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  • Open Access

Improved Calculation of Radiative Corrections to τ→ππντ Decays

Gilberto Colangelo, Martina Cottini, Martin Hoferichter, and Simon Holz

  • Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern, Sidlerstrasse 5, 3012 Bern, Switzerland

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Phys. Rev. Lett. 136, 101903 – Published 11 March, 2026

DOI: https://doi.org/10.1103/ryk1-x6v1

Abstract

A reliable calculation of radiative corrections to τ→ππντ decays is an important prerequisite for using hadronic τ decays for a data-driven evaluation of the hadronic-vacuum-polarization (HVP) contribution to the anomalous magnetic moment of the muon, aμHVP,LO[ππ,τ]. In this Letter, we present an improved model-independent analysis of these radiative corrections, including, for the first time, effects beyond pointlike pions in the evaluation of the loop diagrams. These structure-dependent corrections, implemented via a dispersive representation of the pion form factor, lead to significant changes compared to previous calculations due to enhancements near the ρ(770) resonance. We also devise strategies for the matching to chiral perturbation theory and a stable implementation of the real corrections down to the two-pion threshold, which shows that some higher-order isospin-breaking corrections need to be kept due to a strong threshold enhancement. Finally, we perform dispersive fits to the currently available τ→ππντ spectra and discuss the consequences for isospin-breaking corrections in the evaluation of aμHVP,LO[ππ,τ].

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References (178)

  1. D. P. Aguillard et al. (Muon g−2 Collaboration), Phys. Rev. Lett. 135, 101802 (2025).
  2. D. P. Aguillard et al. (Muon g−2 Collaboration), Phys. Rev. Lett. 131, 161802 (2023).
  3. D. P. Aguillard et al. (Muon g−2 Collaboration), Phys. Rev. D 110, 032009 (2024).
  4. B. Abi et al. (Muon g−2 Collaboration), Phys. Rev. Lett. 126, 141801 (2021).
  5. T. Albahri et al. (Muon g−2 Collaboration), Phys. Rev. D 103, 072002 (2021).
  6. T. Albahri et al. (Muon g−2 Collaboration), Phys. Rev. A 103, 042208 (2021).
  7. T. Albahri et al. (Muon g−2 Collaboration), Phys. Rev. Accel. Beams 24, 044002 (2021).
  8. G. W. Bennett et al. (Muon g−2 Collaboration), Phys. Rev. D 73, 072003 (2006).
  9. R. Aliberti et al., Phys. Rep. 1143, 1 (2025).
  10. T. Aoyama, M. Hayakawa, T. Kinoshita, and M. Nio, Phys. Rev. Lett. 109, 111808 (2012).
  11. D. W. Hertzog and M. Hoferichter, arXiv:2512.16980.
  12. S. Volkov, Phys. Rev. D 100, 096004 (2019).
  13. S. Volkov, Phys. Rev. D 110, 036001 (2024).
  14. T. Aoyama, M. Hayakawa, A. Hirayama, and M. Nio, Phys. Rev. D 111, L031902 (2025).
  15. R. H. Parker, C. Yu, W. Zhong, B. Estey, and H. Müller, Science 360, 191 (2018).
  16. L. Morel, Z. Yao, P. Cladé, and S. Guellati-Khélifa, Nature (London) 588, 61 (2020).
  17. X. Fan, T. G. Myers, B. A. D. Sukra, and G. Gabrielse, Phys. Rev. Lett. 130, 071801 (2023).
  18. A. Czarnecki, W. J. Marciano, and A. Vainshtein, Phys. Rev. D 67, 073006 (2003); 73, 119901(E) (2006).
  19. C. Gnendiger, D. Stöckinger, and H. Stöckinger-Kim, Phys. Rev. D 88, 053005 (2013).
  20. J. Lüdtke, M. Procura, and P. Stoffer, J. High Energy Phys. 04 (2025) 130.
  21. M. Hoferichter, J. Lüdtke, L. Naterop, M. Procura, and P. Stoffer, Phys. Rev. Lett. 134, 201801 (2025).
  22. T. Blum, P.  A. Boyle, V. Gülpers, T. Izubuchi, L. Jin, C. Jung, A. Jüttner, C. Lehner, A. Portelli, and J.  T. Tsang (RBC, UKQCD Collaborations), Phys. Rev. Lett. 121, 022003 (2018).
