The Schwinger effect, a non-perturbative mechanism for particle production in strong fields, plays a crucial role in understanding quantum vacuum decay and high-energy phenomena, including heavy-ion collisions (HIC). Although holographic quantum chromodynamics (QCD) models have been widely used to study this effect, most treatments assume isotropy or consider only a single type of anisotropy, neglecting the interplay between spatial and magnetic anisotropies that arise in realistic HIC scenarios. A unified framework accounting for both anisotropies is needed to accurately model particle production. We investigate the Schwinger effect in a twice anisotropic holographic QCD model incorporating both spatial and magnetic anisotropies. Using the anti-de Sitter/conformal field theory correspondence, we compute the total potential of a particle-antiparticle pair to quantify how these anisotropies influence pair production. Our results show that the magnetic field (parameterized by $c_B$ and $q_3$ ) enhances the Schwinger effect by lowering and narrowing the potential barrier, while increasing spatial anisotropy (controlled by $\nu$ ) suppresses the process by raising and widening the barrier. These findings demonstrate that magnetic and spatial anisotropies exert competing effects on particle production, emphasizing the necessity of treating both concurrently in holographic models. This work advances the theoretical description of the Schwinger effect in anisotropic environments, with implications for understanding non-equilibrium dynamics in HIC and other strongly coupled systems.

China

Wen-Bin Chang

Defu Hou

Schwinger effect in a twice anisotropic holographic model * Defu Hou's research is supported in part by the National Key Research and Development Program of China (2022YFA1604900). Additionally, Defu Hou receives partial support from the National Natural Science Foundation of China (NSFC) (12435009, 12275104). Wen-Bin Chang is supported by the Ph.D. Research Startup Project at Hubei Minzu University (RZ2500000857)

We show that in an elliptic function based formulation for fields with large amplitudes, the rolling down of solitons towards the degenerate vacua can be described as transitions through local meta-stable potentials; the kink-like solitons constructed locally around the maxima of the potential will roll down into the vacua without changing their profiles and their energies, but amplifying their amplitudes and their topological charges. Furthermore, the cusp-like solitons trapped at vacua will admit a nonlinear decomposition in terms of fundamental solitons with different profiles, energies, amplitudes, and topological charges; a scale-probe is proposed in order to reveal the different scales for those vacuum fundamental solitons. The possibility for a vacuum-vacuum tunneling for solitons is addressed.

Mexico

R. Cartas-Fuentevilla

A. Herrera-Aguilar

M. Aguilar-Gonzalez

P. Fierro-Rojas

M. Roque-Vargas

D. Condado-Hernandez

J. Calvario-Acocal

U. Guerra-Franklin

Spontaneous symmetry breaking for solitons and local meta-stability: an elliptic functions based formulation

$\textit{U}$-spin symmetry, which reflects the symmetry between the down-type $\textit{d}$ and $\textit{s}$ quarks, is a powerful tool for analyzing heavy hadron weak decays. Motivated by recent experimental achievements in the bottom baryon sector, we study the $\textit{U}$-spin sum rules for bottom baryon decays. The effective Hamiltonian for $\textit{b}$ quark decay is zero under the $\textit{U}$-spin lowering operators $$U_-^n$$ , permitting us to derive $\textit{U}$-spin sum rules involving only the $$b\rightarrow d$$ transition or $$b\rightarrow s$$ transition. Moreover, a new operator, $$S_b=U_++rU_3-r^2U_-$$ , is proposed to generate $\textit{U}$-spin sum rules involving both the $$b\rightarrow d$$ and $$b\rightarrow s$$ transitions. The proof that the effective Hamiltonian for $\textit{b}$ quark decay is zero under $$U_-^n$$ and $$S_b$$ is presented. The master formulas for generating $\textit{U}$-spin sum rules for the two-body decays of bottom baryons involving $$b\rightarrow c\overline{c}d/s$$ , $$b\rightarrow c\overline{u}d/s$$ , $$b\rightarrow u\overline{u}d/s$$ , and $$b\rightarrow u\overline{c}d/s$$ transitions are derived. Numerous $\textit{U}$-spin sum rules for the two-body decays of bottom baryons are obtained through these master formulas, which provide hints for new decay modes and enable the extraction of dynamical information. As a phenomenological analysis, some branching fractions are predicted according to $\textit{U}$-spin symmetry. Several rate and decay parameter sum rules beyond the $\textit{U}$-spin limit are found, providing a more precise test of flavor symmetry in the bottom baryon sector. Moreover, some $\textit{CP}$ asymmetry relations for $\textit{U}$-spin conjugate pairs in heavy baryon decays are derived for the first time by taking partial-wave amplitudes into account.

