Contributions of $$ {K}_0^{\ast } $$ (1430) and $$ {K}_0^{\ast } $$ (1950) in the three-body decays B → Kπh

Wang, Wen-Fei; Chai, Jian; Ma, Ai-Jun

doi:10.1007/JHEP03(2020)162

Contributions of $ {K}_0^{\ast } $(1430) and $ {K}_0^{\ast } $(1950) in the three-body decays B → Kπh

Regular Article - Experimental Physics
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Published: 26 March 2020

Volume 2020, article number 162 (2020)
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Contributions of $ {K}_0^{\ast } $(1430) and $ {K}_0^{\ast } $(1950) in the three-body decays B → Kπh

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A preprint version of the article is available at arXiv.

Abstract

We study the contributions of the resonant states $ {K}_0^{\ast } $(1430) and $ {K}_0^{\ast } $(1950) in the three-body decays B → Kπh (with h = π, K) in the perturbative QCD approach. The crucial nonperturbative input F_Kπ(s) in the distribution amplitudes of the S-wave Kπ system is derived from the matrix element of vacuum to Kπ pair. The C P averaged branching fraction of the quasi-two-body decay process B → $ {K}_0^{\ast } $(1950) h → Kπh is about one order smaller than that of the corresponding decay B → $ {K}_0^{\ast } $(1430)h → Kπh. In view of the important contribution from the S-wave Kπ system for the B → Kπh decays, it is not appropriate to neglect the $ {K}_0^{\ast } $(1950) in the theoretical or experimental studies for the relevant three-body B meson decays. The predictions in this work for the relevant decays are consistent with the existing experimental data.