  23. D. Giusti, V. Lubicz, G. Martinelli, F. Sanfilippo, and S. Simula (ETM Collaboration), Phys. Rev. D 99, 114502 (2019).
  24. S. Borsányi et al. (BMWc Collaboration), Nature (London) 593, 51 (2021).
  25. C. Lehner and A. S. Meyer, Phys. Rev. D 101, 074515 (2020).
  26. G. Wang, T. Draper, K.-F. Liu, and Y.-B. Yang (χQCD Collaboration), Phys. Rev. D 107, 034513 (2023).
  27. C. Aubin, T. Blum, M. Golterman, and S. Peris, Phys. Rev. D 106, 054503 (2022).
  28. M. Cè et al., Phys. Rev. D 106, 114502 (2022).
  29. C. Alexandrou et al. (ETM Collaboration), Phys. Rev. D 107, 074506 (2023).
  30. T. Blum et al. (RBC, UKQCD Collaboration), Phys. Rev. D 108, 054507 (2023).
  31. S. Kuberski, M. Cè, G. von Hippel, H. B. Meyer, K. Ottnad, A. Risch, and H. Wittig, J. High Energy Phys. 03 (2024) 172.
  32. A. Boccaletti et al. (BMWc Collaboration), arXiv:2407.10913.
  33. S. Spiegel and C. Lehner, Phys. Rev. D 111, 114517 (2025).
  34. T. Blum et al. (RBC, UKQCD Collaborations), Phys. Rev. Lett. 134, 201901 (2025).
  35. D. Djukanovic, G. von Hippel, S. Kuberski, H. B. Meyer, N. Miller, K. Ottnad, J. Parrino, A. Risch, and H. Wittig, J. High Energy Phys. 04 (2025) 098.
