\begin{document}${B_u}$\end{document} and \begin{document}${B_d}$\end{document}) for the profile density distributions of the up and down quarks instead of using the same width as in the literature. We find that the cross-sections calculated with \begin{document}${B_u \geq B_d}$\end{document} at each collision energy are consistent with each other, which is in agreement with theoretical expectations, whereas those computed with \begin{document}${B_u < B_d}$\end{document} show some discrepancies. This outcome implies that the up quark might emit more gluons than the down quark, leading to \begin{document}${B_u \geq B_d}$\end{document} at high energy. The impact of energy on the outcome is estimated. Our results show that as the collision energy increases, the aforementioned discrepancies are not only significantly broadened, but also shift to a relatively smaller momentum transfer range at the future Electron-Ion Collider (EIC) and Large Hadron Electron Collider (LHeC) energies, which indicates that the EIC and LHeC can provide an unprecedented chance to access the shape of the valence quark of the proton."> Probing valence quark width of the proton in deeply virtual Compton scattering at high energies -
  • [1]

    F. D. Aaronet al. (H1, ZEUS collaboration) , JHEP01, 109 (2010), arXiv:0911.0884[hep-ex]

  • [2]

    H. Abramowiczet al. (H1, ZEUS collaboration) , Eur. Phys. J. C75(12), 580 (2015), arXiv:1506.06042[hep-ex]

  • [3]

    S. Schlichting and B. Schenke, Phys. Lett. B739, 313 (2014), arXiv:1407.8458[hep-ph]

  • [4]

    H. Mäntysaari and B. Schenke, Phys. Rev. Lett.117(5), 052301 (2016), arXiv:1603.04349[hep-ph]

  • [5]

    H. Mäntysaari and B. Schenke, Phys. Rev. D94(3), 034042 (2016), arXiv:1607.01711[hep-ph]

  • [6]

    R. Abdul Khaleket al., arXiv: 2103.05419[physics.ins-det]

  • [7]

    P. Agostiniet al. (LHeC, FCC-he Study Group collaboration) , J. Phys. G48(11), 110501 (2021), arXiv:2007.14491[hep-ex]

  • [8]

    D. P. Anderleet al., Front. Phys. (Beijing)16(6), 64701 (2021), arXiv:2102.09222[nucl-ex]

  • [9]

    K. J. Golec-Biernat and M. Wusthoff, Phys. Rev. D60, 114023 (1999), arXiv:hep-ph/9903358

  • [10]

    E. Iancu, K. Itakura, and S. Munier, Phys. Lett. B590, 199 (2004), arXiv:hep-ph/0310338

  • [11]

    G. Watt and H. Kowalski, Phys. Rev. D78, 014016 (2008), arXiv:0712.2670[hep-ph]

  • [12]

    M. Kozlov, A. Shoshi, and W. Xiang, JHEP10, 020 (2007), arXiv:0707.4142[hep-ph]

  • [13]

    J. L. Albacete, N. Armesto, J. G. Milhanoet al., Phys. Rev. D80, 034031 (2009), arXiv:0902.1112[hep-ph]

  • [14]

    A. H. Rezaeian and I. Schmidt, Phys. Rev. D88, 074016 (2013), arXiv:1307.0825[hep-ph]

  • [15]

    C. Contreras, E. Levin, R. Meneseset al., Phys. Rev. D94(11), 114028 (2016), arXiv:1607.00832[hep-ph]

  • [16]

    J. Cepila, J. G. Contreras, and M. Matas, Phys. Rev. D99(5), 051502 (2019), arXiv:1812.02548[hep-ph]

  • [17]

    B. Ducloué, E. Iancu, G. Soyezet al., Phys. Lett. B803, 135305 (2020), arXiv:1912.09196[hep-ph]

  • [18]

    H. Hänninen, H. Mäntysaari, R. Paatelainenet al., Phys. Rev. Lett.130(19), 192301 (2023), arXiv:2211.03504[hep-ph]

  • [19]

    I. Balitsky, Nucl. Phys. B463, 99 (1996), arXiv:hep-ph/9509348

  • [20]

    Y. V. Kovchegov, Phys. Rev. D61, 074018 (2000), arXiv:hep-ph/9905214

  • [21]

    J. Jalilian-Marian, A. Kovner, A. Leonidovet al., Nucl. Phys. B504, 415 (1997), arXiv:hep-ph/9701284

  • [22]

    J. Jalilian-Marian, A. Kovner, A. Leonidovet al., Phys. Rev. D59, 014014 (1998), arXiv:hep-ph/9706377

  • [23]

    E. Iancu, A. Leonidov, and L. D. McLerran, Nucl. Phys. A692, 583 (2001), arXiv:hep-ph/0011241

  • [24]

