The PQCD approach towards to next-to-leading order: A short review

Abstract

In this short review we elaborate the significance of resummation in k_T factorization theorem, and summarize the recent progresses in the calculations of the next-to-leading order contributions to B meson decays from the perturbative QCD (PQCD) approach. We also comment on the current status of the PQCD approach and highlight some key issues to develop it in the near future for more phenomenological applications.

Keywords

flavor physics / perturbative QCD / k _T factorization / next-to-leading order

References

[1] M. Bauer and B. Stech, Exclusive D-decays, Phys. Lett. B 152, 380 (1985)

[2] G. Buchalla, A. J. Buras, and M. E. Lautenbacher, Weak decays beyond leading logarithms, Rev. Mod. Phys. 68, 1125 (1996)

[3] M. Bauer, B. Stech, and M. Wirbel, Exclusive nonleptonic decays of D, D(s), and Bmesons, Z. Phys. C 34, 103 (1987)

[4] A. Ali, G. Kramer, and C. D. Lü, Experimental tests of factorization in charmless nonleptonic two-body Bdecays, Phys. Rev. D 58, 094009 (1998)

[5] A. Ali, G. Kramer, and C. D. Lü, CP violating asymmetries in charmless nonleptonic decays B→ PP, PV, VVin the factorization approach, Phys. Rev. D 59, 014005 (1999)

[6] Y. H. Chen, H. Y. Cheng, B. Tseng, and K. C. Yang, Charmless hadronic two-body decays of B_uand B_dmesons, Phys. Rev. D 60, 094014 (1999)

[7] M. J. Savage and M. B. Wise, SU(3) predictions for nonleptonic Bmeson decays, Phys. Rev. D 39, 3346 (1989), Erratum: [ Phys. Rev. D 40, 3127 (1989)]

[8] L. L. Chau, H. Y. Cheng, W. K. Sze, H. Yao, and B. Tseng, Charmless nonleptonic rare decays of Bmesons, Phys. Rev. D 43, 2176 (1991); Erratum: Phys. Rev. D 58, 019902 (1998)

[9] A. J. Buras and L. Silvestrini, Nonleptonic two-body Bdecays beyond factorization, Nucl. Phys. B 569, 3 (2000)

[10] A. Khodjamirian, B→ ππdecay in QCD, Nucl. Phys. B 605, 558 (2001)

[11] A. Khodjamirian, T. Mannel, and P. Urban, Gluonic penguins in B→ ππfrom QCD light cone sum rules, Phys. Rev. D 67, 054027 (2003)

[12] A. Khodjamirian, T. Mannel, and B. Melic, QCD light cone sum rule estimate of charming penguin contributions in B→ ππ, Phys. Lett. B 571, 75 (2003); Erratum: Phys. Lett. B 572, 171 (2003)

[13] A. Khodjamirian, T. Mannel, M. Melcher, and B. Melic, Annihilation effects in B→ ππfrom QCD light-cone sum rules, Phys. Rev. D 72, 094012 (2005)

[14] M. Beneke, G. Buchalla, M. Neubert, and C. T. Sachrajda, QCD factorization for B→ ππdecays: Strong phases and CP violation in the heavy quark limit, Phys. Rev. Lett. 83, 1914 (1999)

[15] M. Beneke, G. Buchalla, M. Neubert, and C. T. Sachrajda, QCD factorization for exclusive, nonleptonic Bmeson decays: General arguments and the case of heavy light final states, Nucl. Phys. B 591, 313 (2000)

[16] M. Beneke, G. Buchalla, M. Neubert, and C. T. Sachrajda, QCD factorization in B→ πK, ππdecays and extraction of Wolfenstein parameters, Nucl. Phys. B 606, 245 (2001)

[17] M. Beneke and T. Feldmann, Symmetry breaking corrections to heavy to light Bmeson form-factors at large recoil, Nucl. Phys. B 592, 3 (2001)

[18] C. W. Bauer, S. Fleming, D. Pirjol, and I. W. Stewart, An effective field theory for collinear and soft gluons: Heavy to light decays, Phys. Rev. D 63, 114020 (2001)

[19] C. W. Bauer, D. Pirjol, and I. W. Stewart, A Proof of factorization for B→ Dπ, Phys. Rev. Lett. 87, 201806 (2001)

[20] C. W. Bauer, D. Pirjol, and I. W. Stewart, Factorization and endpoint singularities in heavy to light decays, Phys. Rev. D 67, 071502 (2003)

[21] J. Chay and C. Kim, Nonleptonic B decays into two light mesons in soft collinear effective theory,Nucl. Phys. B 680, 302 (2004)

[22] Y. Y. Keum, H. N. Li, and A. I. Sanda, Fat penguins and imaginary penguins in perturbative QCD, Phys. Lett. B 504, 6 (2001)

[23] Y. Y. Keum, H. N. Li, and A. I. Sanda, Penguin enhancement and B→ Kπdecays in perturbative QCD, Phys. Rev. D 63, 054008 (2001)

[24] C. D. Lü, K. Ukai, and M. Z. Yang, Branching ratio and CP violation of B→ ππdecays in perturbative QCD approach, Phys. Rev. D 63, 074009 (2001)