Si-Jia Wen

Wei-Chen Fu

Di Wang

$\textit{U}$-spin sum rules for two-body decays of bottom baryons

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

Neutral triple gauge couplings (nTGCs) first arise from the dimension-8 operators of the Standard Model effective field theory (SMEFT), rather than the dimension-4 SM Lagrangian and dimension-6 SMEFT operators, opening up a unique window for probing new physics at the dimension-8 level. In this work, we formulate the nTGC form factors of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi><mi>Z</mi><msup><mi>V</mi><mo>*</mo></msup></math> (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>V</mi><mo>=</mo><mi>Z</mi></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>γ</mi></mrow></math>) that are compatible with the spontaneous breaking of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>SU</mi><mo stretchy="false">(</mo><mn>2</mn><mo stretchy="false">)</mo><mo stretchy="false">⊗</mo><mi mathvariant="normal">U</mi><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></mrow></math> electroweak gauge symmetry and consistently match the dimension-8 nTGC operators in the broken phase. We study the sensitivities for probing both the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi><mi>Z</mi><msup><mi>V</mi><mo>*</mo></msup></math> form factors and the corresponding new physics scales through <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi><mi>Z</mi></math> production (with visible/invisible fermionic <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi></math> decays) at high energy <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math> colliders including CEPC, FCC-ee, LCF, ILC, and CLIC. In particular, we identify the dimension-8 operator that contributes to the pure triple <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi></math> boson coupling <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi><mi>Z</mi><msup><mi>Z</mi><mo>*</mo></msup></math> alone, but not the mixed <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi><mi>Z</mi><msup><mi>γ</mi><mo>*</mo></msup></math> coupling. We further study the correlations between probes of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi><mi>Z</mi><msup><mi>Z</mi><mo>*</mo></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi><mi>Z</mi><msup><mi>γ</mi><mo>*</mo></msup></math> couplings. Using machine learning, we show that angular distributions of the final-state fermions can play key roles in suppressing the SM backgrounds. The sensitivities can be further improved by using polarized <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>∓</mo></msup></math> beams, and we find that the optimal sensitivity bounds on the nTGC correlations are given by the mixed setting including both the unpolarized operation and the follow-up polarized operation. We demonstrate that machine learning is advantageous for handling the 4-body final states from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi><mi>Z</mi></math> decays and improves significantly the sensitivity reaches of probes of nTGCs in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math> collisions. We find that nTGC new physics scales can be probed up to the multi-TeV scale at the proposed <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math> colliders.

John Ellis

Hong-Jian He

Rui-Qing Xiao

Shi-Ping Zeng

Probing neutral triple gauge couplings via <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi><mi>Z</mi></math> production at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math> colliders with machine learning

We set the scale of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>SU</mi><mo stretchy="false">(</mo><mi>N</mi><mo stretchy="false">)</mo></mrow></math> Yang-Mills theories for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi><mo>=</mo><mn>3</mn></math>, 5, 8 and in the large-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math> limit via gradient flow, as a first step towards the computation of the large-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math> <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Λ</mi></math>-parameter using step scaling. We adopt twisted boundary conditions to achieve large-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math> volume reduction and the Parallel Tempering on Boundary Conditions algorithm to tame topological freezing. This setup allows accurate determinations of the gradient-flow scales down to lattice spacings as fine as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>∼</mo><mn>0.025</mn><mtext> </mtext><mtext> </mtext><mi>fm</mi></math> for all the explored values of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math>, a regime that has never been reached with ergodic algorithms. Moreover, we are able to precisely estimate the finite-size systematics related to topological freezing, and to show the suppression of finite-volume effects expected by virtue of large-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math> twisted volume reduction.

Claudio Bonanno

Jorge Luis Dasilva Golán

Margarita García Pérez

Massimo D’Elia

Andrea Giorgieri

Scale setting of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>SU</mi><mo stretchy="false">(</mo><mi>N</mi><mo stretchy="false">)</mo></mrow></math> Yang–Mills theory, topology and large-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math> volume independence

