We investigated the effect of an isospin chemical potential ( $ \mu_{I} $ ) within the quark-meson model, which approximates quantum chromodynamics (QCD) by modeling low-energy phenomena such as chiral symmetry breaking and phase structure under varying conditions of temperature and chemical potential. Using the functional renormalization group (FRG) flow equations, we calculated the phase diagram in the chiral limit within the two-flavor quark-meson model in a finite $ \mu_{I} $ with $\textit{ρ}$ vector meson interactions. Fluctuation effects significantly decrease the critical chemical potential from the mean-field (MF) value $\mu_{I,{\rm MF}} \gt m_\rho$ to a lower value at which the $\textit{ρ}$ vector meson condensates alongside the chiral condensate once the isospin chemical potential exceeds the critical value $ \mu_{I}^{{\rm{crit}}} $ . This $\textit{ρ}$ condensation was investigated numerically for different meson coupling strengths. The $\textit{ρ}$ meson dominated region is delineated from other phases by a second-order phase transition at lower $ \mu_{I} $ and a first-order transition at slightly higher $ \mu_{I} $ .

China

Mohammed Osman

Defu Hou

Wentao Wang

United States

Hui Zhang

Functional renormalization group study of $\textit{ρ}$ meson condensate at a finite isospin chemical potential in the quark meson model * Supported in part by the National Key Research and Development Program of China (2022YFA1604900). This work is also partly supported by the National Natural Science Foundation of China (NSFC) (12435009, 12275104). Hui Zhang acknowledges the financial support from the Guangdong Major Project of Basic and Applied Basic Research (2020B0301030008) and the National Natural Science Foundation of China (12047523, 12105107)

In this work we study the axion/axion-like particle production from the lepton–nucleon scattering in the low-energy region, i.e., the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>ℓ</mo><mi>N</mi><mo stretchy="false">→</mo><mo>ℓ</mo><mi>N</mi><mi>a</mi></math> processes, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>ℓ</mo></math> being the electron or muon and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math> the proton or neutron. We simultaneously include three different types of axion interaction couplings within the chiral effective field theory, namely the axion–nucleon–nucleon couplings <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>g</mi><mrow><mi>a</mi><mi>N</mi><mi>N</mi></mrow></msub></math>, axion–photon–photon coupling <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>g</mi><mrow><mi>a</mi><mi>γ</mi><mi>γ</mi></mrow></msub></math>, and axion–photon–vector meson resonance couplings <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>g</mi><mrow><mi>ρ</mi><mi>a</mi><mi>γ</mi></mrow></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>g</mi><mrow><mi>ω</mi><mi>a</mi><mi>γ</mi></mrow></msub></math>. Vast inputs from the lattice QCD and hadron phenomenological studies are used to fix the unknown couplings. The relative strengths of different axion interactions in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>ℓ</mo><mi>N</mi><mo stretchy="false">→</mo><mo>ℓ</mo><mi>N</mi><mi>a</mi></math> processes are then revealed. We provide detailed predictions for the differential cross sections with respect to various angles and axion energy, as well as the total cross sections in the low-energy region around production thresholds, both for the Kim-Shifman-Vainstein-Zakharov (KSVZ) and Dine-Fischler-Srednicki-Zhitnitsky (DFSZ) axion models.

Qian-Qian Guo

Xiong-Hui Cao

Zhi-Hui Guo

Hai-Qing Zhou

Axion-like particle production from lepton-nucleon scattering in chiral effective theory

In this work we focus on the evaluation of the leading-order hadronic vacuum polarization contribution from the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>π</mi></math> channel to the muon anomalous magnetic moment <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>a</mi><mi>μ</mi></msub></math> by using the experimental <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>τ</mi><mo stretchy="false">→</mo><mi>π</mi><mi>π</mi><msub><mi>ν</mi><mi>τ</mi></msub></math> data. The isospin breaking corrections play the decisive role in this approach of computing <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>a</mi><mi>μ</mi></msub></math>. One of such important isospin breaking sources is the long-distance electromagnetic correction factor <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>G</mi><mrow><mi>EM</mi></mrow></msub></math> of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>τ</mi><mo stretchy="false">→</mo><mi>π</mi><mi>π</mi><msub><mi>ν</mi><mi>τ</mi></msub></math> process from the real photon radiation. The latter effect can be calculated from the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>τ</mi><mo stretchy="false">→</mo><mi>π</mi><mi>π</mi><msub><mi>ν</mi><mi>τ</mi></msub><mi>γ</mi></math> amplitude, which is revised in this work within the resonance chiral theory by simultaneously including the even-intrinsic-parity and odd-intrinsic-parity resonance operators. We update the determination of the only unknown resonance coupling through the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ω</mi><mo stretchy="false">→</mo><msup><mi>π</mi><mn>0</mn></msup><msup><mi>π</mi><mn>0</mn></msup><mi>γ</mi></math> decay by including contributions from both the vector and scalar resonances. By taking other remaining contributions from the muon <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>g</mi><mo>−</mo><mn>2</mn></math> White Paper 2025, we further revise the complete value of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>a</mi><mi>μ</mi></msub></math>, which turns out to deviate from the newest world average result after Fermilab’s measurement at the level of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2.7</mn><mi>σ</mi></mrow></math>.