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References

M. Gronau and J.L. Rosner, I-spin, U-spin and penguin dominance in B → $ KK\overline{K}, $ Phys. Lett. B 564 (2003) 90 [hep-ph/0304178] [INSPIRE].
G. Engelhard, Y. Nir and G. Raz, SU(3) relations and the CP asymmetry in B → K_SK_SK_S, Phys. Rev. D 72 (2005) 075013 [hep-ph/0505194] [INSPIRE].
M. Gronau and J.L. Rosner, Symmetry relations in charmless B → PPP decays, Phys. Rev. D 72 (2005) 094031 [hep-ph/0509155] [INSPIRE].
M. Imbeault and D. London, SU(3) breaking in charmless B decays, Phys. Rev. D 84 (2011) 056002 [arXiv:1106.2511] [INSPIRE].
M. Gronau, U-spin breaking in CP asymmetries in B decays, Phys. Lett. B 727 (2013) 136 [arXiv:1308.3448] [INSPIRE].
Article ADS Google Scholar
B. Bhattacharya, M. Gronau and J.L. Rosner, CP asymmetries in three-body B^± decays to charged pions and kaons, Phys. Lett. B 726 (2013) 337 [arXiv:1306.2625] [INSPIRE].
Article ADS Google Scholar
B. Bhattacharya et al., Charmless B → PPP decays: the fully-symmetric final state, Phys. Rev. D 89 (2014) 074043 [arXiv:1402.2909] [INSPIRE].
D. Xu, G.-N. Li and X.-G. He, U-spin analysis of CP-violation in B⁻ decays into three charged light pseudoscalar mesons, Phys. Lett. B 728 (2014) 579 [arXiv:1311.3714] [INSPIRE].
Article ADS Google Scholar
D. Xu, G.-N. Li and X.-G. He, Large SU(3) breaking effects and CP-violation in B⁺ decays into three charged octet pseudoscalar mesons, Int. J. Mod. Phys. A 29 (2014) 1450011 [arXiv:1307.7186] [INSPIRE].
Article ADS MATH Google Scholar
X.-G. He, G.-N. Li and D. Xu, SU(3) and isospin breaking effects on B → PPP amplitudes, Phys. Rev. D 91 (2015) 014029 [arXiv:1410.0476] [INSPIRE].
A. Furman, R. Kaminski, L. Lesniak and B. Loiseau, Long-distance effects and final state interactions in B → ππKand B → $ K\overline{K}K $ decays, Phys. Lett. B 622 (2005) 207 [hep-ph/0504116] [INSPIRE].
B. El-Bennich et al., Interference between f₀ (980) and ρ(770)⁰ resonances in B → π⁺ π⁻ K decays, Phys. Rev. D 74 (2006) 114009 [hep-ph/0608205] [INSPIRE].
B. El-Bennich et al., CP violation and kaon-pion interactions in B → Kπ⁺ π⁻ decays, Phys. Rev. D 79 (2009) 094005 [Erratum ibid. D 83 (2011) 039903] [arXiv:0902.3645] [INSPIRE].
O. Leitner, J.P. Dedonder, B. Loiseau and R. Kaminski, K^* resonance effects on direct CP-violation in B → ππK, Phys. Rev. D 81 (2010) 094033 [Erratum ibid. D 82 (2010) 119906] [arXiv:1001.5403] [INSPIRE].
J.P. Dedonder, A. Furman, R. Kaminski, L. Lesniak and B. Loiseau, S-, P - and D-wave ππ final state interactions and C P violation in B^± → π^± π^∓ π^± decays, Acta Phys. Polon. B 42 (2011) 2013 [arXiv:1011.0960] [INSPIRE].
Article Google Scholar
H.-Y. Cheng, C.-K. Chua and A. Soni, C P -violating asymmetries in B⁰ decays to K⁺ K⁻ $ {K}_{S(L)}^0 $ and $ {K}_S^0{K}_S^0{K}_{S(L)}^0, $ Phys. Rev. D 72 (2005) 094003 [hep-ph/0506268] [INSPIRE].
H.-Y. Cheng, C.-K. Chua and A. Soni, Charmless three-body decays of B mesons, Phys. Rev. D 76 (2007) 094006 [arXiv:0704.1049] [INSPIRE].
H.-Y. Cheng and C.-K. Chua, Branching fractions and direct CP-violation in charmless three-body decays of B mesons, Phys. Rev. D 88 (2013) 114014 [arXiv:1308.5139] [INSPIRE].
ADS Google Scholar
H.-Y. Cheng and C.-K. Chua, Charmless three-body decays of B_s mesons, Phys. Rev. D 89 (2014) 074025 [arXiv:1401.5514] [INSPIRE].
Y. Li, Comprehensive study of $ {\overline{B}}^0\to {K}^0\left({\overline{K}}^0\right){K}^{\mp }{\pi}^{\pm } $ decays in the factorization approach, Phys. Rev. D 89 (2014) 094007 [arXiv:1402.6052] [INSPIRE].
H.-Y. Cheng, C.-K. Chua and Z.-Q. Zhang, Direct CP-violation in charmless three-body decays of B mesons, Phys. Rev. D 94 (2016) 094015 [arXiv:1607.08313] [INSPIRE].
S. Kränkl, T. Mannel and J. Virto, Three-body non-leptonic B decays and QCD factorization, Nucl. Phys. B 899 (2015) 247 [arXiv:1505.04111] [INSPIRE].
Article ADS MathSciNet MATH Google Scholar
C. Wang, Z.-H. Zhang, Z.-Y. Wang and X.-H. Guo, Localized direct CP-violation in B^± → ρ⁰ (ω)π^± → π⁺ π⁻ π^± , Eur. Phys. J. C 75 (2015) 536 [arXiv:1506.00324] [INSPIRE].
Article ADS Google Scholar
Z.-H. Zhang, X.-H. Guo and Y.-D. Yang, CP violation in B^± → π^± π⁺ π⁻ in the region with low invariant mass of one π⁺ π⁻ pair, Phys. Rev. D 87 (2013) 076007 [arXiv:1303.3676] [INSPIRE].
J.-J. Qi et al., Study of CP-violations in B⁻ → K⁻ π⁺ π⁻ and B⁻ → K⁻ f₀ (500) decays in the QCD factorization approach, Eur. Phys. J. C 78 (2018) 845 [arXiv:1805.09534] [INSPIRE].