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>

A search for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>K</mi><mrow><mi mathvariant="normal">S</mi><mo stretchy="false">(</mo><mi mathvariant="normal">L</mi><mo stretchy="false">)</mo></mrow><mn>0</mn></msubsup><mo stretchy="false">→</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><msup><mi>μ</mi><mo>+</mo></msup><msup><mi>μ</mi><mo>−</mo></msup></math> decays is performed using proton-proton collision data collected by the LHCb experiment at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>5.4</mn><mtext> </mtext><mtext> </mtext><msup><mi>fb</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math>. No <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>K</mi><mrow><mi mathvariant="normal">S</mi><mo stretchy="false">(</mo><mi mathvariant="normal">L</mi><mo stretchy="false">)</mo></mrow><mn>0</mn></msubsup><mo stretchy="false">→</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><msup><mi>μ</mi><mo>+</mo></msup><msup><mi>μ</mi><mo>−</mo></msup></math> signals are found and upper limits are set for the first time on the branching fractions <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msubsup><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">S</mi></mrow><mrow><mn>0</mn></mrow></msubsup><mo stretchy="false">→</mo><mrow><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup><mrow><msup><mrow><mi>μ</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>μ</mi></mrow><mrow><mo>−</mo></mrow></msup><mo stretchy="false">)</mo></mrow></mrow><mo>&lt;</mo><mn>1.4</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>9</mn></mrow></msup></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msubsup><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">L</mi></mrow><mrow><mn>0</mn></mrow></msubsup><mo stretchy="false">→</mo><mrow><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup><mrow><msup><mrow><mi>μ</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>μ</mi></mrow><mrow><mo>−</mo></mrow></msup><mo stretchy="false">)</mo></mrow></mrow><mo>&lt;</mo><mn>6.6</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>7</mn></mrow></msup></mrow></math>, at the 90% confidence level.

R. Aaij

A.S.W. Abdelmotteleb

C. Abellan Beteta

F. Abudinén

T. Ackernley

A.A. Adefisoye

B. Adeva

M. Adinolfi

P. Adlarson

C. Agapopoulou

C.A. Aidala

Z. Ajaltouni

S. Akar

K. Akiba

P. Albicocco

J. Albrecht

R. Aleksiejunas

F. Alessio

P. Alvarez Cartelle

R. Amalric

S. Amato

J.L. Amey

Y. Amhis

L. An

L. Anderlini

M. Andersson

P. Andreola

M. Andreotti

S. Andres Estrada

A. Anelli

D. Ao

C. Arata

F. Archilli

Z. Areg

M. Argenton

S. Arguedas Cuendis

L. Arnone

A. Artamonov

M. Artuso

E. Aslanides

R. Ataíde Da Silva

M. Atzeni

B. Audurier

J.A. Authier

D. Bacher

I. Bachiller Perea

S. Bachmann

M. Bachmayer

J.J. Back

P. Baladron Rodriguez

V. Balagura

A. Balboni

W. Baldini

Z. Baldwin

L. Balzani

H. Bao

J. Baptista de Souza Leite

C. Barbero Pretel

M. Barbetti

I.R. Barbosa

R.J. Barlow

M. Barnyakov

S. Barsuk

W. Barter

J. Bartz

S. Bashir

B. Batsukh

P.B. Battista

A. Bay

A. Beck

M. Becker

F. Bedeschi

I.B. Bediaga

N.A. Behling

S. Belin

A. Bellavista

K. Belous

I. Belov

I. Belyaev

G. Benane

G. Bencivenni

E. Ben-Haim

A. Berezhnoy

R. Bernet

S. Bernet Andres

A. Bertolin

F. Betti

J. Bex

O. Bezshyyko

S. Bhattacharya

J. Bhom

M.S. Bieker

N.V. Biesuz

A. Biolchini

M. Birch

F.C.R. Bishop

A. Bitadze

A. Bizzeti

T. Blake

F. Blanc

Search for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>K</mi></mrow><mrow><mrow><mi mathvariant="normal">S</mi><mo stretchy="false">(</mo><mi mathvariant="normal">L</mi><mo stretchy="false">)</mo></mrow></mrow><mn>0</mn></msubsup><mo stretchy="false">→</mo><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mi>μ</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>μ</mi></mrow><mrow><mo>−</mo></mrow></msup></mrow></math> decays at LHCb

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

The associated production of a photon and a top-antitop quark pair $$ \left(t\overline{t}\gamma \right) $$ is important for measuring the top-quark charge and probing the top-photon interaction, and it requires improved theoretical predictions. We focus on the calculation of two-loop amplitudes for $$ t\overline{t}\gamma $$ production at hadron colliders. The infrared singularities with full top-quark mass dependence are derived from universal anomalous dimensions combined with one-loop massive amplitudes expanded to higher orders in the dimensional regulator $\textit{ϵ}$. The finite remainders are approximated in the high-energy boosted limit using the mass-factorization formula. To validate our approach, we compare approximate one-loop amplitudes up to $$ \mathcal{O}\left({\epsilon}^2\right) $$ , as well as the two-loop infrared poles, against our exact results. The results in this paper serve as an important step toward next-to-next-to-leading order predictions for $$ t\overline{t}\gamma $$ production.

France

Guoxing Wang

Li Yang

Two-loop QCD amplitudes for $$ t\overline{t}\gamma $$ production at hadron colliders