Lepton number violating meson decays, such as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>M</mi><mn>1</mn><mo>−</mo></msubsup><mo stretchy="false">→</mo><msubsup><mi>M</mi><mn>2</mn><mo>+</mo></msubsup><msubsup><mo>ℓ</mo><mn>1</mn><mo>−</mo></msubsup><msubsup><mo>ℓ</mo><mn>2</mn><mo>−</mo></msubsup></math>, provide constraints on <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>d</mi><mo>=</mo><mn>9</mn></math> <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Δ</mi><mi>L</mi><mo>=</mo><mn>2</mn></math> operators. Renormalization group equation (RGE)-improved bounds on the Wilson coefficients of these operators have been presented in the literature, taking into account perturbative quantum chromodynamics (QCD) one-loop corrections and the corresponding operator mixing. Here, we present for the first time the contribution of connected diagrams to the hadronic matrix elements <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">⟨</mo><msub><mrow><mi>M</mi></mrow><mrow><mn>2</mn></mrow></msub><mo stretchy="false">|</mo><msub><mrow><mi mathvariant="script">O</mi></mrow><mrow><mi>h</mi></mrow></msub><mo stretchy="false">|</mo><msub><mrow><mi>M</mi></mrow><mrow><mn>1</mn></mrow></msub><mo stretchy="false">⟩</mo></mrow></math>. These diagrams, usually overlooked under the assumption that <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">⟨</mo><msub><mi>M</mi><mn>2</mn></msub><mo stretchy="false">|</mo><msub><mi mathvariant="script">O</mi><mi>h</mi></msub><mo stretchy="false">|</mo><msub><mi>M</mi><mn>1</mn></msub><mo stretchy="false">⟩</mo><mo>∼</mo><mo stretchy="false">⟨</mo><msub><mi>M</mi><mn>2</mn></msub><mo stretchy="false">|</mo><msub><mi>J</mi><mrow><msub><mi>q</mi><mn>3</mn></msub><msub><mi>q</mi><mn>4</mn></msub></mrow></msub><mo stretchy="false">|</mo><mn>0</mn><mo stretchy="false">⟩</mo><mo>×</mo><mspace linebreak="goodbreak"></mspace><mo stretchy="false">⟨</mo><mn>0</mn><mo stretchy="false">|</mo><msub><mi>J</mi><mrow><msub><mi>q</mi><mn>1</mn></msub><msub><mi>q</mi><mn>2</mn></msub></mrow></msub><mo stretchy="false">|</mo><msub><mi>M</mi><mn>1</mn></msub><mo stretchy="false">⟩</mo><mo>≫</mo><mo stretchy="false">⟨</mo><msub><mi>M</mi><mn>2</mn></msub><mo stretchy="false">|</mo><msub><mi>J</mi><mrow><msub><mi>q</mi><mn>3</mn></msub><msub><mi>q</mi><mn>2</mn></msub></mrow></msub><mo>×</mo><msub><mi>J</mi><mrow><msub><mi>q</mi><mn>1</mn></msub><msub><mi>q</mi><mn>4</mn></msub></mrow></msub><mo stretchy="false">|</mo><msub><mi>M</mi><mn>1</mn></msub><mo stretchy="false">⟩</mo></math>, can give indeed a significant contribution to the matrix element. Including these connected diagrams is but the first step toward a full nonperturbative computation of the long-range QCD effects in these operators, that should be performed using lattice field theory techniques. However, connected diagrams represent the leading order in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mo>/</mo><msub><mi>N</mi><mi>c</mi></msub></math> expansion of the QCD nonperturbative effects and thus our work can be understood as a realistic, first approximation to a complete calculation of the long-range part of the matrix elements.