[25] Y.Y. Keum and H. N. Li, Nonleptonic charmless B decays: Factorization versus perturbative QCD, Phys. Rev. D 63, 074006 (2001)

[26] T. Becher, A. Broggio, and A. Ferroglia, Introduction to soft-collinear effective theory, Lect. Notes Phys. 896, pp 1–206 (2015), arXiv: 1410.1892 [hep-ph]

[27] M. Beneke, Soft-collinear factorization in Bdecays, Nucl. Part. Phys. Proc. 261–262, 311 (2015)

[28] A. Khodjamirian, T. Mannel, and N. Offen, Form-factors from light-cone sum rules with B-meson distribution amplitudes, Phys. Rev. D 75, 054013 (2007)

[29] N. Gubernari, A. Kokulu, and D. van Dyk, B→ Pand B→ Vform factors from B-meson light-cone sum rules beyond leading twist, J. High Energy Phys. 1901, 150 (2019)

[30] Y. M. Wang and Y. L. Shen, QCD corrections to B→ πform factors from light-cone sum rules, Nucl. Phys. B 898, 563 (2015)

[31] C. D. Lü, Y. L. Shen, Y. M. Wang, and Y. B. Wei, QCD calculations of B→ π, K form factors with higher-twist corrections, J. High Energy Phys. 1901, 024 (2019)

[32] M. Beneke, Y. Kiyo, and D. S. Yang, Loop corrections to subleading heavy quark currents in SCET, Nucl. Phys. B 692, 232 (2004)

[33] M. Beneke, T. Huber, and X. Q. Li, NNLO vertex corrections to non-leptonic Bdecays: Tree amplitudes, Nucl. Phys. B 832, 109 (2010)

[34] G. Bell, M. Beneke, T. Huber, and X. Q. Li, Two-loop current–current operator contribution to the non-leptonic QCD penguin amplitude, Phys. Lett. B 750, 348–355 (2015)

[35] G. Bell, M. Beneke, T. Huber, and X. Q. Li, Non-leptonic B-decays at two loops in QCD factorization, PoS RADCOR2019, 032 (2019), arXiv: 1912.08429 [hep-ph]

[36] G. Bell, M. Beneke, T. Huber, and X. Q. Li, Two-loop non-leptonic penguin amplitude in QCD factorization, J. High Energy Phys. 04, 055 (2020)

[37] T. Kurimoto, H. N. Li, and A. I. Sanda, Leading power contributions to B → π, ρtransition form-factors, Phys. Rev. D 65, 014007 (2002)

[38] C. D. Lü and M. Z. Yang, B to light meson transition form-factors calculated in perturbative QCD approach, Eur. Phys. J. C 28, 515 (2003)

[39] H. N. Li, Y. L. Shen, and Y. M. Wang, Next-to-leadingorder corrections to B→ πform factors in k_Tfactorization, Phys. Rev. D 85, 074004 (2012)

[40] S. Cheng, Y. Y. Fan, X. Yu, C. D. Lü, and Z. J. Xiao, The NLO twist-3 contributions to B → π form factors in k_Tfactorization, Phys. Rev. D 89, 094004 (2014)

[41] E. Dalgic, A. Gray, M. Wingate, C. T. H. Davies, G. P. Lepage, and J. Shigemitsu, B meson semileptonic form-factors from unquenched lattice QCD, Phys. Rev. D 73, 074502 (2006); Erratum: Phys. Rev. D 75, 119906 (2007)

[42] R. R. Horgan, Z. Liu, S. Meinel, and M. Wingate, Lattice QCD calculation of form factors describing the rare decays B → K^∗ℓ⁺ℓ⁻ and B_s → ϕℓ⁺ℓ⁻, Phys. Rev. D 89, 9–094501 (2014)

[43] J. M. Flynn, T. Izubuchi, T. Kawanai, C. Lehner, A. Soni, R. S. Van de Water, and O. Witzel, B→ πℓν and B_s → Kℓν form factors and |V_ub| from 2+1-flavor lattice QCD with domain-wall light quarks and relativistic heavy quarks, Phys. Rev. D 91(7) 074510 (2015)

[44] J. A. Bailey, et al. [Fermilab Lattice and MILC], |V_ub| from B → πℓν decays and (2+1)-flavor lattice QCD, Phys. Rev. D 92(1) 014024 (2015)

[45] J. A. Bailey, et al. [MILC], B → Dlν form factors at nonzero recoil and |V_cb| from 2+1-flavor lattice QCD, Phys. Rev. D 92(3) 034506 (2015)

[46] T. Kaneko, Lattice QCD: Hadron spectroscopy and flavor physics, arXiv: 1807.04134 [hep-lat]

[47] S. Aoki, et al. [Flavour Lattice Averaging Group], FLAG review 2019, Eur. Phys. J. C 80, 113 (2020), and references therein

[48] V. V. Sudakov, Vertex parts at very high-energies in quantum electrodynamics, Sov. Phys. JETP 3, 65 (1956), [Zh. Eksp. Teor. Fiz. 30, 87 (1956)]