Zhi-Xin Li

Ao Li

Jin Hao

Chun-Gui Duan

Revisit of the electromagnetic correction to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>τ</mi><mo stretchy="false">→</mo><mi>π</mi><mi>π</mi><msub><mrow><mi>ν</mi></mrow><mrow><mi>τ</mi></mrow></msub></mrow></math> and its implication for muon <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>g</mi><mo>−</mo><mn>2</mn></math> based on <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>τ</mi></math> data

This paper presents a systematic study of hyperon non-leptonic two-body decays induced by light quark transitions, particularly the $ s \rightarrow u\bar{u}d $ process, within the framework of $\textit{SU}$(3) flavor symmetry. The effective weak Hamiltonian is decomposed into irreducible $\textit{SU}$(3) representations, including the 27-plet and octet components, and applied to analyze decays of octet and decuplet baryons and charmed baryons. Both the irreducible representation amplitude (IRA) approach and the topological diagrammatic analysis (TDA) are employed to construct decay amplitudes and constrain the parameter space. $\textit{SU}$(3) symmetry-breaking effects arising from the strange quark mass are incorporated systematically. A global fit to current experimental data allows us to extract form factors and predict branching ratios and asymmetry parameters for several decay channels. Our results demonstrate the predictive power of $\textit{SU}$(3) flavor symmetry while highlighting significant symmetry-breaking effects, especially in amplitudes related to the 27-plet. Notably, the $ \Sigma^+ \rightarrow p\pi^0 $ decay channel exhibits a deviation exceeding $ 1\sigma $ from experimental measurements, suggesting the possible presence of new decay mechanisms or contributions beyond the Standard Model. Besides, we also evaluate the size of symmetry breaking. However, the large uncertainty of the experimental data makes it difficult to precisely determine the value of symmetry breaking. We strongly recommend that future experimental efforts aim to reduce the measurement uncertainties, especially for the processes $ \Lambda^0\to p\pi^- $ and $ \Lambda^0\to n\pi^0 $ , which have larger experimental errors compared to other data and play an important role in determining the symmetry breaking parameter. This study provides a systematic framework for future tests of the Standard Model and the search for new physics in hyperon decays.

Xin Wu

Qi Chen

Ye Xing

Zhi-Peng Xing

Ruilin Zhu

$\textit{SU}$(3) flavor symmetry analysis of hyperon non-leptonic two body decays * Ruilin Zhu is supported by NSFC (12322503, 12075124) and the Natural Science Foundation of Jiangsu (BK20211267). Zhi-Peng Xing is supported by NSFC (12375088, 12335003, 12405113). Ye Xing is supported by NSFC (12005294)

We discuss the landscape of flavor physics at the Circular Electron-Positron Collider (CEPC), based on the nominal luminosity outlined in its Technical Design Report. The CEPC is designed to operate in multiple modes to address a variety of tasks. At the $\textit{Z}$ pole, the expected production of 4 Tera $\textit{Z}$ bosons will provide unique and highly precise measurements of $\textit{Z}$ boson couplings, while the substantial number of boosted heavy-flavored quarks and leptons produced in clean $\textit{Z}$ decays will facilitate investigations into their flavor physics with unprecedented precision. We investigate the prospects of measuring various physics benchmarks and discuss their implications for particle theories and phenomenological models. Our studies indicate that, with its highlighted advantages and anticipated excellent detector performance, the CEPC can explore beauty and $\textit{τ}$ physics in ways that are superior to or complementary with the Belle II and Large-Hadron-Collider-beauty experiments, potentially enabling the detection of new physics at energy scales of 10 TeV and above. This potential also extends to the observation of yet-to-be-discovered rare and exotic processes, as well as testing fundamental principles such as lepton flavor universality, lepton and baryon number conservation, etc., making the CEPC a vibrant platform for flavor physics research. The $\textit{WW}$ threshold scan, Higgs-factory operation and top-pair productions of the CEPC further enhance its merits in this regard, especially for measuring the Cabibbo-Kobayashi-Maskawa matrix elements, and Flavor-Changing-Neutral-Current physics of Higgs boson and top quarks. We outline the requirements for detector performance and considerations for future development to achieve the anticipated scientific goals. The role of machine learning for innovative detector design and advanced reconstruction algorithms is also stressed. The CEPC flavor physics program not only develops new capabilities for exploring flavor physics beyond existing projects but also enriches the physics opportunities of this machine. It should be remarked that, given the richness of the CEPC flavor physics, this manuscript is not meant to be a comprehensive survey, but rather an investigation of representative cases. Uncovering the full potential of flavor physics at the CEPC will require further dedicated explorations in the future.

