⚛️ high-energy experiments

Precision measurements of semleptonic decays $D^0 \to π^-\ell^+ν_\ell$ and $D^+ \to π^0\ell^+ν_\ell$ ( $\ell =e,μ$ )

Using 20.3 fb $^{-1}$ of $e^+e^-$ collision data collected by the BESIII detector, this study presents the most precise measurements to date of branching fractions, partial decay rates, and forward-backward asymmetries for the semileptonic decays $D^0 \to \pi^-\ell^+\nu_\ell$ and $D^+\to \pi^0\ell^+\nu_\ell$ ( $\ell=e, \mu$ ), from which the product $f^{D\to\pi}_+(0)|V_{cd}|$ is determined and used to extract the CKM matrix element $|V_{cd}|$ and the form factor $f^{D\to\pi}_+(0)$ while also testing lepton flavor universality and searching for scalar current contributions.

Original authors: BESIII Collaboration, M. Ablikim, M. N. Achasov, P. Adlarson, X. C. Ai, C. S. Akondi, R. Aliberti, A. Amoroso, Q. An, Y. H. An, M. S. Anderson, Y. Bai, O. Bakina, H. R. Bao, X. L. Bao, M. BarbagiovannBESIII Collaboration, M. Ablikim, M. N. Achasov, P. Adlarson, X. C. Ai, C. S. Akondi, R. Aliberti, A. Amoroso, Q. An, Y. H. An, M. S. Anderson, Y. Bai, O. Bakina, H. R. Bao, X. L. Bao, M. Barbagiovanni, V. Batozskaya, K. Begzsuren, N. Berger, M. Berlowski, M. B. Bertani, D. Bettoni, F. Bianchi, E. Bianco, A. Bortone, I. Boyko, R. A. Briere, A. Brueggemann, D. Cabiati, H. Cai, M. H. Cai, X. Cai, A. Calcaterra, G. F. Cao, N. Cao, S. A. Cetin, X. Y. Chai, J. F. Chang, T. T. Chang, G. R. Che, Y. Z. Che, C. H. Chen, Chao Chen, G. Chen, H. S. Chen, H. Y. Chen, M. L. Chen, S. J. Chen, S. M. Chen, T. Chen, W. Chen, X. R. Chen, X. T. Chen, X. Y. Chen, Y. B. Chen, Y. Q. Chen, Z. K. Chen, J. Cheng, L. N. Cheng, S. K. Choi, X. Chu, G. Cibinetto, F. Cossio, J. Cottee-Meldrum, H. L. Dai, J. P. Dai, X. C. Dai, A. Dbeyssi, R. E. de Boer, D. Dedovich, C. Q. Deng, Z. Y. Deng, A. Denig, I. Denisenko, M. Destefanis, F. De Mori, E. Di Fiore, X. X. Ding, Y. Ding, Y. X. Ding, J. Dong, L. Y. Dong, M. Y. Dong, X. Dong, Z. J. Dong, M. C. Du, S. X. Du, Shaoxu Du, X. L. Du, Y. Q. Du, Y. Y. Duan, Z. H. Duan, P. Egorov, G. F. Fan, J. J. Fan, K. X. Fan, Y. H. Fan, J. Fang, Jin Fang, S. S. Fang, W. X. Fang, Y. Q. Fang, L. Fava, F. Feldbauer, G. Felici, C. Q. Feng, J. H. Feng, Q. X. Feng, Y. T. Feng, M. Fritsch, C. D. Fu, J. L. Fu, Y. W. Fu, H. Gao, Xu Gao, Y. Gao, Y. N. Gao, Y. Y. Gao, Yunong