- Open Access
All-charm tetraquarks at hadron colliders: A high-precision fragmentation perspective
Phys. Rev. D 113, 114037 – Published 22 June, 2026
DOI: https://doi.org/10.1103/t5j1-84y2
Abstract
We present the TQ4Q2.0 fragmentation functions for the production of all-heavy (fully heavy) -wave tetraquarks () with scalar (), axial-vector (), and tensor () quantum numbers in high-energy hadronic collisions. This work extends the previous TQ4Q1.1 framework by incorporating nonconstituent heavy-quark contributions and introducing a replica-based uncertainty-quantification strategy derived from multiscale variations (MHOUs). The construction follows a nonrelativistic quantum chromodynamics (QCD) factorization approach, combining gluon- and heavy-quark-initiated fragmentation channels at leading power. Initial-scale inputs are modeled through updated potential-inspired wave functions, while the subsequent Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution is performed via the threshold-aware HF-NRevo scheme. A comprehensive systematic analysis of uncertainties is carried out, with contributions from color-composite long-distance matrix elements (LDMEs) and perturbative multiscale inputs. The resulting TQ4Q2.0 grids, publicly released in LHAPDF6 format, provide the first complete phenomenological set for all-heavy exotics, enabling precise studies of all-charm tetraquark production and jet-associated observables within the jethad environment. This article completes the high-energy resummation-driven generation of the TQ4Q program and establishes a definitive baseline for future collider-oriented analyses of all-heavy multiquark dynamics.
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References (344)
- R. Abdul Khalek et al., Nucl. Phys. A1026, 122447 (2022).
- R. Abdul Khalek et al., in 2022 Snowmass Summer Study (2022), arXiv:2203.13199.
- M. Hentschinski et al., Acta Phys. Pol. B 54, A2 (2023).
- S. Amoroso et al., Acta Phys. Pol. B 53, A1 (2022).
- R. Abir et al., arXiv:2305.14572.
- C. Allaire et al., Comput. Software Big Sci. 8, 5 (2024).
- M. Benedikt et al. (FCC Collaboration), Eur. Phys. J. C 85, 1468 (2025).
- M. Benedikt et al. (FCC Collaboration), Eur. Phys. J. Special Topics 234, 5713 (2025).
- M. Benedikt et al. (FCC Collaboration), Eur. Phys. J. Special Topics 234, 5113 (2025); 234, 33(E) (2025).
- F. Feng, Y. Huang, Y. Jia, W.-L. Sang, X. Xiong, and J.-Y. Zhang, Phys. Rev. D 106, 114029 (2022).
- F. Feng, Y. Huang, Y. Jia, W.-L. Sang, and J.-Y. Zhang, Phys. Lett. B 818, 136368 (2021).
- F. Feng, Y. Huang, Y. Jia, W.-L. Sang, D.-S. Yang, and J.-Y. Zhang, Phys. Rev. D 108, L051501 (2023).
- F. Feng, Y. Huang, Y. Jia, W.-L. Sang, D.-S. Yang, and J.-Y. Zhang, Phys. Rev. D 110, 054007 (2024).
- X.-W. Bai, F. Feng, C.-M. Gan, Y. Huang, W.-L. Sang, and H.-F. Zhang, J. High Energy Phys. 09 (2024) 002.
- X.-W. Bai, Y. Huang, and W.-L. Sang, Phys. Rev. D 111, 054006 (2025).
- S. M. Moosavi Nejad and N. Amiri, Phys. Rev. D 105, 034001 (2022).
- F. G. Celiberto and A. Papa, Phys. Lett. B848, 138406 (2024).
- F. G. Celiberto, G. Gatto, and A. Papa, Eur. Phys. J. C 84, 1071 (2024).
- F. G. Celiberto and G. Gatto, Phys. Rev. D 111, 034037 (2025).
- F. G. Celiberto, Phys. Rev. D 111, L111501 (2025).
- F. G. Celiberto, Eur. Phys. J. C 85, 1395 (2025).
- F. G. Celiberto, Phys. Rev. D 112, 074041 (2025).
- F. G. Celiberto, A. V. Giannini, V. P. Gonçalves, and Y. N. Lima, Phys. Rev. D 113, 054014 (2026).
- Y. Wang and R. Zhu, arXiv:2510.02085.
- X. Liu, Y. Wang, and R. Zhu, arXiv:2512.22070.
- F. Feng and M.-M. Liu, Phys. Rev. D 113, 054010 (2026).
- E. Kou and O. Pene, Phys. Lett. B631, 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).
- T. Csörgő, T. Novak, R. Pasechnik, A. Ster, and I. Szanyi, Eur. Phys. J. C 81, 180 (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).
- R. L. Jaffe, Phys. Rev. D 15, 281 (1977).
- R. L. Jaffe, Phys. Rev. Lett. 38, 195 (1977); 38, 617(E) (1977).
