Access by Xinjiang University

Evaluation of CKM matrix elements from exclusive $P_{ℓ 4}$ decays

C. S. Kim^*

G. López Castro^† and S. L. Tostado^‡

Department of Physics and IPAP, Yonsei University, Seoul 120-749, Korea

Departamento de Física, Centro de Investigación y de Estudios Avanzados, Apartado Postal 14-740, 07000 México Distrito Federal, México

^*cskim@yonsei.ac.kr
^†glopez@fis.cinvestav.mx
^‡stostado@fis.cinvestav.mx

PDF

Phys. Rev. D 95, 073003 – Published 10 April, 2017

DOI: https://doi.org/10.1103/PhysRevD.95.073003

Abstract

We consider the exclusive $P_{ℓ 4}$ decays, $P \to (P_{1} P_{2})_{V} ℓ ν_{ℓ}$ , where the subindex $V$ means that the invariant mass of the pseudoscalar pair is taken within a small window around the mass of the vector meson $V$ . Pole contributions beyond the dominant $P \to V (\to P_{1} P_{2}) ℓ ν_{ℓ}$ amplitude of $P_{ℓ 4}$ decays are identified, which, in turn, affect the determination of the CKM matrix elements $| V_{q q^{'}} |$ . We evaluate the effects of those contributions in the extraction of bottom and charm quark mixings. An application to $B \to (π π)_{ρ} ℓ ν_{ℓ}$ data from the Belle Collaboration shows an increase in the extracted value of $| V_{u b} |$ in better agreement with determinations based on $B \to π ℓ ν_{ℓ}$ decays. The effect of the $ρ$ and $D^{*}$ pole contributions in the determination of $| V_{c d} |$ from the decay $D \to π π ℓ^{-} {\bar{ν}}_{ℓ}$ has also been investigated.

Physics Subject Headings (PhySH)

Article Text

References (34)

