- Letter
- Open Access
Fragmentation functions for axial-vector heavy tetraquarks: A TQ4Q1.1 update
Phys. Rev. D 111, L111501 – Published 3 June, 2025
DOI: https://doi.org/10.1103/ympl-ly2l
Abstract
We present and discuss the release of novel sets of collinear, variable-flavor-number-scheme fragmentation functions for axial-vector, fully heavy and tetraquarks. Working within the single-parton approximation at leading power and employing nonrelativistic QCD factorization adapted for tetraquark Fock states, we model the initial-scale fragmentation input using a recent calculation for the constituent heavy-quark channel. Standard Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution is then applied, ensuring consistent implementation of evolution thresholds. To support phenomenology, we investigate rates for tetraquark-jet systems at the High-Luminosity LHC and Future Circular Collider from (sym)jethad. This study further integrates exotic matter explorations with precision QCD calculations.
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References (141)
- A. Esposito, A. Pilloni, and A. D. Polosa, Phys. Rep. 668, 1 (2017).
- S. L. Olsen, T. Skwarnicki, and D. Zieminska, Rev. Mod. Phys. 90, 015003 (2018).
- N. Brambilla, S. Eidelman, C. Hanhart, A. Nefediev, C.-P. Shen, C. E. Thomas, A. Vairo, and C.-Z. Yuan, Phys. Rep. 873, 1 (2020).
- M. Karliner, J. L. Rosner, and T. Skwarnicki, Annu. Rev. Nucl. Part. Sci. 68, 17 (2018).
- R. F. Lebed, R. E. Mitchell, and E. S. Swanson, Prog. Part. Nucl. Phys. 93, 143 (2017).
- E. Kou and O. Pene, Phys. Lett. B 631, 164 (2005).
- E. Braaten, Phys. Rev. Lett. 111, 162003 (2013).
- M. Berwein, N. Brambilla, J. Tarrús Castellà, and A. Vairo, Phys. Rev. D 92, 114019 (2015).
- P. Minkowski and W. Ochs, Eur. Phys. J. C 9, 283 (1999).
- V. Mathieu, N. Kochelev, and V. Vento, Int. J. Mod. Phys. E 18, 1 (2009).
- H.-X. Chen, W. Chen, and S.-L. Zhu, Phys. Rev. D 103, L091503 (2021).
- V. M. Abazov et al. (D0 and TOTEM Collaborations), Phys. Rev. Lett. 127, 062003 (2021).
- M. Gell-Mann, Phys. Lett. 8, 214 (1964).
- R. L. Jaffe, Phys. Rev. D 15, 267 (1977).
- J. P. Ader, J. M. Richard, and P. Taxil, Phys. Rev. D 25, 2370 (1982).
- L. Maiani, A. D. Polosa, and V. Riquer, Phys. Lett. B 749, 289 (2015).
- S. K. Choi et al. (Belle Collaboration), Phys. Rev. Lett. 91, 262001 (2003).
- H.-X. Chen, W. Chen, X. Liu, and S.-L. Zhu, Phys. Rep. 639, 1 (2016).
- Y.-R. Liu, H.-X. Chen, W. Chen, X. Liu, and S.-L. Zhu, Prog. Part. Nucl. Phys. 107, 237 (2019).
- A. Esposito, E. G. Ferreiro, A. Pilloni, A. D. Polosa, and C. A. Salgado, Eur. Phys. J. C 81, 669 (2021).
- A. Esposito, A. Glioti, D. Germani, and A. D. Polosa, arXiv:2502.02505.
- N. A. Tornqvist, Z. Phys. C 61, 525 (1994).
- E. Braaten and M. Kusunoki, Phys. Rev. D 69, 074005 (2004).
- F.-K. Guo, C. Hidalgo-Duque, J. Nieves, and M. P. Valderrama, Phys. Rev. D 88, 054007 (2013).
- Z.-G. Wang, Eur. Phys. J. C 74, 2963 (2014).
- H. Mutuk, Eur. Phys. J. C 82, 1142 (2022).
- A. Esposito, D. Germani, A. Glioti, A. D. Polosa, R. Rattazzi, and M. Tarquini, Phys. Lett. B 847, 138285 (2023).
- L. Maiani, F. Piccinini, A. D. Polosa, and V. Riquer, Phys. Rev. D 71, 014028 (2005).
- G. ’t Hooft, G. Isidori, L. Maiani, A. D. Polosa, and V. Riquer, Phys. Lett. B 662, 424 (2008).
- L. Maiani, A. D. Polosa, and V. Riquer, Phys. Lett. B 778, 247 (2018).
- Z.-G. Wang, Eur. Phys. J. C 74, 2874 (2014).
