Model-agnostic likelihood for the reinterpretation of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:msup> <mml:mrow> <mml:mi>B</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> </mml:mrow> </mml:msup>

We recently measured the branching fraction of the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msup> <a:mi>B</a:mi> <a:mo>+</a:mo> </a:msup> <a:mo stretchy="false">→</a:mo> <a:msup> <a:mi>K</a:mi> <a:mo>+</a:mo> </a:msup> <a:mi>ν</a:mi> <a:mover accent="true"> <a:mi>ν</a:mi> <a:mo stretchy="false">¯</a:mo> </a:mover> </a:math> decay using <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"> <f:mrow> <f:mn>362</f:mn> <f:mtext> </f:mtext> <f:mtext> </f:mtext> <f:msup> <f:mrow> <f:mi>fb</f:mi> </f:mrow> <f:mrow> <f:mo>−</f:mo> <f:mn>1</f:mn> </f:mrow> </f:msup> </f:mrow> </f:math> of on-resonance <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"> <h:msup> <h:mi>e</h:mi> <h:mo>+</h:mo> </h:msup> <h:msup> <h:mi>e</h:mi> <h:mo>−</h:mo> </h:msup> </h:math> collision data under the assumption of Standard Model kinematics, providing the first evidence for this decay. To facilitate future reinterpretations and maximize the scientific impact of this measurement, we publicly release the full analysis likelihood along with all necessary material required for reinterpretation under arbitrary theoretical models sensitive to this measurement. In this work, we demonstrate how the measurement can be reinterpreted within the framework of the weak effective theory. Using a kinematic reweighting technique in combination with the published likelihood, we derive marginal posterior distributions for the Wilson coefficients, construct credible intervals, and assess the goodness of fit to the Belle II data. For the weak effective theory Wilson coefficients, the posterior mode of the magnitudes <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"> <j:mrow> <j:mo stretchy="false">|</j:mo> <j:msub> <j:mrow> <j:mi>C</j:mi> </j:mrow> <j:mrow> <j:mi>VL</j:mi> </j:mrow> </j:msub> <j:mo>+</j:mo> <j:msub> <j:mrow> <j:mi>C</j:mi> </j:mrow> <j:mrow> <j:mi>VR</j:mi> </j:mrow> </j:msub> <j:mo stretchy="false">|</j:mo> </j:mrow> </j:math> , <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"> <n:mo stretchy="false">|</n:mo> <n:msub> <n:mi>C</n:mi> <n:mi>SL</n:mi> </n:msub> <n:mo>+</n:mo> <n:msub> <n:mi>C</n:mi> <n:mi>SR</n:mi> </n:msub> <n:mo stretchy="false">|</n:mo> </n:math> , and <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"> <r:mo stretchy="false">|</r:mo> <r:msub> <r:mi>C</r:mi> <r:mi>TL</r:mi> </r:msub> <r:mo stretchy="false">|</r:mo> </r:math> corresponds to the point (11.3, 0.0, 8.2). The respective 95% credible intervals are [1.9, 16.2], [0.0, 15.4], and [0.0, 11.2].

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Publication Details

Journal
Physical review. D/Physical review. D.
Published
2025-11-24
DOI
https://doi.org/10.1103/pr66-sd36
Primary Topic
Atomic and Subatomic Physics Research
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article
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Model-agnostic likelihood for the reinterpretation of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:msup> <mml:mrow> <mml:mi>B</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> </mml:mrow> </mml:msup>

K. Ravindran, D. Greenwald, C. Cecchi, T. E. Browder et al.
Physical review. D/Physical review. D.
Atomic and Subatomic Physics Research
article

Model-agnostic likelihood for the reinterpretation of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:msup> <mml:mrow> <mml:mi>B</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> </mml:mrow> </mml:msup>