- J. P. Ader, J. M. Richard, and P. Taxil, Phys. Rev. D 25, 2370 (1982).
- J. L. Rosner, Phys. Rev. D 33, 2043 (1986).
- S. Pepin and F. Stancu, Phys. Rev. D 57, 4475 (1998).
- J. Vijande, A. Valcarce, and J. M. Richard, Phys. Rev. D 85, 014019 (2012).
- A. Esposito, A. Pilloni, and A. D. Polosa, Phys. Rep. 668, 1 (2017).
- R. F. Lebed, R. E. Mitchell, and E. S. Swanson, Prog. Part. Nucl. Phys. 93, 143 (2017).
- 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).
- W. Lucha, D. Melikhov, and H. Sazdjian, Phys. Rev. D 96, 014022 (2017).
- A. Ali, L. Maiani, and A. D. Polosa, Multiquark Hadrons (Cambridge University Press, Cambridge, England, 2019).
- S. K. Choi et al. (Belle Collaboration), Phys. Rev. Lett. 91, 262001 (2003).
- D. Acosta et al. (CDF Collaboration), Phys. Rev. Lett. 93, 072001 (2004).
- R. Aaij et al. (LHCb Collaboration), Phys. Rev. Lett. 110, 222001 (2013).
- A. M. Sirunyan et al. (CMS Collaboration), Phys. Rev. Lett. 128, 032001 (2022).
- E. S. Swanson, Phys. Rep. 429, 243 (2006).
- 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).
- R. Aaij et al. (LHCb Collaboration), Phys. Rev. Lett. 125, 242001 (2020).
- R. Aaij et al. (LHCb Collaboration), Nat. Phys. 18, 751 (2022).
- R. Aaij et al. (LHCb Collaboration), Nat. Commun. 13, 3351 (2022).
- S. Fleming, R. Hodges, and T. Mehen, Phys. Rev. D 104, 116010 (2021).
- L. Dai, S. Fleming, R. Hodges, and T. Mehen, Phys. Rev. D 107, 076001 (2023).
- R. Hodges, Studies of decays and transverse-momentum-dependent production using effective field theory, Ph.D. thesis, 2024, arXiv:2404.18907.
- T. Mehen, Phys. Rev. D 92, 034019 (2015).
- E. Braaten, L.-P. He, K. Ingles, and J. Jiang, Phys. Rev. D 101, 096020 (2020).
- R. Aaij et al. (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).
- S. S. Agaev, K. Azizi, B. Barsbay, and H. Sundu, Eur. Phys. J. C 83, 994 (2023).
- A. Hayrapetyan et al. (CMS Collaboration), Phys. Rev. Lett. 132, 111901 (2024).
- A. Hayrapetyan et al. (CMS Collaboration), Nature (London) 648, 58 (2025).
- A. Hayrapetyan et al. (CMS Collaboration), arXiv:2602.02252.
- F. Zhu, G. Bauer, and K. Yi, Chin. Phys. Lett. 41, 111201 (2024).
- P. Nogga (LHCb Collaboration), Proc. Sci. QNP2024 (2025) 118.
- M. Aaboud et al. (ATLAS Collaboration), Eur. Phys. J. C 77, 76 (2017).
- V. Khachatryan et al. (CMS Collaboration), J. High Energy Phys. 09 (2014) 094.
- A. Hayrapetyan et al. (CMS Collaboration), Phys. Rev. D 110, 092002 (2024).
- S. S. Agaev, K. Azizi, B. Barsbay, and H. Sundu, Phys. Lett. B 844, 138089 (2023).
- R. Oncala and J. Soto, arXiv:2511.14016.
- A. Pineda, Prog. Part. Nucl. Phys. 67, 735 (2012).
- L. Maiani, A. D. Polosa, and V. Riquer, Phys. Rev. D 100, 014002 (2019).
- R. Maciuła, W. Schäfer, and A. Szczurek, Phys. Lett. B 812, 136010 (2021).
- A. V. Berezhnoy, A. K. Likhoded, A. V. Luchinsky, and A. A. Novoselov, Phys. Rev. D 84, 094023 (2011).
- M. Karliner, S. Nussinov, and J. L. Rosner, Phys. Rev. D 95, 034011 (2017).
- C. Becchi, A. Giachino, L. Maiani, and E. Santopinto, Phys. Lett. B 806, 135495 (2020).
- 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).
- W.-L. Wu, L. Meng, and S.-L. Zhu, arXiv:2506.20555.
- A. Bondar et al. (Belle Collaboration), Phys. Rev. Lett. 108, 122001 (2012).
- L. C. Bland et al. (ANDY Collaboration), arXiv:1909.03124.
- R. Vogt and A. Angerami, Phys. Rev. D 104, 094025 (2021).
- A. Francis, R. J. Hudspith, R. Lewis, and K. Maltman, arXiv:1810.10550.
- M. Padmanath, A. Radhakrishnan, and N. Mathur, Phys. Rev. Lett. 132, 201902 (2024).
