Letter
Open Access

Model-independent description of $B \to D π ℓ ν$ decays

Erik J. Gustafson ¹, Florian Herren ^1,2, Ruth S. Van de Water ¹, Raynette van Tonder ^3,4, and Michael L. Wagman¹

¹Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
²Physics Institute, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
³Department of Physics, McGill University, 3600 rue University, Montréal, Québec H3A 2T8, Canada
⁴Institut für Experimentelle Teilchenphysik, Karlsruhe Institute of Technology (KIT), D-76131 Karlsruhe, Germany

Phys. Rev. D 110, L091502 – Published 18 November, 2024

DOI: https://doi.org/10.1103/PhysRevD.110.L091502

Abstract

We introduce a new parametrization of $B \to D π ℓ ν$ form factors using a partial-wave expansion and derive bounds on the series coefficients using analyticity and unitarity. This is the first generalization of the model-independent formalism developed by Boyd, Grinstein, and Lebed for $B \to D ℓ ν$ to semileptonic decays with multihadron final states, and enables data-driven form-factor determinations with robust, systematically improvable uncertainties. Using this formalism, we extract the form-factor parameters for $B \to D_{2}^{*} (\to D π) ℓ ν$ decays in a model-independent way from fits of data from the Belle Experiment. We find that the semileptonic data are compatible with the presence of two poles in the $D π$ S-wave channel, which is the scenario preferred by nonleptonic decays and unitarized chiral perturbation theory.

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References (77)