K. Ravindran, D. Greenwald, C. Cecchi, T. E. Browder, Q. M. Li, S. Pardi, X. Dong, Y. Onuki, G. Dujany, Z. Gruberová, R. Leboucher, C. Z. Yuan, M. Hohmann, D. Ricalde Herrmann, Shinichi Ogawa, S. Tanaka, M. Alhakami, J. S. Lange, V. Zhilich, T. Iijima, G. Mancinelli, R. Volpe, J. Libby, X. L. Wang, Y. B. Li, K. Kumara, W. Gradl, V. Bhardwaj, S. Patra, D. A. Sanders, S. A. Al‐Ghamdi, N. K. Baghel, H. Ghumaryan, A. L. Moreira De Carvalho, K. Kojima, Feng Zeng, G. Raeuber, S. Dey, Y. Nakazawa, S. Paul, M. E. Sevior, J. Kandra, A. Ishikawa, S. Raiz, S. P. Maharana, T. Higuchi, J. V. Bennett, H. Svidras, M. Reif, S. Moneta, L. Corona, M. Starič, K. Chirapatpimol, K. Chilikin, D. Marcantonio, J. B. Singh, M. Bertemes, L. Zani, C. Lyu, S. A. De La Motte, M. Masuda, Y. Seino, P. Cheema, Lawrence M. Gartner, A. Beaubien, H. Bae, B. Gobbo, A. Natochii, L. Aggarwal, A. Budano, Z. Liu, T. Kuhr, T. K. Pedlar, J. Park, S. Mondal, F. Keil, L. Chen, M. Sobotzik, S. Stefkova, S. Korpar, F. Tenchini, C. Praz, M. Mirra, K. Miyabayashi, Q. Y. Liu, E. Ganiev, M. J. Lee, P. L. M. Podesta-Lerma, J. Borah, Paul Leo, M. Kaleta, A. Aloisio, S. Kohani, D. Bodrov, J. A. McKenna, Yunhao Ma, E. Prencipe, V. Bonvicini, S. Wallner, S. Sandilya, F. Simon, K. Amos, G. Karyan, S. H. Robertson, C. Schmitt, R. Maiti, Michael H. Bartl, V. Bertacchi, X. T. Hou, Y. Kulii, E. Solovieva, R. Mussa, S. -J. Cho, H. Atmacan, R. Manfredi, G. De Pietro, R. Žlebčík, P. Branchini, Q. Zhou, T. Podobnik, I. Ueda, J. Lin, T. Lueck, R. Giordano, A. Korobov, R. Mehta, D. Liventsev, P. Gironella Gironell, M. Schnepf, K. Schoenning, L. K. Li, P. Goldenzweig, K. Unger, R. Okubo, M. Laurenza, M. Hoek, S. Bettarini, D. Biswas, V. Babu, Z. Doležal, I. Adachi, A. Lozar, Y. Han, Y. Yusa, A. Rostomyan, G. Rizzo, P. Urquijo, K. Cho, K. H. Kang, D. Y. Kim, H. Kindo, J. Baudot, N. Anh Ky, T. Lam, S. Nishida, A. Frey, S. S. Tang, P. Rados, V. Raj, D. M. Asner, R. Godang, M. Barrett, M. Campajola, A. Sibidanov, A. Kuzmin, R. Pestotnik, R. de Sangro, C. Li, S. Kohani, K. Yoshihara, C. Hearty, Francesco Testa, I. Tsaklidis, M. Nayak, A. Martens, A. Thaller, T. V. Dong, B. Bhuyan, K. E. Varvell, A. Boschetti, E. Kovalenko, M. Wakai, S. Choudhury, T. Shillington, Y. Unno, L. Cao, E. Graziani, K. Uno, J. Serrano, G. Gaudino, H. Purwar, S. Hazra, C. Miller, P. Kodyš, G. Finocchiaro, M. Takizawa, K. Gudkova, W. W. Jacobs, M. Iwasaki, Y.B Li, K. Matsuoka, P. Bambade, G. Pakhlova, K. Tanida, C. Mariñas, D. Matvienko, K. Senyo, R. Kowalewski, K. Inami, B. Yabsley, H. Hayashii, R. van Tonder, K. Lalwani, W. Shan, C. Kiesling, P. Krokovny, A. Baur, T. Humair, S. Bussino, P. Horak, L. Šantelj, B. Spruck, J. Chin, Mary P. Neu, A. Selce, A. Bondar, S. K. Maurya, G. de Marino, F. F. Trantou, R. Tiwary, P. Ecker, L. Zhu, R. Kumar, J. Yelton, T. Shimasaki, I. Nakamura, A. Gabrielli, S. Yamada, A. Bozek, L. Vitale, Q. Campagna, N. Althubiti, P. Jackson, D. Shtol, O. Tittel, J. S. Zhou, C. Finck, J. H. Yin, M. T. Hedges, K. Dugic, H. Ono, N. Ipsita, M. Bračko, N. Rout, A. Sokolov, V. S. Vismaya, R. Hoppe, B. G. Fulsom, Y. Li, R. Garg, C. Sfienti, B. Scavino, M. Mantovano, M. T. Prim, F. Forti, R. Ayad, R. Farkas, S. Spataro, V. Savinov, M. H. Liu, F. Becherer, I. Haide, D. Meleshko, G. Heine, S. Privalov, Jae-Young Kim, I. Heredia-De La Cruz, F. Bianchi, J. Kumar, F. Meier, Yuxia Jin, B. Yu, E. Torassa, M. Nakao, L. Massaccesi, E. Bertholet, B. Zhang, J. U. Rehman, Hideaki Miyake, S. B. Yang, Jia Yuan, J. Skorupa, Dilip Ghosh, Y. P. Liao, X. D. Shi, D. Jacobi, R. J. Sobie, L. E. Piilonen, T. S. Lau, V. Gautam, M. Merola, G. Casarosa, P. Stavroulakis, G. Giakoustidis, A. Warburton, V. Gaur, T. Ferber, S. Uno, S. H. Robertson, C. Martellini, A. Gellrich, M. Maggiora, E. Manoni, M. Destefanis, E. De La Cruz–Burelo, H. Nakazawa, F. U. Bernlochner, A. Johnson, R. Itoh, S. Longo, S. Prell, J. A. Becker, S.-W. Lin, G. De Nardo, T. Kunigo, C. Schwanda, M. Veronesi, S. Marcello, A. Soffer, C. Wessel, W. B. Yan, M. Sumihama, N. Akopov, T. Fillinger, A. Giri, S. Reiter, M. Bessner, C. Santos, K. K. Joo, B. G. Cheon, A. Gale, T. Martinov, C. Harris, M. Garcia-Hernandez, J. X. Cui, J. Dingfelder, K. Kinoshita, H. Ahmed, Y. H. Ahn, N. Suwonjandee, S. Vahsen, Y. Ushiroda, Z. Natkaniec, R. Stroili, J. M. Roney, P. Križan, M. Maushart, Sw. Banerjee, L. Stoetzer, M. Abumusabh, L. Salutari
article en