  36. C. Alexandrou et al. (ETM Collaboration), Phys. Rev. D 111, 054502 (2025).
  37. A. Bazavov et al. (Fermilab Lattice, HPQCD, MILC Collaborations), Phys. Rev. D 111, 094508 (2025).
  38. A. Bazavov et al. (Fermilab Lattice, HPQCD, MILC Collaborations), Phys. Rev. Lett. 135, 011901 (2025).
  39. A. Keshavarzi, D. Nomura, and T. Teubner, Phys. Rev. D 101, 014029 (2020).
  40. L. Di Luzio, A. Keshavarzi, A. Masiero, and P. Paradisi, Phys. Rev. Lett. 134, 011902 (2025).
  41. A. Kurz, T. Liu, P. Marquard, and M. Steinhauser, Phys. Lett. B 734, 144 (2014).
  42. G. Colangelo, M. Hoferichter, M. Procura, and P. Stoffer, J. High Energy Phys. 09 (2015) 074.
  43. P. Masjuan and P. Sánchez-Puertas, Phys. Rev. D 95, 054026 (2017).
  44. G. Colangelo, M. Hoferichter, M. Procura, and P. Stoffer, Phys. Rev. Lett. 118, 232001 (2017).
  45. G. Colangelo, M. Hoferichter, M. Procura, and P. Stoffer, J. High Energy Phys. 04 (2017) 161.
  46. M. Hoferichter, B.-L. Hoid, B. Kubis, S. Leupold, and S. P. Schneider, Phys. Rev. Lett. 121, 112002 (2018).
  47. M. Hoferichter, B.-L. Hoid, B. Kubis, S. Leupold, and S. P. Schneider, J. High Energy Phys. 10 (2018) 141.
  48. G. Eichmann, C. S. Fischer, E. Weil, and R. Williams, Phys. Lett. B 797, 134855 (2019); 799, 135029(E) (2019).
  49. J. Bijnens, N. Hermansson-Truedsson, and A. Rodríguez-Sánchez, Phys. Lett. B 798, 134994 (2019).
  50. J. Leutgeb and A. Rebhan, Phys. Rev. D 101, 114015 (2020).
  51. L. Cappiello, O. Catà, G. D’Ambrosio, D. Greynat, and A. Iyer, Phys. Rev. D 102, 016009 (2020).
  52. P. Masjuan, P. Roig, and P. Sánchez-Puertas, J. Phys. G 49, 015002 (2022).
  53. J. Bijnens, N. Hermansson-Truedsson, L. Laub, and A. Rodríguez-Sánchez, J. High Energy Phys. 10 (2020) 203.
  54. J. Bijnens, N. Hermansson-Truedsson, L. Laub, and A. Rodríguez-Sánchez, J. High Energy Phys. 04 (2021) 240.
  55. I. Danilkin, M. Hoferichter, and P. Stoffer, Phys. Lett. B 820, 136502 (2021).
  56. D. Stamen, D. Hariharan, M. Hoferichter, B. Kubis, and P. Stoffer, Eur. Phys. J. C 82, 432 (2022).
  57. J. Leutgeb, J. Mager, and A. Rebhan, Phys. Rev. D 107, 054021 (2023).
  58. M. Hoferichter, B. Kubis, and M. Zanke, J. High Energy Phys. 08 (2023) 209.
  59. M. Hoferichter, P. Stoffer, and M. Zillinger, J. High Energy Phys. 04 (2024) 092.
  60. E. J. Estrada, S. Gonzàlez-Solís, A. Guevara, and P. Roig, J. High Energy Phys. 12 (2024) 203.
  61. O. Deineka, I. Danilkin, and M. Vanderhaeghen, Phys. Rev. D 111, 034009 (2025).
  62. G. Eichmann, C. S. Fischer, T. Haeuser, and O. Regenfelder, Eur. Phys. J. C 85, 445 (2025).
  63. J. Bijnens, N. Hermansson-Truedsson, and A. Rodríguez-Sánchez, J. High Energy Phys. 03 (2025) 094.
  64. M. Hoferichter, P. Stoffer, and M. Zillinger, Phys. Rev. Lett. 134, 061902 (2025).
  65. M. Hoferichter, P. Stoffer, and M. Zillinger, J. High Energy Phys. 02 (2025) 121.
  66. S. Holz, M. Hoferichter, B.-L. Hoid, and B. Kubis, Phys. Rev. Lett. 134, 171902 (2025).
  67. S. Holz, M. Hoferichter, B.-L. Hoid, and B. Kubis, J. High Energy Phys. 04 (2025) 147.
  68. L. Cappiello, J. Leutgeb, J. Mager, and A. Rebhan, J. High Energy Phys. 07 (2025) 033.
  69. G. Colangelo, M. Hoferichter, A. Nyffeler, M. Passera, and P. Stoffer, Phys. Lett. B 735, 90 (2014).
  70. T. Blum, N. Christ, M. Hayakawa, T. Izubuchi, L. Jin, C. Jung, and C. Lehner (RBC, UKQCD Collaborations), Phys. Rev. Lett. 124, 132002 (2020).
  71. E.-H. Chao, R. J. Hudspith, A. Gérardin, J. R. Green, H. B. Meyer, and K. Ottnad, Eur. Phys. J. C 81, 651 (2021).
  72. E.-H. Chao, R. J. Hudspith, A. Gérardin, J. R. Green, and H. B. Meyer, Eur. Phys. J. C 82, 664 (2022).
  73. T. Blum, N. Christ, M. Hayakawa, T. Izubuchi, L. Jin, C. Jung, C. Lehner, and C. Tu (RBC, UKQCD Collaborations), Phys. Rev. D 111, 014501 (2025).
  74. Z. Fodor, A. Gerardin, L. Lellouch, K. K. Szabó, B. C. Toth, and C. Zimmermann (BMWc Collaboration), Phys. Rev. D 111, 114509 (2025).
