Estimating the production rates of D-wave charmed mesons via the semileptonic decays of bottom mesons
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摘要
Using the covariant light-front approach with conventional vertex functions, we estimate the production rates of D-wave charmed/charmed-strange mesons via the B_((s)) semileptonic decays. As the calculated production rates are significant, it seems possible to experimentally search for D-wave charmed/charmed-strange mesons via semileptonic decays, which may provide an additional approach for exploring D-wave charmed/charmed-strange mesons.
Using the covariant light-front approach with conventional vertex functions, we estimate the production rates of D-wave charmed/charmed-strange mesons via the B_((s)) semileptonic decays. As the calculated production rates are significant, it seems possible to experimentally search for D-wave charmed/charmed-strange mesons via semileptonic decays, which may provide an additional approach for exploring D-wave charmed/charmed-strange mesons.
Using the covariant light-front approach with conventional vertex functions, we estimate the production rates of D-wave charmed/charmed-strange mesons via the B_((s)) semileptonic decays. As the calculated production rates are significant, it seems possible to experimentally search for D-wave charmed/charmed-strange mesons via semileptonic decays, which may provide an additional approach for exploring D-wave charmed/charmed-strange mesons.
引文
1 H. X. Chen, W. Chen, X. Liu, Y. R. Liu, and S. L. Zhu, A review of the open charm and open bottom systems,arXiv:1609.08928
2 R. Aaij et al([LHCb Collaboration], Study of D_J meson decays to D~+π~-, D~0π~+and D~(*+)π~-final states in pp collision), JHEP,1309:145(2013)
3 P. del Amo Sanchez et al([BaBar Collaboration], Observation of new resonances decaying to Dπand D~*πin inclusive e~+e~-collisions near s~(1/2)=10.58 GeV), Phys. Rev. D, 82:111101(2010)
4 R. Aaij et al([LHCb Collaboration], Observation of overlapping spin-1 and spin-3D.0K.-resonances at mass 2.86GeV/c.2), Phys.Rev. Lett., 113:162001(2014)
5 R. Aaij et al([LHCb Collaboration], Dalitz plot analysis of B_s~0→D~0K~-π~+decays), Phys. Rev. D, 90(7):072003(2014)
6 M. Di Pierro and E. Eichten(Excited heavy-light systems and hadronic transitions), Phys. Rev. D, 64:114004(2001)
7 Z. F. Sun, J. S. Yu, X. Liu, and T. Matsuki(Newly observed D(2550), D(2610), and D(2760)as 2S and 1D charmed mesons),Phys. Rev. D, 82:111501(2010)
8 X. H. Zhong(Strong decays of the newly observed D(2550),D(2600), D(2750), and D(2760)), Phys. Rev. D, 82:114014(2010)
9 D. M. Li, P. F. Ji, and B. Ma(The newly observed open-charm states in quark model), Eur. Phys. J. C, 71:1582(2011)
10 P. Colangelo, F. De Fazio, F. Giannuzzi, and S. Nicotri(New meson spectroscopy with open charm and beauty), Phys. Rev. D,86:054024(2012)
11 B. Chen, L. Yuan, and A. Zhang(Possible 2S and 1D charmedand charmed-strange mesons), Phys. Rev. D, 83:114025(2011)