Gao, Z. Gao, S. Garbolino, I. Garzia, L. Ge, P. T. Ge, Z. W. Ge, C. Geng, A. Gilman, K. Goetzen, J. Gollub, J. B. Gong, J. D. Gong, L. Gong, W. X. Gong, W. Gradl, M. Greco, M. D. Gu, M. H. Gu, C. Y. Guan, A. Q. Guo, H. Guo, J. N. Guo, L. B. Guo, M. J. Guo, R. P. Guo, X. Guo, Y. P. Guo, Z. Guo, A. Guskov, J. Gutierrez, J. Y. Han, T. T. Han, X. Han, F. Hanisch, K. D. Hao, X. Q. Hao, F. A. Harris, C. Z. He, K. K. He, K. L. He, F. H. Heinsius, C. H. Heinz, Y. K. Heng, C. Herold, P. C. Hong, G. Y. Hou, X. T. Hou, Y. R. Hou, Z. L. Hou, H. M. Hu, J. F. Hu, Q. P. Hu, S. L. Hu, T. Hu, Y. Hu, Y. X. Hu, Z. M. Hu, G. S. Huang, K. X. Huang, L. Q. Huang, P. Huang, X. T. Huang, Y. P. Huang, Y. S. Huang, T. Hussain, N. Hüsken, N. in der Wiesche, J. Jackson, Q. Ji, Q. P. Ji, W. Ji, X. B. Ji, X. L. Ji, Y. Y. Ji, L. K. Jia, X. Q. Jia, D. Jiang, S. J. Jiang, X. S. Jiang, Y. Jiang, J. B. Jiao, J. K. Jiao, Z. Jiao, L. C. L. Jin, S. Jin, Y. Jin, M. Q. Jing, X. M. Jing, T. Johansson, S. Kabana, X. L. Kang, X. S. Kang, B. C. Ke, V. Khachatryan, A. Khoukaz, O. B. Kolcu, B. Kopf, L. Kröger, L. Krümmel, Y. Y. Kuang, X. Kui, N. Kumar, A. Kupsc, W. Kühn, Q. Lan, W. N. Lan, T. T. Lei, M. Lellmann, T. Lenz, C. Li, C. H. Li, C. K. Li, Chunkai Li, Cong Li, D. M. Li, F. Li, G. Li, H. B. Li, H. J. Li, H. L. Li, H. N. Li, H. P. Li, Hui Li, J. N. Li, J. S. Li, J. W. Li, K. Li, K. L. Li, L. J. Li, L. K. Li, Lei Li, M. H. Li, M. R. Li, M. T. Li, P. L. Li, P. R. Li, Q. M. Li, Q. X. Li, R. Li, S. Li, S. X. Li, S. Y. Li, Shanshan Li, T. Li, T. Y. Li, W. D. Li, W. G. Li, X. Li, X. H. Li, X. K. Li, X. L. Li, X. Y. Li, X. Z. Li, Y. Li, Y. H. Li, Y. B. Li, Y. C. Li, Y. G. Li, Y. P. Li, Z. H. Li, Z. J. Li, Z. L. Li, Z. X. Li, Z. Y. Li, C. Liang, H. Liang, Y. F. Liang, Y. T. Liang, Z. Z. Liang, G. R. Liao, L. B. Liao, M. H. Liao, Y. P. Liao, J. Libby, A. Limphirat, C. C. Lin, C. X. Lin, D. X. Lin, T. Lin, B. J. Liu, B. X. Liu, C. Liu, C. X. Liu, F. Liu, F. H. Liu, Feng Liu, G. M. Liu, H. Liu, H. B. Liu, H. M. Liu, Huihui Liu, J. B. Liu, J. J. Liu, K. Liu, K. Y. Liu, Ke Liu, Kun Liu, L. Liu, L. C. Liu, Lu Liu, M. H. Liu, P. L. Liu, Q. Liu, S. B. Liu, T. Liu, W. M. Liu, W. T. Liu, X. Liu, X. K. Liu, X. L. Liu, X. P. Liu, X. T. Liu, X. Y. Liu, Y. Liu, Y. B. Liu, Yi Liu, Z. A. Liu, Z. D. Liu, Z. L. Liu, Z. Q. Liu, Z. X. Liu, Z. Y. Liu, X. C. Lou, H. J. Lu, J. G. Lu, X. L. Lu, Y. Lu, Y. H. Lu, Y. P. Lu, Z. H. Lu, C. L. Luo, J. R. Luo, J. S. Luo, M. X. Luo, T. Luo, X. L. Luo, Z. Y. Lv, X. R. Lyu, Y. F. Lyu, Y. H. Lyu, F. C. Ma, H. L. Ma, Heng