  75. T. Aoyama et al., Phys. Rep. 887, 1 (2020).
  76. M. Davier, A. Hoecker, B. Malaescu, and Z. Zhang, Eur. Phys. J. C 77, 827 (2017).
  77. A. Keshavarzi, D. Nomura, and T. Teubner, Phys. Rev. D 97, 114025 (2018).
  78. G. Colangelo, M. Hoferichter, and P. Stoffer, J. High Energy Phys. 02 (2019) 006.
  79. M. Hoferichter, B.-L. Hoid, and B. Kubis, J. High Energy Phys. 08 (2019) 137.
  80. M. Davier, A. Hoecker, B. Malaescu, and Z. Zhang, Eur. Phys. J. C 80, 241 (2020); 80, 410(E) (2020).
  81. B.-L. Hoid, M. Hoferichter, and B. Kubis, Eur. Phys. J. C 80, 988 (2020).
  82. F. V. Ignatov et al. (CMD-3 Collaboration), Phys. Rev. D 109, 112002 (2024).
  83. F. V. Ignatov et al. (CMD-3 Collaboration), Phys. Rev. Lett. 132, 231903 (2024).
  84. G. Colangelo et al., arXiv:2203.15810.
  85. L. Polat, arXiv:2601.16587.
  86. F. Campanario, H. Czyż, J. Gluza, T. Jeliński, G. Rodrigo, S. Tracz, and D. Zhuridov, Phys. Rev. D 100, 076004 (2019).
  87. F. Ignatov and R. N. Lee, Phys. Lett. B 833, 137283 (2022).
  88. G. Colangelo, M. Hoferichter, J. Monnard, and J. Ruiz de Elvira, J. High Energy Phys. 08 (2022) 295; 03 (2025) 217(E).
  89. J. Monnard, Ph.D. thesis, Universität Bern, 2021, https://boristheses.unibe.ch/2825/.
  90. G. Abbiendi et al., arXiv:2201.12102.
  91. J. P. Lees et al. (BABAR Collaboration), Phys. Rev. D 108, L111103 (2023).
  92. E. Budassi, C. M. Carloni Calame, M. Ghilardi, A. Gurgone, G. Montagna, M. Moretti, O. Nicrosini, F. Piccinini, and F. P. Ucci, J. High Energy Phys. 05 (2025) 196.
  93. R. Aliberti et al., SciPost Phys. Commun. Rep. 9, 1 (2025).
  94. Y. Fang, S. Kollatzsch, M. Rocco, A. Signer, Y. Ulrich, and M. Zoller, arXiv:2512.10709.
  95. E. Budassi, C. M. Carloni Calame, M. Ghilardi, A. Gurgone, G. Montagna, M. Moretti, O. Nicrosini, F. Piccinini, and F. P. Ucci, arXiv:2601.19530.
  96. R. Alemany, M. Davier, and A. Hoecker, Eur. Phys. J. C 2, 123 (1998).
  97. G. Colangelo, M. Hoferichter, and P. Stoffer, Phys. Lett. B 814, 136073 (2021).
  98. G. Colangelo, M. Hoferichter, B. Kubis, and P. Stoffer, J. High Energy Phys. 10 (2022) 032.
  99. M. Hoferichter, G. Colangelo, B.-L. Hoid, B. Kubis, J. Ruiz de Elvira, D. Schuh, D. Stamen, and P. Stoffer, Phys. Rev. Lett. 131, 161905 (2023).
  100. P. Stoffer, G. Colangelo, and M. Hoferichter, J. Instrum. 18, C10021 (2023).
  101. T. P. Leplumey and P. Stoffer, arXiv:2501.09643.
  102. M. N. Achasov et al. (SND Collaboration), J. Exp. Theor. Phys. 103, 380 (2006).
  103. R. R. Akhmetshin et al. (CMD-2 Collaboration), Phys. Lett. B 648, 28 (2007).
  104. J. P. Lees et al. (BABAR Collaboration), Phys. Rev. D 86, 032013 (2012).
  105. M. Ablikim et al. (BESIII Collaboration), Phys. Lett. B 753, 629 (2016); 812, 135982(E) (2021).
  106. A. Anastasi et al. (KLOE-2 Collaboration), J. High Energy Phys. 03 (2018) 173.
  107. G. Colangelo, M. Cottini, and J. Ruiz de Elvira, J. High Energy Phys. 02 (2026) 098.
  108. V. Cirigliano, G. Ecker, and H. Neufeld, Phys. Lett. B 513, 361 (2001).
  109. V. Cirigliano, G. Ecker, and H. Neufeld, J. High Energy Phys. 08 (2002) 002.
  110. F. Flores-Baéz, A. Flores-Tlalpa, G. López Castro, and G. Toledo Sánchez, Phys. Rev. D 74, 071301 (2006).
  111. F. V. Flores-Baéz, G. López Castro, and G. Toledo Sánchez, Phys. Rev. D 76, 096010 (2007).
  112. M. Davier, A. Hoecker, G. López Castro, B. Malaescu, X. H. Mo, G. Toledo Sánchez, P. Wang, C. Z. Yuan, and Z. Zhang, Eur. Phys. J. C 66, 127 (2010).