- P. Bicudo, K. Cichy, A. Peters, B. Wagenbach, and M. Wagner, Phys. Rev. D 92, 014507 (2015).
- L. Leskovec, S. Meinel, M. Pflaumer, and M. Wagner, Phys. Rev. D 100, 014503 (2019).
- C. Alexandrou, J. Finkenrath, T. Leontiou, S. Meinel, M. Pflaumer, and M. Wagner, Phys. Rev. D 110, 054510 (2024).
- 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.
- B. Mele and P. Nason, Nucl. Phys. B361, 626 (1991); B921, 841(E) (2017).
- M. Cacciari and M. Greco, Nucl. Phys. B421, 530 (1994).
- M. Buza, Y. Matiounine, J. Smith, and W. L. van Neerven, Eur. Phys. J. C 1, 301 (1998).
- F. G. Celiberto and F. Lonigro, Phys. Rev. D 112, 114040 (2025).
- F. G. Celiberto, in Proceedings of the 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. G. Celiberto, Acta Phys. Pol. B Proc. Suppl. 18, 1 (2025).
- F. G. Celiberto and F. Lonigro, Proc. Sci. EPS-HEP2025 (2026) 191 [arXiv:2510.22449].
- F. G. Celiberto and F. Lonigro, arXiv:2603.28389.
- F. G. Celiberto, in Excited QCD 2026 Workshop (2026), arXiv:2604.01867.
- F. G. Celiberto, arXiv:2605.01539.
- 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 and R. L. Pearson, Eur. Phys. J. C 81, 830 (2021).
- J. McGowan, T. Cridge, L. A. Harland-Lang, and R. S. Thorne, Eur. Phys. J. C 83, 185 (2023); 83, 302(E) (2023).
- R. D. Ball et al. (NNPDF Collaboration), Eur. Phys. J. C 84, 517 (2024).
- B. Pasquini, S. Rodini, and S. Venturini (MAP (Multi-dimensional Analyses of Partonic Distributions) Collaboration), Phys. Rev. D 107, 114023 (2023).
- A. Buckley, J. Ferrando, S. Lloyd, K. Nordström, B. Page, M. Rüfenacht, M. Schönherr, and G. Watt, Eur. Phys. J. C 75, 132 (2015).
- F. G. Celiberto, Eur. Phys. J. C 81, 691 (2021).
- F. G. Celiberto, Phys. Rev. D 105, 114008 (2022).
- F. G. Celiberto, Universe 9, 324 (2023).
- F. G. Celiberto, Symmetry 16, 550 (2024).
- F. G. Celiberto, Particles 7, 502 (2024).
- F. G. Celiberto, Symmetry 18, 29 (2026).
- F. G. Celiberto, Particles 9, 23 (2026).
- M. Cacciari, M. Greco, S. Rolli, and A. Tanzini, Phys. Rev. D 55, 2736 (1997).
- R. L. Jaffe and L. Randall, Nucl. Phys. B412, 79 (1994).
- B. A. Kniehl, G. Kramer, I. Schienbein, and H. Spiesberger, Eur. Phys. J. C 41, 199 (2005).
- I. Helenius and H. Paukkunen, J. High Energy Phys. 05 (2018) 196.
- I. Helenius and H. Paukkunen, J. High Energy Phys. 07 (2023) 054.
- T. Generet, -hadron production at higher orders in QCD, Ph.D. thesis, RWTH Aachen University, 2023.
- B. Mele and P. Nason, Phys. Lett. B 245, 635 (1990).
- P. J. Rijken and W. L. van Neerven, Phys. Lett. B 386, 422 (1996).
- A. Mitov and S.-O. Moch, Nucl. Phys. B751, 18 (2006).
- J. Blumlein and V. Ravindran, Nucl. Phys. B749, 1 (2006).
- K. Melnikov and A. Mitov, Phys. Rev. D 70, 034027 (2004).
- A. Mitov, Phys. Rev. D 71, 054021 (2005).
- C. Biello and L. Bonino, Eur. Phys. J. C 84, 1192 (2024).
- V. Kartvelishvili, A. Likhoded, and V. Petrov, Phys. Lett. 78B, 615 (1978).
- M. G. Bowler, Z. Phys. C 11, 169 (1981).
- C. Peterson, D. Schlatter, I. Schmitt, and P. M. Zerwas, Phys. Rev. D 27, 105 (1983).
- B. Andersson, G. Gustafson, and B. Soderberg, Z. Phys. C 20, 317 (1983).
- P. D. B. Collins and T. P. Spiller, J. Phys. G 11, 1289 (1985).
- G. Colangelo and P. Nason, Phys. Lett. B 285, 167 (1992).
- H. Georgi, Phys. Lett. B 240, 447 (1990).
- E. Eichten and B. R. Hill, Phys. Lett. B 234, 511 (1990).
- B. Grinstein, Annu. Rev. Nucl. Part. Sci. 42, 101 (1992).
