Two-body nonleptonic decays of the heavy mesons in the factorization approach

Abstract

In the framework of the factorization approach we calculate the branching fractions of 100 two-body nonleptonic decay channels in total, including 44 channels of the charm meson decays and 56 channels of the bottom meson decays. For charm meson decays, we test and confirm the previous observation that taking the limit for the number of colors N\to \mathrm{\infty } significantly improves theoretical predictions. For bottom meson decays, the penguin contributions are included in addition. As an essential input, we employ the weak decay form factors obtained in the framework of the relativistic quark model based on the quasi-potential approach. These form factors have well been tested by calculating observables in the semileptonic D and B meson decays and confronting obtained results with experimental data. In general, the predictions for the nonleptonic decay branching fractions are acceptable. However, for a quantitative calculation it is necessary to account for a more subtle effects of the final-state interaction.

Keywords

form factor / quark model / nonleptonic decay / factorization method

References

[1] J. D. Bjorken. Topics in B-physics. Nucl. Phys. B Proc. Suppl., 1989, 11: 325

[2] R.N. FaustovV.O. GalkinX.W. Kang, Semileptonic decays of D and D_s mesons in the relativistic quark model, Phys. Rev. D 101(1), 013004 (2020), arXiv: 1911.08209 [hep-ph]

[3] R.N. FaustovV.O. GalkinX.W. Kang, Relativistic description of the semileptonic decays of bottom mesons, Phys. Rev. D 106(1), 013004 (2022), arXiv: 2206.10277 [hep-ph]

[4] D.EbertR. N. FaustovV.O. Galkin, Exclusive nonleptonic decays of B mesons, Phys. Rev. D 56, 312 (1997), arXiv: hep-ph/9701218

[5] R.N. FaustovV.O. Galkin, Weak decays of B_s mesons to D_s mesons in the relativistic quark model, Phys. Rev. D 87(3), 034033 (2013), arXiv: 1212.3167 [hep-ph]

[6] R.N. FaustovV.O. Galkin, Charmless weak B_s decays in the relativistic quark model, Phys. Rev. D 87(9), 094028 (2013), arXiv: 1304.3255 [hep-ph]

[7] J.ChaiS. ChengY.H. JuD.C. YanC.D. LüZ.J. Xiao, Charmless two-body B meson decays in perturbative QCD factorization approach, arXiv: 2207.04190 [hep-ph] (2022)

[8] A.AliG. KramerY.LiC.D. LuY.L. Shen W.WangY. M. Wang, Charmless non-leptonic B_s decays to PP, PV and VV final states in the pQCD approach, Phys. Rev. D 76, 074018 (2007), arXiv: hep-ph/0703162

[9] Y.YangL. LangX.ZhaoJ.HuangJ.Sun, Reinvestigating the B → PP decays by including the contributions from ϕ_B2, Phys. Rev. D 103(5), 056006 (2021), arXiv: 2012.10581 [hep-ph]

[10] Z.J. XiaoW. F. WangY.Y. Fan, Revisiting the pure annihilation decays B_s → π⁺π⁻ and B₀ → K⁺K⁻: The data and the perturbative QCD predictions, Phys. Rev. D 85(9), 094003 (2012), arXiv: 1111.6264 [hep-ph]

[11] A.V. Manohar, Large N QCD, arXiv: hep-ph/9802419 (1998)

[12] Z.H. GuoJ. A. OllerJ.Ruiz. de Elvira, Chiral dynamics in form factors, spectral-function sum rules, meson−meson scattering and semilocal duality, Phys. Rev. D 86(5), 054006 (2012), arXiv: 1206.4163 [hep-ph]

[13] L.Y. DaiU. G. Meißner, A new method to study the number of colors in the final-state interactions of hadrons, Phys. Lett. B 783, 294 (2018), arXiv: 1706.10123 [hep-ph]

[14] D. Tadić, J. Trampetić. Weak meson decays and the expansion. Phys. Lett. B, 1982, 114(2−3): 179

[15] M. Bauer, B. Stech. Exclusive D-decays. Phys. Lett. B, 1985, 152(5−6): 380

[16] A.J. BurasJ. M. GerardR.Ruckl, expansion for exclusive and inclusive charm decays, Nucl. Phys. B 268(1), 16 (1986)

[17] I.E. Halperin, Soft gluon suppression of 1/N_c contributions in color suppressed heavy meson decays, Phys. Lett. B 349, 548 (1995), arXiv: hep-ph/9411422

[18] H.Y. ChengX. W. KangF.Xu, Singly Cabibbo-suppressed hadronic decays of Λc+, Phys. Rev. D 97(7), 074028 (2018), arXiv: 1801.08625 [hep-ph]