Andrea Donini

Marcela González

Martin Hirsch

Nicolás A. Neill

Leading large <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>c</mi></msub></math> contributions to lepton number violating meson decays

We systematically investigate the dibaryons <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 stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup><msubsup><mi mathvariant="normal">Ξ</mi><mrow><mi>c</mi><mi>c</mi></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup></math> (di-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</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 mathvariant="normal">Ξ</mi><mrow><mi>b</mi><mi>b</mi></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup><msubsup><mi mathvariant="normal">Ξ</mi><mrow><mi>b</mi><mi>b</mi></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup></math> (di-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mrow><mi>b</mi><mi>b</mi></mrow></msub></math>), with various isospin-spin configurations <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>I</mi><mo stretchy="false">(</mo><msup><mi>J</mi><mi>P</mi></msup><mo stretchy="false">)</mo></math> in a nonrelativistic quark model. For the di-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub></math> system, only the single channels <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub><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">Ξ</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>*</mo></msubsup><msubsup><mi mathvariant="normal">Ξ</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>*</mo></msubsup></math> with <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> are capable of forming deuteronlike bound states, with the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>σ</mi></math> meson exchange playing a decisive role. Those states have binding energies of approximately <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>−</mo><mn>1.5</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>−</mo><mn>3.3</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math> and sizes of 2.37 fm and 1.87 fm, respectively. The coupled channel effect in the di-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub></math> system with <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> enhances the attraction. As a result, this di-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub></math> system can establish a deuteronlike configuration, with the binding energy of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>−</mo><mn>7.5</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math> relative to the threshold <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub><msub><mi mathvariant="normal">Ξ</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub></math> and the size of approximately 1.40 fm. For the di-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mrow><mi>b</mi><mi>b</mi></mrow></msub></math> system, the single channels with <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>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>0</mn><mo stretchy="false">(</mo><msup><mn>2</mn><mo>+</mo></msup><mo stretchy="false">)</mo></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>0</mn><mo stretchy="false">(</mo><msup><mn>3</mn><mo>+</mo></msup><mo stretchy="false">)</mo></math> can give rise to deuteronlike bound states with binding energies ranging from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>−</mo><mn>6.1</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math> to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>−</mo><mn>14.3</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>. Additionally, the di-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mrow><mi>b</mi><mi>b</mi></mrow></msub></math> system with <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> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mo stretchy="false">(</mo><msup><mn>2</mn><mo>+</mo></msup><mo stretchy="false">)</mo></math> can also establish deuteronlike bound states with binding energies of around <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>−</mo><mn>0.5</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>. When considering the coupled channel effect in the di-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mrow><mi>b</mi><mi>b</mi></mrow></msub></math> system with <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>, a compact hexaquark state is formed, exhibiting a binding energy of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>−</mo><mn>21.2</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math> relative to the threshold <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mrow><mi>b</mi><mi>b</mi></mrow></msub><msub><mi mathvariant="normal">Ξ</mi><mrow><mi>b</mi><mi>b</mi></mrow></msub></math> and a size of 0.53 fm. In this state, the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi></math> meson exchange provides a very powerful attractive force. The meson exchange interactions in the quark model is dispensable in the di-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mrow><mi>b</mi><mi>b</mi></mrow></msub></math> bound states, except for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mrow><mi>b</mi><mi>b</mi></mrow><mo>*</mo></msubsup><msubsup><mi mathvariant="normal">Ξ</mi><mrow><mi>b</mi><mi>b</mi></mrow><mo>*</mo></msubsup></math> with <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>.

An-Su Lu

Mao-Jun Yan

Chun-Sheng An

Cheng-Rong Deng

Heavy dibaryons <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 stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup><msubsup><mi mathvariant="normal">Ξ</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 mathvariant="normal">Ξ</mi><mrow><mi>b</mi><mi>b</mi></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup><msubsup><mi mathvariant="normal">Ξ</mi><mrow><mi>b</mi><mi>b</mi></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup></math>

We present the nonrelativistic QCD (NRQCD) calculations at the next-to-leading order (NLO) of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>α</mi><mi>s</mi></msub></math> for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>c</mi><mo>*</mo></msubsup><mo stretchy="false">→</mo><msub><mi>η</mi><mi>c</mi></msub></math> vector, axial-vector, tensor, and axial-tensor form factors, and obtain complete analytical expressions for the form factors, along with their asymptotic forms in the hierarchical heavy quark limit. Our results show that the NLO corrections are both sizable and well behaved in the low squared transfer momentum <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><msup><mi>q</mi><mn>2</mn></msup><mo stretchy="false">)</mo></math> region. Using the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>NRQCD</mi><mo>+</mo><mtext>lattice</mtext></mrow><mo>+</mo><mi>z</mi></math>-series method, we further provide theoretical predictions for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>c</mi><mo>*</mo></msubsup><mo stretchy="false">→</mo><msub><mi>η</mi><mi>c</mi></msub></math> form factors across the full physical <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>q</mi><mn>2</mn></msup></math> range. Based on these predicted form factors, we finally compute the decay widths and branching fractions for the semileptonic decays <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>c</mi><mo>*</mo></msubsup><mo stretchy="false">→</mo><msub><mi>η</mi><mi>c</mi></msub><mo>+</mo><mi>l</mi><msub><mi>ν</mi><mi>l</mi></msub></math>.