12 Q. T. Song, D. Y. Chen, X. Liu, and T. Matsuki(D_(s1)~*(2860)and D_(s3)~*(2860):candidates for 1D charmed-strange mesons), Eur.Phys. J. C, 75:30(2015)
13 S. Godfrey and K. Moats(The D_(sJ·)*(2860)Mesons as Excited Dwave cs States), Phys. Rev. D, 90:117501(2014)
14 D. Zhou, E. L. Cui, H. X. Chen, L. S. Geng, X. Liu, and S. L. Zhu(D-wave heavy-light mesons from QCD sum rules), Phys. Rev.D, 90:114035(2014)
15 Z. G. Wang(D_(s3·)*(2860)and D_(s1·)*(2860)as the 1D cs states),Eur. Phys. J. C, 75:25(2015)
16 B. Aubert et al([BaBar Collaboration], Observation of a New DS Meson Decaying to DK at a Mass of 2.86 GeV/c2), Phys. Rev.Lett., 97:222001(2006)
17 B. Aubert et al([BaBar Collaboration], Study of D_(sJ)decays to D~*K in inclusive e~+e~-interactions), Phys. Rev. D, 80:092003(2009)
18 B. Zhang, X. Liu, W. Z. Deng, and S. L. Zhu(D_(sJ)(2860)and D_(sJ)(2715)), Eur. Phys. J. C, 50:617(2007)
19 P. Colangelo, F. De Fazio, S. Nicotri, and M. Rizzi(Identifying D_(sJ)(2700)through its decay modes), Phys. Rev. D, 77:014012(2008)
20 D. M. Li and B. Ma(Implication of BaBar's new data on the D_(s1)(2710)and D_(sJ)(2860)), Phys. Rev. D, 81:014021(2010)
21 X. H. Zhong and Q. Zhao(Strong decays of newly observed D_(sJ)states in a constituent quark model with effective Lagrangians),Phys. Rev. D, 81:014031(2010)
22 D. M. Li, B. Ma, and Y. H. Liu(Understanding masses of c anti-sstates in Regge phenomenology), Eur. Phys. J. C, 51:359(2007)
23 X. h. Zhong and Q. Zhao(Strong decays of heavy-light mesons in a chiral quark model), Phys. Rev. D, 78:014029(2008)
24 B. Chen, D. X. Wang, and A. Zhang(Interpretation of D_(sJ)~+(2632),D_(sJ)~(+-)(2700), D_(sJ)~(*+)(2860)and D_(sJ)~+(3040)), Phys. Rev. D, 80:071502(2009)
25 E. van Beveren and G. Rupp(Comment on'Study of D_(sJ)decays to D~*in inclusive e~+e~-interactions'), Phys. Rev. D, 81:118101(2010)
26 Q. T. Song, D. Y. Chen, X. Liu, and T. Matsuki, Higher radial and orbital excitations in the charmed meson family, Phys. Rev.D, 92 no. 7:074011(2015)
27 Q. T. Song, D. Y. Chen, X. Liu and T. Matsuki(Charmed-strange mesons revisited:mass spectra and strong decays), Phys. Rev. D,91:054031(2015)
28 W. Jaus(Semileptonic Decays of B and D Mesons in the Light Front Formalism), Phys. Rev. D, 41:3394(1990)
29 W. Jaus(Relativistic constituent quark model of electroweak properties of light mesons), Phys. Rev. D, 44:2851(1991)
30 C. R. Ji, P. L. Chung and S. R. Cotanch(Light cone quark model axial vector meson wave function), Phys. Rev. D, 45:4214(1992)
31 W. Jaus, Semileptonic, radiative, and pionic(decays of B, B*and D,D~*mesons), Phys. Rev. D, 53, 1349(1996)Erratum:[Phys.Rev. D 54, 5904(1996)]
32 H. Y. Cheng, C. Y. Cheung and C. W. Hwang(Mesonic formfactors and the Isgur-Wise function on the light front), Phys. Rev.D, 55:1559(1997)
33 B. Q. Ma(Spin structure of the pion in a light cone representation), Z. Phys. A, 345:321(1993)
34 H. J. Melosh(Quarks:Currents and constituents), Phys. Rev. D,9:1095(1974)