[19] A.N. KamalA. B. SantraT.UppalR.C. Verma, Nonfactorization in hadronic two-body Cabibbo-favored decays of D⁰ and D⁺, Phys. Rev. D 53, 2506 (1996), arXiv: hep-ph/9503390

[20] L.ZhangX. W. KangX.H. GuoL.Y. DaiT.Luo C.Wang, A comprehensive study on the semileptonic decay of heavy flavor mesons, J. High Energy Phys. 02, 179 (2021), arXiv: 2012.04417 [hep-ph]

[21] G.BuchallaA. J. BurasM.E. Lautenbacher, Weak decays beyond leading logarithms, Rev. Mod. Phys. 68, 1125 (1996), arXiv: hep-ph/9512380

[22] T.FeldmannP. KrollB.Stech, Mixing and decay constants of pseudoscalar mesons, Phys. Rev. D 58, 114006 (1998), arXiv: hep-ph/9802409

[23] H.Y. ChengX. W. Kang, Branching fractions of semileptonic D and D_s decays from the covariant light-front quark model, Eur. Phys. J. C 77 (9), 587 (2017) [Erratum: Eur. Phys. J. C 77(12), 863 (2017)], arXiv: 1707.02851 [hep-ph]

[24] H.Y. ChengX. W. Kang, The semileptonic baryonic decay D_s⁺ → p p ¯e⁺ν_e, Phys. Lett. B 780, 100 (2018), arXiv: 1712.00566 [hep-ph]

[25] J.HietalaD. Cronin-HennessyT.Pedlar I.Shipsey, Exclusive D_s semileptonic branching fraction measurements, Phys. Rev. D 92(1), 012009 (2015), arXiv: 1505.04205 [hep-ex]

[26] M.AblikimM. N. AchasovS.AhmedM.AlbrechtM.Alekseev, ., Measurement of the dynamics of the decays D_s⁺ → η(′)e⁺ν_e, Phys. Rev. Lett. 122(12), 121801 (2019), arXiv: 1901.02133 [hep-ex]

[27] J.L. RosnerS. StoneR.S. Van de Water, Leptonic decays of charged pseudoscalar mesons – 2015, arXiv: 1509.02220 [hep-ph] (2015)

[28] D.EbertR. N. FaustovV.O. Galkin, Relativistic treatment of the decay constants of light and heavy mesons, Phys. Lett. B 635, 93 (2006), arXiv: hep-ph/0602110

[29] A.BazavovC. BernardN.BrownC.DetarA.X. El-KhadraE.GámizS.GottliebU.M. HellerJ.KomijaniA.S. KronfeldJ.Laiho P.B. MackenzieE.T. NeilJ.N. SimoneR.L. SugarD.ToussaintR.S. Van de Water, B- and D-meson leptonic decay constants from four-flavor lattice QCD, Phys. Rev. D 98(7), 074512 (2018), arXiv: 1712.09262 [hep-lat]

[30] P.MarisP. C. Tandy, Bethe−Salpeter study of vector meson masses and decay constants, Phys. Rev. C 60, 055214 (1999), arXiv: nucl-th/9905056

[31] P.BallR. Zwicky, B_d,s→ρ, ω, K^∗, ϕ decay form factors from light-cone sum rules revisited, Phys. Rev. D 71, 014029 (2005), arXiv: hep-ph/0412079

[32] P.BallG. W. JonesR.Zwicky, B→V gamma beyond QCD factorisation, Phys. Rev. D 75, 054004 (2007), arXiv: hep-ph/0612081

[33] J.C. R. BlochY.L. KalinovskyC.D. RobertsS.M. Schmidt, Describing a₁ and b₁ decays, Phys. Rev. D 60, 111502 (1999), arXiv: nucl-th/9906038

[34] H.Y. ChengB. Tseng, Nonfactorizable effects in spectator and penguin amplitudes of hadronic charmless B decays, Phys. Rev. D 58, 094005 (1998), arXiv: hep-ph/9803457

[35] A.AliC. Greub, An analysis of two-body non-leptonic B decays involving light mesons in the standard model, Phys. Rev. D 57, 2996 (1998), arXiv: hep-ph/9707251

[36] R.AkhouryJ. M. Frere, η, η′ mixing and anomalies, Phys. Lett. B 220(1–2), 258 (1989)

[37] Z.XingH. ZhangS.Zhou, Updated values of running quark and lepton masses, Phys. Rev. D 77(11), 113016 (2008), arXiv: 0712.1419 [hep-ph]

[38] P. A. Zyla, . [Particle Data Group]. . Review of particle physics. Prog. Theor. Exp. Phys., 2020, 2020(8): 083C01

[39] A.BiswasN. SinhaG.Abbas, Nonleptonic decays of charmed mesons into two pseudoscalars, Phys. Rev. D 92(1), 014032 (2015), arXiv: 1503.08176 [hep-ph]