[49] J. C. Collins, In perturbative quantum chromodynamics, Ed. A. H. Mueller, World Scientific, Singapore, 1989

[50] G. P. Lepage and S. J. Brodsky, Exclusive processes in perturbative quantum chromodynamics, Phys. Rev. D 22, 2157 (1980)

[51] P. V. Landshoff and D. J. Pritchard, Higher order QCD corrections to exclusive processes: The multiple scattering mechanism, Z. Phys. C 6, 69 (1980)

[52] A. H. Mueller, Perturbative QCD at high-energies, Phys. Rep. 73, 237 (1981)

[53] A. Sen, Asymptotic behavior of the Sudakov form-factor in quantum chromodynamics, Phys. Rev. D 24, 3281 (1981)

[54] A. Sen, Asymptotic behavior of the wide angle on-shell quark scattering amplitudes in nonabelian gauge theories, Phys. Rev. D 28, 860 (1983)

[55] J. C. Collins and D. E. Soper, Back-to-back jets in QCD, Nucl. Phys. B 193, 381 (1981); Erratum: Nucl. Phys. B 213, 545 (1983)

[56] J. C. Collins, D. E. Soper, and G. F. Sterman, Factorization for one loop corrections in the Drell–Yan process, Nucl. Phys. B 223, 381 (1983)

[57] J. Botts and G. F. Sterman, Hard elastic scattering in QCD: Leading behavior, Nucl. Phys. B 325, 62 (1989)

[58] N. Isgur, and C. H. L. Smith, The applicability of perturbative QCD to exclusive processes, Nucl. Phys. B 317, 526 (1989)

[59] T. Huang, Q. X. Shen, and P. Kroll, A study of the applicability of perturbative QCD to the pion form factor, Z. Phys. C 50, 139 (1991)

[60] H. N. Li and G. F. Sterman, The perturbative pion formfactor with Sudakov suppression, Nucl. Phys. B 381, 129 (1992)

[61] H. N. Li, Unification of the k_T and threshold resummations, Phys. Lett. B 454, 328 (1999)

[62] F. Feng, J. P. Ma, and Q. Wang, Resummation of large logarithms in γ^∗π⁰ → γ, J. High Energy Phys. 0706, 039 (2007)

[63] H. Georgi, An effective field theory for heavy quarks at low-energies, Phys. Lett. B 240, 447 (1990)

[64] A. F. Falk, H. Georgi, B. Grinstein, and M. B. Wise, Heavy meson form-factors from QCD, Nucl. Phys. B 343, 1 (1990)

[65] A. V. Efremov and A. V. Radyushkin, Factorization and asymptotical behavior of pion form-factor in QCD, Phys. Lett. B 94, 245 (1980)

[66] G. P. Lepage and S. J. Brodsky, Exclusive processes in quantum chromodynamics: the form-factors of baryons at large momentum transfer, Phys. Rev. Lett. 43, 545 (1979); Erratum: Phys. Rev. Lett. 43, 1625 (1979)

[67] R. Akhoury, G. F. Sterman, and Y. P. Yao, Exclusive semileptonic decays of Bmesons into light mesons, Phys. Rev. D 50, 358 (1994)

[68] H. N. Li and H. L. Yu, Extraction of V_ubfrom decay B→ πlν, Phys. Rev. Lett. 74, 4388 (1995)

[69] H. N. Li and H. L. Yu, Perturbative QCD analysis of Bmeson decays, Phys. Rev. D 53, 2480 (1996)

[70] Z. J. Xiao, Y. Y. Fan, W. F. Wang, and S. Cheng, The semileptonic decays of B/B_s meson in the perturbative QCD approach: A short review, Chin. Sci. Bull. 59, 3787 (2014)

[71] M. S. Alam, et al. [CLEO Collaboration], Exclusive hadronic B decays to charm and charmonium final states, Phys. Rev. D 50, 43 (1994)

[72] H. Y. Cheng and B. Tseng, Extraction of a₁ and a₂ from B → ΨK(K^∗), D(D^∗)π(ρ) decays, Phys. Rev. D 51, 6259 (1995)

[73] H. N. Li, Study of the decay B → ππ via perturbative QCD, Phys. Lett. B 348, 597 (1995)

[74] C. H. Chang and H. N. Li, Three-scale factorization theorem and effective field theory, Phys. Rev. D 55, 5577 (1997)

[75] T. W. Yeh and H. N. Li, Factorization theorems, effective field theory, and nonleptonic heavy meson decays, Phys. Rev. D 56, 1615 (1997)

[76] H. N. Li and B. Tseng, Nonfactorizable soft gluons in nonleptonic heavy meson decays, Phys. Rev. D 57, 443 (1998)

[77] H. Y. Cheng, H. N. Li, and K. C. Yang, Gauge invariant and infrared finite theory of nonleptonic heavy meson decays, Phys. Rev. D 60, 094005 (1999)

[78] Y. M. Wang and Y. L. Shen, Subleading power corrections to the pion-photon transition form factor in QCD, J. High Energy Phys. 12, 037 (2017)