Wei Tao

Ya-Hui Zhao

Li-Ting Wang

Qin Chang

Zhen-Jun Xiao

Form factors for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>c</mi><mo>*</mo></msubsup><mo stretchy="false">→</mo><msub><mi>η</mi><mi>c</mi></msub><mo>+</mo><mi>l</mi><msub><mi>ν</mi><mi>l</mi></msub></math> at NLO in QCD

In this study, we investigate the possibility of enhancing the di-jet resonance searches by tagging the final state radiation (FSR) jet using an event-level deep neural network. It is found that solely relying on the 4-momenta of the leading three jets allows the algorithm to achieve good discriminating power that can identify the hardest FSR jet in the signal while rejecting other soft jets. Once the invariant mass is corrected with the tagged FSR jet, the mass resolution of the signal is greatly enhanced, and the sensitivity of the search is also improved by more than 10%. By crafting the input variables carefully, the algorithm introduces minimal mass sculpting for the background, and its applicability extends to a broad mass range. This work proves that FSR jet tagging can potentially enhance di-jet resonance searches, suiting various stages of the physics programmes at the Large Hadron Collider (LHC) and High-Luminosity LHC (HL-LHC).

China

Bingxuan Liu

Yuxuan Shen

Yuanshunzi Sui

Enhancing di-jet resonance searches via a final-state radiation jet tagging algorithm * Bingxuan Liu is supported by Shenzhen Campus of the Sun Yat-sen University under project 74140-12255011, and by the Young Scientists Fund (C Class) of the National Natural Science Foundation of China (12405122). Both Yuxuan Shen and Yuanshunzi Sui are supported by College Students’ Innovative Entrepreneurial Training Plan Program

We analyze the latest cosmic microwave background (CMB) constraints on the scalar spectral index <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>n</mi><mi>s</mi></msub></math> and tensor-to-scalar ratio <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>r</mi></math> from Planck 2018, BICEP/Keck 2018, the Atacama Cosmology Telescope Data Release 6 (ACT DR6), and the South Pole Telescope (SPT-3G) data, focusing on their implications for attractor models of inflation. We compare systematically observational bounds with theoretical predictions for both E-model (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>α</mi></math>-Starobinsky) and T-model potentials. The observational constraints accommodate E-models with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>α</mi><mo>≲</mo><mn>25</mn></math>, with the canonical Starobinsky model (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>α</mi><mo>=</mo><mn>1</mn></math>) predicting <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>n</mi><mi>s</mi></msub><mo>=</mo><mn>0.958</mn><mi>–</mi><mn>0.963</mn></math> for reheating temperatures between <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>100</mn><mo>−</mo><msup><mn>10</mn><mn>10</mn></msup><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>, in good agreement with Planck 2018 data and within the 95% CL region determined by the Planck-ACT-SPT combination, but below the 95% confidence region of the Planck-ACT-DESI combination. Higher reheating temperatures from near-instantaneous reheating improve the compatibility. T-models predict slightly lower <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>n</mi><mi>s</mi></msub></math> values (0.956–0.961), in some tension with Planck 2018 data, and we find an upper limit of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>α</mi><mo>≲</mo><mn>11</mn></math> in these models. We extend our analysis to generalized <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>α</mi></math>-attractors with monomial potentials <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>V</mi><mo stretchy="false">(</mo><mi>φ</mi><mo stretchy="false">)</mo><mo>∝</mo><msup><mi>φ</mi><mi>k</mi></msup></math> near the minimum, demonstrating that models with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>k</mi><mo>≥</mo><mn>6</mn></math> naturally predict <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>n</mi><mi>s</mi></msub><mo>≃</mo><mn>0.965</mn><mi>–</mi><mn>0.968</mn></math> for typical number of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>e</mi></math>-folds, in better agreement with the ACT DR6 data. We also consider deformed E- and T-models, which allow significantly higher values of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>n</mi><mi>s</mi></msub></math> for low values of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>α</mi><mo>≃</mo><mn>1</mn></math>.