  113. J. A. Miranda and P. Roig, Phys. Rev. D 102, 114017 (2020).
  114. M. Davier, A. Hoecker, A.-M. Lutz, B. Malaescu, and Z. Zhang, Eur. Phys. J. C 84, 721 (2024).
  115. G. López Castro, A. Miranda, and P. Roig, Phys. Rev. D 111, 073004 (2025).
  116. M. Bruno, T. Izubuchi, C. Lehner, and A. Meyer, Proc. Sci. LATTICE2018 (2018) 135 [arXiv:1811.00508].
  117. M. Fujikawa et al. (Belle Collaboration), Phys. Rev. D 78, 072006 (2008).
  118. S. Schael et al. (ALEPH Collaboration), Phys. Rep. 421, 191 (2005).
  119. M. Davier, A. Höcker, B. Malaescu, C.-Z. Yuan, and Z. Zhang, Eur. Phys. J. C 74, 2803 (2014).
  120. S. Anderson et al. (CLEO Collaboration), Phys. Rev. D 61, 112002 (2000).
  121. K. Ackerstaff et al. (OPAL Collaboration), Eur. Phys. J. C 7, 571 (1999).
  122. S. Navas et al. (Particle Data Group), Phys. Rev. D 110, 030001 (2024).
  123. S. Banerjee et al. (HFLAV Collaboration), Phys. Rev. D 113, 012008 (2026).
  124. A. Sirlin, Nucl. Phys. B196, 83 (1982).
  125. W. J. Marciano and A. Sirlin, Phys. Rev. Lett. 56, 22 (1986).
  126. W. J. Marciano and A. Sirlin, Phys. Rev. Lett. 61, 1815 (1988).
  127. W. J. Marciano and A. Sirlin, Phys. Rev. Lett. 71, 3629 (1993).
  128. E. Braaten and C.-S. Li, Phys. Rev. D 42, 3888 (1990).
  129. J. Erler, Rev. Mex. Fis. 50, 200 (2004); arXiv:hep-ph/0211345.
  130. M. Davier, S. Eidelman, A. Hocker, and Z. Zhang, Eur. Phys. J. C 27, 497 (2003).
  131. V. Cirigliano, W. Dekens, E. Mereghetti, and O. Tomalak, Phys. Rev. D 108, 053003 (2023).
  132. G. Colangelo, S. Lanz, H. Leutwyler, and E. Passemar, Eur. Phys. J. C 78, 947 (2018).
  133. R. Urech, Nucl. Phys. B433, 234 (1995).
  134. M. Knecht, H. Neufeld, H. Rupertsberger, and P. Talavera, Eur. Phys. J. C 12, 469 (2000).
  135. R. García-Martín and B. Moussallam, Eur. Phys. J. C 70, 155 (2010).
  136. M. Hoferichter, D. R. Phillips, and C. Schat, Eur. Phys. J. C 71, 1743 (2011).
  137. B. Moussallam, Eur. Phys. J. C 73, 2539 (2013).
  138. I. Danilkin and M. Vanderhaeghen, Phys. Lett. B 789, 366 (2019).
  139. M. Hoferichter and P. Stoffer, J. High Energy Phys. 07 (2019) 073.
  140. I. Danilkin, O. Deineka, and M. Vanderhaeghen, Phys. Rev. D 101, 054008 (2020).
  141. G. Passarino and M. J. G. Veltman, Nucl. Phys. B160, 151 (1979).
  142. W. Beenakker and A. Denner, Nucl. Phys. B338, 349 (1990).
  143. G. Colangelo, M. Cottini, M. Hoferichter, and S. Holz, J. High Energy Phys. 02 (2026) 181.
  144. S. Descotes-Genon and B. Moussallam, Eur. Phys. J. C 42, 403 (2005).
  145. P.-X. Ma, X. Feng, M. Gorchtein, L.-C. Jin, and C.-Y. Seng, Phys. Rev. D 103, 114503 (2021).
  146. V. Cirigliano, M. Hoferichter, and N. Valori, arXiv:2602.11253.
  147. X. Feng, M. Gorchtein, L.-C. Jin, P.-X. Ma, and C.-Y. Seng, Phys. Rev. Lett. 124, 192002 (2020).