[79] J. Gao, C. D. Lü, Y. L. Shen, Y. M. Wang, and Y. B. Wei, Precision calculations of B → V form factors from softcollinear effective theory sum rules on the light-cone, Phys. Rev. D 101, 074035 (2020)

[80] H. N. Li, QCD aspects of exclusive B meson decays, Prog.Part. Nucl. Phys. 51, 85 (2003)

[81] Z. J. Xiao, The B Meson Physics, Beijing: Science Press, 2013 (in Chinese)

[82] Ed. A. J. Bevan, B. Golob, Th. Mannel, S. Prell, and B. D. Yabsley, The physics of the B factories, Eur. Phys. J. C 74, 3026 (2014); SLAC-PUB-15968, KEK Preprint2014-3

[83] Y. Amhis, et al. [Heavy Flavor Averaging group (HFLAV)], Averages of b-hadron, c-hadron and τ-lepton properties as summer of 2016, Eur. Phys. J. C 77, 895 (2017)

[84] Y. Amhis, et al. [Heavy Flavor Averaging group (HFLAV)], Averages of b-hadron, c-hadron and τ-lepton properties as of 2018, arXiv: 1909.12524V2 [hep-ex]

[85] P. A. Zyla, et al. [Particle Data Group], The review of particle physics, Prog. Theor. Exp. Phys. 2020, 083C01 (2020)

[86] H. N. Li, Perturbative QCD factorization of πγ^∗ → γ(π) and B→ γ(π)lv¯, Phys. Rev. D 64, 014019 (2001)

[87] M. Nagashima and H. N. Li, Two parton twist three factorization in perturbative QCD, Eur. Phys. J. C 40, 395 (2005)

[88] M. Nagashima and H. N. Li, k_Tfactorization of exclusive processes, Phys. Rev. D 67, 034001 (2003)

[89] F. Feng, J. P. Ma, and Q. Wang, Gauge invariance and k_T-factorization of exclusive processes, Phys. Lett. B 674, 176 (2009)

[90] H. N. Li and S. Mishima, Comment on “Gauge invariance and k_T-factorization of exclusive processes” Phys. Lett. B 674, 182 (2009)

[91] Y. C. Chen and H. N. Li, Three-parton contribution to pion form factor in k_Tfactorization, Phys. Rev. D 84, 034018 (2011)

[92] Y. C. Chen and H. N. Li, Three-parton contribution to the B → π form factors in k_T factorization, Phys. Lett. B 712, 63 (2012)

[93] S. Cheng, Pion and Kaon form factors in the perturbative QCD approach, Phys. Rev. D 100, 013007 (2019)

[94] Y. L. Zhang, S. Cheng, J. Hua, and Z. J. Xiao, ργ^∗ → π(ρ) transition form factors in the perturbative QCD factorization approach, Phys. Rev. D 92, 094031 (2015)

[95] S. Cheng, Y. L. Zhang, J. Hua, H. N. Li, and Z. J. Xiao, Revisiting the factorization theorem for ργ^∗ → π(ρ) at twist 3, Phys. Rev. D 95, 076005 (2017)

[96] J. Hua, S. Cheng, Y. L. Zhang, and Z. J. Xiao, Rho-pion transition form factors in the k_T factorization formulism revisited, Phys. Rev. D 97, 113002 (2018)

[97] S. Nandi and H. N. Li, Next-to-leading-order corrections to exclusive processes in k_T factorization, Phys. Rev. D 76, 034008 (2007)

[98] H. N. Li, Y. L. Shen, Y. M. Wang, and H. Zou, Next-toleading-order correction to pion form factor in k_T factorization, Phys. Rev. D 83, 054029 (2011)

[99] S. Cheng, Y. Y. Fan, and Z. J. Xiao, NLO twist-3 contribution to the pion electromagnetic form factors in k_T factorization, Phys. Rev. D 89, 054015 (2014)

[100] B. O. Lange and M. Neubert, Renormalization group evolution of the B meson light cone distribution amplitude, Phys. Rev. Lett. 91, 102001 (2003)

[101] V. M. Braun, D. Y. Ivanov, and G. P. Korchemsky, The B meson distribution amplitude in QCD, Phys. Rev. D 69, 034014 (2004)

[102] H. N. Li and H. S. Liao, B meson wave function in kT factorization, Phys. Rev. D 70, 074030 (2004)

[103] J. C. Collins, What exactly is a parton density? Acta Phys. Polon. B 34, 3103 (2003)

[104] H. N. Li, Y. L. Shen, and Y. M. Wang, Resummation of rapidity logarithms in B meson wave functions, J. High Energy Phys. 1302, 008 (2013)

[105] H. N. Li, Y. L. Shen, and Y. M. Wang, Joint resummation for pion wave function and pion transition form factor, J. High Energy Phys. 1401, 004 (2014)

[106] X. D. Ji, J. P. Ma, and F. Yuan, QCD factorization for semi-inclusive deep-inelastic scattering at low transverse momentum, Phys. Rev. D 71, 034005 (2005)

[107] H. N. Li and Y. M. Wang, Non-dipolar Wilson links for transverse-momentum-dependent wave functions, J. High Energy Phys. 1506, 013 (2015)