CERN

John Ellis

Mexico

Marcos A.G. Garcia

United States

Keith A. Olive

Sarunas Verner

Constraints on attractor models of inflation and reheating from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>P</mi><mi>l</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>k</mi></math>, BICEP/Keck, ACT DR6, and SPT-3G data

In this work, we perform a comprehensive investigation of the production of high-spin <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ω</mi><mi>J</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ρ</mi><mi>J</mi></msub></math> mesons (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>=</mo><mn>2</mn></math>, 3, 4, 5) in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>π</mi><mo>−</mo></msup><mi>p</mi></math> reactions using an effective Lagrangian approach. By constructing the relevant <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>t</mi></math>-channel processes and calibrating the model with a single adjustable parameter fitted to existing data, we successfully reproduce the measured total and differential cross sections for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>=</mo><mn>3</mn></math> states <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ω</mi><mn>3</mn></msub><mo stretchy="false">(</mo><mn>1670</mn><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ρ</mi><mn>3</mn></msub><mo stretchy="false">(</mo><mn>1690</mn><mo stretchy="false">)</mo></math>. Within the same framework, we predict the production cross sections for their lower- and higher-spin partners; <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ω</mi><mn>2</mn></msub><mo stretchy="false">(</mo><mn>1975</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ρ</mi><mn>2</mn></msub><mo stretchy="false">(</mo><mn>1940</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ω</mi><mn>4</mn></msub><mo stretchy="false">(</mo><mn>2250</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ρ</mi><mn>4</mn></msub><mo stretchy="false">(</mo><mn>2230</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ω</mi><mn>5</mn></msub><mo stretchy="false">(</mo><mn>2350</mn><mo stretchy="false">)</mo></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ρ</mi><mn>5</mn></msub><mo stretchy="false">(</mo><mn>2350</mn><mo stretchy="false">)</mo></math>. Our results show that these states exhibit measurable cross sections with characteristically forward-peaked angular distributions, underscoring their strong potential for observation in future <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>p</mi></math> meson-beam experiments.

Ting-Yan Li

Zi-Yue Bai

Xiang Liu

Production of high-spin <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ω</mi><mi>J</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ρ</mi><mi>J</mi></msub></math> (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>J</mi><mo>=</mo><mn>2</mn></mrow></math>, 3, 4, 5) mesons in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>π</mi><mo>−</mo></msup><mi>p</mi></math> reactions

Based on a sample of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><mn>10087</mn><mo>±</mo><mn>44</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup><mtext> </mtext><mtext> </mtext><mi>J</mi><mo>/</mo><mi>ψ</mi></math> events collected with the BESIII detector, a partial-wave analysis of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi><mo stretchy="false">→</mo><mi mathvariant="normal">Λ</mi><msup><mover accent="true"><mi mathvariant="normal">Σ</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup><mi>η</mi><mo>+</mo><mi mathvariant="normal">c</mi><mo>.</mo><mi mathvariant="normal">c</mi><mo>.</mo></math> is performed for the first time. The dominant contributions are found to be excited <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Λ</mi></math> states with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>+</mo></msup></math> in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>η</mi><mi mathvariant="normal">Λ</mi></math> mass spectra. The measured masses and widths are <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>M</mi><mo>=</mo><mn>1668.8</mn><mo>±</mo><mn>3.1</mn><mo>±</mo><mn>21.2</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi><mo>/</mo><msup><mi>c</mi><mn>2</mn></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Γ</mi><mo>=</mo><mn>52.7</mn><mo>±</mo><mn>4.2</mn><mo>±</mo><mn>17.8</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math> for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Λ</mi><mo stretchy="false">(</mo><mn>1670</mn><mo stretchy="false">)</mo></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>M</mi><mo>=</mo><mn>1881.5</mn><mo>±</mo><mn>16.5</mn><mo>±</mo><mn>20.3</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi><mo>/</mo><msup><mi>c</mi><mn>2</mn></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Γ</mi><mo>=</mo><mn>82.4</mn><mo>±</mo><mn>18.2</mn><mo>±</mo><mn>8.9</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math> for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Λ</mi><mo stretchy="false">(</mo><mn>1810</mn><mo stretchy="false">)</mo></math>, respectively. The branching fraction is determined to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mo stretchy="false">→</mo><mi mathvariant="normal">Λ</mi><msup><mover accent="true"><mi mathvariant="normal">Σ</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup><mi>η</mi><mo>+</mo><mi mathvariant="normal">c</mi><mo>.</mo><mi mathvariant="normal">c</mi><mo>.</mo><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mn>3.44</mn><mo>±</mo><mn>0.11</mn><mo>±</mo><mn>0.13</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>5</mn></mrow></msup></math>. The first uncertainties are statistical and the second systematic.