Ma, J. L. Ma, L. L. Ma, L. R. Ma, Q. M. Ma, R. Q. Ma, R. Y. Ma, T. Ma, X. T. Ma, X. Y. Ma, F. E. Maas, I. MacKay, M. Maggiora, S. Maity, S. Malde, L. M. Mansur, Y. J. Mao, Z. P. Mao, S. Marcello, A. Marshall, F. M. Melendi, Y. H. Meng, Z. X. Meng, G. Mezzadri, H. Miao, T. J. Min, R. E. Mitchell, X. H. Mo, A. F. Mohammad, B. Moses, N. Yu. Muchnoi, J. Muskalla, Y. Nefedov, F. Nerling, H. Neuwirth, Z. Ning, S. Nisar, Q. L. Niu, W. D. Niu, Y. Niu, C. Normand, S. L. Olsen, Q. Ouyang, I. V. Ovtin, S. Pacetti, Y. Pan, C. Y. Pang, A. Pathak, Y. P. Pei, M. Pelizaeus, G. L. Peng, H. P. Peng, X. J. Peng, Y. Y. Peng, K. Peters, K. Petridis, J. L. Ping, R. G. Ping, S. Plura, V. Prasad, L. Pöpping, F. Z. Qi, H. R. Qi, S. Qian, W. B. Qian, C. F. Qiao, J. H. Qiao, J. J. Qin, J. L. Qin, L. Q. Qin, L. Y. Qin, P. B. Qin, X. P. Qin, X. S. Qin, Z. H. Qin, J. F. Qiu, Z. H. Qu, J. Rademacker, K. Ravindran, C. F. Redmer, A. Rivetti, M. Rolo, G. Rong, S. S. Rong, F. Rosini, Ch. Rosner, M. Q. Ruan, W. R. Ruangyoo, N. Salone, A. Sarantsev, Y. Schelhaas, M. Schernau, K. Schoenning, M. Scodeggio, W. Shan, X. Y. Shan, Z. J. Shang, J. F. Shangguan, L. G. Shao, M. Shao, C. P. Shen, H. F. Shen, W. H. Shen, X. Y. Shen, B. A. Shi, Ch. Y. Shi, H. Shi, J. L. Shi, J. Y. Shi, M. H. Shi, S. Shi, S. Y. Shi, X. Shi, H. L. Song, J. J. Song, M. H. Song, T. Z. Song, W. M. Song, Y. X. Song, Zirong Song, S. Sosio, S. Spataro, S. Stansilaus, F. Stieler, M. Stolte, S. S Su, G. B. Sun, G. X. Sun, H. Sun, H. K. Sun, J. F. Sun, K. Sun, L. Sun, R. Sun, S. S. Sun, T. Sun, W. Y. Sun, Y. C. Sun, Y. H. Sun, Y. J. Sun, Y. Z. Sun, Z. Q. Sun, Z. T. Sun, H. Tabaharizato, N. T. Tagsinsit, C. J. Tang, G. Y. Tang, J. Tang, J. J. Tang, L. F. Tang, Y. A. Tang, Z. H. Tang, L. Y. Tao, M. Tat, J. X. Teng, J. Y. Tian, W. H. Tian, Y. Tian, Z. F. Tian, K. Yu. Todyshev, I. Uman, E. van der Smagt, B. Wang, Bin Wang, Bo Wang, C. Wang, Chao Wang, Cong Wang, D. Y. Wang, F. K. Wang, H. J. Wang, H. R. Wang, J. Wang, J. H. Wang, J. J. Wang, J. P. Wang, K. Wang, L. L. Wang, L. W. Wang, M. Wang, Mi Wang, N. Y. Wang, P. Wang, S. Wang, Shun Wang, T. Wang, W. Wang, W. P. Wang, X. F. Wang, X. L. Wang, X. N. Wang, Xin Wang, Y. Wang, Y. D. Wang, Y. F. Wang, Y. H. Wang, Y. J. Wang, Y. L. Wang, Y. N. Wang, Yanning Wang, Yaqian Wang, Yi Wang, Yuan