- M. Neubert, Phys. Rep. 245, 259 (1994).
- W. E. Caswell and G. P. Lepage, Phys. Lett. 167B, 437 (1986).
- B. A. Thacker and G. P. Lepage, Phys. Rev. D 43, 196 (1991).
- G. T. Bodwin, E. Braaten, and G. P. Lepage, Phys. Rev. D 51, 1125 (1995); 55, 5853(E) (1997).
- P. L. Cho and A. K. Leibovich, Phys. Rev. D 53, 150 (1996).
- P. L. Cho and A. K. Leibovich, Phys. Rev. D 53, 6203 (1996).
- A. K. Leibovich, Phys. Rev. D 56, 4412 (1997).
- G. T. Bodwin, E. Braaten, and J. Lee, Phys. Rev. D 72, 014004 (2005).
- B. Grinstein, Int. J. Mod. Phys. A 15, 461 (2000).
- M. Krämer, Prog. Part. Nucl. Phys. 47, 141 (2001).
- N. Brambilla et al. (Quarkonium Working Group), 10.5170/CERN-2005-005 (2004).
- J.-P. Lansberg, Quarkonium production at high-energy hadron colliders: A systematic gauge-invariant approach to relativistic effects of , and production, Ph.D. thesis, Liege University, 2005, arXiv:hep-ph/0507175.
- J.-P. Lansberg, Phys. Rep. 889, 1 (2020).
- S. Alekhin, J. Blumlein, S. Klein, and S. Moch, Phys. Rev. D 81, 014032 (2010).
- 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).
- M. G. Echevarria, J. High Energy Phys. 10 (2019) 144.
- D. Boer, J. Bor, L. Maxia, C. Pisano, and F. Yuan, J. High Energy Phys. 08 (2023) 105.
- E. Braaten and T. C. Yuan, Phys. Rev. Lett. 71, 1673 (1993).
- E. Braaten, K.-m. Cheung, and T. C. Yuan, Phys. Rev. D 48, 4230 (1993).
- X.-C. Zheng, C.-H. Chang, T.-F. Feng, and X.-G. Wu, Phys. Rev. D 100, 034004 (2019).
- X.-C. Zheng, C.-H. Chang, and X.-G. Wu, J. High Energy Phys. 05 (2022) 036.
- 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).
- R. Aaij et al. (LHCb Collaboration), Phys. Rev. Lett. 114, 041801 (2015).
- R. Aaij et al. (LHCb Collaboration), Phys. Rev. Lett. 118, 052002 (2017); 119, 169901(E) (2017).
- G. Aad et al. (ATLAS Collaboration), Phys. Rev. Lett. 131, 151902 (2023).
- H.-F. Zhang, Y.-Q. Ma, and W.-L. Sang, Sci. Bull. 70, 1915 (2025).
- R. Zhu, Nucl. Phys. B966, 115393 (2021).
- F. G. Celiberto, Universe 12, 13 (2026).
- H.-H. Ma, Z.-K. Tao, and J.-J. Niu, Eur. Phys. J. C 85, 397 (2025).
- H. S. Nakhaei and G. R. Boroun, Phys. Rev. D 112, 054039 (2025).
- F. G. Celiberto, Phys. Rev. D 112, 074023 (2025).
- M. A. Shifman, A. I. Vainshtein, and V. I. Zakharov, Nucl. Phys. B147, 385 (1979).
- F. J. Gilman and M. B. Wise, Phys. Rev. D 20, 2392 (1979).
- M. Cacciari, M. Greco, M. L. Mangano, and A. Petrelli, Phys. Lett. B 356, 553 (1995).
- P. Artoisenet, J. P. Lansberg, and F. Maltoni, Phys. Lett. B 653, 60 (2007).
- Y.-Q. Ma, J.-W. Qiu, G. Sterman, and H. Zhang, Phys. Rev. Lett. 113, 142002 (2014).
- M. Cacciari and M. Greco, Phys. Rev. Lett. 73, 1586 (1994).
- M. Cacciari and M. Krämer, Phys. Rev. Lett. 76, 4128 (1996).
- K. Kolodziej, A. Leike, and R. Ruckl, Phys. Lett. B 355, 337 (1995).
- B. Ducloué, L. Szymanowski, and S. Wallon, Phys. Rev. D 92, 076002 (2015).
- J.-P. Lansberg and H.-S. Shao, Phys. Lett. B 751, 479 (2015).
- J.-P. Lansberg, H.-S. Shao, N. Yamanaka, Y.-J. Zhang, and C. Noûs, Phys. Lett. B 807, 135559 (2020).
- J.-P. Lansberg and H.-S. Shao, J. High Energy Phys. 10 (2016) 153.
- J.-P. Lansberg, H.-S. Shao, and N. Yamanaka, Phys. Lett. B 781, 485 (2018).
- D. d’Enterria and A. M. Snigirev, Phys. Rev. Lett. 118, 122001 (2017).