M. Ablikim

Russia

M.N. Achasov

Sweden

P. Adlarson

X.C. Ai

Italy

C.S. Akondi

Germany

R. Aliberti

A. Amoroso

Q. An

Y.H. An

Y. Bai

JINR

O. Bakina

Y. Ban

H.R. Bao

X.L. Bao

Poland

V. Batozskaya

Mongolia

K. Begzsuren

N. Berger

M. Berlowski

M.B. Bertani

D. Bettoni

F. Bianchi

E. Bianco

A. Bortone

I. Boyko

R.A. Briere

A. Brueggemann

H. Cai

M.H. Cai

X. Cai

A. Calcaterra

G.F. Cao

N. Cao

Türkiye

S.A. Cetin

X.Y. Chai

J.F. Chang

T.T. Chang

G.R. Che

Y.Z. Che

C.H. Chen

Chao Chen

G. Chen

H.S. Chen

H.Y. Chen

M.L. Chen

S.J. Chen

S.M. Chen

T. Chen

W. Chen

X.R. Chen

X.T. Chen

X.Y. Chen

Y.B. Chen

Y.Q. Chen

Z.K. Chen

J. Cheng

L.N. Cheng

South Korea

S.K. Choi

X. Chu

G. Cibinetto

F. Cossio

United Kingdom

J. Cottee-Meldrum

H.L. Dai

J.P. Dai

X.C. Dai

A. Dbeyssi

R.E. de Boer

D. Dedovich

C.Q. Deng

Z.Y. Deng

A. Denig

I. Denisenko

M. Destefanis

F. De Mori

X.X. Ding

Y. Ding

Y.X. Ding

J. Dong

L.Y. Dong

M.Y. Dong

X. Dong

M.C. Du

S.X. Du

X.L. Du

Y.Q. Du

Y.Y. Duan

Z.H. Duan

P. Egorov

G.F. Fan

J.J. Fan

Y.H. Fan

J. Fang

S.S. Fang

W.X. Fang

Y.Q. Fang

L. Fava

F. Feldbauer

G. Felici

C.Q. Feng

Amplitude analysis and branching fraction measurement of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi><mo stretchy="false">→</mo><mi mathvariant="normal">Λ</mi><msup><mover accent="true"><mi mathvariant="normal">Σ</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup><mi>η</mi><mo>+</mo><mi mathvariant="normal">c</mi><mo>.</mo><mi mathvariant="normal">c</mi><mo>.</mo></math>