[40] Y.H. ChenH. Y. ChengB.TsengK.C. Yang, Charmless hadronic two-body decays of B_u and B_d mesons, Phys. Rev. D 60, 094014 (1999), arXiv: hep-ph/9903453

[41] H.LiC.D. LüF.S. Yu, Branching ratios and direct CP asymmetries in D → PP decays, Phys. Rev. D 86(3), 036012 (2012), arXiv: 1203.3120 [hep-ph]

[42] Q.QinH. N. LiC.D. LüF.S. Yu, Branching ratios and direct CP asymmetries in D→PV decays, Phys. Rev. D 89(5), 054006 (2014), arXiv: 1305.7021 [hep-ph]

[43] S.H. ZhouY. B. WeiQ.QinY.LiF.S. Yu C.D. Lü, Analysis of two-body charmed b meson decays in factorization-assisted topological-amplitude approach, Phys. Rev. D 92(9), 094016 (2015), arXiv: 1509.04060 [hep-ph]

[44] S.H. ZhouQ. A. ZhangW.R. LyuC.D. Lü, Analysis of charmless two-body B decays in factorization assisted topological amplitude approach, Eur. Phys. J. C 77(2), 125 (2017), arXiv: 1608.02819 [hep-ph]

[45] H.Y. ChengC. W. Chiang, Two-body hadronic charmed meson decays, Phys. Rev. D 81(7), 074021 (2010), arXiv: 1001.0987 [hep-ph]

[46] H.Y. ChengC. W. ChiangA.L. Kuo, Updating B → PP, VP decays in the framework of flavor symmetry, Phys. Rev. D 91(1), 014011 (2015), arXiv: 1409.5026 [hep-ph]

[47] Y.H. ChenH. Y. ChengB.Tseng, Charmless hadronic two-body decays of the B_s mesons, Phys. Rev. D 59, 074003 (1999), arXiv: hep-ph/9809364

[48] Z.Q. WangX. W. KangJ.A. OllerL.Zhang, Analysis on the composite nature of the light scalar mesons f₀ (980) and a₀ (980), Phys. Rev. D 105(7), 074016 (2022), arXiv: 2201.00492 [hep-ph]

[49] L.Y. DaiX. W. KangU.G. Meißner, Test of semilocal duality in a large NC framework, Phys. Rev. D 98(7), 074033 (2018), arXiv: 1808.05057 [hep-ph]

[50] X.W. KangB. KubisC.HanhartU.G. Meißner, ^l4B decays and the extraction of |V_ub|, Phys. Rev. D 89(5), 053015 (2014), arXiv: 1312.1193 [hep-ph]

[51] L. Y. DaiX. W. Kang, U. G. Meißner, X. Y. Song , D. L. Yao., Amplitude analysis of the anomalous decay η′ → π⁺π⁻γ, Phys. Rev. D 97(3), 036012 (2018), arXiv: 1712.02119 [hep-ph]

[52] L.Y. DaiM. R. Pennington, Comprehensive amplitude analysis of γγ → π⁺π⁻, π₀π₀ and K ¯K below 1.5 GeV, Phys. Rev. D 90(3), 036004 (2014), arXiv: 1404.7524 [hep-ph]

[53] D.S. DuM. Z. YangD.Z. Zhang, Space-like Penguin effects in B→PP decays, Phys. Rev. D 53, 249 (1996), arXiv: hep-ph/9507280

[54] A.AliG. KramerC.D. Lü, Experimental tests of factorization in charmless non-leptonic two-body B decays, Phys. Rev. D 58, 094009 (1998), arXiv: hep-ph/9804363

[55] M.BenekeM. Neubert, QCD factorization for B→PP and B→PV decays, Nucl. Phys. B 675, 333 (2003), arXiv: hep-ph/0308039

[56] M.BenekeG. BuchallaM.NeubertC.T. Sachrajda, QCD factorization for exclusive, non-leptonic B meson decays: General arguments and the case of heavy-light final states, Nucl. Phys. B 591, 313 (2000), arXiv: hep-ph/0006124

[57] C.Amsler, The Quark Structure of Hadrons, Lecture Notes in Physics 949, Springer, 2018

[58] Section “Quark Model” in Ref. [38]

[59] H.Y. ChengC. K. ChuaC.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(7), 074025 (2004), arXiv: hep-ph/0310359

[60] W. Jaus. Covariant analysis of the light-front quark model. Phys. Rev. D, 1999, 60(5): 054026

Acknowledgements

We are grateful to Prof. Hai-Yang Cheng for very valuable discussions on his paper [40] and answering our questions quickly. V.O.G. thanks Profs. Dietmar Ebert and Rudolf Faustov for usefull discussions. The author X.W.K. acknowledges the support from the National Natural Science Foundation of China (NSFC) under Project Nos. 11805012 and 12275023.

RIGHTS & PERMISSIONS

2023 Higher Education Press