- H.-S. Shao and Y.-J. Zhang, Phys. Rev. Lett. 122, 192002 (2019).
- A. Petrelli, M. Cacciari, M. Greco, F. Maltoni, and M. L. Mangano, Nucl. Phys. B514, 245 (1998).
- N. Brambilla et al., Eur. Phys. J. C 71, 1534 (2011).
- A. Andronic et al., Eur. Phys. J. C 76, 107 (2016).
- M. Beneke and I. Z. Rothstein, Phys. Rev. D 54, 2005 (1996).
- M. Butenschoen and B. A. Kniehl, Phys. Rev. Lett. 106, 022003 (2011).
- K.-T. Chao, Y.-Q. Ma, H.-S. Shao, K. Wang, and Y.-J. Zhang, Phys. Rev. Lett. 108, 242004 (2012).
- B. Gong, L.-P. Wan, J.-X. Wang, and H.-F. Zhang, Phys. Rev. Lett. 110, 042002 (2013).
- H. Han, Y.-Q. Ma, C. Meng, H.-S. Shao, and K.-T. Chao, Phys. Rev. Lett. 114, 092005 (2015).
- R. Aaij et al. (LHCb Collaboration), Eur. Phys. J. C 75, 311 (2015).
- R. Aaij et al. (LHCb Collaboration), Eur. Phys. J. C 80, 191 (2020).
- R. Aaij et al. (LHCb Collaboration), J. High Energy Phys. 07 (2023) 069.
- P. Artoisenet, J. M. Campbell, J. P. Lansberg, F. Maltoni, and F. Tramontano, Phys. Rev. Lett. 101, 152001 (2008).
- B. Gong, J.-X. Wang, and H.-F. Zhang, Phys. Rev. D 83, 114021 (2011).
- E. Braaten and S. Fleming, Phys. Rev. Lett. 74, 3327 (1995).
- E. Eichten, K. Gottfried, T. Kinoshita, J. B. Kogut, K. D. Lane, and T.-M. Yan, Phys. Rev. Lett. 34, 369 (1975); 36, 1276(E) (1976).
- E. Eichten, K. Gottfried, T. Kinoshita, K. D. Lane, and T.-M. Yan, Phys. Rev. D 17, 3090 (1978); 21, 313(E) (1980).
- J. Zhao, S. Shi, and P. Zhuang, Phys. Rev. D 102, 114001 (2020).
- Q.-F. Lü, D.-Y. Chen, and Y.-B. Dong, Eur. Phys. J. C 80, 871 (2020).
- M.-S. Liu, F.-X. Liu, X.-H. Zhong, and Q. Zhao, Phys. Rev. D 109, 076017 (2024).
- G.-L. Yu, Z.-Y. Li, Z.-G. Wang, J. Lu, and M. Yan, Eur. Phys. J. C 83, 416 (2023).
- G.-J. Wang, L. Meng, and S.-L. Zhu, Phys. Rev. D 100, 096013 (2019).
- E. J. Eichten and C. Quigg, Phys. Rev. D 99, 054025 (2019).
- W. Buchmuller and S. H. H. Tye, Phys. Rev. D 24, 132 (1981).
- V. Bertone, S. Carrazza, and J. Rojo, Comput. Phys. Commun. 185, 1647 (2014).
- S. Carrazza, A. Ferrara, D. Palazzo, and J. Rojo, J. Phys. G 42, 057001 (2015).
- V. Bertone, Proc. Sci. DIS2017 (2018) 201 [arXiv:1708.00911].
- A. Candido, F. Hekhorn, and G. Magni, Eur. Phys. J. C 82, 976 (2022).
- F. Hekhorn and G. Magni, arXiv:2306.15294.
- M. Suzuki, Phys. Lett. 71B, 139 (1977).
- J. D. Bjorken, Phys. Rev. D 17, 171 (1978).
- 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).
- F. G. Celiberto, Acta Phys. Pol. B Proc. Suppl. 16, 41 (2023).
- 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).
- V. S. Fadin and L. N. Lipatov, Phys. Lett. B 429, 127 (1998).
- M. Ciafaloni and G. Camici, Phys. Lett. B 430, 349 (1998).
- D. Colferai, F. Schwennsen, L. Szymanowski, and S. Wallon, J. High Energy Phys. 12 (2010) 026.
- F. G. Celiberto, D. Yu. Ivanov, B. Murdaca, and A. Papa, Eur. Phys. J. C 75, 292 (2015).
- F. G. Celiberto, D. Yu. Ivanov, B. Murdaca, and A. Papa, Eur. Phys. J. C 77, 382 (2017).
- A. H. Mueller and H. Navelet, Nucl. Phys. B282, 727 (1987).
- B. Ducloué, L. Szymanowski, and S. Wallon, J. High Energy Phys. 05 (2013) 096.
- D. Colferai and A. Niccoli, J. High Energy Phys. 04 (2015) 071.