35 H. Y. Cheng, C. K. Chua, and C. W. Hwang(Covariant light front approach for s wave and p wave mesons:Its application to decay constants and form-factors), Phys. Rev. D, 69:074025(2004)
36 H. Xu, Q. Huang, H. W. Ke, and X. Liu(Numerical analysis of the production of D~*(3000), D_(sJ)(3040)and their partners through the semileptonic decays of B_s mesons in terms of the light front quark model), Phys. Rev. D, 90:094017(2014)
37 G. Li, F. 1. Shao, and W. Wang(B_s→D_s(3040)form factors and B_s decays into D_s(3040)), Phys. Rev. D, 82:094031(2010),arXiv:1008.3696[hep-ph]
38 H. Y. Cheng and C. K. Chua,(Covariant light front approach for B→K~*γ,K_(1γ), K_2~*γdecays), Phys. Rev. D. 69:094007(2004)Erratum:[Phys. Rev. D, 81:059901(2010)]
39 H. W. Ke, X. Q. Li, and Z. T. Wei(Whether new data on D_s→f_0(980)e~+v_e can be understood if f_0(980)consists of only the conventional q anti-q structure), Phys. Rev. D, 80:074030(2009)
40 H. W. Ke, X. Q. Li, and Z. T. Wei(Determining theη-η'mixing by the newly measured BR(D(D_s)→η(η')+(?)+v_l), Eur. Phys. J. C,69:133(2010)
41 C. D. Lu, W. Wang, and Z. T. Wei(Heavy-to-light form factors on the light cone), Phys. Rev. D, 76:014013(2007)
42 W. Wang, Y. L. Shen, and C. D. Lu(The Study of B_c~-→X(3872)π~-(K~-)decays in the covariant light-front approach), Eur. Phys. J. C, 51:841(2007)
43 W. Wang and Y. L. Shen(D_s→K, K~*,φform factors in the Covariant Light-Front Approach and Exclusive Ds Decays), Phys.Rev. D, 78:054002(2008)
44 Y. L. Shen and Y. M. Wang(J/Ψweak decays in the covariant light-front quark model), Phys. Rev. D, 78:074012(2008)
45 W. Wang, Y. L. Shen, and C. D. Lu(Covariant Light-Front Approach for B_c transition form factors), Phys. Rev. D, 79:054012(2009)
46 X. X. Wang, W. Wang, and C. D. Lu(B_c to p-Wave CharmoniaTransitions in Covariant Light-Front Approach), Phys. Rev. D,79:114018(2009)
47 C. H. Chen, Y. L. Shen, and W. Wang(|V_(ub)|and B→η'Form Factors in Covariant Light Front Approach), Phys. Lett. B, 686:118(2010), arXiv:0911.2875[hep-ph]
48 W. Wang(Hindered Magnetic Dipole Transition in the Covariant Light-Front Approach), arXiv:[hep-ph].
49 W. Jaus(Covariant analysis of the light front quark model), Phys.Rev. D, 60:054026(1999)
50 T. Matsuki, T. Morii, and K. Seo(Mixing angle between~3P_1 and~1P_1 in HQET), Prog. Theor. Phys., 124:285(2010),arXiv:1001.4248[hep-ph]
51 Q. Li, T. Wang, Y. Jiang, H. Yuan, T. Zhou, and G. L. Wang(Decays of B, Bs and B_c to D-wave heavy-light mesons), Eur.Phys. J. C, 77(1):12(2017)
52 H. W. Ke and X. Q. Li(Vertex functions for D-wave mesons in the light-front approach), Eur. Phys. J. C, 71:1776(2011)
53 H. M. Choi and C. R. Ji(Light-front dynamic analysis of transition form factors in the process of P→Vev_e), Nucl. Phys.A, 856:95(2011), arXiv:1007.2502[hep-ph]
54 H. M. Choi and C. R. Ji(Semileptonic and radiative decays of the B(c)meson in light-front quark model), Phys. Rev. D, 80:054016(2009), arXiv:0903.0455[hep-ph]
55 H. M. Choi and C. R. Ji(Semileptonic B/c decays in the lightfront quark model), Nucl. Phys. Proc. Suppl., 199:240(2010)
