- Letter
- Open Access
Reviving the energy-dependent partonic structure of via two-pion distribution amplitudes
Phys. Rev. D 113, L031901 – Published 18 February, 2026
DOI: https://doi.org/10.1103/5vty-jdbh
Abstract
We present a novel framework for analyzing four-body semileptonic weak decays, performing the first high-twist analysis of the form factors using light cone distribution amplitudes for the isoscalar two-pion state (). It is motivated by persistent tensions between phenomenological cascade analyses and QCD-based interpretations of the partonic structure of the meson. Our study reveals that the twist-three DAs incorporate an asymmetry in the partial-wave expansion, a feature absent in single distribution amplitudes, that drives a substantial cancellation between twist-two and twist-three contributions to the form factors. As a result, the predicted decay rate falls significantly below the experimental value. These findings indicate that the isoscalar two-pion system near the charm scale is not primarily a state, reviving the energy-dependent partonic structures of light scalar mesons by highlighting a fundamental limitation of the single-meson light cone distribution amplitude approach in describing such complex systems.
Physics Subject Headings (PhySH)
Article Text
Supplemental Material
References (79)
- S. Navas et al. (Particle Data Group), Phys. Rev. D 110, 030001 (2024).
- F. E. Close and N. A. Tornqvist, J. Phys. G 28, R249 (2002).
- C. Amsler and N. A. Tornqvist, Phys. Rep. 389, 61 (2004).
- J. R. Pelaez, Phys. Rep. 658, 1 (2016).
- A. Bramon and E. Masso, Phys. Lett. 93B, 65 (1980); 107B, 455(E) (1981).
- D. Morgan and M. R. Pennington, Phys. Rev. D 48, 1185 (1993).
- N. A. Tornqvist and M. Roos, Phys. Rev. Lett. 76, 1575 (1996).
- P. J. A. Bicudo, Phys. Rev. C 60, 035209 (1999).
- T. Umekawa, K. Naito, M. Oka, and M. Takizawa, Phys. Rev. C 70, 055205 (2004).
- E. Ruiz Arriola and W. Broniowski, Phys. Rev. D 81, 054009 (2010).
- J. A. Oller and E. Oset, Nucl. Phys. A620, 438 (1997); A652, 407(E) (1999).
- M. G. Alford and R. L. Jaffe, Nucl. Phys. B578, 367 (2000).
- N. N. Achasov and A. V. Kiselev, Phys. Rev. D 73, 054029 (2006); 74, 059902(E) (2006); 83, 054008 (2011).
- L. Maiani, F. Piccinini, A. D. Polosa, and V. Riquer, Phys. Rev. Lett. 93, 212002 (2004).
- G. ’t Hooft, G. Isidori, L. Maiani, A. D. Polosa, and V. Riquer, Phys. Lett. B 662, 424 (2008).
- S. S. Agaev, K. Azizi, and H. Sundu, Phys. Lett. B 781, 279 (2018).
- R. L. Jaffe, Phys. Rev. D 15, 267 (1977).
- R. A. Briceno, J. J. Dudek, R. G. Edwards, and D. J. Wilson, Phys. Rev. D 97, 054513 (2018).
- R. A. Briceno, J. J. Dudek, R. G. Edwards, and D. J. Wilson, Phys. Rev. Lett. 118, 022002 (2017).
- J. D. Weinstein and N. Isgur, Phys. Rev. Lett. 48, 659 (1982); Phys. Rev. D 27, 588 (1983); 41, 2236 (1990).
- G. Janssen, B. C. Pearce, K. Holinde, and J. Speth, Phys. Rev. D 52, 2690 (1995).
- J. A. Oller, E. Oset, and J. R. Pelaez, Phys. Rev. Lett. 80, 3452 (1998).
- M. P. Locher, V. E. Markushin, and H. Q. Zheng, Eur. Phys. J. C 4, 317 (1998).
- V. Bernard, M. Lage, U. G. Meissner, and A. Rusetsky, J. High Energy Phys. 01 (2011) 019.
- W. Wang and C. D. Lu, Phys. Rev. D 82, 034016 (2010).
- H. W. Ke, X. Q. Li, and Z. T. Wei, Phys. Rev. D 80, 074030 (2009).
- T. Sekihara and E. Oset, Phys. Rev. D 92, 054038 (2015).
- Y. J. Shi and W. Wang, Phys. Rev. D 92, 074038 (2015).
- Y. J. Shi, C. Y. Seng, F. K. Guo, B. Kubis, U. G. Meißner, and W. Wang, J. High Energy Phys. 04 (2021) 086.
- X. D. Cheng, H. B. Li, B. Wei, Y. G. Xu, and M. Z. Yang, Phys. Rev. D 96, 033002 (2017).
- C. D. Lu, Y. M. Wang, and H. Zou, Phys. Rev. D 75, 056001 (2007).
- Z. H. Wu, H. B. Fu, T. Zhong, D. Huang, D. D. Hu, and X. G. Wu, Nucl. Phys. A1036, 122671 (2023).
- J. Bijnens and A. Khodjamirian, Eur. Phys. J. C 26, 67 (2002).
- P. Ball, V. M. Braun, and A. Lenz, J. High Energy Phys. 05 (2006) 004.