- F. G. Celiberto, D. Yu. Ivanov, B. Murdaca, and A. Papa, Acta Phys. Pol. B Proc. Suppl. 8, 935 (2015).
- F. G. Celiberto, D. Yu. Ivanov, B. Murdaca, and A. Papa, Eur. Phys. J. C 76, 224 (2016).
- F. G. Celiberto, High-energy resummation in semi-hard processes at the LHC, Ph.D. thesis, Università della Calabria and INFN-Cosenza, 2017, arXiv:1707.04315.
- F. Caporale, F. G. Celiberto, G. Chachamis, D. Gordo Gómez, and A. Sabio Vera, Nucl. Phys. B935, 412 (2018).
- N. B. de León, G. Chachamis, and A. Sabio Vera, Eur. Phys. J. C 81, 1019 (2021).
- F. G. Celiberto and A. Papa, Phys. Rev. D 106, 114004 (2022).
- C. Baldenegro, G. Chachamis, M. Kampshoff, M. Klasen, G. J. Milhano, C. Royon, and A. Sabio Vera, Phys. Rev. D 110, 114027 (2024).
- F. G. Celiberto, D. Yu. Ivanov, B. Murdaca, and A. Papa, Phys. Rev. D 94, 034013 (2016).
- F. G. Celiberto, D. Yu. Ivanov, and A. Papa, Phys. Rev. D 102, 094019 (2020).
- A. D. Bolognino, F. G. Celiberto, D. Yu. Ivanov, M. M. A. Mohammed, and A. Papa, Eur. Phys. J. C 78, 772 (2018).
- A. D. Bolognino, F. G. Celiberto, D. Yu. Ivanov, M. M. A. Mohammed, and A. Papa, Proc. Sci. DIS2019 (2019) 049 [arXiv:1906.11800].
- A. D. Bolognino, F. G. Celiberto, D. Yu. Ivanov, M. M. A. Mohammed, and A. Papa, Acta Phys. Pol. B Proc. Suppl. 12, 773 (2019).
- F. G. Celiberto, Eur. Phys. J. C 83, 332 (2023).
- F. Caporale, F. G. Celiberto, G. Chachamis, and A. Sabio Vera, Eur. Phys. J. C 76, 165 (2016).
- F. Caporale, F. G. Celiberto, G. Chachamis, D. Gordo Gómez, and A. Sabio Vera, Nucl. Phys. B910, 374 (2016).
- F. Caporale, F. G. Celiberto, G. Chachamis, D. Gordo Gómez, and A. Sabio Vera, Eur. Phys. J. C 77, 5 (2017).
- F. G. Celiberto, Frascati Phys. Ser. 63, 43 (2016).
- F. Caporale, F. G. Celiberto, G. Chachamis, D. Gordo Gómez, and A. Sabio Vera, Phys. Rev. D 95, 074007 (2017).
- M. Hentschinski, K. Kutak, and A. van Hameren, Eur. Phys. J. C 81, 112 (2021); 81, 262(E) (2021).
- F. G. Celiberto, M. Fucilla, D. Yu. Ivanov, M. M. A. Mohammed, and A. Papa, J. High Energy Phys. 08 (2022) 092.
- F. G. Celiberto, D. Yu. Ivanov, M. M. A. Mohammed, and A. Papa, Eur. Phys. J. C 81, 293 (2021).
- M. M. A. Mohammed, Hunting stabilization effects of the high-energy resummation at the LHC, Ph.D. thesis, Università della Calabria and INFN-Cosenza, 2022, arXiv:2204.11606.
- F. G. Celiberto and A. Papa, arXiv:2305.00962.
- F. G. Celiberto, L. Delle Rose, M. Fucilla, G. Gatto, and A. Papa, in Proceedings of the 57th Rencontres de Moriond on QCD and High Energy Interactions (2023), arXiv:2305.05052.
- F. G. Celiberto, L. Delle Rose, M. Fucilla, G. Gatto, and A. Papa, Proc. Sci. RADCOR2023 (2024) 069 [arXiv:2309.11573].
- F. G. Celiberto, L. Delle Rose, M. Fucilla, G. Gatto, and A. Papa, Proc. Sci. EPS-HEP2023 (2024) 390 [arXiv:2310.16967].
- F. G. Celiberto, M. Fucilla, M. M. A. Mohammed, D. Yu. Ivanov, and A. Papa, Proc. Sci. RADCOR2023 (2024) 091 [arXiv:2309.07570].
- F. G. Celiberto, M. Fucilla, M. M. A. Mohammed, and A. Papa, Phys. Rev. D 105, 114056 (2022).
- F. G. Celiberto, L. Delle Rose, M. Fucilla, G. Gatto, and A. Papa, J. High Energy Phys. 12 (2024) 061.
- F. G. Celiberto, D. Gordo Gómez, and A. Sabio Vera, Phys. Lett. B 786, 201 (2018).