In this work, we investigate the productions of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mn>2910</mn><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mn>2940</mn><mo stretchy="false">)</mo></math> in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>p</mi><mover accent="true"><mrow><mi>p</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><mo stretchy="false">→</mo><msub><mrow><mover accent="true"><mrow><mi mathvariant="normal">Λ</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mi>c</mi></mrow></msub><msup><mrow><mi>D</mi></mrow><mrow><mn>0</mn></mrow></msup><mi>p</mi></mrow></math> process by utilizing an effective Lagrangian approach, where both <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mn>2910</mn><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mn>2940</mn><mo stretchy="false">)</mo></math> are considered as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mo>*</mo></msup><mi>N</mi></math> molecular states with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></math>, respectively. In addition to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>t</mi></math>-channel <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mo>*</mo></msup></math> exchanges, the contribution from light-meson exchange is also considered. At <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>10</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>, our estimations indicate that the total cross sections for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi><mover accent="true"><mi>p</mi><mo stretchy="false">¯</mo></mover><mo stretchy="false">→</mo><msub><mover accent="true"><mi mathvariant="normal">Λ</mi><mo stretchy="false">¯</mo></mover><mi>c</mi></msub><msup><mi>D</mi><mn>0</mn></msup><mi>p</mi></math> are <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><msubsup><mn>130.7</mn><mrow><mo>−</mo><mn>103.9</mn></mrow><mrow><mo>+</mo><mn>397.1</mn></mrow></msubsup><mo stretchy="false">)</mo><mtext> </mtext><mtext> </mtext><mi>nb</mi></math>, where the central value is estimated with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>r</mi></msub><mo>=</mo><mn>1.1</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>, and the uncertainties are resulted from the variation of parameter <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>r</mi></msub></math> from 1.0 to 1.2 GeV. Our results indicate that the light-meson exchange diagrams are very important, which provide a very large, smooth background. Moreover, the estimations of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mn>0</mn></msup><mi>p</mi></math> invariant mass spectrum reveal that the peak structure between 2.9 and 3.0 GeV primarily originates from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mn>2910</mn><mo stretchy="false">)</mo></math>, while the signal of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mn>2940</mn><mo stretchy="false">)</mo></math> is about 1 order smaller than that of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mn>2910</mn><mo stretchy="false">)</mo></math>. Furthermore, the resulting Dalitz plot is estimated with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>8</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>. It is expected that our estimations in the present work can be tested by future experiments at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mover accent="true"><mrow><mi mathvariant="normal">P</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><mi>ANDA</mi></mrow></math>.

Quan-Yun Guo

Dian-Yong Chen

<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mn>2910</mn><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mn>2940</mn><mo stretchy="false">)</mo></math> productions in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>p</mi><mover accent="true"><mrow><mi>p</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow></math> annihilation

Dark matter (DM) and the baryon asymmetry of the Universe (BAU) are among the most compelling indications of physics beyond the Standard Model. We revisit the inelastic Higgs-portal complex singlet, a minimal framework in which a complex scalar splits into two nearly degenerate real states, with an off-diagonal Higgs-portal interaction that drives coannihilation to set the relic density, while the elastic DM-Higgs coupling can be tuned small enough to evade direct-detection limits. This setup naturally supports a strong first-order electroweak phase transition (SFOEWPT) and can account for the longstanding Galactic Center gamma-ray excess (GCE) via present-day DM annihilation into Higgs pairs. In this work, we show that the same framework, extended by a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>Z</mi><mn>2</mn></msub></math>-symmetric dimension-6 <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>C</mi><mi>P</mi></mrow></math>-violating top Yukawa operator, can also generate the BAU via the electroweak baryogenesis (EWBG) mechanism. The cosmological history involves a two-step electroweak phase transition: first, the singlet fields acquire nonzero vacuum expectation values (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mrow><mi>v</mi><mi>e</mi><mi>v</mi><mi>s</mi></mrow></mrow></math>); then a strongly first-order transition occurs in which the Higgs develops its nonzero <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mrow><mi>v</mi><mi>e</mi><mi>v</mi></mrow></mrow></math> while the singlet <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mrow><mi>v</mi><mi>e</mi><mi>v</mi><mi>s</mi></mrow></mrow></math> vanish. During this second step, both fields remain nonzero only within the advancing bubble wall, generating wall-localized <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violation that biases sphaleron transitions and enables EWBG. After the phase transition, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>Z</mi><mn>2</mn></msub></math> symmetries are restored: the lightest singlet state becomes a stable DM candidate, while the vanishing singlet <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mrow><mi>v</mi><mi>e</mi><mi>v</mi><mi>s</mi></mrow></mrow></math> allow the model to naturally satisfy the stringent constraints on <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violation. We delineate the SFOEWPT-favored parameter space, identifying the criteria for the two-step phase transition region that simultaneously yields the observed BAU and relic density, explains the GCE, and predicts gravitational wave spectra accessible to next-generation space-based detectors.