Wang, Z. Wang, Z. L. Wang, Z. Q. Wang, Z. Y. Wang, Zhi Wang, Ziyi Wang, D. Wei, D. H. Wei, D. J. Wei, H. R. Wei, F. Weidner, H. R. Wen, S. P. Wen, U. Wiedner, G. Wilkinson, J. F. Wu, L. H. Wu, L. J. Wu, Lianjie Wu, S. G. Wu, S. M. Wu, X. W. Wu, Z. Wu, H. L. Xia, L. Xia, B. H. Xiang, D. Xiao, G. Y. Xiao, H. Xiao, Y. L. Xiao, Z. J. Xiao, C. Xie, K. J. Xie, Y. Xie, Y. G. Xie, Y. H. Xie, Z. P. Xie, T. Y. Xing, D. B. Xiong, G. F. Xu, H. Y. Xu, Q. J. Xu, Q. N. Xu, T. D. Xu, X. P. Xu, Y. Xu, Y. C. Xu, Z. S. Xu, F. Yan, L. Yan, W. B. Yan, W. C. Yan, W. H. Yan, W. P. Yan, X. Q. Yan, Y. Y. Yan, H. J. Yang, H. L. Yang, H. X. Yang, J. H. Yang, L. Y. Yang, R. J. Yang, X. Y. Yang, Y. Yang, Y. G. Yang, Y. H. Yang, Y. M. Yang, Y. Q. Yang, Y. Z. Yang, Youhua Yang, Z. Y. Yang, W. J. Yao, Z. P. Yao, M. Ye, M. H. Ye, Z. J. Ye, K. Yi, Junhao Yin, Qiqin Yin, Z. Y. You, B. X. Yu, C. X. Yu, G. Yu, J. S. Yu, L. W. Yu, T. Yu, X. D. Yu, Y. C. Yu, Yongchao Yu, C. Z. Yuan, H. Yuan, J. Yuan, Jie Yuan, L. Yuan, M. K. Yuan, S. H. Yuan, Y. Yuan, C. X. Yue, Ying Yue, A. A. Zafar, F. R. Zeng, S. H. Zeng, X. Zeng, Y. J. Zeng, Yujie Zeng, Y. C. Zhai, Y. H. Zhan, B. L. Zhang, B. X. Zhang, D. H. Zhang, G. Y. Zhang, Gengyuan Zhang, H. Zhang, H. C. Zhang, H. H. Zhang, H. L. Zhang, H. Q. Zhang, H. R. Zhang, H. Y. Zhang, Han Zhang, J. Zhang, J. J. Zhang, J. L. Zhang, J. Q. Zhang, J. S. Zhang, J. W. Zhang, J. X. Zhang, J. Y. Zhang, J. Z. Zhang, Jianyu Zhang, Jin Zhang, Jiyuan Zhang, L. M. Zhang, Lei Zhang, N. Zhang, P. Zhang, Q. Zhang, Q. Y. Zhang, Q. Z. Zhang, R. Y. Zhang, S. H. Zhang, S. N. Zhang, Shulei Zhang, X. M. Zhang, X. Y. Zhang, Y. T. Zhang, Y. H. Zhang, Y. P. Zhang, Yao Zhang, Yu Zhang, Yu Zhang, Z. Zhang, Z. D. Zhang, Z. H. Zhang, Z. L. Zhang, Z. X. Zhang, Z. Y. Zhang, Zh. Zh. Zhang, Zhilong Zhang, Ziyang Zhang, Ziyu Zhang, G. Zhao, J. -P. Zhao, J. Y. Zhao, J. Z. Zhao, L. Zhao, Lei Zhao, M. G. Zhao, R. P. Zhao, S. J. Zhao, Y. B. Zhao, Y. L. Zhao, Y. P. Zhao, Y. X. Zhao, Z. G. Zhao, A. Zhemchugov, B. Zheng, B. M. Zheng, J. P. Zheng, W. J. Zheng, W. Q. Zheng, X. R. Zheng, Y. H. Zheng, B. Zhong, C. Zhong, X. Zhong, H. Zhou, J. Q. Zhou, S. Zhou, X. Zhou, X. K. Zhou, X. R. Zhou, X. Y. Zhou, Y. X. Zhou, Y. Z. Zhou, A. N. Zhu, J. Zhu, K. Zhu, K. J. Zhu, K. S. Zhu, L. X. Zhu, Lin Zhu, S. H. Zhu, T. J. Zhu, W. D. Zhu, W. J. Zhu, W. Z. Zhu, Y. C. Zhu, Z. A. Zhu, X. Y. Zhuang, M. Zhuge, J. H. Zou, J. Zu