- K. Golec-Biernat, L. Motyka, and T. Stebel, J. High Energy Phys. 12 (2018) 091.
- F. G. Celiberto, D. Yu. Ivanov, B. Murdaca, and A. Papa, Phys. Lett. B 777, 141 (2018).
- R. Boussarie, B. Ducloué, L. Szymanowski, and S. Wallon, Phys. Rev. D 97, 014008 (2018).
- A. D. Bolognino, F. G. Celiberto, M. Fucilla, D. Yu. Ivanov, B. Murdaca, and A. Papa, Proc. Sci. DIS2019 (2019) 067 [arXiv:1906.05940].
- A. D. Bolognino, F. G. Celiberto, M. Fucilla, D. Yu. Ivanov, and A. Papa, Eur. Phys. J. C 79, 939 (2019).
- A. D. Bolognino, F. G. Celiberto, M. Fucilla, D. Yu. Ivanov, and A. Papa, Phys. Rev. D 103, 094004 (2021).
- F. G. Celiberto and M. Fucilla, in Proceedings of the 29th International Workshop on Deep-Inelastic Scattering and Related Subjects (2022), arXiv:2208.07206.
- G. Gatto, High-energy dynamics of QCD: Theoretical and phenomenological results, Ph.D. thesis, Università della Calabria and INFN-Cosenza, 2025, arXiv:2506.03222.
- I. Anikin, A. Besse, D. Yu. Ivanov, B. Pire, L. Szymanowski, and S. Wallon, Phys. Rev. D 84, 054004 (2011).
- A. Besse, L. Szymanowski, and S. Wallon, J. High Energy Phys. 11 (2013) 062.
- A. D. Bolognino, F. G. Celiberto, D. Yu. Ivanov, and A. Papa, Eur. Phys. J. C 78, 1023 (2018).
- A. D. Bolognino, F. G. Celiberto, D. Yu. Ivanov, and A. Papa, Frascati Phys. Ser. 67, 76 (2018).
- A. D. Bolognino, A. Szczurek, and W. Schaefer, Phys. Rev. D 101, 054041 (2020).
- F. G. Celiberto, Nuovo Cimento Soc. Ital. Fis. 42C, 220 (2019).
- A. D. Bolognino, From semi-hard processes to the unintegrated gluon distribution: A phenomenological path in the high-energy framework, Ph.D. thesis, Calabria University, 2021, arXiv:2109.03033.
- A. Łuszczak, M. Łuszczak, and W. Schäfer, Phys. Lett. B 835, 137582 (2022).
- A. D. Bolognino, F. G. Celiberto, D. Yu. Ivanov, A. Papa, W. Schäfer, and A. Szczurek, Eur. Phys. J. C 81, 846 (2021).
- A. D. Bolognino, F. G. Celiberto, D. Yu. Ivanov, and A. Papa, SciPost Phys. Proc. 8, 089 (2022).
- A. D. Bolognino, F. G. Celiberto, M. Fucilla, D. Yu. Ivanov, A. Papa, W. Schäfer, and A. Szczurek, Rev. Mex. Fis. Suppl. 3, 0308109 (2022).
- A. D. Bolognino, F. G. Celiberto, D. Yu. Ivanov, A. Papa, W. Schäfer, and A. Szczurek, in Proceedings of the 29th International Workshop on Deep-Inelastic Scattering and Related Subjects (2022), arXiv:2207.05726.
- R. D. Ball, V. Bertone, M. Bonvini, S. Marzani, J. Rojo, and L. Rottoli, Eur. Phys. J. C 78, 321 (2018).
- H. Abdolmaleki et al. (xFitter Developers’ Team), Eur. Phys. J. C 78, 621 (2018).
- M. Bonvini and F. Giuli, Eur. Phys. J. Plus 134, 531 (2019).
- F. Silvetti and M. Bonvini, Eur. Phys. J. C 83, 267 (2023).
- F. G. Celiberto and M. Bonvini, Proc. Sci. EPS-HEP2025 (2026) 222 [arXiv:2512.01961].
- F. Silvetti, Resummation phenomenology and PDF determination for precision QCD at the LHC, Ph.D. thesis, Rome University, 2023, arXiv:2403.20315.
- A. Rinaudo, Towards the resummation of high-energy next-to-leading logarithms in QCD, Ph.D. thesis, Genoa University, 2024.
- 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, Nuovo Cimento Soc. Ital. Fis. 44C, 36 (2021).
- X.-C. Zheng, C.-H. Chang, and X.-G. Wu, Phys. Rev. D 100, 014005 (2019).
- C.-H. Chang and Y.-Q. Chen, Phys. Rev. D 46, 3845 (1992); 50, 6013(E) (1994).
- E. Braaten, K.-m. Cheung, and T. C. Yuan, Phys. Rev. D 48, R5049 (1993).
- J. P. Ma, Phys. Lett. B 332, 398 (1994).
- F. Feng, Y. Jia, and D. Yang, Phys. Rev. D 106, 054030 (2022).