Abstract

We recently measured the branching fraction of the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msup> <a:mi>B</a:mi> <a:mo>+</a:mo> </a:msup> <a:mo stretchy="false">→</a:mo> <a:msup> <a:mi>K</a:mi> <a:mo>+</a:mo> </a:msup> <a:mi>ν</a:mi> <a:mover accent="true"> <a:mi>ν</a:mi> <a:mo stretchy="false">¯</a:mo> </a:mover> </a:math> decay using <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"> <f:mrow> <f:mn>362</f:mn> <f:mtext> </f:mtext> <f:mtext> </f:mtext> <f:msup> <f:mrow> <f:mi>fb</f:mi> </f:mrow> <f:mrow> <f:mo>−</f:mo> <f:mn>1</f:mn> </f:mrow> </f:msup> </f:mrow> </f:math> of on-resonance <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"> <h:msup> <h:mi>e</h:mi> <h:mo>+</h:mo> </h:msup> <h:msup> <h:mi>e</h:mi> <h:mo>−</h:mo> </h:msup> </h:math> collision data under the assumption of Standard Model kinematics, providing the first evidence for this decay. To facilitate future reinterpretations and maximize the scientific impact of this measurement, we publicly release the full analysis likelihood along with all necessary material required for reinterpretation under arbitrary theoretical models sensitive to this measurement. In this work, we demonstrate how the measurement can be reinterpreted within the framework of the weak effective theory. Using a kinematic reweighting technique in combination with the published likelihood, we derive marginal posterior distributions for the Wilson coefficients, construct credible intervals, and assess the goodness of fit to the Belle II data. For the weak effective theory Wilson coefficients, the posterior mode of the magnitudes <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"> <j:mrow> <j:mo stretchy="false">|</j:mo> <j:msub> <j:mrow> <j:mi>C</j:mi> </j:mrow> <j:mrow> <j:mi>VL</j:mi> </j:mrow> </j:msub> <j:mo>+</j:mo> <j:msub> <j:mrow> <j:mi>C</j:mi> </j:mrow> <j:mrow> <j:mi>VR</j:mi> </j:mrow> </j:msub> <j:mo stretchy="false">|</j:mo> </j:mrow> </j:math> , <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"> <n:mo stretchy="false">|</n:mo> <n:msub> <n:mi>C</n:mi> <n:mi>SL</n:mi> </n:msub> <n:mo>+</n:mo> <n:msub> <n:mi>C</n:mi> <n:mi>SR</n:mi> </n:msub> <n:mo stretchy="false">|</n:mo> </n:math> , and <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"> <r:mo stretchy="false">|</r:mo> <r:msub> <r:mi>C</r:mi> <r:mi>TL</r:mi> </r:msub> <r:mo stretchy="false">|</r:mo> </r:math> corresponds to the point (11.3, 0.0, 8.2). The respective 95% credible intervals are [1.9, 16.2], [0.0, 15.4], and [0.0, 11.2].

Physical review. D/Physical review. D.Vol. 112(9)
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Atomic and Subatomic Physics Research
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