- B. Grinstein, L. Maiani, and A. D. Polosa, Phys. Rev. D 109, 074009 (2024).
- S. Dubynskiy and M. B. Voloshin, Phys. Lett. B 666, 344 (2008).
- M. B. Voloshin, Phys. Rev. D 87, 091501 (2013).
- F.-K. Guo, C. Hanhart, U.-G. Meißner, Q. Wang, Q. Zhao, and B.-S. Zou, Rev. Mod. Phys. 90, 015004 (2018); 94, 029901(E) (2022).
- J. Ferretti, E. Santopinto, M. Naeem Anwar, and M. A. Bedolla, Phys. Lett. B 789, 562 (2019).
- J. Ferretti and E. Santopinto, J. High Energy Phys. 04 (2020) 119.
- R. Aaij et al. (LHCb Collaboration), Nat. Phys. 18, 751 (2022).
- R. Aaij et al. (LHCb Collaboration), Nat. Commun. 13, 3351 (2022).
- LHCb Collaboration, Sci. Bull. 65, 1983 (2020).
- H.-X. Chen, W. Chen, X. Liu, Y.-R. Liu, and S.-L. Zhu, Rep. Prog. Phys. 86, 026201 (2023).
- I. Belov, A. Giachino, and E. Santopinto, J. High Energy Phys. 01 (2025) 093.
- A. Pineda, Prog. Part. Nucl. Phys. 67, 735 (2012).
- J. Wu, Y.-R. Liu, K. Chen, X. Liu, and S.-L. Zhu, Phys. Rev. D 97, 094015 (2018).
- R. Maciuła, W. Schäfer, and A. Szczurek, Phys. Lett. B 812, 136010 (2021).
- F. Carvalho, E. R. Cazaroto, V. P. Gonçalves, and F. S. Navarra, Phys. Rev. D 93, 034004 (2016).
- L. M. Abreu, F. Carvalho, J. V. C. Oliveira, and V. P. Gonçalves, Eur. Phys. J. C 84, 470 (2024).
- A. Cisek, W. Schäfer, and A. Szczurek, Eur. Phys. J. C 82, 1062 (2022).
- S. Chatrchyan et al. (CMS Collaboration), J. High Energy Phys. 04 (2013) 154.
- M. Aaboud et al. (ATLAS Collaboration), J. High Energy Phys. 01 (2017) 117.
- R. Aaij et al. (LHCb Collaboration), J. High Energy Phys. 01 (2022) 131.
- F. G. Celiberto and G. Gatto, Phys. Rev. D 111, 034037 (2025).
- B. Mele and P. Nason, Nucl. Phys. B361, 626 (1991); B921, 841(E) (2017).
- M. Cacciari and M. Greco, Nucl. Phys. B421, 530 (1994).
- F. Feng, Y. Huang, Y. Jia, W.-L. Sang, X. Xiong, and J.-Y. Zhang, Phys. Rev. D 106, 114029 (2022).
- X.-W. Bai, F. Feng, C.-M. Gan, Y. Huang, W.-L. Sang, and H.-F. Zhang, J. High Energy Phys. 09 (2024) 002.
- W. E. Caswell and G. P. Lepage, Phys. Lett. 167B, 437 (1986).
- G. T. Bodwin, E. Braaten, and G. P. Lepage, Phys. Rev. D 51, 1125 (1995); 55, 5853(E) (1997).
- F. G. Celiberto, in 58th Rencontres de Moriond on QCD and High Energy Interactions (2024), arXiv:2405.08221.
- F. G. Celiberto, Proc. Sci. DIS2024 (2025) 168 [arXiv:2406.10779].
- F. Giacosa, Phys. Rev. D 75, 054007 (2007).
- H. Kim, K. S. Kim, M.-K. Cheoun, and M. Oka, Phys. Rev. D 97, 094005 (2018).
- H. Kim, K. S. Kim, M.-K. Cheoun, D. Jido, and M. Oka, Phys. Rev. D 99, 014005 (2019).
- F.-Y. Zhang and L.-M. Wang, arXiv:2503.01443.
- E. S. Swanson, Phys. Rev. D 107, 074028 (2023).
- P. Wang, S. R. Cotanch, and I. J. General, Eur. Phys. J. C 55, 409 (2008).
- H. Kim and K. S. Kim, Eur. Phys. J. C 82, 1113 (2022).
- N. Isgur and M. B. Wise, Phys. Rev. Lett. 66, 1130 (1991).
- M. Neubert, Phys. Rep. 245, 259 (1994).
- X.-Z. Weng, X.-L. Chen, W.-Z. Deng, and S.-L. Zhu, Phys. Rev. D 103, 034001 (2021).