Subhojit Roy

Dark matter and electroweak baryogenesis with spontaneous <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>C</mi><mi>P</mi></mrow></math> violation in the early Universe

We perform an improved perturbative QCD study of the decays <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><msub><mi>η</mi><mi>c</mi></msub><msup><mi>L</mi><mo>+</mo></msup></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>L</mi></math> denotes the light ground-state pseudoscalar, vector mesons and the corresponding <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi></math>-wave scalar, axial-vector, and tensor ones, and predict their branching ratios (BRs) associated with relative ratios at leading order in the strong coupling <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>α</mi><mi>s</mi></msub></math>. Our results <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>BR</mi></mrow><mo stretchy="false">(</mo><msubsup><mi>B</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><msub><mi>η</mi><mi>c</mi></msub><msup><mi>π</mi><mo>+</mo></msup><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mn>2.0</mn><msubsup><mn>3</mn><mrow><mo>−</mo><mn>0.41</mn></mrow><mrow><mo>+</mo><mn>0.53</mn></mrow></msubsup><mo stretchy="false">)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>BR</mi></mrow><mo stretchy="false">(</mo><msubsup><mi>B</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><msub><mi>η</mi><mi>c</mi></msub><msup><mi>π</mi><mo>+</mo></msup><mo stretchy="false">)</mo><mo>/</mo><mrow><mi>BR</mi></mrow><mo stretchy="false">(</mo><msubsup><mi>B</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><msup><mi>π</mi><mo>+</mo></msup><mo stretchy="false">)</mo><mo>=</mo><mn>1.7</mn><msubsup><mn>4</mn><mrow><mo>−</mo><mn>0.50</mn></mrow><mrow><mo>+</mo><mn>0.66</mn></mrow></msubsup></math> are consistent with several available predictions in different approaches within uncertainties. Inputting the measured <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>η</mi><mi>c</mi></msub><mo stretchy="false">→</mo><mi>p</mi><mover accent="true"><mi>p</mi><mo stretchy="false">¯</mo></mover></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>η</mi><mi>c</mi></msub><mo stretchy="false">→</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><mo stretchy="false">(</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><mo>,</mo><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup><mo>,</mo><mi>p</mi><mover accent="true"><mi>p</mi><mo stretchy="false">¯</mo></mover><mo stretchy="false">)</mo></math> BRs with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi></math> here being a proton, we derive the multibody <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><msub><mi>η</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mi>π</mi><mo>,</mo><mi>ρ</mi><msup><mo stretchy="false">)</mo><mo>+</mo></msup></math> BRs through secondary decay chains via resonance <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>η</mi><mi>c</mi></msub></math> under the narrow-width approximation, which might facilitate the (near-)future tests of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mi>c</mi></msub><mo stretchy="false">→</mo><msub><mi>η</mi><mi>c</mi></msub></math> decays. Under the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>q</mi><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover></math> assignment for light scalars, different to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mi>c</mi></msub></math> decaying into <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi></math> plus a scalar meson and other <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><msub><mi>η</mi><mi>c</mi></msub><msup><mi>L</mi><mo>+</mo></msup></math> modes, surprisingly small <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Δ</mi><mi>S</mi><mo>=</mo><mn>0</mn></math> BRs around <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>7</mn></mrow></msup><mo>−</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>9</mn></mrow></msup><mo stretchy="false">)</mo></math> and highly large ratios near <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><msup><mn>10</mn><mn>2</mn></msup><mo stretchy="false">)</mo></math> between the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Δ</mi><mi>S</mi><mo>=</mo><mn>1</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Δ</mi><mi>S</mi><mo>=</mo><mn>0</mn></math> BRs are found in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mi>c</mi></msub></math> decays to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>η</mi><mi>c</mi></msub></math> plus light scalars, with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi></math> being strange number. Many large BRs and interesting ratios presented in this work could be tested by the Large Hadron Collider experiments, which would help us to examine the reliability of this improved perturbative QCD formalism for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mi>c</mi></msub></math>-meson decays and further understand the QCD dynamics in the considered decay modes as well as in the related hadrons.

Wen-Jing Zhang

Xin Liu

Improved perturbative QCD study of the decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><msub><mi>η</mi><mi>c</mi></msub><msup><mi>L</mi><mo>+</mo></msup></math>