- F. Feng and Y. Jia, Chin. Phys. C 47, 033103 (2023).
- V. M. Abazov et al. (D0 Collaboration), Phys. Rev. D 90, 111101 (2014).
- R. D. Ball et al. (NNPDF Collaboration), Eur. Phys. J. C 81, 958 (2021).
- R. D. Ball et al. (NNPDF Collaboration), Eur. Phys. J. C 82, 428 (2022).
- S. Chatrchyan et al. (CMS Collaboration), Phys. Lett. B 714, 136 (2012).
- V. Khachatryan et al. (CMS Collaboration), J. High Energy Phys. 08 (2016) 139.
- V. Khachatryan et al. (CMS Collaboration), J. Instrum. 16, P02010 (2021).
- A. Giraldi (CMS Collaboration), Proc. Sci. ICHEP2022 (2022) 638 [arXiv:2208.08214].
- A. J. Rádl (CMS Collaboration), Proc. Sci. LHCP2023 (2024) 283 [arXiv:2401.10763].
- F. G. Celiberto, TQ4Q2.0: HF-NRevo FFs for scalar, axial-vector, and tensor fully heavy tetraquarks (2026), https://github.com/FGCeliberto/Collinear_FFs/tree/main/TQ4Q20.
- E. Chapon et al., Prog. Part. Nucl. Phys. 122, 103906 (2022).
- A. Accardi et al. (LHCspin Collaboration), arXiv:2504.16034.
- L. A. Anchordoqui et al., Phys. Rep. 968, 1 (2022).
- J. L. Feng et al., J. Phys. G 50, 030501 (2023).
- I. Adachi et al. (ILC International Development Team and ILC Community Collaboration), arXiv:2203.07622.
- C. Balazs et al. (Linear Collider Collaboration), arXiv:2503.24049.
- H. Abramowicz et al. (Linear Collider Vision Collaboration), Eur. Phys. J. Special Topics 235, 1641 (2026).
- A. Arbuzov et al., Prog. Part. Nucl. Phys. 119, 103858 (2021).
- C. Accettura et al., Eur. Phys. J. C 83, 864 (2023); 84, 36(E) (2024).
- C. Accettura et al. (International Muon Collider Collaboration), CERN Yellow Rep. Monogr. 2/2024, 1 (2024).
- C. Accettura et al. (MuCoL Collaboration), 10.5281/zenodo.13970100 (2024).
- A. Chancé et al. (MuCoL Collaboration), 10.5281/zenodo.17476875 (2025).
- K. M. Black et al., J. Instrum. 19, T02015 (2024).
- C. Accettura et al. (International Muon Collider Collaboration), arXiv:2504.21417.
- A. Accardi et al., Eur. Phys. J. A 60, 173 (2024).
- T. Bose et al., in 2022 Snowmass Summer Study (2022), arXiv:2209.13128.
- S. Gessner et al., arXiv:2503.20214.
- J. Altmann et al., CERN Yellow Rep. Monogr. 5/2025 (2025).
- S. J. Brodsky, P. Hoyer, C. Peterson, and N. Sakai, Phys. Lett. 93B, 451 (1980).
- S. J. Brodsky, A. Kusina, F. Lyonnet, I. Schienbein, H. Spiesberger, and R. Vogt, Adv. High Energy Phys. 2015, 231547 (2015).
- P. Jimenez-Delgado, T. J. Hobbs, J. T. Londergan, and W. Melnitchouk, Phys. Rev. Lett. 114, 082002 (2015).
- R. D. Ball, V. Bertone, M. Bonvini, S. Carrazza, S. Forte, A. Guffanti, N. P. Hartland, J. Rojo, and L. Rottoli (NNPDF Collaboration), Eur. Phys. J. C 76, 647 (2016).
- T.-J. Hou, S. Dulat, J. Gao, M. Guzzi, J. Huston, P. Nadolsky, C. Schmidt, J. Winter, K. Xie, and C. P. Yuan, J. High Energy Phys. 02 (2018) 059.
- 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. 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. Vogt, Phys. Rev. D 110, 074036 (2024).
- Y. L. Dokshitzer, V. A. Khoze, and S. I. Troian, J. Phys. G 17, 1602 (1991).
- S. Acharya et al. (ALICE Collaboration), Nature (London) 605, 440 (2022); 607, E22 (2022).
- F.-K. Guo, U.-G. Meißner, and W. Wang, Commun. Theor. Phys. 61, 354 (2014).
- F. G. Celiberto, https://github.com/FGCeliberto/Collinear_FFs/.
- W. A. Bardeen, A. J. Buras, D. W. Duke, and T. Muta, Phys. Rev. D 18, 3998 (1978).
- D. Yu. Ivanov and A. Papa, J. High Energy Phys. 07 (2012) 045.
- A. Tumasyan et al. (CMS Collaboration), J. High Energy Phys. 03 (2022) 189.