Article ADS Google Scholar
C.-H. Chen and H.-n. Li, Three body nonleptonic B decays in perturbative QCD, Phys. Lett. B 561 (2003) 258 [hep-ph/0209043] [INSPIRE].
C.-H. Chen and H.-n. Li, Vector pseudoscalar two meson distribution amplitudes in three body B meson decays, Phys. Rev. D 70 (2004) 054006 [hep-ph/0404097] [INSPIRE].
W.-F. Wang, H.-C. Hu, H.-n. Li and C.-D. Lü, Direct CP asymmetries of three-body B decays in perturbative QCD, Phys. Rev. D 89 (2014) 074031 [arXiv:1402.5280] [INSPIRE].
Belle collaboration, Dalitz analysis of the three-body charmless decays B⁺ → K⁺ π⁺ π⁻and B⁺ → K⁺ K⁺ K⁻ , Phys. Rev. D 71 (2005) 092003 [hep-ex/0412066] [INSPIRE].
Belle collaboration, Evidence for large direct CP violation in B^± → ρ(770)⁰ K^± from analysis of three-body charmless B^± → K^± π^± π^± decay, Phys. Rev. Lett. 96 (2006) 251803 [hep-ex/0512066] [INSPIRE].
Belle collaboration, Dalitz analysis of three-body charmless B⁰ → K⁰ π⁺ π⁻ decay, Phys. Rev. D 75 (2007) 012006 [hep-ex/0610081] [INSPIRE].
Belle collaboration, Time-dependent Dalitz plot measurement of CP parameters in B⁰ → $ {K}_S^0 $π⁺ π⁻ decays, Phys. Rev. D 79 (2009) 072004 [arXiv:0811.3665] [INSPIRE].
Belle collaboration, Measurement of branching fraction and direct C P asymmetry in charmless B⁺ → K⁺ K⁻ π⁺ decays at Belle, Phys. Rev. D 96 (2017) 031101 [arXiv:1705.02640] [INSPIRE].
Belle collaboration, Measurements of branching fraction and direct C P asymmetry in $ {B}^{\pm}\to {K}_S^0{K}_S^0{K}^{\pm } $ and a search for B± → $ {B}^{\pm}\to {K}_S^0{K}_S^0{\pi}^{\pm }, $ Phys. Rev. D 99 (2019) 031102 [arXiv:1812.10221] [INSPIRE].
Belle collaboration, Measurement of branching fraction and final-state asymmetry for the $ {B}^0\to {K}_S^0{K}^{\mp }{\pi}^{\pm } $ decay, Phys. Rev. D 100 (2019) 011101 [arXiv:1904.06835] [INSPIRE].
BaBar collaboration, Dalitz-plot analysis of the decays B^± → K^± π^∓ π^±, Phys. Rev. D 72 (2005) 072003 [Erratum ibid. D 74 (2006) 099903] [hep-ex/0507004] [INSPIRE].
BaBar collaboration, Observation of the decay B⁺ → K⁺ K⁻ π⁺, Phys. Rev. Lett. 99 (2007) 221801 [arXiv:0708.0376] [INSPIRE].
BaBar collaboration, Evidence for direct CP-violation from Dalitz-plot analysis of B^± → K^± π^∓ π^±, Phys. Rev. D 78 (2008) 012004 [arXiv:0803.4451] [INSPIRE].
BaBar collaboration, Dalitz plot analysis of the decay B⁰ $ \left({\overline{B}}^0\right) $ → K^± π^∓ π⁰, Phys. Rev. D 78 (2008) 052005 [arXiv:0711.4417] [INSPIRE].
BaBar collaboration, Time-dependent amplitude analysis of B⁰ → $ {K}_S^0{\pi}^{+}{\pi}^{-}, $ Phys. Rev. D 80 (2009) 112001 [arXiv:0905.3615] [INSPIRE].
BaBar collaboration, Observation of the rare decay B⁰ → $ {K}_S^0{K}^{\pm }{\pi}^{\mp }, $ Phys. Rev. D 82 (2010) 031101 [arXiv:1003.0640] [INSPIRE].
BaBar collaboration, Amplitude analysis of B⁰ → K⁺ π⁻ π⁰ and evidence of direct CP-violation in B → K^∗π decays, Phys. Rev. D 83 (2011) 112010 [arXiv:1105.0125] [INSPIRE].
BaBar collaboration, Evidence for C P violation in B⁺ → K^∗ (892)⁺ π⁰ from a Dalitz plot analysis of B⁺ → $ {K}_{\mathrm{S}}^0{\pi}^{+}{\pi}^0, $ decays, Phys. Rev. D 96 (2017) 072001 [arXiv:1501.00705] [INSPIRE].
LHCb collaboration, Study of $ {B}_{(s)}^0\to {K}_{\mathrm{S}}^0{h}^{+}h{\prime}^{-} $ decays with first observation of $ {B}_s^0\to {K}_{\mathrm{S}}^0{K}^{\pm }{\pi}^{\mp } $ and $ {B}_s^0\to {K}_{\mathrm{S}}^0{\pi}^{+}{\pi}^{-}, $ JHEP 10 (2013) 143 [arXiv:1307.7648] [INSPIRE].
LHCb collaboration, Measurement of CP-violation in the phase space of B^± → K^± π⁺ π⁻ and B^± → K^± K⁺ K⁻ decays, Phys. Rev. Lett. 111 (2013) 101801 [arXiv:1306.1246] [INSPIRE].
LHCb collaboration, Measurement of CP-violation in the phase space of B^± → K⁺ K⁻ π^± and B^± → π⁺ π⁻ π^± decays, Phys. Rev. Lett. 112 (2014) 011801 [arXiv:1310.4740] [INSPIRE].
LHCb collaboration, Measurements of C P violation in the three-body phase space of charmless B^± decays, Phys. Rev. D 90 (2014) 112004 [arXiv:1408.5373] [INSPIRE].
LHCb collaboration, Search for the suppressed decays B⁺ → K⁺ K⁺ π⁻ and B⁺ → π⁺ π⁺ K⁻, Phys. Lett. B 765 (2017) 307 [arXiv:1608.01478] [INSPIRE].
LHCb collaboration, Updated branching fraction measurements of $ {B}_{(s)}^0\to {K}_S^0{h}^{+}h{\prime}^{-} $ decays,JHEP 11 (2017) 027 [arXiv:1707.01665] [INSPIRE].
LHCb collaboration, Amplitude analysis of the decay $ {\overline{B}}^0\to {K}_S^0{\pi}^{+}{\pi}^{-} $ and first observation of the CP asymmetry in $ {\overline{B}}^0 $ → K^* (892)⁻ π⁺, Phys. Rev. Lett. 120 (2018) 261801 [arXiv:1712.09320] [INSPIRE].