[108] M. Bander, D. Silverman, and A. Soni, CP noninvariance in the decays of the heavy charged quark systems, Phys. Rev. Lett. 43, 242 (1979)

[109] H. C. Hu and H. N. Li, Next-to-leading-order time-like pion form factors in k_T factorization, Phys. Lett. B 718, 1351 (2013)

[110] S. Cheng and Z. J. Xiao, Time-like pion electromagnetic form factors in k_T factorization with the next-to-leadingorder twist-3 contribution, Phys. Lett. B 749, 1 (2015)

[111] S. Cheng, Z. J. Xiao, and Y. L. Zhang, The NLO contributions to the scalar pion form factors and the O(αs2) annihilation corrections to the B → ππ decays, Nucl. Phys. B 896, 255 (2015)

[112] S. Cheng and Q. Qin, Z → π⁺π⁻, K⁺K⁻: A touchstone of the perturbative QCD approach, Phys. Rev. D 99, 016019 (2019)

[113] C. D. Lü and M. Z. Yang, B → πρ, πω decays in perturbative QCD approach, Eur. Phys. J. C 23, 275 (2002)

[114] H. N. Li and S. Mishima, Polarizations in B → VV decays, Phys. Rev. D 71, 054025 (2005)

[115] Y. Li and C. D. Lü, Branching ratio and polarization of B → ρ(ω)ρ(ω) decays in perturbative QCD approach, Phys. Rev. D 73, 014024 (2006)

[116] Z. J. Xiao, D. Q. Guo, and X. F. Chen, Branching ratio and CP asymmetry of B → η(′)η(′) decays in the perturbative QCD approach, Phys. Rev. D 75, 014018 (2007)

[117] Y. Y. Keum, T. Kurimoto, H. N. Li, C. D. Lü, and A. I. Sanda, Nonfactorizable contributions to B → D^(∗)Mdecays, Phys. Rev. D 69, 094018 (2004)

[118] R. H. Li, X. X. Wang, A. I. Sanda, and C. D. Lü, Decays of B meson to two charmed mesons, Phys. Rev. D 81, 034006 (2010)

[119] A. Ali, G. Kramer, Y. Li, C. D. Lü, Y. L. Shen, W. Wang, and Y. 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)

[120] Z. T. Zou, A. Ali, C. D. Lü, X. Liu, and Y. Li, Improved estimates of the B(s) → VV decays in perturbative QCD approach, Phys. Rev. D 91, 054033 (2015)

[121] Y. Li, C. D. Lü, Z. J. Xiao, and X. Q. Yu, Branching ratio and CP asymmetry of B_s → π⁺π⁻ decays in the perturbative QCD approach, Phys. Rev. D 70, 034009 (2004)

[122] Z. J. Xiao, W. F. Wang, and Y. 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, 094003 (2012)

[123] X. Liu, Z. J. Xiao, and C. D. Lü, Pure annihilation type B_c→ M₂M₃ decays in the perturbative QCD approach, Phys. Rev. D 81, 014022 (2010)

[124] X. Liu and Z. J. Xiao, Branching ratios of B_c → AP decays in the perturbative QCD approach, Phys. Rev. D 81, 074017(2010)

[125] Z. J. Xiao and X. Liu, The two-body hadronic decays of B_c meson in the perturbative QCD approach: A short review, Chin. Sci. Bull. 59, 3748 (2014), and references therein

[126] X. Liu and Z. J. Xiao, Light scalar mesons and charmless hadronic B_c → SP, SVdecays in the perturbative QCD approach, Phys. Rev. D 82, 054029 (2010)

[127] Z. Rui, W. F. Wang, G. X. Wang, L. H. Song, and C. D. Lü, The B_c → ψ(2S)π, η_c(2S)πdecays in the perturbative QCD approach, Eur. Phys. J. C 75, 293 (2015)

[128] Z. Rui, H. Li, G. X. Wang, and Y. Xiao, Semileptonic decays of B_c meson to S-wave charmonium states in the perturbative QCD approach, Eur. Phys. J. C 76, 564 (2016)

[129] X. Liu, H. N. Li, and Z. J. Xiao, Improved perturbative QCD formalism for B_c meson decays, Phys. Rev. D 97, 113001 (2018)

[130] X. Liu, R. H. Li, Z. T. Zou, and Z. J. Xiao, Nonleptonic charmless decays of B_c → TP, TV in the perturbative QCD approach, Phys. Rev. D 96, 013005 (2017)

[131] Z. T. Zou and C. D. Lü, The nonleptonic two body B decays involving a light tensor meson in fnal states, Chin. Sci. Bull. 59, 3738 (2014)

[132] C. H. Chen and H. N. Li, Three body nonleptonic B decays in perturbative QCD, Phys. Lett. B 561, 258 (2003)

[133] 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, 074031 (2014)

[134] R. Aaij, et al. [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, 101801 (2013)

[135] R. Aaij, et al. [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, 011801 (2014)

[136] Y. Li, A. J. Ma, W. F. Wang, and Z. J. Xiao, Quasi-twobody decays B_(s) → P_ρ→ Pππin the perturbative QCD approach, Phys. Rev. D 95, 056008 (2017)

