On the constituent counting rule for hard exclusive processes involving multi-quark states

  • At high energy, the cross section at finite scattering angle of a hard exclusive process falls off as a power of the Manderstam variable s. If all involved quark-gluon compositions undergo hard momentum transfers, the fall-off scaling is determined by the underlying valence structures of the initial and final hadrons, known as the constituent counting rule. In spite of the complication due to helicity conservation, it has been argued that when applied to exclusive process with exotic multiquark states, the counting rule is a powerful way to determine the valence degrees of freedom inside hadron exotics. In this work, we demonstrate that for hadrons with hidden flavors, the naive application of the constituent counting rule is problematic, since it is not mandatory for all components to participate in hard scattering at the scale \sqrts. We illustrate the problems in the viewpoint based on effective field theory. We clarify the misleading results that may be obtained from the constituent counting rule in exclusive processes with exotic candidates such as Zc±(ccud/ccdu), Zb±(bbud/bbdu), X(3872), etc.
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  • [1] E. Witten, Nucl. Phys. B, 160: 57 (1979). doi:10.1016/0550-3213(79)90232-3
    [2] S. Coleman, Aspects of Symmetry (Cambridge: Cambridge University Press 1985)
    [3] S. Weinberg, Phys. Rev. Lett., 110: 261601 (2013) doi:10.1103/PhysRevLett.110.261601 [arXiv:1303.0342 [hep-ph]]
    [4] N. Brambilla { et al}, Eur. Phys. J. C, 71: 1534 (2011) doi:10.1140/epjc/s10052-010-1534-9 [arXiv:1010.5827 [hep-ph]]
    [5] A. Esposito, A. L. Guerrieri, F. Piccinini, A. Pilloni, and A. D. Polosa, Int. J. Mod. Phys. A, 30: 1530002 (2015) doi:10.1142/S0217751X15300021 [arXiv:1411.5997 [hep-ph]]
    [6] H. X. Chen, W. Chen, X. Liu, and S. L. Zhu, Phys. Rept., 639: 1 (2016) doi:10.1016/j.physrep.2016.05.004 [arXiv:1601.02092 [hep-ph]]
    [7] A. Ali, arXiv:1605.05954 [hep-ph]
    [8] S. K. Choi { et al} (Belle Collaboration), Phys. Rev. Lett., 91: 262001 (2003) doi:10.1103/PhysRevLett.91.262001 [hep-ex/0309032]
    [9] D. Acosta {et al} (CDF Collaboration), Phys. Rev. Lett., 93: 072001 (2004) doi:10.1103/PhysRevLett.93.072001 [hep-ex/0312021]
    [10] B. Aubert { et al} (BaBar Collaboration), Phys. Rev. D, 71: 071103 (2005) doi:10.1103/PhysRevD.71.071103 [hep-ex/0406022]
    [11] V. M. Abazov { et al} (D0 Collaboration), Phys. Rev. Lett., 93: 162002 (2004) doi:10.1103/PhysRevLett.93.162002 [hep-ex/0405004]
    [12] H. Kawamura, S. Kumano, and T. Sekihara, Phys. Rev. D, 88: 034010 (2013) doi:10.1103/PhysRevD.88.034010 [arXiv:1307.0362 [hep-ph]]
    [13] H. Kawamura and S. Kumano, Phys. Rev. D, 89: 054007 (2014) doi:10.1103/PhysRevD.89.054007 [arXiv:1312.1596 [hep-ph]]
    [14] S. H. Blitz and R. F. Lebed, Phys. Rev. D, 91: 094025 (2015) doi:10.1103/PhysRevD.91.094025 [arXiv:1503.04802 [hep-ph]]
    [15] S. J. Brodsky and R. F. Lebed, Phys. Rev. D, 91: 114025 (2015) doi:10.1103/PhysRevD.91.114025 [arXiv:1505.00803 [hep-ph]]
    [16] W. C. Chang, S. Kumano, and T. Sekihara, Phys. Rev. D, 93: 034006 (2016) doi:10.1103/PhysRevD.93.034006 [arXiv:1512.06647 [hep-ph]]
    [17] G. P. Lepage and S. J. Brodsky, Phys. Rev. D, 22: 2157 (1980). doi:10.1103/PhysRevD.22.2157
    [18] C. P. Shen { et al} (Belle Collaboration), Phys. Rev. D, 88: 052019 (2013) doi:10.1103/PhysRevD.88.052019 [arXiv:1309.0575 [hep-ex]]
    [19] N. E. Adam { et al} (CLEO Collaboration), Phys. Rev. Lett., 94: 012005 (2005) doi:10.1103/PhysRevLett.94.012005 [hep-ex/0407028]
    [20] M. Ablikim { et al} (BES Collaboration), Phys. Rev. D, 70: 112007 (2004); [Phys. Rev. D, 71: 019901 (2005)] doi: 10.1103/PhysRevD.71.019901,10.1103/PhysRevD.70.112007 [hep-ex/0410031]
    [21] B. Aubert { et al} (BaBar Collaboration), Phys. Rev. D, 74: 111103 (2006) doi:10.1103/PhysRevD.74.111103 [hep-ex/0611028]
    [22] C. D. Lu, W. Wang, and Y. M. Wang, Phys. Rev. D, 75: 094020 (2007) doi:10.1103/PhysRevD.75.094020 [hep-ph/0702085]
    [23] F. E. Close and P. R. Page, Phys. Lett. B, 578: 119 (2004) doi:10.1016/j.physletb.2003.10.032 [hep-ph/0309253]
    [24] C. Meng and K. T. Chao, Phys. Rev. D, 75: 114002 (2007) doi:10.1103/PhysRevD.75.114002 [hep-ph/0703205]
    [25] B. Q. Li, C. Meng, and K. T. Chao, Phys. Rev. D, 80: 014012 (2009) doi:10.1103/PhysRevD.80.014012 [arXiv:0904.4068 [hep-ph]]
    [26] M. Butenschoen, Z. G. He, and B. A. Kniehl, Phys. Rev. D, 88: 011501 (2013) doi:10.1103/PhysRevD.88.011501 [arXiv:1303.6524 [hep-ph]]
    [27] C. Meng, H. Han, and K. T. Chao, arXiv:1304.6710 [hep-ph]
    [28] G. Y. Chen, W. S. Huo, and Q. Zhao, Chin. Phys. C, 39: 093101 (2015) doi:10.1088/1674-1137/39/9/093101 [arXiv:1309.2859 [hep-ph]]
    [29] N. N. Achasov and E. V. Rogozina, JETP Lett., 100: 227 (2014) doi:10.1134/S0021364014160024 [arXiv:1310.1436 [hep-ph]]
    [30] N. N. Achasov and E. V. Rogozina, Mod. Phys. Lett. A, 30: 1550181 (2015) doi:10.1142/S0217732315501813 [arXiv:1501.03583 [hep-ph]]
    [31] N. N. Achasov and E. V. Rogozina, arXiv:1510.07251 [hep-ph]
    [32] R. H. Dalitz, T. C. Wong, and G. Rajasekaran, Phys., Rev., 153: 1617 (1967)
    [33] E. Oset and A. Ramos, Nucl. Phys. A, 635: 99 (1998) [nucl-th/9711022]
    [34] D. Jido, J. A. Oller, E. Oset, A. Ramos, and U. G. Meissner, Nucl. Phys. A, 725: 181 (2003) doi:10.1016/S0375-9474(03)01598-7 [nucl-th/0303062]
    [35] E. Braaten, Phys. Rev. D, 73: 011501 (2006) doi:10.1103/PhysRevD.73.011501 [hep-ph/0408230]
    [36] W. Wang and Q. Zhao, Phys. Lett. B, 755: 261 (2016) doi:10.1016/j.physletb.2016.02.012 [arXiv:1512.03123 [hep-ph]]
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Feng-Kun Guo, Ulf-G. Meißner and Wei Wang. On the constituent counting rule for hard exclusive processes involving multi-quark states[J]. Chinese Physics C, 2017, 41(5): 053108. doi: 10.1088/1674-1137/41/5/053108
Feng-Kun Guo, Ulf-G. Meißner and Wei Wang. On the constituent counting rule for hard exclusive processes involving multi-quark states[J]. Chinese Physics C, 2017, 41(5): 053108.  doi: 10.1088/1674-1137/41/5/053108 shu
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Received: 2016-12-07
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    Supported in part by DFG and NSFC through funds provided to the Sino-German CRC 110 Symmetries and the Emergence of Structure in QCD(NSFC Grant No. 11261130311), Thousand Talents Plan for Young Professionals, Chinese Academy of Sciences (CAS) President's International Fellowship Initiative (PIFI) (2015VMA076), National Natural Science Foundation of China (11575110, 11655002), Natural Science Foundation of Shanghai (15DZ2272100, 15ZR1423100), Open Project Program of State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, China (Y5KF111CJ1), and by Key Laboratory for Particle Physics, Astrophysics and Cosmology, Ministry of Education.