LHCb collaboration, Amplitude analysis of $ {B}_s^0\to {K}_S^0{K}^{\pm }{\pi}^{\mp } $ decays, JHEP 06 (2019) 114 [arXiv:1902.07955] [INSPIRE].
N. Cabibbo, Unitary symmetry and leptonic decays, Phys. Rev. Lett. 10 (1963) 531 [INSPIRE].
Article ADS Google Scholar
M. Kobayashi and T. Maskawa, CP violation in the renormalizable theory of weaKinteraction, Prog. Theor. Phys. 49 (1973) 652 [INSPIRE].
Article ADS Google Scholar
M. Ciuchini, M. Pierini and L. Silvestrini, New bounds on the CKM matrix from B → Kππ Dalitz plot analyses, Phys. Rev. D 74 (2006) 051301 [hep-ph/0601233] [INSPIRE].
M. Gronau, D. Pirjol, A. Soni and J. Zupan, Improved method for CKM constraints in charmless three-body B and B_s decays, Phys. Rev. D 75 (2007) 014002 [hep-ph/0608243] [INSPIRE].
I. Bediaga, G. Guerrer and J.M. de Miranda, Extracting the quarKmixing phase γ from B^± → K^± π⁺ π^−, B⁰ → K_Sπ⁺ π⁻ and $ {\overline{B}}^0 $ → K_Sπ⁺ π⁻, Phys. Rev. D 76 (2007) 073011 [hep-ph/0608268] [INSPIRE].
M. Ciuchini, M. Pierini and L. Silvestrini, Hunting the CKM weaKphase with time-integrated Dalitz analyses of B_s → Kππ decays, Phys. Lett. B 645 (2007) 201 [hep-ph/0602207] [INSPIRE].
M. Imbeault, N. R.-L. Lorier and D. London, Measuring gamma in B → Kππ decays, Phys. Rev. D 84 (2011) 034041 [arXiv:1011.4973] [INSPIRE].
N. Rey-Le Lorier and D. London, Measuring gamma with B → Kππ and B → $ KK\overline{k} $ decays, Phys. Rev. D 85 (2012) 016010 [arXiv:1109.0881] [INSPIRE].
B. Bhattacharya, M. Imbeault and D. London, Extraction of the CP-violating phase γ using B → Kππ and B → $ KK\overline{K} $ decays, Phys. Lett. B 728 (2014) 206 [arXiv:1303.0846] [INSPIRE].
Article ADS Google Scholar
B. Bhattacharya and D. London, Using U spin to extract γ from charmless B → PPP decays, JHEP 04 (2015) 154 [arXiv:1503.00737] [INSPIRE].
Article ADS Google Scholar
G.N. Fleming, Recoupling effects in the isobar model. 1. General formalism for three-pion scattering, Phys. Rev. 135 (1964) B551 [INSPIRE].
D. Morgan, Phenomenological analysis of I = 1/2 single-pion production processes in the energy range 500 to 700 MeV, Phys. Rev. 166 (1968) 1731 [INSPIRE].
Article ADS Google Scholar
D. Herndon, P. Soding and R.J. Cashmore, A generalized isobar model formalism, Phys. Rev. D 11 (1975) 3165 [INSPIRE].
ADS Google Scholar
S. Fajfer, R.J. Oakes and T.N. Pham, The Penguin operators in nonresonant B⁻ → $ M\overline{M}{\pi}^{-} $ (M = π⁻, K⁻, K⁰) decays, Phys. Rev. D 60 (1999) 054029 [hep-ph/9812313] [INSPIRE].
H.-Y. Cheng and K.-C. Yang, Nonresonant three-body decays of D and B mesons, Phys. Rev. D 66 (2002) 054015 [hep-ph/0205133] [INSPIRE].
I. Bediaga et al., Final state hadronic interactions and non-resonant B^± → K^± π⁺ π⁻ decays, Phys. Lett. B 665 (2008) 30 [arXiv:0709.0075] [INSPIRE].
Article ADS Google Scholar
W.-F. Wang and H.-n. Li, Quasi-two-body decays B → Kρ → Kππ in perturbative QCD approach, Phys. Lett. B 763 (2016) 29 [arXiv:1609.04614] [INSPIRE].
Article ADS Google Scholar
J.H. Alvarenga Nogueira et al., Summary of the 2015 LHCb workshop on multi-body decays of D and B mesons, arXiv:1605.03889 [INSPIRE].
D. Boito et al., Parametrizations of three-body hadronic B- and D-decay amplitudes in terms of analytic and unitary meson-meson form factors, Phys. Rev. D 96 (2017) 113003 [arXiv:1709.09739] [INSPIRE].
ADS Google Scholar
I. Bediaga and P.C. Magalhães, Final state interaction on B⁺ → π⁻ π⁺ π⁺, arXiv:1512.09284 [INSPIRE].
K.S.F.F. Guimaraes et al., Three-body model of the final state interaction in heavy meson decay, Nucl. Phys. Proc. Suppl. 199 (2010) 341 [INSPIRE].
Article ADS Google Scholar
P.C. Magalhaes et al., Towards three-body unitarity in D⁺ → K⁻ π⁺ π⁺, Phys. Rev. D 84 (2011) 094001 [arXiv:1105.5120] [INSPIRE].
J.R. Peláez, A. Rodas and J. Ruiz de Elvira, Strange resonance poles from Kπ scattering below 1.8 GeV, Eur. Phys. J. C 77 (2017) 91 [arXiv:1612.07966] [INSPIRE].
J.R. Pelaez and A. Rodas, Pion-kaon scattering amplitude constrained with forward dispersion relations up to 1.6 GeV, Phys. Rev. D 93 (2016) 074025 [arXiv:1602.08404] [INSPIRE].
D.J. Wilson et al., The quark-mass dependence of elastic πK scattering from QCD, Phys. Rev. Lett. 123 (2019) 042002 [arXiv:1904.03188] [INSPIRE].
R. Brett et al., Determination of s- and p-wave I = 1/2 Kπ scattering amplitudes in N_f = 2 + 1 lattice QCD, Nucl. Phys. B 932 (2018) 29 [arXiv:1802.03100] [INSPIRE].