56 M. A. DeWitt, H. M. Choi, and C. R. Ji(Radiative scalar meson decays in the light front quark model), Phys. Rev. D, 68:054026(2003), arXiv:hep-ph/0306060[hep-ph]
57 B. L. G. Bakker, H. M. Choi, and C. R. Ji(The Vector meson form-factor analysis in light front dynamics), Phys. Rev. D, 65:116001(2002), arXiv:hep-ph/0202217[hep-ph]
58 B. L. G. Bakker, H. M. Choi, and C. R. Ji(Regularizing the fermion loop divergencies in the light front meson currents),Phys. Rev. D, 63:074014(2001), arXiv:hep-ph/0008147[hepph]
59 H. M. Choi and C. R. Ji(The Light-front zero-mode contribution to the good current in weak transition), Phys. Rev. D, 72:013004(2005), arXiv:hep-ph/0504219[hep-ph]
60 P. L. Chung, F. Coester, and W. N. Polyzou(Charge FormFactors of Quark Model Pions), Phys. Lett. B, 205:545(1988)
61 E. Gamiz et al([HPQCD Collaboration], Neutral B Meson Mixing in Unquenched Lattice QCD), Phys. Rev. D, 80:014503(2009)
62 A. Khodjamirian, C. Klein, T. Mannel, and N. Offen(Semileptonic charm decays D→πev_e and D→Kev_e from QCD Light-Cone Sum Rules), Phys. Rev. D, 80:114005(2009)
63 C. Bourrely, I. Caprini, and L. Lellouch(Model-independent description of B→πev decays and a determination of|V(ub)|),Phys. Rev. D, 79:013008(2009)
64 Y. M. Wang, Y. B. Wei, Y. L. Shen, and C. D. L(Perturbative corrections to B→D form factors in QCD), JHEP, 1706:062(2017)
65 P. Colangelo, F. De Fazio, and G. Nardulli(B meson transitions into higher mass charmed resonances), Phys. Lett. B, 478:408(2000)
66 L. F. Gan and M. Q. Huang(Semileptonic Decays of B Meson Transition Into D-wave Charmed Meson Doublets), Phys. Rev.D, 79:034025(2009)
67 L. F. Gan, J. R. Zhang, M. Q. Huang, H. B. Zhuo, Y. Y. Ma, Q. J.Zhu, J. X. Liu, and G. B. Zhang(D_(sJ)(2860)From The Semileptonic Decays Of Bs Mesons), Eur. Phys. J. C, 75(5):232(2015), arXiv:1412.7969[hep-ph]
68 S. J. Brodsky, H. C. Pauli, and S. S. Pinsky(Quantum chromodynamics and other field theories on the light cone), Phys.Rept., 301:299(1998)
69 J. h. Yu, B. W. Xiao, and B. Q. Ma(Space-like and time-like pion-rho ransition form factors in the light-cone formalism), J.Phys. G, 34:1845(2007)
1)We should mention that there is a typo in Ref.[35] for the A_9~((4))function, whose correct expression is given by A_9~((4))=A_2~((1))A_6~((3))-3/q~2A_4~((4)).
1)We need to mention that a minus sign is needed in front ofω_(3_(D_2)~c which is a typo in Ref.[52].
1)When reproducing the coefficients A_i~((4)),B_j~((4))and C_k~((4)), we find a typo in Ref.[35] whose correct expression is given by A_9~((4))=A_2~((1))A_6~((3))-3/q~2A_4~((4)).
2 R. Aaij et al([LHCb Collaboration], Study of D_J meson decays to D~+π~-, D~0π~+and D~(*+)π~-final states in pp collision), JHEP,1309:145(2013)
3 P. del Amo Sanchez et al([BaBar Collaboration], Observation of new resonances decaying to Dπand D~*πin inclusive e~+e~-collisions near s~(1/2)=10.58 GeV), Phys. Rev. D, 82:111101(2010)