Published 2026-07-28

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Original authors: BESIII Collaboration, M. Ablikim, M. N. Achasov, P. Adlarson, X. C. Ai, C. S. Akondi, R. Aliberti, A. Amoroso, Q. An, Y. H. An, M. S. Anderson, Y. Bai, O. Bakina, H. R. Bao, X. L. Bao, M. Barbagiovanni, V. Batozskaya, K. Begzsuren, N. Berger, M. Berlowski, M. B. Bertani, D. Bettoni, F. Bianchi, E. Bianco, A. Bortone, I. Boyko, R. A. Briere, A. Brueggemann, D. Cabiati, H. Cai, M. H. Cai, X. Cai, A. Calcaterra, G. F. Cao, N. Cao, S. A. Cetin, X. Y. Chai, J. F. Chang, T. T. Chang, G. R. Che, Y. Z. Che, C. H. Chen, Chao Chen, G. Chen, H. S. Chen, H. Y. Chen, M. L. Chen, S. J. Chen, S. M. Chen, T. Chen, W. Chen, X. R. Chen, X. T. Chen, X. Y. Chen, Y. B. Chen, Y. Q. Chen, Z. K. Chen, J. Cheng, L. N. Cheng, S. K. Choi, X. Chu, G. Cibinetto, F. Cossio, J. Cottee-Meldrum, H. L. Dai, J. P. Dai, X. C. Dai, A. Dbeyssi, R. E. de Boer, D. Dedovich, C. Q. Deng, Z. Y. Deng, A. Denig, I. Denisenko, M. Destefanis, F. De Mori, E. Di Fiore, X. X. Ding, Y. Ding, Y. X. Ding, J. Dong, L. Y. Dong, M. Y. Dong, X. Dong, Z. J. Dong, M. C. Du, S. X. Du, Shaoxu Du, X. L. Du, Y. Q. Du, Y. Y. Duan, Z. H. Duan, P. Egorov, G. F. Fan, J. J. Fan, K. X. Fan, Y. H. Fan, J. Fang, Jin Fang, S. S. Fang, W. X. Fang, Y. Q. Fang, L. Fava, F. Feldbauer, G. Felici, C. Q. Feng, J. H. Feng, Q. X. Feng, Y. T. Feng, M. Fritsch, C. D. Fu, J. L. Fu, Y. W. Fu, H. Gao, Xu Gao, Y. Gao, Y. N. Gao, Y. Y. Gao, Yunong Gao, Z. Gao, S. Garbolino, I. Garzia, L. Ge, P. T. Ge, Z. W. Ge, C. Geng, A. Gilman, K. Goetzen, J. Gollub, J. B. Gong, J. D. Gong, L. Gong, W. X. Gong, W. Gradl, M. Greco, M. D. Gu, M. H. Gu, C. Y. Guan, A. Q. Guo, H. Guo, J. N. Guo, L. B. Guo, M. J. Guo, R. P. Guo, X. Guo, Y. P. Guo, Z. Guo, A. Guskov, J. Gutierrez, J. Y. Han, T. T. Han, X. Han, F. Hanisch, K. D. Hao, X. Q. Hao, F. A. Harris, C. Z. He, K. K. He, K. L. He, F. H. Heinsius, C. H. Heinz, Y. K. Heng, C. Herold, P. C. Hong, G. Y. Hou, X. T. Hou, Y. R. Hou, Z. L. Hou, H. M. Hu, J. F. Hu, Q. P. Hu, S. L. Hu, T. Hu, Y. Hu, Y. X. Hu, Z. M. Hu, G. S. Huang, K. X. Huang, L. Q. Huang, P. Huang, X. T. Huang, Y. P. Huang, Y. S. Huang, T. Hussain, N. Hüsken, N. in der Wiesche, J. Jackson, Q. Ji, Q. P. Ji, W. Ji, X. B. Ji, X. L. Ji, Y. Y. Ji, L. K. Jia, X. Q. Jia, D. Jiang, S. J. Jiang, X. S. Jiang, Y. Jiang, J. B. Jiao, J. K. Jiao, Z. Jiao, L. C. L. Jin, S. Jin, Y. Jin, M. Q. Jing, X. M. Jing, T. Johansson, S. Kabana, X. L. Kang, X. S. Kang, B. C. Ke, V. Khachatryan, A. Khoukaz, O. B. Kolcu, B. Kopf, L. Kröger, L. Krümmel, Y. Y. Kuang, X. Kui, N. Kumar, A. Kupsc, W. Kühn, Q. Lan, W. N. Lan, T. T. Lei, M. Lellmann, T. Lenz, C. Li, C. H. Li, C. K. Li, Chunkai