Article ADS Google Scholar
D.J. Wilson, J.J. Dudek, R.G. Edwards and C.E. Thomas, Resonances in coupled πK, ηK scattering from lattice QCD, Phys. Rev. D 91 (2015) 054008 [arXiv:1411.2004] [INSPIRE].
C.B. Lang, L. Leskovec, D. Mohler and S. Prelovsek, Kπ scattering for isospin 1/2 and 3/2 in lattice QCD, Phys. Rev. D 86 (2012) 054508 [arXiv:1207.3204] [INSPIRE].
A.H. Fariborz, E. Pourjafarabadi, S. Zarepour and S.M. Zebarjad, Chiral nonet mixing in πKscattering, Phys. Rev. D 92 (2015) 113002 [arXiv:1511.01623] [INSPIRE].
ADS Google Scholar
D. Aston et al., A study of K⁻ π⁺ scattering in the reaction K⁻ p → K⁻ π⁺ n at 11 GeV/c, Nucl. Phys. B 296 (1988) 493 [INSPIRE].
Article ADS Google Scholar
E791 collaboration, Model independent measurement of S-wave K⁻ π⁺ systems using D⁺ → Kππ decays from Fermilab E791, Phys. Rev. D 73 (2006) 032004 [Erratum ibid. D 74 (2006) 059901] [hep-ex/0507099] [INSPIRE].
FOCUS collaboration, Dalitz plot analysis of the D⁺ → K⁻ π⁺ π⁺ decay in the FOCUS experiment, Phys. Lett. B 653 (2007) 1 [arXiv:0705.2248] [INSPIRE].
FOCUS collaboration, The K⁻ π⁺ S-wave from the D⁺ → K⁻ π⁺ π⁺ decay, Phys. Lett. B 681 (2009) 14 [arXiv:0905.4846] [INSPIRE].
CLEO collaboration, Dalitz plot analysis of the D⁺ → K⁻ π⁺ π⁺ decay, Phys. Rev. D 78 (2008) 052001 [arXiv:0802.4214] [INSPIRE].
BaBar collaboration, Measurement of the I = 1/2 Kπ S -wave amplitude from Dalitz plot analyses of η_c → $ K\overline{K}\pi $ in two-photon interactions, Phys. Rev. D 93 (2016) 012005 [arXiv:1511.02310] [INSPIRE].
Belle collaboration, Study of τ⁻ → K_Sπ⁻ ν_τ decay at Belle, Phys. Lett. B 654 (2007) 65 [arXiv:0706.2231] [INSPIRE].
G. Breit and E. Wigner, Capture of slow neutrons, Phys. Rev. 49 (1936) 519 [INSPIRE].
Article ADS MATH Google Scholar
E.P. Wigner, Resonance reactions and anomalous scattering, Phys. Rev. 70 (1946) 15 [INSPIRE].
Article ADS Google Scholar
I.J.R. Aitchison, K-matrix formalism for overlapping resonances, Nucl. Phys. A 189 (1972) 417 [INSPIRE].
Article ADS Google Scholar
S.U. Chung et al., Partial wave analysis in Kmatrix formalism, Annalen Phys. 4 (1995) 404 [INSPIRE].
Article ADS Google Scholar
BaBar collaboration, Dalitz plot analysis of η_c → K⁺ K⁻ η and η_c → K⁺ K⁻ π⁰ in two-photon interactions, Phys. Rev. D 89 (2014) 112004 [arXiv:1403.7051] [INSPIRE].
Particle Data Group collaboration, Review of particle physics, Phys. Rev. D 98 (2018) 030001 [INSPIRE].
E791 collaboration, Dalitz plot analysis of the decay D⁺ → K⁻ π⁺ π⁺ and the study of the Kπ scalar amplitudes, Phys. Rev. Lett. 89 (2002) 121801 [hep-ex/0204018] [INSPIRE].
D.V. Bugg, The kappa in E791 data for D → Kππ, Phys. Lett. B 632 (2006) 471 [hep-ex/0510019] [INSPIRE].
BES collaboration, Evidence for kappa meson production in J/ψ → $ {\overline{K}}^{\ast } $(892)⁰ K⁺ π⁻ process, Phys. Lett. B 633 (2006) 681 [hep-ex/0506055] [INSPIRE].
S. Descotes-Genon and B. Moussallam, The $ {K}_0^{\ast } $(800) scalar resonance from Roy-Steiner representations of πK scattering, Eur. Phys. J. C 48 (2006) 553 [hep-ph/0607133] [INSPIRE].
D.V. Bugg, An update on the kappa, Phys. Rev. D 81 (2010) 014002 [arXiv:0906.3992] [INSPIRE].
BES collaboration, Observation of charged κ in J/ψ → K^*(892)^∓ K_sπ^±, K^* (892)^∓ → K_sπ^∓ at BESII, Phys. Lett. B 698 (2011) 183 [arXiv:1008.4489] [INSPIRE].
R.L. Jaffe, Multi-quarKhadrons. 1. The phenomenology of (Q² $ {\overline{Q}}^2 $) mesons, Phys. Rev. D 15 (1977) 267 [INSPIRE].
J.D. WEinstein and N. Isgur, Do multi-quarKhadrons exist?, Phys. Rev. Lett. 48 (1982) 659 [INSPIRE].
Article ADS Google Scholar
J.D. WEinstein and N. Isgur, $ K\overline{K} $ molecules, Phys. Rev. D 41 (1990) 2236 [INSPIRE].
ADS Google Scholar
L. Maiani, F. Piccinini, A.D. Polosa and V. Riquer, A new looKat scalar mesons, Phys. Rev. Lett. 93 (2004) 212002 [hep-ph/0407017] [INSPIRE].
C. Amsler and N.A. Tornqvist, Mesons beyond the naive quarKmodel, Phys. Rept. 389 (2004) 61 [INSPIRE].
Article ADS Google Scholar
R.L. Jaffe, Exotica, Phys. Rept. 409 (2005) 1 [hep-ph/0409065] [INSPIRE].
F. Giacosa, Strong and electromagnetic decays of the light scalar mesons interpreted as tetraquarKstates, Phys. Rev. D 74 (2006) 014028 [hep-ph/0605191] [INSPIRE].
Y.-Y. Keum, H.-n. Li and A.I. Sanda, Fat penguins and imaginary penguins in perturbative QCD, Phys. Lett. B 504 (2001) 6 [hep-ph/0004004] [INSPIRE].
Y.Y. Keum, H.-N. Li and A.I. Sanda, Penguin enhancement and B → Kπ decays in perturbative QCD, Phys. Rev. D 63 (2001) 054008 [hep-ph/0004173] [INSPIRE].