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On the constituent counting rule for hard exclusive processes involving multi-quark states

    Corresponding author: Feng-Kun Guo,
    Corresponding author: Wei Wang,
  • 1. State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
  • 2. Helmholtz-Institut fü
  • 3.  INPAC, Shanghai Key Laboratory for Particle Physics and Cosmology, Department of Physics and Astronomy, ShanghaiJiao-Tong University, Shanghai 200240, China
Fund Project:  Supported in part by DFG and NSFC through funds provided to the Sino-German CRC 110 Symmetries and the Emergence of Structure in QCD(NSFC Grant No. 11261130311), Thousand Talents Plan for Young Professionals, Chinese Academy of Sciences (CAS) President's International Fellowship Initiative (PIFI) (2015VMA076), National Natural Science Foundation of China (11575110, 11655002), Natural Science Foundation of Shanghai (15DZ2272100, 15ZR1423100), Open Project Program of State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, China (Y5KF111CJ1), and by Key Laboratory for Particle Physics, Astrophysics and Cosmology, Ministry of Education.

Abstract: At high energy, the cross section at finite scattering angle of a hard exclusive process falls off as a power of the Manderstam variable s. If all involved quark-gluon compositions undergo hard momentum transfers, the fall-off scaling is determined by the underlying valence structures of the initial and final hadrons, known as the constituent counting rule. In spite of the complication due to helicity conservation, it has been argued that when applied to exclusive process with exotic multiquark states, the counting rule is a powerful way to determine the valence degrees of freedom inside hadron exotics. In this work, we demonstrate that for hadrons with hidden flavors, the naive application of the constituent counting rule is problematic, since it is not mandatory for all components to participate in hard scattering at the scale \sqrts. We illustrate the problems in the viewpoint based on effective field theory. We clarify the misleading results that may be obtained from the constituent counting rule in exclusive processes with exotic candidates such as Zc±(ccud/ccdu), Zb±(bbud/bbdu), X(3872), etc.

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