Li, Cong Li, D. M. Li, F. Li, G. Li, H. B. Li, H. J. Li, H. L. Li, H. N. Li, H. P. Li, Hui Li, J. N. Li, J. S. Li, J. W. Li, K. Li, K. L. Li, L. J. Li, L. K. Li, Lei Li, M. H. Li, M. R. Li, M. T. Li, P. L. Li, P. R. Li, Q. M. Li, Q. X. Li, R. Li, S. Li, S. X. Li, S. Y. Li, Shanshan Li, T. Li, T. Y. Li, W. D. Li, W. G. Li, X. Li, X. H. Li, X. K. Li, X. L. Li, X. Y. Li, X. Z. Li, Y. Li, Y. H. Li, Y. B. Li, Y. C. Li, Y. G. Li, Y. P. Li, Z. H. Li, Z. J. Li, Z. L. Li, Z. X. Li, Z. Y. Li, C. Liang, H. Liang, Y. F. Liang, Y. T. Liang, Z. Z. Liang, G. R. Liao, L. B. Liao, M. H. Liao, Y. P. Liao, J. Libby, A. Limphirat, C. C. Lin, C. X. Lin, D. X. Lin, T. Lin, B. J. Liu, B. X. Liu, C. Liu, C. X. Liu, F. Liu, F. H. Liu, Feng Liu, G. M. Liu, H. Liu, H. B. Liu, H. M. Liu, Huihui Liu, J. B. Liu, J. J. Liu, K. Liu, K. Y. Liu, Ke Liu, Kun Liu, L. Liu, L. C. Liu, Lu Liu, M. H. Liu, P. L. Liu, Q. Liu, S. B. Liu, T. Liu, W. M. Liu, W. T. Liu, X. Liu, X. K. Liu, X. L. Liu, X. P. Liu, X. T. Liu, X. Y. Liu, Y. Liu, Y. B. Liu, Yi Liu, Z. A. Liu, Z. D. Liu, Z. L. Liu, Z. Q. Liu, Z. X. Liu, Z. Y. Liu, X. C. Lou, H. J. Lu, J. G. Lu, X. L. Lu, Y. Lu, Y. H. Lu, Y. P. Lu, Z. H. Lu, C. L. Luo, J. R. Luo, J. S. Luo, M. X. Luo, T. Luo, X. L. Luo, Z. Y. Lv, X. R. Lyu, Y. F. Lyu, Y. H. Lyu, F. C. Ma, H. L. Ma, Heng Ma, J. L. Ma, L. L. Ma, L. R. Ma, Q. M. Ma, R. Q. Ma, R. Y. 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Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the universe as a giant, bustling construction site where tiny building blocks called particles are constantly being assembled and taken apart. In the "charm" sector of this site, there are special, short-lived bricks called D mesons. These bricks are fascinating because they are made of a heavy charm quark and a lighter partner, and when they fall apart, they reveal the secret rules of the universe's weak force—the invisible glue that allows particles to change their identity. One of the most important rules in this game is "lepton flavor universality," which is like a strict bouncer at a cosmic club: it insists that the universe treats electrons and muons (two different types of light particles) exactly the same way, regardless of their slight differences in weight. If the bouncer ever lets one in while turning the other away, it would mean the rulebook is wrong and there's a whole new, undiscovered physics hiding in the shadows. Scientists have been hunting for this "bouncer breaking" in other parts of the construction site, but the charm sector has remained a bit of a mystery, waiting for a closer look.

