We study the inelastic charmonium ( $ J/\psi $ , $ \psi(2S) $ ) and bottomonium ( $ \Upsilon(nS) $ ) photoproduction and fragmentation processes in $\textit{p}$-$\textit{p}$ and $ \rm Pb$ - $\rm Pb$ collisions at LHC energies, where the ultra-incoherent photon emission is included. Using the NRQCD factorization approach, an exact treatment is developed. This approach recovers the Weizsäcker-Williams approximation (WWA) near the $ Q^{2}\sim0 $ region, where the Martin-Ryskin and BCCKL methods are used to avoid double counting. We calculated the $ Q^{2} $ , $\textit{y}$, $\textit{z}$, $ \sqrt{s} $ , and $ p_{T} $ dependent and total cross sections. Inelastic photoproduction and fragmentation were observed to contribute to heavy quarkonium production, particularly at large $ p_{T} $ . In addition, the contribution of the ultra-incoherent photon channel, which increases rapidly with quarkonium mass, is significant and begins to dominate the photoproduction processes for large $ p_{T} $ . We also obtained the complete WWA validity scopes of inelastic heavy quarkonium photoproduction in heavy-ion collisions. The WWA had high accuracy at high energies and for $\rm Pb $ - $\rm Pb $ collisions. However, current photon spectra are derived beyond the WWA scope, and double counting can occur when considering different channels simultaneously.

China

Zhi-Lei Ma

Zhun Lu

Hao Liu

Li Zhang

Inelastic heavy quarkonium photoproduction in $\textit{p}$-$\textit{p}$ and Pb-Pb collisions at LHC energies * Supported in part by the National Natural Science Foundation of China (12305092, 12233006, 12150013), the Xingdian Talent Support Program for Youth Project, and by the Yunnan Fundamental Research Projects (202401AU070206). Hao Liu is supported by the Scientific Research and Innovation Project of Postgraduate Students in the Academic Degree of YunNan University (KC-242410212)

In this study, we investigate a two-component scalar dark matter framework featuring two singlet scalar fields as dark matter candidates. To ensure vacuum stability, we employ copositive criteria for the scalar potential. We analyze four distinct copositive scenarios characterized by specific negative parameter configurations using direct detection constraints. A comprehensive parameter space scan is performed under joint constraints from the observed dark matter relic density and direct detection experiments. The different signs of couplings not only correspond to different copositive criteria but also contribute to different parameter spaces caused by interference. The allowed values of quartic couplings are different for the four different cases; however, they all require the new Higgs to play a dominant role in determining dark matter relic density within the viable parameter space.

Xin-Xin Qi

Hao Sun

Copositive criteria for a two-component dark matter model * Hao Sun is supported by the National Natural Science Foundation of China (12075043 and 12147205). XinXin Qi is supported by the National Natural Science Foundation of China (12447162)

Recent years have seen the development and growth of machine learning in high-energy physics. However, additional effort is required to continue exploring the use of machine learning to its full potential. To simplify the application of the existing algorithms and neural networks and to advance the reproducibility of the analysis, we developed HEP ML LAB ( $ \mathrm{hml}$ ), a Python-based, end-to-end framework for phenomenology studies. It covers the complete workflow from event generation to performance evaluation, and provides a consistent style of use for different approaches. We propose an observable naming convention to streamline the data extraction and conversion processes. In the KERAS style, we provide the traditional cut-and-count and boosted decision trees together with neural networks. We take the $W^+ $ tagging as an example and evaluate all built-in approaches with the metrics of significance and background rejection. With its modular design, HEP ML LAB is easy to extend and customize, and can be used as a tool for both beginners and experienced researchers.

Jing Li

HEP ML LAB: An end-to-end framework for applying machine learning to phenomenology studies * Hao Sun is supported by the National Natural Science Foundation of China (12075043)

We develop a mathematical theory of separable higher categories based on Gaiotto and Johnson-Freyd’s work on condensation completion. Based on this theory, we prove some fundamental results on E  m -multi-fusion higher categories and their higher centers. We also outline a theory of unitary higher categories based on a ∗-version of condensation completion. After these mathematical preparations, based on the idea of topological Wick rotation, we develop a unified mathematical theory of all quantum liquids, which include topological orders, SPT/SET orders, symmetry-breaking orders and CFT-like gapless phases. We explain that a quantum liquid consists of two parts, the topological skeleton and the local quantum symmetry, and show that all nD quantum liquids form a ∗-condensation complete higher category whose equivalence type can be computed explicitly from a simple coslice 1-category.

Liang Kong

Hao Zheng

Categories of quantum liquids I

In this work, we use Ising chain and Kitaev chain to check the validity of an earlier proposal in  arXiv:2011.02859   that enriched fusion (higher) categories provide a unified categorical description of all gapped/gapless quantum liquid phases, including symmetry-breaking phases, topological orders, SPT/SET orders and CFT-type gapless quantum phases. In particular, we show explicitly that, in each gapped phase realized by these two models, the spacetime observables form a fusion category enriched in a braided fusion category such that its monoidal center is trivial. We also study the categorical descriptions of the boundaries of these models. In the end, we obtain a classification of and the categorical descriptions of all 1-dimensional (spatial dimension) gapped quantum phases with a bosonic/fermionic finite onsite symmetry.