Xiaocong Ai

Wolfgang Altmannshofer

Peter Athron

Xiaozhi Bai

Lorenzo Calibbi

Germany

Lu Cao

Yuzhi Che

Chunhui Chen

Ji-Yuan Chen

Long Chen

Mingshui Chen

Shanzhen Chen

Xuan Chen

Shan Cheng

Cheng-Wei Chiang

Switzerland

Andreas Crivellin

Hanhua Cui

France

Olivier Deschamps

Sébastien Descotes-Genon

Xiaokang Du

Shuangshi Fang

Yu Gao

Yuanning Gao

Li-Sheng Geng

Pablo Goldenzweig

Jiayin Gu

Feng-Kun Guo

Yuchen Guo

Tao Han

Hong-Jian He

Jibo He

Miao He

Xiaogang He

Yanping Huang

Gino Isidori

Quan Ji

Jianfeng Jiang

Xu-Hui Jiang

Slovenia

Jernej F. Kamenik

Tsz Hong Kwok

Gang Li

Geng Li

Haibo Li

Haitao Li

Hengne Li

Honglei Li

Liang Li

Lingfeng Li

Qiang Li

Shu Li

Xiaomei Li

Xin-Qiang Li

Yiming Li

Yubo Li

Yuji Li

Zhao Li

Hao Liang

Zhijun Liang

Libo Liao

Zoltan Ligeti

Jia Liu

Jianbei Liu

Tao Liu

Yi Liu

Yong Liu

Zhen Liu

Xinchou Lou

Peng-Cheng Lu

Italy

Alberto Lusiani

Hong-Hao Ma

Kai Ma

Farvah Mahmoudi

Yajun Mao

Yaxian Mao

David Marzocca

Juan-Juan Niu

Soeren Prell

Huirong Qi

Sen Qian

Zhuoni Qian

Qin Qin

Ariel Rock

Jonathan L. Rosner

Manqi Ruan

Dingyu Shao

Chengping Shen

Xiaoyan Shen

Haoyu Shi

United Kingdom

Liaoshan Shi

Zong-Guo Si

Cristian Sierra

Huayang Song

Shufang Su

Wei Su

Zhijia Sun

Michele Tammaro

Dayong Wang

En Wang

Flavor physics at the CEPC: a general perspective * We acknowledge financial support from the National Natural Science Foundation of China (NSFC) (12125507, 12047503, 12035008, 2211530479, 12475094, 12135006, 12075097, 12375086, 2022YFA1601903, 12061141007, 12375091, 12342502, 12235018, 12335003, 12105100, 12475106, 11961141015, 12188102, 12175245, 12205171, 12321005, tsqn202312052, 2024HWYQ-005, 12405121, 12447167, 12061141006, 12405102, 12125503,12305115, 12075213, 12335005, 12235008); the Chinese Academy of Sciences (YSBR-101, XDB34030000); the National Key R&D Program of China (2022YFE0116900, 2023YFA1606703, 2022YFA1601901); the National Key Research and Development Program of China (2023YFA1606300); the Excellent Postdoctoral Program of Jiangsu Province (2023ZB891); the Shenzhen Science and Technology Program (202206193000001, 20220816094256002); the Natural Science Foundation for Distinguished Young Scholars of Henan Province (242300421046); the Beijing Municipal Natural Science Foundation (JQ22002); the Area of Excellence (AoE/P-404/18-3) and the General Research Fund (16304321) (both grants are issued by the Research Grants Council of Hong Kong S.A.R); the MOST National Key R&D Program (2023YFA1606303); the Shanghai Key Laboratory for Particle Physics and Cosmology, Key Laboratory for Particle Astrophysics and Cosmology (Ministry of Education), Shanghai Jiao Tong University

We analyzed two-loop planar contributions to a three-body form factor at next-to-leading power in the high-energy limit, where the masses of the external particles are much smaller than their energies. Calculations were performed by exploiting differential equations for the expansion coefficients, both to facilitate linear relations among them and to derive their analytic expressions. The results are expressed in terms of generalized polylogarithms involving a few simple symbol letters. Our method can readily be applied to calculations of non-planar contributions as well. Our results provide crucial information for establishing sub-leading factorization theorems for massive scattering amplitudes in the high-energy limit.