- H.-T. An, S.-Q. Luo, Z.-W. Liu, and X. Liu, Eur. Phys. J. C 83, 740 (2023).
- M.-S. Liu, F.-X. Liu, X.-H. Zhong, and Q. Zhao, Phys. Rev. D 109, 076017 (2024).
- R. Abdul Khalek et al., Nucl. Phys. A1026, 122447 (2022).
- F. Feng, Y. Huang, Y. Jia, W.-L. Sang, D.-S. Yang, and J.-Y. Zhang, Phys. Rev. D 110, 054007 (2024).
- F. Feng, Y. Huang, Y. Jia, W.-L. Sang, D.-S. Yang, and J.-Y. Zhang, Phys. Rev. D 108, L051501 (2023).
- H.-H. Ma, Z.-K. Tao, and J.-J. Niu, Eur. Phys. J. C 85, 397 (2025).
- F. G. Celiberto, TQ4Q1.1: Axial-vector tetraquarks with 4 heavy quarks VFNS FFs, https://github.com/FGCeliberto/Collinear_FFs/ (2025).
- H.-X. Chen, W. Chen, X. Liu, and S.-L. Zhu, Sci. Bull. 65, 1994 (2020).
- R. Zhu, Nucl. Phys. B966, 115393 (2021).
- M. Karliner and J. L. Rosner, Phys. Rev. D 102, 114039 (2020).
- C. Becchi, A. Giachino, L. Maiani, and E. Santopinto, Phys. Lett. B 806, 135495 (2020).
- M. Karliner and J. L. Rosner, Phys. Rev. Lett. 119, 202001 (2017).
- R. L. Jaffe and L. Randall, Nucl. Phys. B412, 79 (1994).
- I. Helenius and H. Paukkunen, J. High Energy Phys. 05 (2018) 196.
- L. Bonino, M. Cacciari, and G. Stagnitto, J. High Energy Phys. 06 (2024) 040.
- M. Cacciari, A. Ghira, S. Marzani, and G. Ridolfi, Eur. Phys. J. C 84, 889 (2024).
- M. Czakon, T. Generet, A. Mitov, and R. Poncelet, arXiv:2411.09684.
- E. Braaten and T. C. Yuan, Phys. Rev. Lett. 71, 1673 (1993).
- M. Cacciari and M. Greco, Phys. Rev. Lett. 73, 1586 (1994).
- X.-C. Zheng, C.-H. Chang, and X.-G. Wu, Phys. Rev. D 100, 014005 (2019).
- P. Zhang, C.-Y. Wang, X. Liu, Y.-Q. Ma, C. Meng, and K.-T. Chao, J. High Energy Phys. 04 (2019) 116.
- P. Artoisenet and E. Braaten, J. High Energy Phys. 04 (2015) 121.
- S. Fleming, A. K. Leibovich, T. Mehen, and I. Z. Rothstein, Phys. Rev. D 86, 094012 (2012).
- Z.-B. Kang, Y.-Q. Ma, J.-W. Qiu, and G. Sterman, Phys. Rev. D 90, 034006 (2014).
- D. Boer, J. Bor, L. Maxia, C. Pisano, and F. Yuan, J. High Energy Phys. 08 (2023) 105.
- F. G. Celiberto and M. Fucilla, Eur. Phys. J. C 82, 929 (2022).
- F. G. Celiberto, Phys. Lett. B 835, 137554 (2022).
- F. G. Celiberto, Eur. Phys. J. C 84, 384 (2024).
- H.-F. Zhang and Y.-Q. Ma, arXiv:2009.08376.
- X.-W. Bai, Y. Huang, and W.-L. Sang, Phys. Rev. D 111, 054006 (2025).
- F. G. Celiberto, G. Gatto, and A. Papa, Eur. Phys. J. C 84, 1071 (2024).
- S. M. Moosavi Nejad and N. Amiri, Phys. Rev. D 105, 034001 (2022).
- F. G. Celiberto and A. Papa, Phys. Lett. B 848, 138406 (2024).
- F. G. Celiberto, Eur. Phys. J. C 81, 691 (2021).
- F. G. Celiberto, Phys. Rev. D 105, 114008 (2022).
- F. G. Celiberto, Symmetry 16, 550 (2024).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/ympl-ly2l for additional technical details supporting the Letter. It includes analytic formulas for the short-distance coefficients (SDCs), expressions for high-energy resummed observables, the full list of input parameters, and supplemental plots illustrating the fragmentation functions for scalar and tensor tetraquarks. The content complements and extends the results discussed in the main manuscript.