[137] Y. Li, A. J. Ma, W. F. Wang, and Z. J. Xiao, Quasi-twobody decays B_(s) → Pρ′ (1450), Pρ′′ (1700 → Pππ in the perturbative QCD approach, Phys. Rev. D 96, 036014 (2017)

[138] A. J. Ma, Y. Li, W. F. Wang, and Z. J. Xiao, S-wave resonance contributions to B(s)0→ ηc(2S)π⁺π⁻ in the perturbative QCD factorization approach, Chin. Phys. C 41, 083105 (2017)

[139] Y. Li, D. C. Yan, R. Zhou, and Z. J. Xiao, S, P and D-wave resonance contributions to B_(s) → ηc(1S, 2S)Kπdecays in the perturbative QCD approach, Phys. Rev. D 101, 016015 (2020)

[140] W. F. Wang, Will the subprocesses ρ(770; 1450) → K⁺K^? contribute large branching fractions for B → πK⁺K⁻ decays ? Phys. Rev. D 101, 111901(R) (2020)

[141] H. N. Li, S. Mishima, and A. I. Sanda, Resolution to the B → πK puzzle, Phys. Rev. D 72, 114005 (2005)

[142] S. Mishima and A. I. Sanda, Calculation of magnetic penguin amplitudes in B → ϕK decays using PQCD approach, Prog. Theor. Phys. 110, 549 (2003)

[143] Y. L. Zhang, X. Y. Liu, Y. Y. Fan, S. Cheng, and Z. J. Xiao, B → ππ decays and effects of the next-to-leading order contributions, Phys. Rev. D 90, 014029 (2014)

[144] J. J. Wang, D. T. Lin, W. Sun, Z. J. Ji, S. Cheng, and Z. J. Xiao, B¯s0 → Kπ, KKdecays and effects of the nextto- leading order contributions, Phys. Rev. D 89, 074046 (2014)

[145] Y. Y. Fan, W. F. Wang, S. Cheng, and Z. J. Xiao, Anatomy of B → Kη^(′) decays in different mixing schemes and effects of NLO contributions in the perturbative QCD approach, Phys. Rev. D 87, 094003 (2013)

[146] H. N. Li and S. Mishima, Glauber gluons in spectator amplitudes for B → πM decays, Phys. Rev. D 90, 074018 (2014)

[147] X. Liu, H. N. Li, and Z. J. Xiao, Transverse-momentumdependent wave functions with Glauber gluons in B → ππ, ρρ decays, Phys. Rev. D 91, 114019 (2015)

[148] X. Liu, H. N. Li, and Z. J. Xiao, Resolving the B → Kπ puzzle by Glauber-gluon effects, Phys. Rev. D 93, 014024 (2016)

[149] Z. J. Xiao, Z. Q. Zhang, X. Liu, and L. B. Guo, Branching ratios and CP asymmetries of B → Kη^(′) decays in the perturbative PQCD approach, Phys. Rev. D 78, 114001 (2008)

[150] Z. Q. Zhang, X. Liu, and Z. J. Xiao, B → πη^(′), η^(′)η^(′) decays and NLO contributions in the PQCD approach, Chin. Phys. C 33, 722 (2009)

[151] W. Bai, M Liu, Y. Y. Fan, W. F. Wang, S. Cheng, and Z. J. Xiao, Revisiting the Kπ puzzle in the PQCD factorization approach, Chin. Phys. C 38, 033101 (2014)

[152] D. C. Yan, P. Yang, X. Liu, and Z. J. Xiao, Anatomy of B_s → PV decays and effects of next-to-leading order contributions in the perturbative QCD factorization approach, Nucl. Phys. B 931 , 79 (2018)

[153] D. C. Yan, X. Liu, and Z. J. Xiao, Anatomy of B_s → VV decays and effects of next-to-leading order contributions in the perturbative QCD factorization approach, Nucl. Phys. B 935 , 17 (2018)

[154] D. C. Yan, X. Liu, and Z. J. Xiao, Anatomy of B_s → PP decays and effects of the next-to-leading order contributions in the perturbative QCD approach, Nucl. Phys. B 946 , 114705 (2019)

[155] Z. Q. Zhang, X. Liu, and Z. J. Xiao, B → (J/Ψηc)Kdecays in the perturbative QCD approach, Chin. Phys. C 34, 937 (2010)

[156] Z. J. Xiao, D. C. Yan, and X. Liu, B_(s) → η_c(P, V) decays and effects of the next-to-leading order contributions in the perturbative QCD approach, Nucl. Phys. B 953 , 114954 (2020)

[157] J. P. Lees, et al. [BaBar Collaboration], Evidence for an excess of B¯→ D^(∗)τ−ν¯τ decays, Phys. Rev. Lett. 109, 101802 (2012)

[158] R. Aaij, et al. [LHCb collaboration], Differential branching fraction and angular analysis of the decay B⁰ → K^∗0μ⁺μ⁻, J. High Energy Phys. 1308, 131 (2013)