Now, a massive team of scientists known as the BESIII Collaboration has finally taken a magnifying glass to these specific charm bricks. Using a giant detector in China that acts like a high-speed camera for particle collisions, they analyzed a massive dataset corresponding to an integrated luminosity of 20.3 fb⁻¹ to catch D mesons decaying into pions, a lepton (either an electron or a muon), and a ghostly neutrino. Think of it like trying to figure out the recipe of a cake by watching it bake and then carefully measuring the crumbs left behind. The team measured exactly how often these specific decay recipes happen, finding that the D0 meson decays into a pion and an electron about 2.950 times out of every 1,000 tries, and into a pion and a muon about 2.817 times out of 1,000. For the charged D+ meson, the numbers are slightly higher, around 3.622 and 3.507 times out of 1,000, respectively. These aren't just rough guesses; the team measured them with such precision that they are the best numbers we have ever seen, improving on previous records by a factor of two to three.

But the real magic wasn't just counting the crumbs; it was checking if the universe plays fair. The scientists compared the "electron" recipes to the "muon" recipes to see if the bouncer was being biased. They found that the ratio of muons to electrons is very close to what the Standard Model (the current rulebook of physics) predicts, with no significant bias found. This means that, at least in these specific charm decays, the universe is still treating electrons and muons with equal respect. Furthermore, they looked for a sneaky "scalar current"—a hypothetical extra force that could be hiding in the decay process, acting like a secret ingredient that changes the flavor of the cake. After analyzing the angles and energies of the particles flying out, they found no evidence of this secret ingredient. The data suggests that if this secret force exists, it is incredibly weak, hiding so well that it hasn't left a detectable fingerprint yet. By combining all these precise measurements, the team also calculated a fundamental number called the CKM matrix element, which helps map out how quarks change into one another, giving us a sharper, more accurate map of the universe's fundamental building blocks.

Technical Summary: Precision Measurements of Semileptonic Decays $D^0 \to \pi^- \ell^+ \nu_\ell$ and $D^+ \to \pi^0 \ell^+ \nu_\ell$

Problem and Motivation
Experimental studies of semileptonic decays of charmed mesons are essential for understanding weak and strong interactions within the charm sector. These processes allow for the extraction of the product of the Cabibbo-Kobayashi-Maskawa (CKM) matrix element modulus $|V_{cd}|$ and the hadronic transition form factor $f^{D\to\pi}_+(0)$ . This extraction serves two primary purposes: testing theoretical predictions of form factors (calculated via approaches such as Lattice QCD, QCD light-cone sum rules, and quark models) and testing the unitarity of the CKM matrix.

Furthermore, these decays provide a probe for Lepton Flavor Universality (LFU) and potential New Physics (NP). While the Standard Model (SM) predicts equivalent interactions for all lepton generations, anomalies in $b \to c \ell^+ \bar{\nu}_\ell$ transitions have suggested deviations. Theoretical models, including two-Higgs-doublet models and leptoquark scenarios, propose that scalar current contributions in weak interactions could explain these discrepancies. The $c \to d \ell^+ \nu_\ell$ transition in $D \to \pi \ell^+ \nu_\ell$ decays is particularly promising for constraining these scalar currents due to their relatively large branching fractions and high detection efficiencies. Prior to this work, experimental constraints on scalar currents and forward-backward asymmetries in these specific decays were non-existent, and existing branching fraction measurements lacked the precision required for stringent tests.

Methodology
The analysis utilizes $20.3 \text{ fb}^{-1}$ of $e^+e^-$ collision data collected at a center-of-mass energy of $\sqrt{s} = 3.773 \text{ GeV}$ by the BESIII detector. At this energy, $D\bar{D}$ pairs are produced via the $\psi(3770)$ resonance.

Double-Tag (DT) Method: The study employs the double-tag technique to measure absolute branching fractions. Single-tag (ST) candidates are reconstructed in various hadronic modes ( $\bar{D}^0 \to K^+\pi^-, K^+\pi^-\pi^0$ , etc., and $D^- \to K^+\pi^-\pi^-$ , etc.). Signal events are identified in the recoil system of these ST candidates.
Event Selection: Signal candidates for $D^0 \to \pi^- \ell^+ \nu_\ell$ and $D^+ \to \pi^0 \ell^+ \nu_\ell$ ( $\ell = e, \mu$ ) are selected based on kinematic variables, particle identification (PID) using $dE/dx$, Time-of-Flight (TOF), and Electromagnetic Calorimeter (EMC) information, and specific veto criteria to suppress backgrounds (e.g., $K_S^0$ veto, extra photon/track rejection).
Signal Extraction: The missing mass squared ( $M^2_{miss}$ ) distribution is used to extract signal yields. Fits are performed in ten $q^2$ intervals to determine partial decay rates.
Form Factor Extraction: The hadronic transition form factors are modeled using a two-parameter series expansion. A simultaneous fit is performed on the partial decay rates of all four channels ( $D^0 \to \pi^- e^+ \nu_e, D^0 \to \pi^- \mu^+ \nu_\mu, D^+ \to \pi^0 e^+ \nu_e, D^+ \to \pi^0 \mu^+ \nu_\mu$ ) to extract $f^{D\to\pi}_+(0)|V_{cd}|$ .
Scalar Current and Asymmetry: The forward-backward asymmetry ( $A_{FB}$ ) is measured in $q^2$ bins. A simultaneous fit to partial decay rates and $A_{FB}$ is conducted to constrain the complex Wilson coefficients ( $C_S^\ell$ ) associated with scalar currents.