Yishuai Guo

Zhi-Feng Liu

Mingming Lu

Tianya Xia

Li-Lin Yang

A three-body form factor at sub-leading power in the high-energy limit: planar contributions * Supported in part by the National Natural Science Foundation of China Sunder (12375097, 12347103) and the Fundamental Research Funds for the Central Universities. Zhi-Feng Liu was supported by the China Postdoctoral Science Foundation (2023M733123, 2023TQ0282) and the Postdoctoral Fellowship Program of China Postdoctoral Science Foundation

A comprehensive analysis of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>K</mi><mo stretchy="false">→</mo><mi>π</mi><mi>K</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>π</mi><mo stretchy="false">→</mo><mi>K</mi><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover></math> amplitudes at large unphysical pion mass for all important partial waves is presented. A set of crossing-symmetric partial-wave hyperbolic dispersion relations is used to describe lattice quantum chromodynamics (QCD) data at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><mi>π</mi></msub><mo>=</mo><mn>391</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>. In the present analysis, the amplitudes for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi></math>- and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>P</mi></math>-waves are formulated by combining the constraints of analyticity, unitarity, and crossing symmetry, fulfilling Roy-Steiner-type equations. We use these results to investigate the low-lying strange-meson resonances and resolve the instability problem tied to analytic continuation in prior lattice QCD studies based on the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>K</mi></math>-matrix formalism. At <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><mi>π</mi></msub><mo>=</mo><mn>391</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>, the rigorous Roy-Steiner-type equation approach allows us to determine the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi></math>-wave scattering lengths, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><mi>π</mi></msub><msubsup><mi>a</mi><mn>0</mn><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msubsup><mo>=</mo><mrow><mo stretchy="false">(</mo><mn>0.9</mn><msubsup><mn>2</mn><mrow><mo>−</mo><mn>0.28</mn></mrow><mrow><mo>+</mo><mn>0.06</mn></mrow></msubsup><mo stretchy="false">)</mo></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><mi>π</mi></msub><msubsup><mi>a</mi><mn>0</mn><mrow><mn>3</mn><mo>/</mo><mn>2</mn></mrow></msubsup><mo>=</mo><mo>−</mo><mrow><mo stretchy="false">(</mo><mn>0.3</mn><msubsup><mn>2</mn><mrow><mo>−</mo><mn>0.02</mn></mrow><mrow><mo>+</mo><mn>0.05</mn></mrow></msubsup><mo stretchy="false">)</mo></mrow></math>, and the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>κ</mi></math> [also known as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>K</mi><mn>0</mn><mo>*</mo></msubsup><mo stretchy="false">(</mo><mn>700</mn><mo stretchy="false">)</mo></math>] pole position, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><msub><mi>s</mi><mi>κ</mi></msub></msqrt><mo>=</mo><mrow><mo stretchy="false">(</mo><mn>96</mn><msubsup><mn>6</mn><mrow><mo>−</mo><mn>24</mn></mrow><mrow><mo>+</mo><mn>41</mn></mrow></msubsup><mo>−</mo><mi>i</mi><mn>19</mn><msubsup><mn>8</mn><mrow><mo>−</mo><mn>17</mn></mrow><mrow><mo>+</mo><mn>38</mn></mrow></msubsup><mo stretchy="false">)</mo></mrow><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>. We also provide a detailed analysis of the complex validity domain of the Roy-Steiner-type equations.