[159] R. Aaij, et al. [LHCb collaboration], Measurement of form-factor independent observables in the decay B⁰ → K^∗0μ⁺μ⁻, Phys. Rev. Lett. 111, 191801 (2013)

[160] G. Caria, et al. [Belle collaboration], Measurement of R(D) and R(D^∗) with a semileptonic tagging method, Phys. Rev. Lett. 124, 161803 (2020)

[161] R. Aaij, et al. [LHCb collaboration], Search for leptonuniversality violation in B⁺ → K⁺l⁺l⁻, Phys. Rev. Lett. 122, 191801 (2019)

[162] S. Fajfer, J. F. Kamenik, and I. Nisandzic, On the B → D^∗τν¯τ sensitivity to new physics. Phys. Rev. D 85, 094025 (2012)

[163] S. Descotes-Genona, J. Matiasb, and J. Virtob, Understanding the B→ K^∗μ⁺μ⁻ Anomaly, Phys. Rev. D 88, 074002 (2013)

[164] J. A. Bailey, et al., Refining new-physics searches in B → Dτνdecay with lattice QCD, Phys. Rev. Lett. 109, 071802 (2012)

[165] S. Fajfer, J. F. Kamenik, I. Nisandzic, et al., Implications of lepton flavor universality violations in Bdecays, Phys. Rev. Lett. 109, 161801 (2012)

[166] A. Celis, M. Jung, X. Q. Li, et al., Sensitivity to charged scalars in B → Dτν and B → τν decays, J. High Energy Phys. 1301, 054 (2013)

[167] F. U. Bemlochner, Z. Ligeti, M. Papucci, and D. J. Robinson, Combined analysis of semileptonic B decays to D and D^∗: R(D^(∗)), |V_cb|, and new physics, Phys. Rev. D 95, 115008 (2017)

[168] Y. Li and C. D. Lü, Recent anomalies in B physics, Sci. Bull. 63, 267 (2018)

[169] Y. Y. Fan, W. F. Wang, S. Cheng, and Z. J. Xiao, Semileptonic decays B → D^(∗)lν in the perturbative QCD factorization approach, Chin. Sci. Bull. 59, 125 (2014)

[170] Y. Y. Fan, Z. J. Xiao, R. M. Wang, and B. Z. Li, The B → D^(∗)lνdecays in the pQCD approach with the Lattice QCD input, Chin. Sci. Bull. 60, 2009 (2015)

[171] Y. M. Wang, Y. B. Wei, Y. L. Shen, and C. D. Lü, Perturbative corrections to B → D form factors in QCD, J. High Energy Phys. 06, 062 (2017)

[172] Y. Y. Fan, W. F. Wang, and Z. J. Xiao, Study of B¯s0→ (Ds+, Ds*+)l⁻ν¯ldecays in the perturbative QCD factorization approach, Phys. Rev. D 89, 014030 (2013)

[173] X. Q. Hu, S. P. Jin, and Z. J. Xiao, Semileptonic decays B/B_s→ (D^(∗), Ds(*))lν_lin the PQCD approach with the lattice QCD input, Chin. Phys. C 44, 053102 (2020)

[174] W. F. Wang and Z. J. Xiao, Semileptonic decays of B/B_s→ (π, K)(l⁺l⁻ , lν, νν¯) in the perturbative QCD approach beyond the leading order, Phys. Rev. D 86, 114025 (2012)

[175] W. F. Wang, Y. Y. Fan, M. Liu, and Z. J. Xiao, Semileptonic decays of B/B_s→ (η, η′ G)(l⁺l ⁻ , l⁻ν¯, νν¯) in the perturbative QCD approach beyond the leading order, Phys. Rev. D 87, 097501 (2013)

[176] C. Bourrely, I. Caprini, and L. Lellouch, Modelindependent description of B → πlν decays and a determination of |V_ub|, Phys. Rev. D 79, 013008 (2009); Erratum: Phys. Rev. D 82, 099902 (2010)

[177] S. P. Jin, X. Q. Hu, and Z. J. Xiao, Study of B_s → K^(∗)l⁺l⁻ in the PQCD factorization approach with lattice QCD input , Phys. Rev. D 102, 013001 (2020)

[178] A. Khodjamirian, T. Mannel, A. A. Pivovarov, and Y. M. Wang, Charm-loop effect in B → K^(∗)ℓ⁺ℓ⁻ and B → K^∗γ, J. High Energy Phys. 09, 089 (2010)

[179] A. Khodjamirian, T. Mannel, and Y. M. Wang, B → Kℓ⁺ℓ⁻ decay at large hadronic recoil, J. High Energy Phys. 02, 010 (2013)

[180] W. F. Wang, X. Yu, C. D. Lü, and Z. J. Xiao, Semileptonic decays Bc+→ D(s)*+ (l⁺νl, l⁺l⁻ , νν¯) in the perturbative QCD approach, Phys. Rev. D 90, 094018 (2014)

[181] X. Q. Hu, S. P. Jin, and Z. J. Xiao, Semileptonic decays B_c → (η_c, J/Ψ)lν¯l in the “Lattice+PQCD” approach, Chin. Phys. C 44, 023104 (2020)

[182] R. Aaij, et al. [LHCb collaboration], Measuremnt of the ratio of branching fractions B(Bc+→ J/Ψτ⁺ντ)/B(Bc+ → J/Ψμ⁺ν_μ), Phys. Rev. Lett. 120, 121801 (2018)

[183] M. Mulder, on behalf of the LHCb Collaboration, Experimental status of LFU in b→ slltransitions, talk given at FPCP 2020, June 8, 2020.