N. Cabibbo, Unitary Symmetry and Leptonic Decays, Phys. Rev. Lett. 10, 531 (1963).
M. Kobayashi and T. Maskawa, $C P$ violation in the renormalizable theory of weak interaction, Prog. Theor. Phys. 49, 652 (1973).
C. Patrignani et al. (Particle Data Group), Review of particle physics, Chin. Phys. C 40, 100001 (2016).
C. Bernard et al., The $\bar{B} \to D^{*} ℓ \bar{ν}$ form factor at zero recoil from three-flavor lattice QCD: A model independent determination of $| V_{c b} |$ , Phys. Rev. D 79, 014506 (2009).
H. Na, C. M. Bouchard, G. P. Lepage, C. Monahan, and J. Shigemitsu (HPQCD Collaboration), $B \to D l ν$ form factors at nonzero recoil and extraction of $| V_{c b} |$ , Phys. Rev. D 92, 054510 (2015); H. Na, C. M. Bouchard, G. P. Lepage, C. Monahan, and J. Shigemitsu (HPQCD Collaboration)Erratum, 93, 119906(E) (2016).
J. A. Bailey et al. (MILC Collaboration), $B \to D ℓ ν$ form factors at nonzero recoil and $| V_{c b} |$ from $2 + 1$ -flavor lattice QCD, Phys. Rev. D 92, 034506 (2015).
J. A. Bailey et al. (Fermilab Lattice and MILC Collaborations), $| V_{u b} |$ from $B \to π ℓ ν$ decays and ( $2 + 1$ )-flavor lattice QCD, Phys. Rev. D 92, 014024 (2015).
A. Khodjamirian, T. Mannel, and N. Offen, B-meson distribution amplitude from the $B \to π$ form-factor, Phys. Lett. B 620, 52 (2005).
P. Ball and R. Zwicky, $B_{d, s} \to ρ, ω, K^{*}, ϕ$ decay form-factors from light-cone sum rules revisited, Phys. Rev. D 71, 014029 (2005).
P. Ball and R. Zwicky, New results on $B \to π, K, η$ decay form-factors from light-cone sum rules, Phys. Rev. D 71, 014015 (2005).
S. Faller, T. Feldmann, A. Khodjamirian, T. Mannel, and D. van Dyk, Disentangling the decay observables in $B^{-} \to π^{+} π^{-} ℓ^{-} {\bar{ν}}_{ℓ}$ , Phys. Rev. D 89, 014015 (2014).
X. W. Kang, B. Kubis, C. Hanhart, and U. G. Meiner, $B_{l 4}$ decays and the extraction of $| V_{u b} |$ , Phys. Rev. D 89, 053015 (2014).
U. G. Meiner and W. Wang, $B_{s} \to K^{(*)} ℓ \bar{ν}$ , angular analysis, s-wave contributions and $| V_{u b} |$ , J. High Energy Phys. 01 (2014) 107.
C. Albertus, E. Hernndez, and J. Nieves, $B \to ρ$ semileptonic decays and $| V_{u b} |$ , Phys. Rev. D 90, 013017 (2014); Erratum, 90, 079906(E) (2014).
C. Hambrock and A. Khodjamirian, Form factors in ${\bar{B}}^{0} \to π π ℓ {\bar{ν}}_{ℓ}$ from QCD light-cone sum rules, Nucl. Phys. B905, 373 (2016).
S. Cheng, A. Khodjamirian, and J. Virto, $B \to π π$ form factors from light-cone sum rules with $B$ -meson distribution amplitudes, arXiv:1701.01633.
Y. J. Shi, W. Wang, and S. Zhao, Chiral dynamics, s-wave contributions and angular analysis in $D \to π π ℓ \bar{ν}$ , arXiv:1701.07571.
A. Bharucha, D. M. Straub, and R. Zwicky, $B \to V ℓ^{+} ℓ^{-}$ in the standard model from light-cone sum rules, J. High Energy Phys. 08 (2016) 098.
M. Ablikim et al. (BESIII Collaboration), Study of $D^{+} \to K^{-} π^{+} e^{+} ν_{e}$ , Phys. Rev. D 94, 032001 (2016).
J. Bijnens, G. Colangelo, G. Ecker, and J. Gasser, Semileptonic kaon decays, arXiv:hep-ph/9411311.
N. Cabibbo and A. Maksymowicz, Angular correlations in Ke-4 decays and determination of low-energy $π π$ phase shifts, Phys. Rev. 137, B438 (1965); Erratum, 168, 1926(E) (1968); A. Flores-Tlalpa, G. López Castro, and G. Sánchez Toledo, Radiative two-pion decay of the tau lepton, Phys. Rev. D 72, 113003 (2005).
Q. Chang, J. Zhu, X. L. Wang, J. F. Sun, and Y. L. Yang, Study of semileptonic ${\bar{B}}^{*} \to P ℓ {\bar{ν}}_{ℓ}$ decays, Nucl. Phys. B909, 921 (2016).
B. H. Behrens et al. (CLEO Collaboration), Measurement of $B \to ρ$ lepton neutrino decay and $| V_{u b} |$ , Phys. Rev. D 61, 052001 (2000).
P. del Amo Sanchez et al. (BABAR Collaboration), Study of $B \to π ℓ ν$ and $B \to ρ ℓ ν$ decays and determination of $| V_{u b} |$ , Phys. Rev. D 83, 032007 (2011).
A. Sibidanov et al. (Belle Collaboration), Study of exclusive $B \to X_{u} ℓ ν$ decays and extraction of $∥ V_{u b} ∥$ using full reconstruction tagging at the Belle experiment, Phys. Rev. D 88, 032005 (2013).
P. del Amo Sanchez et al. (BABAR Collaboration), Analysis of the $D^{+} \to K^{-} π^{+} e^{+} ν_{e}$ decay channel, Phys. Rev. D 83, 072001 (2011).
S. Dobbs et al. (CLEO Collaboration), First Measurement of the Form Factors in the Decays $D^{0} \to ρ^{-} e^{+} ν_{e}$ and $D^{+} \to ρ^{0} e^{+} ν_{e}$ , Phys. Rev. Lett. 110, 131802 (2013).
T. Hokuue et al. (Belle Collaboration), Measurements of branching fractions and $q^{2}$ distributions for $B \to π ℓ ν$ and $B \to ρ ℓ ν$ decays with $B \to D^{*} ℓ ν$ decay tagging, Phys. Lett. B 648, 139 (2007).
C. S. Kim, G. Lopez-Castro, S. L. Tostado, and A. Vicente, Remarks on the standard model predictions for $R (D)$ and $R (D^{*})$ , Phys. Rev. D 95, 013003 (2017).
W. M. Gibson and B. R. Pollard, Symmetry Principles in Elementary Particle Physics (Cambridge University Press, Cambridge, England, 1980).
F. Bernardoni, J. Bulava, M. Donnellan, and R. Sommer (ALPHA Collaboration), Precision lattice QCD computation of the $B^{*} B π$ coupling, Phys. Lett. B 740, 278 (2015).
L. Del Debbio, J. M Flynn, L. Lellouch, and J. Nieves (UKQCD Collaboration), Lattice constrained parametrizations of form-factors for semileptonic and rare radiative $B$ decays, Phys. Lett. B 416, 392 (1998).
M. Wirbel, B. Stech, and M. Bauer, Exclusive semileptonic decays of heavy mesons, Z. Phys. C 29, 637 (1985).
M. Bauer and M. Wirbel, Form-factor effects in exclusive $d$ and $B$ decays, Z. Phys. C 42, 671 (1989).

Physical Review D

Export citation

Export citation

Evaluation of CKM matrix elements from exclusive $P_{ℓ 4}$ decays

Abstract

Physics Subject Headings (PhySH)

Article Text

References (34)

Outline

Information

Filter

Filter

Article Lookup

Enter a citation

Evaluation of CKM matrix elements from exclusive Pℓ4 decays

Abstract

Physics Subject Headings (PhySH)

Article Text

References (34)

Evaluation of CKM matrix elements from exclusive $P_{ℓ 4}$ decays