto Frezzotti

Nazario Tantalo

Giuseppe Gagliardi

Vittorio Lubicz

Guido Martinelli

Chris T. Sachrajda

Francesco Sanfilippo

Silvano Simula

Luca Silvestrini

Theoretical framework for lattice QCD computations of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><mi>K</mi><msup><mo>ℓ</mo><mo>+</mo></msup><msup><mo>ℓ</mo><mo>−</mo></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mi>s</mi></msub><mo stretchy="false">→</mo><msup><mo>ℓ</mo><mo>+</mo></msup><msup><mo>ℓ</mo><mo>−</mo></msup><mi>γ</mi></math> decays rates, including contributions from charming penguin diagrams