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Limits on the luminance of dark matter from xenon recoil data


It is commonly conjectured that dark matter is a charge neutral fundamental particle. However, it may still have minute photon-mediated interactions through millicharge1,2 or higher-order multipole interactions3,4,5,6,7,8,9,10, resulting from new physics at a high energy scale. Here we report a direct search for effective electromagnetic interactions between dark matter and xenon nuclei that produce a recoil of the latter from the PandaX-4T xenon-based detector11,12. Using this technique, the first constraint on the charge radius of dark matter is derived with the lowest excluded value of 1.9 × 10−10 fm2 for a dark matter mass of 40 giga electron volts per speed of light in a vaccum squared (GeV/c2), more stringent than that for neutrinos by four orders of magnitude. Constraints on the magnitudes of millicharge, magnetic dipole moment, electric dipole moment and anapole moment are also improved substantially from previous searches13,14, with corresponding tightest upper limits of 2.6 × 10−11 e, 4.8 × 10−10 Bohr magnetons, 1.2 × 10−23 ecm and 1.6 × 10−33 cm2, respectively, for a dark matter mass of 20–40 GeV/c2.

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Fig. 1: Diagram showing photon-mediated interaction in a xenon detector.
Fig. 2: Expected distributions of photon-mediated interactions in the PandaX-4T detector.
Fig. 3: Constraints on the luminance of dark matter.

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Data availability

The authors declare that the main data supporting the findings of this study are available within the article. Extra data are available from the corresponding author upon request.


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We thank W. Haxton, Y. Bai, Z. Liu and N. Nagata for helpful discussions. This project is supported in part by grants from National Natural Science Foundation of China (grant nos. 12090061, 12005131, 11925502 and 11835005), a grant from the Ministry of Science and Technology of China (grant no. 2016YFA0400301), and by Office of Science and Technology, Shanghai Municipal Government (grant no. 22JCJC1410200). We thank Double First Class Plan of the Shanghai Jiao Tong University and the Tsung-Dao Lee Institute Experimental Platform Development Fund for support. We also thank the sponsorship from the Hongwen Foundation in Hong Kong, Tencent Foundation in China and Yangyang Development Fund. Finally, we thank the CJPL administration and the Yalong River Hydropower Development Company Ltd for indispensable logistical support and other help.

Author information

Authors and Affiliations



This work is the result of the contributions and efforts of all participating institutes of the PandaX Collaboration, under the leadership of the hosting institute, Shanghai Jiao Tong University. The collaboration has constructed and operated the PandaX-4T apparatus, and performed the data processing, calibration and data selections. J.Liu is the Collaboration Spokesperson. N.Z. initiated the effective field theory studies and the application to the dark matter electromagnetic properties with the PandaX data. X.N. and N.Z. performed the calculation of theoretical models, data analysis and hypothesis tests. The paper draft was prepared by X.N. and N.Z., extensively edited by J.Liu and reviewed by X.J., L.Geng and Y.Yang. All authors approved the final version of the manuscript.

Corresponding authors

Correspondence to Jianglai Liu or Ning Zhou.

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The authors declare no competing interests.

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Nature thanks Giuliana Fiorillo, Masaki Yamashita and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data figures and tables

Extended Data Fig. 1 Detector efficiency.

a,b, The nuclear recoil signal efficiency (with shaded band representing the uncertainty) for data in sets 4 and 5, as a function of nuclear recoil energy in keVNR or S1/S2 signal in PE.

Source data

Extended Data Fig. 2 Detector response.

a,b, Light yield for nuclear (a) and electron (b) recoil signal used in this work at 92.8 V/cm, as compared with the nominal NEST v2.3.6 values and uncertainties29,30,31.

Source data

Extended Data Table 1 Detector configurations
Extended Data Table 2 Background components
Extended Data Table 3 Standard Halo Model parameters

Source data

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PandaX Collaboration. Limits on the luminance of dark matter from xenon recoil data. Nature 618, 47–50 (2023).

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