4 R. Aaij et al([LHCb Collaboration], Observation of overlapping spin-1 and spin-3D.0K.-resonances at mass 2.86GeV/c.2), Phys.Rev. Lett., 113:162001(2014)
5 R. Aaij et al([LHCb Collaboration], Dalitz plot analysis of B_s~0→D~0K~-π~+decays), Phys. Rev. D, 90(7):072003(2014)
6 M. Di Pierro and E. Eichten(Excited heavy-light systems and hadronic transitions), Phys. Rev. D, 64:114004(2001)
7 Z. F. Sun, J. S. Yu, X. Liu, and T. Matsuki(Newly observed D(2550), D(2610), and D(2760)as 2S and 1D charmed mesons),Phys. Rev. D, 82:111501(2010)
8 X. H. Zhong(Strong decays of the newly observed D(2550),D(2600), D(2750), and D(2760)), Phys. Rev. D, 82:114014(2010)
9 D. M. Li, P. F. Ji, and B. Ma(The newly observed open-charm states in quark model), Eur. Phys. J. C, 71:1582(2011)
10 P. Colangelo, F. De Fazio, F. Giannuzzi, and S. Nicotri(New meson spectroscopy with open charm and beauty), Phys. Rev. D,86:054024(2012)
11 B. Chen, L. Yuan, and A. Zhang(Possible 2S and 1D charmedand charmed-strange mesons), Phys. Rev. D, 83:114025(2011)
12 Q. T. Song, D. Y. Chen, X. Liu, and T. Matsuki(D_(s1)~*(2860)and D_(s3)~*(2860):candidates for 1D charmed-strange mesons), Eur.Phys. J. C, 75:30(2015)
13 S. Godfrey and K. Moats(The D_(sJ·)*(2860)Mesons as Excited Dwave cs States), Phys. Rev. D, 90:117501(2014)
14 D. Zhou, E. L. Cui, H. X. Chen, L. S. Geng, X. Liu, and S. L. Zhu(D-wave heavy-light mesons from QCD sum rules), Phys. Rev.D, 90:114035(2014)
15 Z. G. Wang(D_(s3·)*(2860)and D_(s1·)*(2860)as the 1D cs states),Eur. Phys. J. C, 75:25(2015)
16 B. Aubert et al([BaBar Collaboration], Observation of a New DS Meson Decaying to DK at a Mass of 2.86 GeV/c2), Phys. Rev.Lett., 97:222001(2006)
17 B. Aubert et al([BaBar Collaboration], Study of D_(sJ)decays to D~*K in inclusive e~+e~-interactions), Phys. Rev. D, 80:092003(2009)
18 B. Zhang, X. Liu, W. Z. Deng, and S. L. Zhu(D_(sJ)(2860)and D_(sJ)(2715)), Eur. Phys. J. C, 50:617(2007)
19 P. Colangelo, F. De Fazio, S. Nicotri, and M. Rizzi(Identifying D_(sJ)(2700)through its decay modes), Phys. Rev. D, 77:014012(2008)
20 D. M. Li and B. Ma(Implication of BaBar's new data on the D_(s1)(2710)and D_(sJ)(2860)), Phys. Rev. D, 81:014021(2010)
21 X. H. Zhong and Q. Zhao(Strong decays of newly observed D_(sJ)states in a constituent quark model with effective Lagrangians),Phys. Rev. D, 81:014031(2010)
22 D. M. Li, B. Ma, and Y. H. Liu(Understanding masses of c anti-sstates in Regge phenomenology), Eur. Phys. J. C, 51:359(2007)
23 X. h. Zhong and Q. Zhao(Strong decays of heavy-light mesons in a chiral quark model), Phys. Rev. D, 78:014029(2008)
24 B. Chen, D. X. Wang, and A. Zhang(Interpretation of D_(sJ)~+(2632),D_(sJ)~(+-)(2700), D_(sJ)~(*+)(2860)and D_(sJ)~+(3040)), Phys. Rev. D, 80:071502(2009)
25 E. van Beveren and G. Rupp(Comment on'Study of D_(sJ)decays to D~*in inclusive e~+e~-interactions'), Phys. Rev. D, 81:118101(2010)
26 Q. T. Song, D. Y. Chen, X. Liu, and T. Matsuki, Higher radial and orbital excitations in the charmed meson family, Phys. Rev.D, 92 no. 7:074011(2015)