C.-D. Lu, K. Ukai and M.-Z. Yang, Branching ratio and CP-violation of B → ππ decays in perturbative QCD approach, Phys. Rev. D 63 (2001) 074009 [hep-ph/0004213] [INSPIRE].
H.-n. Li, QCD aspects of exclusive B meson decays, Prog. Part. Nucl. Phys. 51 (2003) 85 [hep-ph/0303116] [INSPIRE].
LHCb collaboration, Dalitz plot analysis of $ {B}_s^0\to {\overline{D}}^0{K}^{-}{\pi}^{+} $ decays, Phys. Rev. D 90 (2014) 072003 [arXiv:1407.7712] [INSPIRE].
LHCb collaboration, Evidence for an η_c (1S)π⁻ resonance in B⁰ → η_c (1S)K⁺ π⁻ decays, Eur. Phys. J. C 78 (2018) 1019 [arXiv:1809.07416] [INSPIRE].
H.-Y. Cheng, C.-K. Chua and K.-C. Yang, Charmless hadronic B decays involving scalar mesons: Implications to the nature of light scalar mesons, Phys. Rev. D 73 (2006) 014017 [hep-ph/0508104] [INSPIRE].
C.-D. Lu, Y.-M. Wang and H. Zou, Twist-3 distribution amplitudes of scalar mesons from QCD sum rules, Phys. Rev. D 75 (2007) 056001 [hep-ph/0612210] [INSPIRE].
H.-Y. Han, X.-G. Wu, H.-B. Fu, Q.-L. Zhang and T. Zhong, Twist-3 distribution amplitudes of scalar mesons within the QCD sum rules and its application to the B → S transition form factors, Eur. Phys. J. A 49 (2013) 78 [arXiv:1301.3978] [INSPIRE].
Article ADS Google Scholar
Z.-T. Zou, Y. Li and X. liu, Two-body charmed B_s decays involving a light scalar meson, Phys. Rev. D 95 (2017) 016011 [arXiv:1609.06444] [INSPIRE].
B.-Y. Cui, Y.-Y. Fan, F.-H. Liu and W.-F. Wang, Quasi-two-body decays B_(s) → $ {PD}_0^{\ast } $(2400) → PDπ in the perturbative QCD approach, Phys. Rev. D 100 (2019) 014017 [arXiv:1906.09387] [INSPIRE].
Y. Li, W.-F. Wang, A.-J. Ma and Z.-J. Xiao, Quasi-two-body decays B_(s) → K^* (892)h → Kπh in perturbative QCD approach, Eur. Phys. J. C 79 (2019) 37 [arXiv:1809.09816] [INSPIRE].
Article ADS Google Scholar
A.-J. Ma, W.-F. Wang, Y. Li and Z.-J. Xiao, Quasi-two-body decays B → DK^* (892) → DKπ in the perturbative QCD approach, Eur. Phys. J. C 79 (2019) 539 [arXiv:1901.03956] [INSPIRE].
Article Google Scholar
W.-F. Wang and J. Chai, Virtual contributions from D^* (2007)⁰ and D^* (2010)^± in the B → Dπh decays, Phys. Lett. B 791 (2019) 342 [arXiv:1812.08524] [INSPIRE].
Article ADS Google Scholar
W.-F. Wang, Resonant state $ {D}_0^{\ast } $(2400) in the quasi-two-body B meson decays, Phys. Lett. B 788 (2019) 468 [arXiv:1809.02943] [INSPIRE].
Article ADS Google Scholar
A.-J. Ma, Y. Li, W.-F. Wang and Z.-J. Xiao, Quasi-two-body decays B_(s) → D(ρ(1450), ρ(1700)) → Dππ in the perturbative QCD factorization approach, Phys. Rev. D 96 (2017) 093011 [arXiv:1708.01889] [INSPIRE].
Y. Li, A.-J. Ma, W.-F. Wang and Z.-J. Xiao, Quasi-two-body decays B_(s) → Pρ′ (1450), Pρ′′ (1700) → P ππ in the perturbative QCD approach, Phys. Rev. D 96 (2017) 036014 [arXiv:1704.07566] [INSPIRE].
Z. Rui, Y. Li and W.-F. Wang, The S-wave resonance contributions in the $ {B}_s^0 $ decays into ψ(2S, 3S) plus pion pair, Eur. Phys. J. C 77 (2017) 199 [arXiv:1701.02941] [INSPIRE].
Article ADS Google Scholar
Y. Li, A.-J. Ma, W.-F. Wang and Z.-J. Xiao, Quasi-two-body decays B_(s) → Pρ → Pππ in perturbative QCD approach, Phys. Rev. D 95 (2017) 056008 [arXiv:1612.05934] [INSPIRE].
A.-J. Ma, Y. Li, W.-F. Wang and Z.-J. Xiao, The quasi-two-body decays B_(s) → (D_(s),$ \overline{D} $_(s))ρ → (D_(s), $ \overline{D} $_(s))ππ in the perturbative QCD factorization approach, Nucl. Phys. B 923 (2017) 54 [arXiv:1611.08786] [INSPIRE].
M. Wirbel, B. Stech and M. Bauer, Exclusive semileptonic decays of heavy mesons, Z. Phys. C 29 (1985) 637 [INSPIRE].
ADS Google Scholar
ALEPH collaboration, Study of tau decays involving kaons, spectral functions and determination of the strange quarKmass, Eur. Phys. J. C 11 (1999) 599 [hep-ex/9903015] [INSPIRE].
M. Jamin, A. Pich and J. Portoles, Spectral distribution for the decay τ → ν_τ Kπ, Phys. Lett. B 640 (2006) 176 [hep-ph/0605096] [INSPIRE].
M. Jamin, A. Pich and J. Portoles, What can be learned from the Belle spectrum for the decay τ⁻ → ν_τ K_Sπ⁻ , Phys. Lett. B 664 (2008) 78 [arXiv:0803.1786] [INSPIRE].
Article ADS Google Scholar
B. Moussallam, Analyticity constraints on the strangeness changing vector current and applications to τ → Kπν_τ and τ → Kππν_τ , Eur. Phys. J. C 53 (2008) 401 [arXiv:0710.0548] [INSPIRE].
Article ADS Google Scholar
D.R. Boito, R. Escribano and M. Jamin, Kπ vector form-factor, dispersive constraints and τ → ν_τ Kπ decays, Eur. Phys. J. C 59 (2009) 821 [arXiv:0807.4883] [INSPIRE].