  148. J.-S. Yoo, T. Bhattacharya, R. Gupta, S. Mondal, and B. Yoon, Phys. Rev. D 108, 034508 (2023).
  149. J. Gasser and H. Leutwyler, Ann. Phys. (N.Y.) 158, 142 (1984).
  150. J. Gasser and H. Leutwyler, Nucl. Phys. B250, 465 (1985).
  151. J. Wess and B. Zumino, Phys. Lett. 37B, 95 (1971).
  152. E. Witten, Nucl. Phys. B223, 422 (1983).
  153. F. E. Low, Phys. Rev. 110, 974 (1958).
  154. G. Ecker, J. Gasser, H. Leutwyler, A. Pich, and E. de Rafael, Phys. Lett. B 223, 425 (1989).
  155. G. Ecker, J. Gasser, A. Pich, and E. de Rafael, Nucl. Phys. B321, 311 (1989).
  156. G. Colangelo, M. Hoferichter, B. Kubis, M. Niehus, and J. Ruiz de Elvira, Phys. Lett. B 825, 136852 (2022).
  157. M. Zielinski et al., Phys. Rev. Lett. 52, 1195 (1984).
  158. B. Moussallam, Nucl. Phys. B504, 381 (1997).
  159. M. Knecht and A. Nyffeler, Eur. Phys. J. C 21, 659 (2001).
  160. V. Cirigliano, G. Ecker, M. Eidemüller, A. Pich, and J. Portolés, Phys. Lett. B 596, 96 (2004).
  161. G. T. Condo, T. Handler, W. M. Bugg, G. R. Blackett, M. Pisharody, and K. A. Danyo, Phys. Rev. D 48, 3045 (1993).
  162. M. Nozar et al. (CLAS Collaboration), Phys. Rev. Lett. 102, 102002 (2009).
  163. M. Hoferichter, B. Kubis, and M. Zanke, Phys. Rev. D 96, 114016 (2017).
  164. M. Zanke, M. Hoferichter, and B. Kubis, J. High Energy Phys. 07 (2021) 106.
  165. R. Omnès, Nuovo Cimento 8, 316 (1958).
  166. C. Bouchiat and L. Michel, J. Phys. Radium 22, 121 (1961).
  167. S. J. Brodsky and E. de Rafael, Phys. Rev. 168, 1620 (1968).
  168. W. Altmannshofer et al. (Belle-II Collaboration), Prog. Theor. Exp. Phys. 2019, 123C01 (2019); 2020, 029201(E) (2020).
  169. G. Colangelo, M. Cottini, M. Hoferichter, and S. Holz, arXiv.org v1 (2025), https://arxiv.org/src/2511.07507v1/anc.
  170. M. Hoferichter, B. Kubis, S. Leupold, F. Niecknig, and S. P. Schneider, Eur. Phys. J. C 74, 3180 (2014).
  171. M. Hoferichter, B.-L. Hoid, B. Kubis, and D. Schuh, J. High Energy Phys. 08 (2023) 208.
  172. M. Hoferichter, B.-L. Hoid, and B. Kubis, J. High Energy Phys. 07 (2025) 095.
  173. S. M. Roy, Phys. Lett. 36B, 353 (1971).
  174. B. Ananthanarayan, G. Colangelo, J. Gasser, and H. Leutwyler, Phys. Rep. 353, 207 (2001).
  175. I. Caprini, G. Colangelo, and H. Leutwyler, Eur. Phys. J. C 72, 1860 (2012).
  176. M. Kirk, B. Kubis, M. Reboud, and D. van Dyk, Phys. Lett. B 861, 139266 (2025).
  177. G. D’Agostini, Nucl. Instrum. Methods Phys. Res., Sect. A 346, 306 (1994).
  178. R. D. Ball, L. Del Debbio, S. Forte, A. Guffanti, J. I. Latorre, J. Rojo, and M. Ubiali (NNPDF Collaboration), J. High Energy Phys. 05 (2010) 075.

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Phys. Rev. Lett. 136, 101903– Published 11 March, 2026
  • Received 12 November 2025
  • Revised 21 January 2026
  • Accepted 11 February 2026
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