[184] Y. Y. Charng and H. N. Li, B meson wave function from the B → γlν¯ decay, Phys. Rev. D 72, 014003 (2005)

[185] Y. M. Wang, Factorization and dispersion relations for radiative leptonic Bdecay, J. High Energy Phys. 09, 159 (2016)

[186] Y. L. Shen, Z. T. Zou, and Y. B. Wei, Subleading power corrections to B→ γlνdecay in PQCD approach, Phys. Rev. D 99, 016004 (2019)

[187] Y. M. Wang and Y. L. Shen, Subleading-power corrections to the radiative leptonic B → γℓνdecay in QCD, J. High Energy Phys. 05, 184 (2018)

[188] Y. L. Shen, Z. T. Zou, and Y. Li, Power corrections to pion transition form factor in perturbative QCD approach, Phys. Rev. D 100, 016022 (2019)

[189] S. Cheng, A. Khodjamirian, and J. Virto, B → ππ form factors from light-cone sum rules with B-meson distribution amplitudes, J. High Energy Phys. 1705, 157 (2017)

[190] S. Descotes-Genon, A. Khodjamirian, and J. Virto, Lightcone sum rules for B → Kπ form factors and applications to rare decays,J. High Energy Phys. 1912, 083 (2019)

[191] S. Cheng and J. M. Shen, B¯s → f₀ (980) form factors and the width effect from light-cone sum rules, Eur. Phys. J. C 80, 554 (2020)

[192] M. Beneke and M. Neubert, QCD factorization for B → PP and B → PV decays, Nucl. Phys. B 675, 333 (2003)

[193] H. N. Li, Resummation in hard QCD processes, Phys. Rev. D 55, 105 (1997)

[194] H. N. Li and H. L. Yu, Determination of the HQET parameters from the B → X_sγdecay, Phys. Rev. D 55, 2833 (1997)

[195] H. N. Li and B. Melic, Determination of heavy meson wave functions from Bdecays, Eur. Phys. J. C 11, 695 (1999)

[196] C. D. Lü, M. Matsumori, A. I. Sanda, and M. Z. Yang, CP asymmetry, branching ratios and isospin breaking effects in B → ργ and B → ωγ decays with the pQCD approach, Phys. Rev. D 72, 094005 (2005); Erratum: Phys. Rev. D 73, 039902 (2006)

[197] M. Tanabashi, et al. [Particle Data Group], The review of particle physics, Phys. Rev. D 98(3), 030001 (2018)

[198] Y. Li and C. D. Lü, Annihilation type radiative decays of B meson in perturbative QCD approach, Phys. Rev. D 74, 097502 (2006)

[199] C. H. Chang and Y. Q. Chen, The decays of B_c meson, Phys. Rev. D 49, 3399 (1994)

[200] C. H. Chang, C. D. Lü, G. L. Wang, and H. S. Zong, The pure leptonic decays of Bc meson and their radiative corrections, Phys. Rev. D 60, 114013 (1999)

[201] X. Liu, H. N. Li, and Z. J. Xiao, Next-to-leadinglogarithm k_T resummation for B_c → J/ψdecays, Phys. Lett. B 811, 135892 (2020)

[202] H. H. Shih, S. C. Lee, and H. N Li, The Λ_b → plν¯ decay in perturbative QCD, Phys. Rev. D 59, 094014 (1999)

[203] X. G. He, T. Li, X. Q. Li, and Y. M. Wang, PQCD calculation for Λ_b → Λ_γ in the standard model, Phys. Rev. D 74, 034026 (2006)

[204] C. D. Lü, Y. M. Wang, H. Zou, A. Ali, and G. Kramer, Anatomy of the pQCD approach to the baryonic decays Λ_b → pπ, pK, Phys. Rev. D 80, 034011 (2009)

[205] Y. M. Wang, Y. Li, and C. D. Lü, Rare decays of Λ_b → Λ⁺γ and Λ_b → Λl⁺l⁻ in the light-cone sum rules, Eur. Phys. J. C 59, 861 (2009)

[206] A. Khodjamirian, C. Klein, T. Mannel, and Y. M. Wang, Form factors and strong couplings of heavy baryons from QCD light-cone sum rules, J. High Energy Phys. 09, 106 (2011)

[207] Y. M. Wang, Y. L. Shen, and C. D. Lu, Λ_b→ p, Λ transition form factors from QCD light-cone sum rules,Phys. Rev. D 80, 074012 (2009)

[208] Y. M. Wang and Y. L. Shen, Perturbative corrections to Λ_b→ Λ form factors from QCD light-cone sum rules, J. High Energy Phys. 02, 179 (2016)

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