Qu-Zhi Li

Revisiting Roy-Steiner-equation analysis of pion-kaon scattering from lattice QCD data

We perform a rigorous analysis of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>K</mi></math> scattering at an unphysical pion mass 391 MeV using the Roy-Steiner equations, which satisfy unitarity, analyticity, and crossing symmetry, for the first time. Stable solutions of the Roy-Steiner equations with different quantum numbers of isospin and angular momentum are obtained in the elastic energy region, by taking inputs from the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>K</mi></math> lattice data in the inelastic region, the lattice data from the crossed <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>π</mi><mo stretchy="false">→</mo><mi>K</mi><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover></math> channels, the masses of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>500</mn><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>*</mo></msup></math> at the same pion mass from previous study, and the Regge model. Predictions on the elastic <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>K</mi></math> scattering phase shifts and the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>K</mi><mn>0</mn><mo>*</mo></msubsup><mo stretchy="false">(</mo><mn>700</mn><mo stretchy="false">)</mo></math> pole content are made. Contrary to the virtual pole scenario obtained using the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>K</mi></math>-matrix method in the literature, we find that lightest strange scalar meson <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>K</mi></mrow><mrow><mn>0</mn></mrow><mrow><mo>*</mo></mrow></msubsup><mo stretchy="false">(</mo><mn>700</mn><mo stretchy="false">)</mo></mrow></math> remains a broad resonance at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><mi>π</mi></msub><mo>=</mo><mn>391</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>. The cross-channel dynamics is found to play a crucial role in deriving the proper pole position.

Rigorous Roy-Steiner equation analysis of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>K</mi></math> scattering at unphysical quark masses

The axion thermalization rate is a crucial input to determine the hot dark matter bound of axions, resulting from the scattering processes in the thermal bath of early Universe. We demonstrate that the commonly employed axion thermalization rate by including the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>a</mi><mi>π</mi><mo stretchy="false">↔</mo><mi>π</mi><mi>π</mi></math> channel alone is significantly underestimated for the temperature <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>T</mi></math> above 100 MeV. This is obtained through the systematical calculation of the axion-light flavor meson scattering amplitudes within the framework of the chiral unitarization approach, paying special attention to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>a</mi><mi>K</mi><mo stretchy="false">↔</mo><mi>π</mi><mi>K</mi></math> reaction. Hadron resonances appearing in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>a</mi><mi>K</mi><mo stretchy="false">↔</mo><mi>π</mi><mi>K</mi></math> amplitudes significantly enlarge the cross sections, which turn out to be much bigger than that of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>a</mi><mi>π</mi><mo stretchy="false">↔</mo><mi>π</mi><mi>π</mi></math>. The axion thermalization rate is then substantially enhanced by the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>a</mi><mi>K</mi><mo stretchy="false">↔</mo><mi>π</mi><mi>K</mi></math> channel for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>T</mi><mo>≳</mo><mn>100</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>. Especially at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>T</mi><mo>≃</mo><mn>130</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>, the contribution from the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>a</mi><mi>K</mi><mo stretchy="false">↔</mo><mi>π</mi><mi>K</mi></math> reaction to the axion thermalization rate exceeds the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>a</mi><mi>π</mi><mo stretchy="false">↔</mo><mi>π</mi><mi>π</mi></math> one. Obviously more stringent constraints on the axion parameters are obtained, when confronting the number of extra relativistic degrees of freedom <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Δ</mi><msub><mi>N</mi><mi>eff</mi></msub></math> from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>Planck</mi></mrow><mrow><mo>′</mo></mrow></msup><mn>18</mn></mrow></math>.

Jin-Bao Wang

Prominent enhancement of axion thermalization rate from axion-kaon interactions

We study $ \cos2\phi $ azimuthal asymmetry in doubly longitudinally polarized proton-proton Drell-Yan collisions within the transverse momentum dependent factorization framework. The asymmetry arises from the convolution of the longitudinal transversity distribution $ h_{1L}^{\perp} $ for both protons. Using the Bacchetta-Delcarro-Pisano-Radici-Signori parameterization for the nonperturbative Sudakov form factor and the Wandzura-Wilczek approximation for collinear $ h_{1L}^{\perp} $ , we predict the double spin asymmetry $ A_{LL}^{\cos2\phi} $ at RHIC and NICA kinematics. Our results demonstrate sensitivity to sea quark distributions, with the asymmetry reaching up to 25% for maximal sea quark contributions. These predictions highlight the potential of polarized Drell-Yan measurements to probe sea quark dynamics and advance our understanding of nucleon structures.

Hui Li

Ting Hu

Liang-Liang Liu

Xiao-Yu Wang

Zhun Lu

Asymmetry ${{\boldsymbol A}_{\boldsymbol{LL}}^{\bf\cos2\boldsymbol\phi}} $ in the polarized proton-proton Drell-Yan process within TMD factorization * Hui Li is supported by Fundamental Research Program of Shanxi Province (202203021222224) and Natural Science Foundation of Shanxi Normal University (JCYJ2023021). Xiao-Yu Wang is supported by the Natural Science Foundation of Henan Province (242300421377, 232300421140)