- Q.-F. Lü, D.-Y. Chen, and Y.-B. Dong, Eur. Phys. J. C 80, 871 (2020).
- G.-L. Yu, Z.-Y. Li, Z.-G. Wang, J. Lu, and M. Yan, Eur. Phys. J. C 83, 416 (2023).
- V. Bertone, S. Carrazza, and J. Rojo, Comput. Phys. Commun. 185, 1647 (2014).
- A. Buckley, J. Ferrando, S. Lloyd, K. Nordström, B. Page, M. Rüfenacht, M. Schönherr, and G. Watt, Eur. Phys. J. C 75, 132 (2015).
- M. Suzuki, Phys. Lett. 71B, 139 (1977).
- J. D. Bjorken, Phys. Rev. D 17, 171 (1978).
- G. T. Bodwin and A. Petrelli, Phys. Rev. D 66, 094011 (2002); 87, 039902(E) (2013).
- Y.-Q. Ma, J.-W. Qiu, and H. Zhang, J. High Energy Phys. 06 (2015) 021.
- Y.-Z. Xu, S. Chen, Z.-Q. Yao, D. Binosi, Z.-F. Cui, and C. D. Roberts, Eur. Phys. J. C 81, 895 (2021).
- R. Aaij et al. (LHCb Collaboration), arXiv:2410.18018.
- R. N. Faustov, V. O. Galkin, and E. M. Savchenko, Symmetry 14, 2504 (2022).
- F. G. Celiberto, M. Fucilla, D. Yu. Ivanov, and A. Papa, Eur. Phys. J. C 81, 780 (2021).
- F. G. Celiberto, M. Fucilla, D. Yu. Ivanov, M. M. A. Mohammed, and A. Papa, Phys. Rev. D 104, 114007 (2021).
- V. S. Fadin, E. Kuraev, and L. Lipatov, Phys. Lett. 60B, 50 (1975).
- I. Balitsky and L. Lipatov, Sov. J. Nucl. Phys. 28, 822 (1978), https://inspirehep.net/literature/137229.
- D. Colferai and A. Niccoli, J. High Energy Phys. 04 (2015) 071.
- R. Boussarie, B. Ducloué, L. Szymanowski, and S. Wallon, Phys. Rev. D 97, 014008 (2018).
- F. G. Celiberto, D. Yu. Ivanov, B. Murdaca, and A. Papa, Eur. Phys. J. C 75, 292 (2015).
- D. Yu. Ivanov and A. Papa, J. High Energy Phys. 07 (2012) 045.
- A. D. Bolognino, F. G. Celiberto, M. Fucilla, D. Yu. Ivanov, and A. Papa, Phys. Rev. D 103, 094004 (2021).
- F. G. Celiberto, D. Gordo Gómez, and A. Sabio Vera, Phys. Lett. B 786, 201 (2018).
- A. D. Bolognino, F. G. Celiberto, D. Yu. Ivanov, and A. Papa, Eur. Phys. J. C 78, 1023 (2018).
- R. D. Ball, V. Bertone, M. Bonvini, S. Marzani, J. Rojo, and L. Rottoli, Eur. Phys. J. C 78, 321 (2018).
- A. Bacchetta, F. G. Celiberto, M. Radici, and P. Taels, Eur. Phys. J. C 80, 733 (2020).
- A. Bacchetta, F. G. Celiberto, and M. Radici, Eur. Phys. J. C 84, 576 (2024).
- F. G. Celiberto, arXiv:1707.04315.
- V. Khachatryan et al. (CMS Collaboration), J. High Energy Phys. 08 (2016) 139.
- Z. Kassabov, M. Ubiali, and C. Voisey, J. High Energy Phys. 03 (2023) 148.
- L. A. Harland-Lang and R. S. Thorne, Eur. Phys. J. C 79, 225 (2019).
- R. D. Ball et al. (NNPDF Collaboration), Eur. Phys. J. C 84, 517 (2024).
- R. D. Ball, A. Candido, J. Cruz-Martinez, S. Forte, T. Giani, F. Hekhorn, G. Magni, E. R. Nocera, J. Rojo, and R. Stegeman (NNPDF Collaboration), Phys. Rev. D 109, L091501 (2024).
- R. D. Ball, A. Candido, J. Cruz-Martinez, S. Forte, T. Giani, F. Hekhorn, K. Kudashkin, G. Magni, and J. Rojo (NNPDF Collaboration), Nature (London) 608, 483 (2022).
- M. Guzzi, T. J. Hobbs, K. Xie, J. Huston, P. Nadolsky, and C. P. Yuan, Phys. Lett. B 843, 137975 (2023).
- R. Vogt, Phys. Rev. D 110, 074036 (2024).