- I. I. Balitsky and V. M. Braun, Nucl. Phys. B311, 541 (1989).
- V. M. Braun, G. P. Korchemsky, and D. Müller, Prog. Part. Nucl. Phys. 51, 311 (2003).
- P. Colangelo, F. De Fazio, and W. Wang, Phys. Rev. D 81, 074001 (2010).
- H. Y. Cheng, C. K. Chua, and K. C. Yang, Phys. Rev. D 73, 014017 (2006).
- S. Cheng and J. M. Shen, Eur. Phys. J. C 80, 554 (2020).
- S. Cheng and S. L. Zhang, Eur. Phys. J. C 84, 379 (2024).
- D. D. Hu, X. G. Wu, H. J. Tian, T. Zhong, and H. B. Fu, Phys. Rev. D 112, 056023 (2025).
- M. Ablikim et al. (BESIII Collaboration), Phys. Rev. Lett. 132, 141901 (2024).
- M. Diehl, T. Gousset, B. Pire, and O. Teryaev, Phys. Rev. Lett. 81, 1782 (1998).
- M. V. Polyakov, Nucl. Phys. B555, 231 (1999).
- S. Cheng, Phys. Rev. D 99, 053005 (2019).
- S. Cheng, Phys. Rev. D 112, L111301 (2025).
- C. Lorcé, B. Pire, and Q. T. Song, Phys. Rev. D 106, 094030 (2022).
- P. Ball and V. M. Braun, Phys. Rev. D 54, 2182 (1996).
- P. Ball, V. M. Braun, Y. Koike, and K. Tanaka, Nucl. Phys. B529, 323 (1998).
- P. Ball and V. M. Braun, Nucl. Phys. B543, 201 (1999).
- V. L. Chernyak and A. R. Zhitnitsky, JETP Lett. 25, 510 (1977).
- G. P. Lepage and S. J. Brodsky, Phys. Lett. 87B, 359 (1979).
- A. V. Efremov and A. V. Radyushkin, Phys. Lett. 94B, 245 (1980).
- R. Omnes, Nuovo Cimento 8, 316 (1958).
- D. Alde et al. (GAMS Collaboration), Z. Phys. C 66, 375 (1995).
- N. N. Achasov and G. N. Shestakov, Phys. Rev. D 58, 054011 (1998).
- R. Garcia-Martin, R. Kaminski, J. R. Pelaez, J. Ruiz de Elvira, and F. J. Yndurain, Phys. Rev. D 83, 074004 (2011).
- L. Y. Dai and M. R. Pennington, Phys. Rev. D 90, 036004 (2014).
- D. Diakonov and V. Y. Petrov, Nucl. Phys. B272, 457 (1986).
- B. Lehmann-Dronke, P. V. Pobylitsa, M. V. Polyakov, A. Schafer, and K. Goeke, Phys. Lett. B 475, 147 (2000).
- See Supplement Material at http://link.aps.org/supplemental/10.1103/5vty-jdbh for the constraints of nonperturbative parameters of from low-energy effective theory, which includes Refs. [1,44,62–71].
- P. V. Pobylitsa, Phys. Lett. B 226, 387 (1989).
- D. Diakonov, M. V. Polyakov, and C. Weiss, Nucl. Phys. B461, 539 (1996).
- E. V. Shuryak, Nucl. Phys. B203, 116 (1982).
- V. Y. Petrov, M. V. Polyakov, R. Ruskov, C. Weiss, and K. Goeke, Phys. Rev. D 59, 1140 (1999).
- D. Diakonov, V. Petrov, P. Pobylitsa, M. V. Polyakov, and C. Weiss, Nucl. Phys. B480, 341 (1996).
- D. Diakonov, V. Y. Petrov, P. V. Pobylitsa, M. V. Polyakov, and C. Weiss, Phys. Rev. D 56, 4069 (1997).
- M. V. Polyakov and C. Weiss, Phys. Rev. D 59, 091502 (1999).
- M. V. Polyakov and C. Weiss, Phys. Rev. D 60, 114017 (1999).
- J. Balla, M. V. Polyakov, and C. Weiss, Nucl. Phys. B510, 327 (1998).
- J. F. Donoghue, J. Gasser, and H. Leutwyler, Nucl. Phys. B343, 341 (1990).
- S. Faller, T. Feldmann, A. Khodjamirian, T. Mannel, and D. van Dyk, Phys. Rev. D 89, 014015 (2014).
- X. W. Kang, B. Kubis, C. Hanhart, and U. G. Meißner, Phys. Rev. D 89, 053015 (2014).
- U. G. Meißner and W. Wang, Phys. Lett. B 730, 336 (2014).
- P. Böer, T. Feldmann, and D. van Dyk, J. High Energy Phys. 02 (2017) 133.
- C. Hambrock and A. Khodjamirian, Nucl. Phys. B905, 373 (2016).
- S. Cheng, A. Khodjamirian, and J. Virto, Phys. Rev. D 96, 051901 (2017).
- S. Cheng, A. Khodjamirian, and J. Virto, J. High Energy Phys. 05 (2017) 157.
- C. Bourrely, I. Caprini, and L. Lellouch, Phys. Rev. D 79, 013008 (2009); 82, 099902(E) (2010).