Exact Solution of Schrödinger Equation for Pentaquark Systems

[1] C. Alt, T. Anticic, B. Baatar, D. Barna, J. Bartke, L. Betev, H. Białkowska,
A. Billmeier, C. Blume, B. Boimska and M. Botje, J. Bracinik, R. Bramm,
R. Brun, P. Buncic, V. Cerny, P. Christakoglou, O. Chvala, JG. Cramer, P.
Csato, N. Darmenov, A. Dimitrov, P. Dinkelaker, V. Eckardt, G. Farantatos,
P. Filip, D. Flierl, Z. Fodor, P. Foka, P. Freund, V. Friese, J. Gal, M. Gazdzicki, G. Georgopoulos, E. Gladysz, S. Hegyi, C. Hohne, K. Kadija, A. Karev,
S. Kniege, V. I. Kolesnikov, T. Kollegger, R. Korus, M. Kowalski, I. Kraus,
M. Kreps, M. van Leeuwen, P. Levai, L. Litov, M. Makariev, A. I. Malakhov,
C. Markert, M. Mateev, BW. Mayes, G. L. Melkumov, C. Meurer, A. Mischke, M. Mitrovski, J. Molnar, S. Mrowczynski, G. Palla, A. D. Panagiotou,
D. Panayotov, K. Perl, A. Petridis, M. Pikna, L. Pinsky, F. Puhlhofer, J.
G. Reid, R. Renfordt, W. Retyk, C. Roland, G. Roland, M. Rybczynski, A.
Rybicki, A. Sandoval, H. Sann, N. Schmitz, P. Seyboth, F. Sikler, B. Sitar,
E. Skrzypczak, G. Stefanek, R. Stock, H. Strobele, T. Susa, I. Szentpetery,
J. Sziklai, T. A. Trainor, D. Varga, M. Vassiliou, G. I. Veres, G. Vesztergombi, D. Vranic, A. Wetzler, Z. Wlodarczyk, I. K. Yoo, J. Zaranek and J.
Zimanyi, Evidence for an exotic S = −2, Q = −2 baryon resonance in protonproton collisions at the CERN SPS, Phys. Rev. Lett. 92 (4) (2004) p. 042003,
https://doi.org/10.1103/PhysRevLett.92.042003.
[2] F. Stancu, Positive parity pentaquarks in a Goldstone boson exchange model, Phys. Rev. D 58 (11) (1998) p. 111501,
https://doi.org/10.1103/PhysRevD.58.111501.
[3] R. Jaffe and F. Wilczek, Diquarks and exotic spectroscopy, Phys. Rev. Lett.
91 (23) (2003) p. 232003, https://doi.org/10.1103/PhysRevLett.91.232003.
[4] D. Diakonov, V. Petrov and M. Polyakov, Exotic anti-decuplet of baryons:
prediction from chiral solitons, Z. Phys. A 359 (1997) 305 − 314,
https://doi.org/10.1007/s002180050406.
[5] B. K. Jennings and K. Maltman, Z^*
resonances: Phenomenology and models, Phys. Rev. D 69 (9) (2004) p. 094020,
https://doi.org/10.1103/PhysRevD.69.094020.
[6] I. Schmidt and M. Siddikov, Production of pentaquarks
in pA-collisions, Phys. Rev. D 93 (9) (2016) p. 094005,
https://doi.org/10.1103/PhysRevD.93.094005.
[7] K. Azizi, Y. Sarac and H. Sundu, Analysis of P^{+}_{c}
(4380) and P^{+}_{c} (4450) as pentaquark states in the molecular picture with QCD sum rules, Phys. Rev.
D 95 (9) (2017) p. 094016, https://doi.org/10.1103/PhysRevD.95.094016.