    E. Ferreiro, E. Iancu, A. Leonidovet al., Nucl. Phys. A703, 489 (2002), arXiv:hep-ph/0109115

  • [25]

    C. Marquet, R. B. Peschanski, and G. Soyez, Phys. Rev. D76, 034011 (2007), arXiv:hep-ph/0702171

  • [26]

    Y. Cai, W. Xiang, M. Wanget al., Chin. Phys. C44(7), 074110 (2020), arXiv:2002.12610[hep-ph]

  • [27]

    S. Zhang, S. Cai, W. Xianget al., Chin. Phys. C45(7), 073110 (2021)

  • [28]

    J. L. Albacete and A. Soto-Ontoso, Phys. Lett. B770, 149 (2017), arXiv:1605.09176[hep-ph]

  • [29]

    J. Cepila, J. G. Contreras, and J. D. Tapia Takaki, Phys. Lett. B766, 186 (2017), arXiv:1608.07559[hep-ph]

  • [30]

    M. C. Traini and J.-P. Blaizot, Eur. Phys. J. C79(4), 327 (2019), arXiv:1804.06110[hep-ph]

  • [31]

    A. Kumar and T. Toll, Eur. Phys. J. C82(9), 837 (2022), arXiv:2106.12855[hep-ph]

  • [32]

    S. Demirci, T. Lappi, and S. Schlichting, Phys. Rev. D103(9), 094025 (2021), arXiv:2101.03791[hep-ph]

  • [33]

    S. Demirci, T. Lappi, and S. Schlichting, Phys. Rev. D106(7), 074025 (2022), arXiv:2206.05207[hep-ph]

  • [34]

    A. Kumar and T. Toll, Phys. Rev. D105(11), 114011 (2022), arXiv:2202.06631[hep-ph]

  • [35]

    J.-P. Blaizot and M. C. Traini, arXiv: 2209.15545[hep-ph]

  • [36]

    S. Bhattacharya, K. Cichy, M. Constantinouet al., Phys. Rev. D108(1), 014507 (2023), arXiv:2305.11117[hep-lat]

  • [37]

    W. Xiang, Y. Cai, and D. Zhou, Nucl. Phys. A1042, 122810 (2024), arXiv:2308.10136[hep-ph]

  • [38]

    H. Kowalski, L. Motyka, and G. Watt, Phys. Rev. D74, 074016 (2006), arXiv:hep-ph/0606272

  • [39]

    H. I. Miettinen and J. Pumplin, Phys. Rev. D18, 1696 (1978)

  • [40]

    L. Frankfurt, G. A. Miller, and M. Strikman, Phys. Rev. Lett.71, 2859 (1993), arXiv:hep-ph/9309285

  • [41]

    I. Balitsky, Phys. Rev. D75, 014001 (2007), arXiv:hep-ph/0609105

  • [42]

    I. Balitsky and G. A. Chirilli, Phys. Rev. D77, 014019 (2008), arXiv:0710.4330[hep-ph]

  • [43]

    E. Iancu, J. D. Madrigal, A. H. Muelleret al., Phys. Lett. B744, 293 (2015), arXiv:1502.05642[hep-ph]

  • [44]

    D.-X. Zheng and J. Zhou, JHEP11, 177 (2019), arXiv:1906.06825[hep-ph]

  • [45]

    E. Levin and K. Tuchin, Nucl. Phys. B573, 833 (2000), arXiv:hep-ph/9908317

  • [46]

    Y. Hatta and J. Zhou, Phys. Rev. Lett.129(25), 252002 (2022), arXiv:2207.03378[hep-ph]

  • [47]

    W. Xiang, Y. Cai, M. Wanget al., Phys. Rev. D101(7), 076005 (2020), arXiv:1911.06744[hep-ph]

  • [48]

    W. Xiang, Y. Cai, M. Wanget al., Phys. Rev. D104(1), 016018 (2021), arXiv:2102.03789[hep-ph]

  • [49]

    T. Lappi and H. Mäntysaari, Phys. Rev. D91(7), 074016 (2015), arXiv:1502.02400[hep-ph]

  • [50]

    T. Lappi and H. Mäntysaari, Phys. Rev. D93(9), 094004 (2016), arXiv:1601.06598[hep-ph]

  • [51]

    H. Kowalski and D. Teaney, Phys. Rev. D68, 114005 (2003), arXiv:hep-ph/0304189

  • [52]

    A. H. Rezaeian, M. Siddikov, M. Van de Klundertet al., Phys. Rev. D87(3), 034002 (2013), arXiv:1212.2974[hep-ph]

  • [53]

    F. D. Aaronet al. (H1 collaboration) , Phys. Lett. B681, 391 (2009), arXiv:0907.5289[hep-ex]

  • [54]

    A. Aktaset al. (H1 collaboration) , Eur. Phys. J. C44, 1 (2005), arXiv:hep-ex/0505061

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