Article ADS Google Scholar
D.R. Boito, R. Escribano and M. Jamin, Kπ vector form factor constrained by τ → Kpiν_τ and K_l3 decays, JHEP 09 (2010) 031 [arXiv:1007.1858] [INSPIRE].
Article ADS MATH Google Scholar
R. Escribano, S. González-Solís, M. Jamin and P. Roig, Combined analysis of the decays τ ⁻ → K_Sπ⁻ ν_τ and τ ⁻ → K⁻ ην_τ , JHEP 09 (2014) 042 [arXiv:1407.6590] [INSPIRE].
Article ADS Google Scholar
S. Descotes-Genon, A. Khodjamirian and J. Virto, Light-cone sum rules for B → Kπ form factors and applications to rare decays, JHEP 12 (2019) 083 [arXiv:1908.02267] [INSPIRE].
Article ADS Google Scholar
M. Jamin, J.A. Oller and A. Pich, Strangeness changing scalar form-factors, Nucl. Phys. B 622 (2002) 279 [hep-ph/0110193] [INSPIRE].
D.R. Boito and R. Escribano, Kpi form-factors and final state interactions in D⁺ → K⁻ π⁺ π⁺ decays, Phys. Rev. D 80 (2009) 054007 [arXiv:0907.0189] [INSPIRE].
U.-G. Meissner and W. Wang, Generalized heavy-to-light form factors in light-cone sum rules, Phys. Lett. B 730 (2014) 336 [arXiv:1312.3087] [INSPIRE].
Article ADS Google Scholar
D. Delepine, J.L. Lucio M., J.A. Mendoza S. and C.A. Ramirez, A consistent scenario for B → PS decays, Phys. Rev. D 78 (2008) 114016 [arXiv:0808.2305] [INSPIRE].
K. Maltman, The a₀ (980), a₀ (1450) and $ {K}_0^{\ast } $(1430) scalar decay constants and the isovector scalar spectrum, Phys. Lett. B 462 (1999) 14 [hep-ph/9906267] [INSPIRE].
C.M. Shakin and H. Wang, Calculation of the decay constants of scalar mesons, Phys. Rev. D 63 (2001) 074017 [INSPIRE].
H.-Y. Cheng, C.-K. Chua, K.-C. Yang and Z.-Q. Zhang, Revisiting charmless hadronic B decays to scalar mesons, Phys. Rev. D 87 (2013) 114001 [arXiv:1303.4403] [INSPIRE].
ADS Google Scholar
W.-F. Wang, H.-n. Li, W. Wang and C.-D. Lü, S-wave resonance contributions to the $ {B}_{(s)}^0 $→ J/ψπ⁺ π⁻ and B_s → π⁺ π⁻ μ⁺ μ⁻ decays, Phys. Rev. D 91 (2015) 094024 [arXiv:1502.05483] [INSPIRE].
A. Bazavov et al., B- and D-meson leptonic decay constants from four-flavor lattice QCD, Phys. Rev. D 98 (2018) 074512 [arXiv:1712.09262] [INSPIRE].
H.-Y. Cheng, Comments on the quarKcontent of the scalar meson f₍₀₎ (1370), Phys. Rev. D 67 (2003) 054021 [hep-ph/0212361] [INSPIRE].
H.-n. Li and S. Mishima, Penguin-dominated B → P V decays in NLO perturbative QCD, Phys. Rev. D 74 (2006) 094020 [hep-ph/0608277] [INSPIRE].
Y.-L. Shen, W. Wang, J. Zhu and C.-D. Lu, Study of $ {K}_0^{\ast } $(1430) and a₀ (980) from B → $ {K}_0^{\ast } $(1430)π and B → a₀ (980)K decays, Eur. Phys. J. C 50 (2007) 877 [hep-ph/0610380] [INSPIRE].
Y. Li, H.-Y. Zhang, Y. Xing, Z.-H. Li and C.-D. Lu, Study of B → $ {K}_0^{\ast } $1430)K^(*) decays in QCD Factorization Approach, Phys. Rev. D 91 (2015) 074022 [arXiv:1501.03865] [INSPIRE].
M. Gronau, A precise sum rule among four B → Kπ CP asymmetries, Phys. Lett. B 627 (2005) 82 [hep-ph/0508047] [INSPIRE].
M. Beneke and T. Feldmann, Symmetry breaking corrections to heavy to light B meson form-factors at large recoil, Nucl. Phys. B 592 (2001) 3 [hep-ph/0008255] [INSPIRE].
C.-D. Lu and M.-Z. Yang, B to light meson transition form-factors calculated in perturbative QCD approach, Eur. Phys. J. C 28 (2003) 515 [hep-ph/0212373] [INSPIRE].
A. Ali et al., Charmless non-leptonic B_s decays to PP, PV and VV final states in the pQCD approach, Phys. Rev. D 76 (2007) 074018 [hep-ph/0703162] [INSPIRE].
P. Ball, B → π and B → Ktransitions from QCD sum rules on the light cone, JHEP 09 (1998) 005 [hep-ph/9802394] [INSPIRE].
P. Ball, Theoretical update of pseudoscalar meson distribution amplitudes of higher twist: the nonsinglet case, JHEP 01 (1999) 010 [hep-ph/9812375] [INSPIRE].
P. Ball and R. Zwicky, New results on B → π, K, η decay formfactors from light-cone sum rules, Phys. Rev. D 71 (2005) 014015 [hep-ph/0406232] [INSPIRE].
P. Ball, V.M. Braun and A. Lenz, Higher-twist distribution amplitudes of the Kmeson in QCD, JHEP 05 (2006) 004 [hep-ph/0603063] [INSPIRE].
W.-F. Wang and Z.-J. Xiao, The semileptonic decays B/B_s → (π, K) (ℓ⁺ ℓ⁻, ℓν, ν$ \overline{v} $) in the perturbative QCD approach beyond the leading-order, Phys. Rev. D 86 (2012) 114025 [arXiv:1207.0265] [INSPIRE].
T. Kurimoto, H.-n. Li and A.I. Sanda, Leading power contributions to B → π, ρ transition form-factors, Phys. Rev. D 65 (2002) 014007 [hep-ph/0105003] [INSPIRE].
H.-n. Li and S. Mishima, Pion transition form factor in k_T factorization, Phys. Rev. D 80 (2009) 074024 [arXiv:0907.0166] [INSPIRE].