27 Q. T. Song, D. Y. Chen, X. Liu and T. Matsuki(Charmed-strange mesons revisited:mass spectra and strong decays), Phys. Rev. D,91:054031(2015)
28 W. Jaus(Semileptonic Decays of B and D Mesons in the Light Front Formalism), Phys. Rev. D, 41:3394(1990)
29 W. Jaus(Relativistic constituent quark model of electroweak properties of light mesons), Phys. Rev. D, 44:2851(1991)
30 C. R. Ji, P. L. Chung and S. R. Cotanch(Light cone quark model axial vector meson wave function), Phys. Rev. D, 45:4214(1992)
31 W. Jaus, Semileptonic, radiative, and pionic(decays of B, B*and D,D~*mesons), Phys. Rev. D, 53, 1349(1996)Erratum:[Phys.Rev. D 54, 5904(1996)]
32 H. Y. Cheng, C. Y. Cheung and C. W. Hwang(Mesonic formfactors and the Isgur-Wise function on the light front), Phys. Rev.D, 55:1559(1997)
33 B. Q. Ma(Spin structure of the pion in a light cone representation), Z. Phys. A, 345:321(1993)
34 H. J. Melosh(Quarks:Currents and constituents), Phys. Rev. D,9:1095(1974)
35 H. Y. Cheng, C. K. Chua, and C. W. Hwang(Covariant light front approach for s wave and p wave mesons:Its application to decay constants and form-factors), Phys. Rev. D, 69:074025(2004)
36 H. Xu, Q. Huang, H. W. Ke, and X. Liu(Numerical analysis of the production of D~*(3000), D_(sJ)(3040)and their partners through the semileptonic decays of B_s mesons in terms of the light front quark model), Phys. Rev. D, 90:094017(2014)
37 G. Li, F. 1. Shao, and W. Wang(B_s→D_s(3040)form factors and B_s decays into D_s(3040)), Phys. Rev. D, 82:094031(2010),arXiv:1008.3696[hep-ph]
38 H. Y. Cheng and C. K. Chua,(Covariant light front approach for B→K~*γ,K_(1γ), K_2~*γdecays), Phys. Rev. D. 69:094007(2004)Erratum:[Phys. Rev. D, 81:059901(2010)]
39 H. W. Ke, X. Q. Li, and Z. T. Wei(Whether new data on D_s→f_0(980)e~+v_e can be understood if f_0(980)consists of only the conventional q anti-q structure), Phys. Rev. D, 80:074030(2009)
40 H. W. Ke, X. Q. Li, and Z. T. Wei(Determining theη-η'mixing by the newly measured BR(D(D_s)→η(η')+(?)+v_l), Eur. Phys. J. C,69:133(2010)
41 C. D. Lu, W. Wang, and Z. T. Wei(Heavy-to-light form factors on the light cone), Phys. Rev. D, 76:014013(2007)
42 W. Wang, Y. L. Shen, and C. D. Lu(The Study of B_c~-→X(3872)π~-(K~-)decays in the covariant light-front approach), Eur. Phys. J. C, 51:841(2007)
43 W. Wang and Y. L. Shen(D_s→K, K~*,φform factors in the Covariant Light-Front Approach and Exclusive Ds Decays), Phys.Rev. D, 78:054002(2008)
44 Y. L. Shen and Y. M. Wang(J/Ψweak decays in the covariant light-front quark model), Phys. Rev. D, 78:074012(2008)
45 W. Wang, Y. L. Shen, and C. D. Lu(Covariant Light-Front Approach for B_c transition form factors), Phys. Rev. D, 79:054012(2009)
46 X. X. Wang, W. Wang, and C. D. Lu(B_c to p-Wave CharmoniaTransitions in Covariant Light-Front Approach), Phys. Rev. D,79:114018(2009)
47 C. H. Chen, Y. L. Shen, and W. Wang(|V_(ub)|and B→η'Form Factors in Covariant Light Front Approach), Phys. Lett. B, 686:118(2010), arXiv:0911.2875[hep-ph]
