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We use a hadronic $B$-tagging technique, and search for the signal decay in the system recoiling against the fully reconstructed $B$ meson. We find no evidence for $B^0 \\rightarrow K_S^0 \\tau^\\pm \\ell^\\mp$ decays and set 90\\% confidence level upper limits on the branching fractions in the range of $[0.8,\\,3.6]\\times10^{-5}$.","authors_text":"A. Aloisio, A. Baur, A. Beaubien, A. B. Kaliyar, A. Bobrov, A. Bolz, A. Boschetti, A. Bozek, A. Budano, A. Di Canto, A. Fodor, A. Gabrielli, A. Gaz, A. Gellrich, A. Giri, A. Glazov, A. Heidelbach, A. Ishikawa, A. Johnson, A. Korobov, A. Kuzmin, A. Martens, A. Martini, A. Natochii, A. Passeri, A. Rostomyan, A. Selce, A. Sibidanov, A. Soffer, A. Sokolov, A. Thaller, A. Vinokurova, A. Warburton, B. Bhuyan, B. D. Yabsley, Belle, Belle II Collaborations: I. Adachi, B. G. Cheon, B. G. Fulsom, B. Gobbo, B. Paschen, B. Scavino, B. Spruck, B. Zhang, C. Cecchi, C. Finck, C. Harris, C. Hearty, C.-H. Kim, C. Ketter, C. Kiesling, C. Lemettais, C.-L. Hsu, C. Li, C. Lyu, C. Madaan, C. Marinas, C. Martellini, C. Miller, C. Praz, C. Schwanda, C. Sfienti, C. Sharma, C. Wessel, C. Z. Yuan, D. A. Sanders, D. Biswas, D. Bodrov, D. Dossett, D. E. Jaffe, D. Ghosh, D. Greenwald, D. Jacobi, D. Kumar, D. Liventsev, D. M. Asner, D. Matvienko, D. Meleshko, D. Ricalde Herrmann, D. Shtol, D. Y. Kim, E. Bertholet, E. De La Cruz-Burelo, E. Ganiev, E. Graziani, E.-J. Jang, E. Kovalenko, E. Manoni, E. Paoloni, E. Prencipe, E. Solovieva, E. Torassa, E. Won, F. Becherer, F. Bianchi, F. Di Capua, F. Forti, F. Keil, F. Meier, F. Otani, F. R. Le Diberder, F. Simon, F. Tenchini, F. U. Bernlochner, F. Zeng, G. B. Mohanty, G. Casarosa, G. de Marino, G. De Nardo, G. De Pietro, G. Dujany, G. Finocchiaro, G. Gaudino, G. Ghevondyan, G. Giakoustidis, G. Inguglia, G. Karyan, G. Mancinelli, G. Nazaryan, G. Pakhlova, G. Raeuber, G. Rizzo, G. Schnell, H. Ahmed, H. Aihara, H. Atmacan, H. Bae, H.-E. Cho, H. Ghumaryan, H.-G. Moser, H. Hayashii, H. Junkerkalefeld, H. Miyake, H. Ono, H. Park, H. Purwar, H. Svidras, I. Dom\\'inguez Jim\\'enez, I. Haide, I. Heredia de la Cruz, I. Nakamura, I. Peruzzi, I. Prudiiev, I. Ripp-Baudot, I. Tsaklidis, I. Ueda, J. A. McKenna, J. Baudot, J. Becker, J. B. Singh, J. Cerasoli, J. Cochran, J. Dingfelder, J.-G. Shiu, J. H. Yin, J. Kandra, J. Libby, J. Lin, J. M. Roney, J. Park, J. Serrano, J. Skorupa, J. S. Lange, J. Strube, J. S. Zhou, J. U. Rehman, J. V. Bennett, J. Wiechczynski, J. X. Cui, J. Yelton, J.-Y. Kim, J. Yuan, K. Adamczyk, K. Chilikin, K. Chirapatpimol, K. Cho, K. Dugic, K. E. Varvell, K. Gudkova, K. Hayasaka, K. H. Kang, K.