United States

Xiao-Gang Wen

One dimensional gapped quantum phases and enriched fusion categories

This is the second part of a two-part work on the unified mathematical theory of gapped and gapless edges of 2+1D topological orders. In Part I, we have developed the mathematical theory of chiral gapless edges. In Part II, we study boundary-bulk relation and non-chiral gapless edges. In particular, we explain how the notion of the center of an enriched monoidal category naturally emerges from the boundary-bulk relation. After the study of 0+1D gapless walls, we give the complete boundary-bulk relation for 2+1D topological orders with chiral gapless edges (including gapped edges) and 0d walls between edges. This relation is stated precisely and proved rigorously as a monoidal equivalence, which generalizes the functoriality of the usual Drinfeld center to an enriched setting. We also develop the mathematical theory of non-chiral gapless edges and 0+1D walls, and explain how to gap out certain non-chiral 1+1D gapless edges and 0+1D gapless walls categorically. In the end, we show that all anomaly-free 1+1D boundary-bulk rational CFT's can be recovered from 2d topological orders with chiral gapless edges via a dimensional reduction process. This provides physical meanings to some mysterious connections between mathematical results in fusion categories and those in rational CFT's.

A mathematical theory of gapless edges of 2d topological orders. Part II

We develop a mathematical theory of symmetry protected trivial (SPT) orders and anomaly-free symmetry enriched topological (SET) orders in all dimensions via two different approaches with an emphasis on the second approach. The first approach is to gauge the symmetry in the same dimension by adding topological excitations as it was done in the 2d case, in which the gauging process is mathematically described by the minimal modular extensions of unitary braided fusion 1-categories. This 2d result immediately generalizes to all dimensions except in 1d, which is treated with special care. The second approach is to use the 1-dimensional higher bulk of the SPT/SET order and the boundary-bulk relation. This approach also leads us to a precise mathematical description and a classification of SPT/SET orders in all dimensions. The equivalence of these two approaches, together with known physical results, provides us with many precise mathematical predictions.

Canada

Tian Lan

Zhi-Hao Zhang

Classification of topological phases with finite internal symmetries in all dimensions

This is the first part of a two-part work on a unified mathematical theory of gapped and gapless edges of 2d topological orders. We analyze all the possible observables on the 1+1D world sheet of a chiral gapless edge of a 2d topological order, and show that these observables form an enriched unitary fusion category, the Drinfeld center of which is precisely the unitary modular tensor category associated to the bulk. This mathematical description of a chiral gapless edge automatically includes that of a gapped edge (i.e. a unitary fusion category) as a special case. Therefore, we obtain a unified mathematical description and a classification of both gapped and chiral gapless edges of a given 2d topological order. In the process of our analysis, we encounter an interesting and reoccurring phenomenon: spatial fusion anomaly, which leads us to propose the Principle of Universality at RG fixed points for all quantum field theories. Our theory also implies that all chiral gapless edges can be obtained from a so-called topological Wick rotations. This fact leads us to propose, at the end of this work, a surprising correspondence between gapped and gapless phases in all dimensions.

A mathematical theory of gapless edges of 2d topological orders. Part I

In this work, we give a mathematical description of a chiral gapless edge of a 2d topological order (without symmetry). We show that the observables on the 1+1D world sheet of such an edge consist of a family of topological edge excitations, boundary CFT's and walls between boundary CFT's. These observables can be described by a chiral algebra and an enriched monoidal category. This mathematical description automatically includes that of gapped edges as special cases. Therefore, it gives a unified framework to study both gapped and gapless edges. Moreover, the boundary-bulk duality also holds for gapless edges. More precisely, the unitary modular tensor category that describes the 2d bulk phase is exactly the Drinfeld center of the enriched monoidal category that describes the gapless/gapped edge. We propose a classification of all gapped and chiral gapless edges of a given bulk phase. In the end, we explain how modular-invariant bulk rational conformal field theories naturally emerge on certain gapless walls between two trivial phases.

Gapless edges of 2d topological orders and enriched monoidal categories

In this paper, we study the relation between an anomaly-free n+1 D topological order, which are often called n+1 D topological order in physics literature, and its n D gapped boundary phases. We argue that the n+1 D bulk anomaly-free topological order for a given n D gapped boundary phase is unique. This uniqueness defines the notion of the “ bulk ” for a given gapped boundary phase. In this paper, we show that the n+1 D “ bulk ” phase is given by the “center” of the n D boundary phase. In other words, the geometric notion of the “ bulk ” corresponds precisely to the algebraic notion of the “center”. We achieve this by first introducing the notion of a morphism between two (potentially anomalous) topological orders of the same dimension, then proving that the notion of the “ bulk ” satisfies the same universal property as that of the “center” of an algebra in mathematics, i.e. “ bulk = center”. The entire argument does not require us to know the precise mathematical description of a (potentially anomalous) topological order. This result leads to concrete physical predictions.