48 W. Wang(Hindered Magnetic Dipole Transition in the Covariant Light-Front Approach), arXiv:[hep-ph].
49 W. Jaus(Covariant analysis of the light front quark model), Phys.Rev. D, 60:054026(1999)
50 T. Matsuki, T. Morii, and K. Seo(Mixing angle between~3P_1 and~1P_1 in HQET), Prog. Theor. Phys., 124:285(2010),arXiv:1001.4248[hep-ph]
51 Q. Li, T. Wang, Y. Jiang, H. Yuan, T. Zhou, and G. L. Wang(Decays of B, Bs and B_c to D-wave heavy-light mesons), Eur.Phys. J. C, 77(1):12(2017)
52 H. W. Ke and X. Q. Li(Vertex functions for D-wave mesons in the light-front approach), Eur. Phys. J. C, 71:1776(2011)
53 H. M. Choi and C. R. Ji(Light-front dynamic analysis of transition form factors in the process of P→Vev_e), Nucl. Phys.A, 856:95(2011), arXiv:1007.2502[hep-ph]
54 H. M. Choi and C. R. Ji(Semileptonic and radiative decays of the B(c)meson in light-front quark model), Phys. Rev. D, 80:054016(2009), arXiv:0903.0455[hep-ph]
55 H. M. Choi and C. R. Ji(Semileptonic B/c decays in the lightfront quark model), Nucl. Phys. Proc. Suppl., 199:240(2010)
56 M. A. DeWitt, H. M. Choi, and C. R. Ji(Radiative scalar meson decays in the light front quark model), Phys. Rev. D, 68:054026(2003), arXiv:hep-ph/0306060[hep-ph]
57 B. L. G. Bakker, H. M. Choi, and C. R. Ji(The Vector meson form-factor analysis in light front dynamics), Phys. Rev. D, 65:116001(2002), arXiv:hep-ph/0202217[hep-ph]
58 B. L. G. Bakker, H. M. Choi, and C. R. Ji(Regularizing the fermion loop divergencies in the light front meson currents),Phys. Rev. D, 63:074014(2001), arXiv:hep-ph/0008147[hepph]
59 H. M. Choi and C. R. Ji(The Light-front zero-mode contribution to the good current in weak transition), Phys. Rev. D, 72:013004(2005), arXiv:hep-ph/0504219[hep-ph]
60 P. L. Chung, F. Coester, and W. N. Polyzou(Charge FormFactors of Quark Model Pions), Phys. Lett. B, 205:545(1988)
61 E. Gamiz et al([HPQCD Collaboration], Neutral B Meson Mixing in Unquenched Lattice QCD), Phys. Rev. D, 80:014503(2009)
62 A. Khodjamirian, C. Klein, T. Mannel, and N. Offen(Semileptonic charm decays D→πev_e and D→Kev_e from QCD Light-Cone Sum Rules), Phys. Rev. D, 80:114005(2009)
63 C. Bourrely, I. Caprini, and L. Lellouch(Model-independent description of B→πev decays and a determination of|V(ub)|),Phys. Rev. D, 79:013008(2009)
64 Y. M. Wang, Y. B. Wei, Y. L. Shen, and C. D. L(Perturbative corrections to B→D form factors in QCD), JHEP, 1706:062(2017)
65 P. Colangelo, F. De Fazio, and G. Nardulli(B meson transitions into higher mass charmed resonances), Phys. Lett. B, 478:408(2000)
66 L. F. Gan and M. Q. Huang(Semileptonic Decays of B Meson Transition Into D-wave Charmed Meson Doublets), Phys. Rev.D, 79:034025(2009)
67 L. F. Gan, J. R. Zhang, M. Q. Huang, H. B. Zhuo, Y. Y. Ma, Q. J.Zhu, J. X. Liu, and G. B. Zhang(D_(sJ)(2860)From The Semileptonic Decays Of Bs Mesons), Eur. Phys. J. C, 75(5):232(2015), arXiv:1412.7969[hep-ph]
68 S. J. Brodsky, H. C. Pauli, and S. S. Pinsky(Quantum chromodynamics and other field theories on the light cone), Phys.Rept., 301:299(1998)
69 J. h. Yu, B. W. Xiao, and B. Q. Ma(Space-like and time-like pion-rho ransition form factors in the light-cone formalism), J.Phys. G, 34:1845(2007)
1)We should mention that there is a typo in Ref.[35] for the A_9~((4))function, whose correct expression is given by A_9~((4))=A_2~((1))A_6~((3))-3/q~2A_4~((4)).
1)We need to mention that a minus sign is needed in front ofω_(3_(D_2)~c which is a typo in Ref.[52].
1)When reproducing the coefficients A_i~((4)),B_j~((4))and C_k~((4)), we find a typo in Ref.[35] whose correct expression is given by A_9~((4))=A_2~((1))A_6~((3))-3/q~2A_4~((4)).