-H. Kim, K. Inami, K. Kinoshita, K. K. Joo, K. Kojima, K. Kumara, K. Lalwani, K. Miyabayashi, K. Parham, K. Park, K. Ravindran, K. R. Nakamura, K. Senyo, K. Sumisawa, K. Tanida, K. Trabelsi, K. Unger, K. Uno, K. Yoshihara, L. Aggarwal, L. Cao, L. Corona, L. E. Piilonen, L. K. Li, L. Lanceri, L. Massaccesi, L. Reuter, L. Santelj, L. Vitale, L. Zani, L. Zhu, M. Alhakami, M. Aversano, M. Barrett, M. Bartl, M. Bertemes, M. Bessner, M. Bra\\v{c}ko, M. Campajola, M.-C. Chang, M. Destefanis, M. Dorigo, M. E. Sevior, M. Garcia-Hernandez, M. Hern\\'andez Villanueva, M. H. Liu, M. Hoek, M. Hohmann, M. Iwasaki, M. J. Lee, M. Kaleta, M. Laurenza, M. Maggiora, M. Mantovano, M. Masuda, M. Maushart, M. Merola, M. Mirra, M. Nakao, M. Naruki, M. Nayak, M. Neu, M. Piccolo, M. Reif, M. Remnev, M. Roehrken, M. Sobotzik, M. Stari\\v{c}, M. Sumihama, M. Takahashi, M. Takizawa, M. T. Hedges, M. T. Prim, M. Veronesi, M. Wakai, M. Watanabe, M.-Z. Wang, N. Akopov, N. Althubiti, N. Anh Ky, N. Ipsita, N. K. Baghel, N. Rauls, N. Rout, N. Suwonjandee, O. Gogota, O. Tittel, P. Bambade, P. Branchini, P. Chang, P. Cheema, P. Ecker, P. Feichtinger, P. Gironella Gironell, P. Goldenzweig, P. Horak, P. Kody\\v{s}, P. Kri\\v{z}an, P. Krokovny, P. Leo, P. L. M. Podesta-Lerma, P. M. Lewis, P. Rados, P. Stavroulakis, P. Urquijo, Q. Campagna, Q. D. Zhou, Q. M. Li, Q. P. Ji, Q. Y. Liu, R. A. Briere, R. Ayad, R. Cheaib, R. de Sangro, R. Dhamija, R. Garg, R. Giordano, R. Godang, R. Hoppe, R. Itoh, R. J. Sobie, R. Kowalewski, R. Kumar, R. Leboucher, R. Maiti, R. Manfredi, R. Mehta, R. Mussa, R. Peschke, R. Pestotnik, R. Stroili, R. Tiwary, R. van Tonder, R. Volpe, R. \\v{Z}leb\\v{c}\\'ik, S. A. De La Motte, S. Bahinipati, S. Bansal, S. Bettarini, S. Bussino, S. Choudhury, S. Dey, S. Dubey, S. E. Vahsen, S. Granderath, S. Hazra, S.-H. Park, S. H. Robertson, S.-J. Cho, S. Jia, S. Kang, S.-K. Choi, S. K. Maurya, S. Kohani, S. Korpar, S. Lacaprara, S. Lin, S. Longo, S. Marcello, S. Mitra, S. Mondal, S. Moneta, S. Nishida, S. Ogawa, S. Pardi, S. Patra, S. P. Maharana, S. Pokharel, S. Prell, S. Raiz, S. Reiter, S. Sandilya, S. Schneider, S. Spataro, S. Stefkova, S. Uno, S. Wallner, S. Watanuki, Sw. Banerjee, S. Yamada, T. E. Browder, T. Ferber, T. Fillinger, T. Hara, T. Higuchi, T. Humair, T. Iijima, T. Kawasaki, T. Koga, T. K. Pedlar, T. Kuhr, T. Kunigo, T. Lam, T. Lueck, T. Luo, T. Martinov, T. Podobnik, T. Shillington, T. Shimasaki, T. S. Lau, T. Uglov, T. V. Dong, U. Tamponi, V. Aushev, V. Babu, V. Bertacchi, V. Bhardwaj, V. Gaur, V. I. Zhukova, V. Savinov, V. S. Vismaya, V. Vobbilisetti, W. Gradl, W. Shan, W. Song, W. Sutcliffe, W. W. Jacobs, W. Yan, W. Z. Li, X. Dong, X. D. Shi, X. P. Xu, Y. B. Li, Y. Guan, Y. Han, Y. Jin, Y.-J. Kwon, Y.-K. Kim, Y. Kulii, Y. Li, Y. Liu, Y. Ma, Y. Nakazawa, Y. Onuki, Y. P. Liao, Y. Seino, Y. Sue, Y.-T. Lai, Y. Unno, Y. Ushiroda, Z. Dole\\v{z}al, Z. Gruberov\\'a, Z. Natkaniec, Z. Q. Liu, Z. 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