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Institute of Theoretical Physics, Shanxi University, Taiyuan, 030006, Shanxi, China
Wen-Fei Wang & Jian Chai
State Key Laboratory of Quantum Optics and Quantum Optics Devices, Shanxi University, Taiyuan, 030006, Shanxi, China
Wen-Fei Wang & Jian Chai
Department of Mathematics and Physics, Nanjing Institute of Technology, Nanjing, 211167, Jiangsu, China
Ai-Jun Ma

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Wang, WF., Chai, J. & Ma, AJ. Contributions of $ {K}_0^{\ast } $(1430) and $ {K}_0^{\ast } $(1950) in the three-body decays B → Kπh. J. High Energ. Phys. 2020, 162 (2020). https://doi.org/10.1007/JHEP03(2020)162

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Received: 04 January 2020
Revised: 22 February 2020
Accepted: 13 March 2020
Published: 26 March 2020
Version of record: 26 March 2020
DOI: https://doi.org/10.1007/JHEP03(2020)162

Contributions of \( {K}_0^{\ast } \)(1430) and \( {K}_0^{\ast } \)(1950) in the three-body decays B → Kπh

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Contributions of \( {K}_0^{\ast } \)(1430) and \( {K}_0^{\ast } \)(1950) in the three-body decays B → Kπh

Abstract

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Resonant contributions to three-body \(B\rightarrow KKK\) decays in perturbative QCD approach

Contributions of S-, P-, and D-wave resonances to the quasi-two-body decays \(B^{0}_{s} \rightarrow \psi (3686,3770)K \pi \) in the perturbative QCD approach

Four-body decays B(s) → (Kπ)S/P(Kπ)S/P in the perturbative QCD approach

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Four-body decays B_(s) → (Kπ)_S/P(Kπ)_S/P in the perturbative QCD approach