Na Cai | Searcharxiv

arXiv2026

Resolved photoproduction of the $B_c$ meson in electron-proton collisions

We present a systematic study of $B_c$ meson photoproduction at electron--proton colliders within the framework of nonrelativistic QCD (NRQCD) factorization. In addition to the dominant direct channel $\gamma+g\to B_c+X$, we include resolved contributions initiated by $g+g$ and $q+\bar q (q=u,d,s)$ subprocesses. Total cross sections and transverse-momentum distributions are calculated for several collider configurations, including HERA, LHeC, FCC-$ep$, and EIC. The numerical results show that the direct $\gamma+g$ channel provides the leading contribution over the entire kinematic range. However, the resolved $g+g$ channel yields a non-negligible correction, reaching the level of $\mathcal{O}(10\%)$ in the low-$p_T$ region where most events are produced, and it becomes increasingly important at higher collision energies. The $q+\bar q$ channel is found to be numerically insignificant.

hep-ph↗

arXiv2025

Confucius3-Math: A Lightweight High-Performance Reasoning LLM for Chinese K-12 Mathematics Learning

We introduce Confucius3-Math, an open-source large language model with 14B parameters that (1) runs efficiently on a single consumer-grade GPU; (2) achieves SOTA performances on a range of mathematical reasoning tasks, outperforming many models with significantly larger sizes. In particular, as part of our mission to enhancing education and knowledge dissemination with AI, Confucius3-Math is specifically committed to mathematics learning for Chinese K-12 students and educators. Built via post-training with large-scale reinforcement learning (RL), Confucius3-Math aligns with national curriculum and excels at solving main-stream Chinese K-12 mathematical problems with low cost. In this report we share our development recipe, the challenges we encounter and the techniques we develop to overcome them. In particular, we introduce three technical innovations: Targeted Entropy Regularization, Recent Sample Recovery and Policy-Specific Hardness Weighting. These innovations encompass a new entropy regularization, a novel data scheduling policy, and an improved group-relative advantage estimator. Collectively, they significantly stabilize the RL training, improve data efficiency, and boost performance. Our work demonstrates the feasibility of building strong reasoning models in a particular domain at low cost. We open-source our model and code at https://github.com/netease-youdao/Confucius3-Math.

cs.LG↗