[8] R. Zhu, X. Liu, H. Huang and C. F. Qiao, Analyzing doubly heavy tetraand penta-quark states by variational method, Phys. Lett. B 797 (2019) p.
134869, https://doi.org/10.1016/j.physletb.2019.134869.
[9] F. Okiharu, T. Doi, H. Ichie, H. Iida, N. Ishii, M. Oka, H. Suganuma and T.
T. Takahashi, Tetraquark and pentaquark systems in lattice QCD, J. Modern
Phys. 7 (8) (2016) 774 − 789, https://doi.org/10.4236/jmp.2016.78072.
[10] M. Monemzadeh, N. Tazimi and P. Sadeghi, Tetraquarks as diquarkantidiquark bound systems, Phys. Lett. B 741 (2015) 124 − 127,
https://doi.org/10.1016/j.physletb.2014.12.001.
[11] M. Radin and N. Tazimi, Quark-antiquark bound state in momentumhelicity representation, Phys. Rev. D 90 (8) (2014) p. 085020,
https://doi.org/10.1103/PhysRevD.90.085020.
[12] M. Radin, Sh. Babaghodrat and M. Monemzadeh, Estimation of heavy
baryon masses Ω^{++}_{ccc} and Ω^{−}_{bbb} by solving the Faddeev equation in
a three-dimensional approach, Phys. Rev. D 90 (2014) p. 047701,
https://doi.org/10.1103/PhysRevD.90.047701.
[13] P. Sadeghi Alavijeh, N. Tazimi and M. Monemzadeh, Calculation of the topquark Yukawa coupling constant, Int J. Mod. Phys. A 36 (19) (2021) p.
2150124, https://doi.org/10.1142/S0217751X21501244.
[14] A. Khalaghi, M. Monemzadeh and N. Tazimi, Investigation of binding energy and potential in mesons, Commun. Theor. Phys. 71 (7) (2019) p. 813,
https://doi.org/10.1088/0253-6102/71/7/813.
[15] E. Santopinto, F. Iachello and M. M. Giannini, Exactly solvable models of baryon spectroscopy, Nucl. Phys. A 623 (1-2) (1997) 100 − 109,
https://doi.org/10.1016/S0375-9474(97)00427-2.
[16] T. Hyodo and W. Weise, Effective KN¯ interaction based on chiral SU(3) dynamics, Phys. Rev. C 77 (3) (2008) p. 035204,
https://doi.org/10.1103/PhysRevC.77.035204.
[17] T. Hyodo, D. Jido and T. Kunihiro, Nature of the σ meson as revealed by its softening process, Nucl. Phys. A 848 (3-4) (2010) 341 − 365,
https://doi.org/10.1016/j.nuclphysa.2010.09.016.
[18] A. Doté, T. Hyodo and W. Weise, Variational calculation of the ppK− system
based on chiral SU(3) dynamics, Phys. Rev. C 79 (1) (2009) p. 014003,
https://doi.org/10.1103/PhysRevC.79.014003.
[19] S. Yasui and K. Sudoh, Exotic nuclei with open heavy
flavor mesons, Phys. Rev. D 80 (3) (2009) p. 034008,
https://doi.org/10.1103/PhysRevD.80.034008.

[20] Y. Sarac, H. Kim and S. H. Lee, QCD sum rules for the anticharmed pentaquark, Phys. Rev. D 73 (1) (2006) p. 014009,
https://doi.org/10.1103/PhysRevD.73.014009.
[21] S. H. Lee, S. Yasui, W. Liu and C. M. Ko, Charmed exotics
in heavy ion collisions, Eur. Phys. J. C 54 (2008) 259 − 265,
https://doi.org/10.1140/epjc/s10052-007-0516-z.
[22] H. Yukawa, On the interaction of elementary particles, Proc. Phys. Math. Soc.
Jap. 17 (1935) 48 − 57.
[23] C. Stubbins, Bound states of the Hulthén and Yukawa potentials, Phys. Rev.
A 48 (1) (1993) p. 220, https://doi.org/10.1103/PhysRevA.48.220.
[24] J. Stein, A. Ron, I. B. Goldberg and R. H. Pratt, Generalized WKB
approximation to nonrelativistic normalizations and phase shifts in a
screened Coulomb potential, Phys. Rev. A 36 (12) (1987) p. 5523,
https://doi.org/10.1103/PhysRevA.36.5523.
[25] F. J. Rogers, H. C. Graboske, Jr. and D. J. Harwood, Bound eigenstates of
the static screened Coulomb potential, Phys. Rev. A 1 (6) (1970) p. 1577,
https://doi.org/10.1103/PhysRevA.1.1577.
[26] B. Gönül, K. Köksal and E. Bakir, An alternative treatment for Yukawa-type
potentials, Phys. Scr. 73 (3) (2006) p. 279, https://doi.org/10.1088/0031-
8949/73/3/007.
[27] M. Karakoc and I. Boztosun, Accurate iterative and perturbative solutions
of the yukawa potential, Int. J. Mod. Phys. E 15 (06) (2006) 1253 − 1262,
https://doi.org/10.1142/S0218301306004806.
[28] S. Özçelik and M. Simsek, Exact solutions of the radial Schrödinger equation for inverse-power potentials, Phys. Lett. A 152 (3-4) (1991) 145 − 150,
https://doi.org/10.1016/0375-9601(91)91081-N.
[29] M. Karliner, Quark masses, hyperfine interactions and exotic baryons, In
Pentaquark Workshop, Jlab, hep-ph/0307243 and hep-ph/0307343, 7 (2003),
https://doi.org/10.11429/ppmsj1919.17.0_48.
[30] M. Karliner and H. J. Lipkin, The anticharmed exotic baryon
Θc and its 281 relatives, arXiv preprint hep-ph/0307343, (2003),
https://doi.org/10.48550/arXiv.hep-ph/0307343.