Key Contributions and Results

Branching Fractions: The paper reports the first precision measurements of the branching fractions for all four decay modes using the full dataset. The results are:
- $\mathcal{B}(D^0 \to \pi^- e^+ \nu_e) = (2.950 \pm 0.017_{\text{stat}} \pm 0.017_{\text{syst}}) \times 10^{-3}$
- $\mathcal{B}(D^0 \to \pi^- \mu^+ \nu_\mu) = (2.817 \pm 0.037_{\text{stat}} \pm 0.019_{\text{syst}}) \times 10^{-3}$
- $\mathcal{B}(D^+ \to \pi^0 e^+ \nu_e) = (3.622 \pm 0.034_{\text{stat}} \pm 0.018_{\text{syst}}) \times 10^{-3}$
- $\mathcal{B}(D^+ \to \pi^0 \mu^+ \nu_\mu) = (3.507 \pm 0.043_{\text{stat}} \pm 0.026_{\text{syst}}) \times 10^{-3}$
  These measurements improve upon previous BESIII results by a factor of 2–3.
Form Factor and CKM Element: Through a simultaneous fit, the product of the form factor at zero momentum transfer and the CKM element is determined:
- $f^{D\to\pi}_+(0)|V_{cd}| = 0.1425 \pm 0.0005_{\text{stat}} \pm 0.0003_{\text{syst}}$
  Using the SM global fit value for $|V_{cd}|$ , the form factor is extracted as $f^{D\to\pi}_+(0) = 0.6339 \pm 0.0024_{\text{stat}} \pm 0.0014_{\text{syst}}$ . Conversely, using Lattice QCD calculations for the form factor, the CKM element is determined as $|V_{cd}| = 0.2262 \pm 0.0008_{\text{stat}} \pm 0.0005_{\text{syst}} \pm 0.0018_{\text{LQCD}}$ .
Lepton Flavor Universality (LFU): The ratios of semimuonic to semielectronic branching fractions are measured:
- $R^0_{\text{LFU}} = 0.947 \pm 0.014_{\text{stat}} \pm 0.005_{\text{syst}}$
- $R^+_{\text{LFU}} = 0.973 \pm 0.015_{\text{stat}} \pm 0.006_{\text{syst}}$
  These results are consistent with SM predictions within $2.5\sigma$ and $0.7\sigma$ , respectively.
Forward-Backward Asymmetries: This work presents the first experimental measurements of the forward-backward asymmetries ( $A_{FB}$ ) for $D \to \pi \ell^+ \nu_\ell$ decays in $q^2$ bins. The measured asymmetries are consistent with SM predictions.
Scalar Current Constraints: By fitting the partial decay rates and $A_{FB}$ , the paper establishes the first experimental constraints on the scalar current contribution in the $c \to d \ell^+ \nu_\ell$ transition. The results for the muon channel are:
- $\text{Re}(C_S^\mu) = 0.022 \pm 0.023_{\text{stat}} \pm 0.003_{\text{syst}}$
- $|\text{Im}(C_S^\mu)| = 0.000 \pm 0.038_{\text{stat}} \pm 0.012_{\text{syst}}$
  No evidence for scalar currents beyond the SM is found. The significance of a non-zero $C_S^\mu$ is estimated at $1.6\sigma$ .

Significance
The paper claims that these results represent the most precise measurements to date for these decay modes, superseding previous BESIII analyses. The improved precision on $f^{D\to\pi}_+(0)$ and $|V_{cd}|$ provides a stringent test for theoretical calculations, particularly Lattice QCD. The first-time measurement of forward-backward asymmetries and the resulting constraints on scalar currents offer critical new data for investigating potential New Physics in the charm sector, specifically regarding the scalar current contributions that could explain anomalies observed in other flavor sectors. The consistency of the LFU ratios with the Standard Model further supports the SM description of these interactions within the current experimental precision.

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