J. Charles, A. Hocker, H. Lacker, S. Laplace, F. R. Le Diberder, J. Malcles, J. Ocariz, M. Pivk, and L. Roos (CKMfitter Group), $C P$ violation and the CKM matrix: Assessing the impact of the asymmetric $B$ factories, Eur. Phys. J. C 41, 1 (2005).
Y. S. Amhis et al. (HFLAV Collaboration), Averages of b-hadron, c-hadron, and $τ$ -lepton properties as of 2018, Eur. Phys. J. C 81, 226 (2021).
M. Bona et al. (UTfit Collaboration), New UTfit analysis of the unitarity triangle in the Cabibbo-Kobayashi-Maskawa scheme, Rend. Lincei Sci. Fis. Nat. 34, 37 (2023).
A. Di Canto and S. Meinel, Weak decays of $b$ and $c$ quarks, arXiv:2208.05403.
M. Artuso et al., Report of the frontier for rare processes and precision measurements, arXiv:2210.04765.
R. L. Workman et al. (Particle Data Group), Review of particle physics, Prog. Theor. Exp. Phys. 2022, 083C01 (2022).
R. van Tonder et al. (Belle Collaboration), Measurements of $q^{2}$ moments of inclusive $B \to X_{c} ℓ^{+} ν_{ℓ}$ decays with hadronic tagging, Phys. Rev. D 104, 112011 (2021).
C. Schwanda et al. (Belle Collaboration), Moments of the hadronic invariant mass spectrum in $B \to X_{c} ℓ ν$ decays at BELLE, Phys. Rev. D 75, 032005 (2007).
P. Urquijo et al. (Belle Collaboration), Moments of the electron energy spectrum and partial branching fraction of B— $>$ X(c) e nu decays at Belle, Phys. Rev. D 75, 032001 (2007).
L. Cao et al. (Belle Collaboration), Measurements of partial branching fractions of inclusive $B \to X_{u} ℓ^{+} ν_{ℓ}$ decays with hadronic tagging, Phys. Rev. D 104, 012008 (2021).
F. Abudinén et al. (Belle-II Collaboration), Measurement of lepton mass squared moments in $B \to X_{c} ℓ {\bar{ν}}_{ℓ}$ decays with the Belle II experiment, Phys. Rev. D 107, 072002 (2023).
M. Feindt, F. Keller, M. Kreps, T. Kuhr, S. Neubauer, D. Zander, and A. Zupanc, A hierarchical NeuroBayes-based algorithm for full reconstruction of B mesons at B factories, Nucl. Instrum. Methods Phys. Res., Sect. A 654, 432 (2011).
T. Keck et al., The full event interpretation: An exclusive tagging algorithm for the Belle II experiment, Comput. Software Big Sci. 3, 6 (2019).
F. Abudinén et al. (Belle-II Collaboration), A calibration of the Belle II hadronic tag-side reconstruction algorithm with $B \to X ℓ ν$ decays, arXiv:2008.06096.
F. Abudinén et al. (Belle-II Collaboration), Study of exclusive $B \to π e^{+} ν_{e}$ decays with hadronic full-event-interpretation tagging in $189.3 {fb}^{- 1}$ of Belle II data, arXiv:2206.08102.
F. Abudinén et al. (Belle II Collaboration), Measurement of the $B^{0} \to D^{* -} ℓ^{+} ν_{ℓ}$ branching ratio and $| V_{c b} |$ with a fully reconstructed accompanying $B$ meson in 2019-2021 Belle II data, arXiv:2301.04716.
M. T. Prim et al. (Belle Collaboration), Measurement of differential distributions of $B \to D^{*} ℓ {\bar{ν}}_{ℓ}$ and implications on $| V_{c b} |$ , Phys. Rev. D 108, 012002 (2023).
I. Adachi et al. (Belle-II Collaboration), Evidence for $B^{+} \to K^{+} ν \bar{ν}$ Decays, Phys. Rev. D 109, 112006 (2024).
I. Adachi et al. (Belle-II Collaboration), First measurement of $R (X_{τ / ℓ})$ as an inclusive test of the $b \to c τ ν$ anomaly, Phys. Rev. Lett. 132, 211804 (2024).
R. Aaij et al. (LHCb Collaboration), Test of lepton flavor universality using $B_{0} \to D^{* -} τ^{+} ν_{τ}$ decays with hadronic $τ$ channels, Phys. Rev. D 108, 012018 (2023).
Measurement of the ratios of branching fractions $R (D^{*})$ and $R (D^{0})$ , Phys. Rev. Lett. 131, 111802 (2023).
A. K. Leibovich, Z. Ligeti, I. W. Stewart, and M. B. Wise, Predictions for $B \to D_{1} (2420) ℓ \bar{ν}$ and $B \to D_{2}^{*} (2460) ℓ \bar{ν}$ at order $Λ_{QCD} / m_{c, b}$ , Phys. Rev. Lett. 78, 3995 (1997).
A. K. Leibovich, Z. Ligeti, I. W. Stewart, and M. B. Wise, Semileptonic B decays to excited charmed mesons, Phys. Rev. D 57, 308 (1998).
F. U. Bernlochner and Z. Ligeti, Semileptonic $B_{(s)}$ decays to excited charmed mesons with $e$ , $μ$ , $τ$ and searching for new physics with $R (D^{* *})$ , Phys. Rev. D 95, 014022 (2017).
F. U. Bernlochner, Z. Ligeti, and D. J. Robinson, Model independent analysis of semileptonic $B$ decays to $D^{* *}$ for arbitrary new physics, Phys. Rev. D 97, 075011 (2018).
M. Albaladejo, P. Fernandez-Soler, F.-K. Guo, and J. Nieves, Two-pole structure of the $D_{0}^{*} (2400)$ , Phys. Lett. B 767, 465 (2017).
M.-L. Du, M. Albaladejo, P. Fernández-Soler, F.-K. Guo, C. Hanhart, U.-G. Meißner, J. Nieves, and D.-L. Yao, Towards a new paradigm for heavy-light meson spectroscopy, Phys. Rev. D 98, 094018 (2018).
F.-K. Guo, C. Hanhart, U.-G. Meißner, Q. Wang, Q. Zhao, and B.-S. Zou, Hadronic molecules, Rev. Mod. Phys. 90, 015004 (2018); 94, 029901(E) (2022).
G. Moir, M. Peardon, S. M. Ryan, C. E. Thomas, and D. J. Wilson, Coupled-channel $D π$ , $D η$ and $D_{s} \bar{K}$ scattering from lattice QCD, J. High Energy Phys. 10 (2016) 011.
L. Gayer, N. Lang, S. M. Ryan, D. Tims, C. E. Thomas, and D. J. Wilson (Hadron Spectrum Collaboration), Isospin- $1 / 2$ D $π$ scattering and the lightest $D_{0}^{*}$ resonance from lattice QCD, J. High Energy Phys. 07 (2021) 123.
H. Yan, C. Liu, L. Liu, Y. Meng, and H. Xing, Isospin- $\frac{1}{2} D π$ scattering and the $D_{0}^{*}$ resonance, Proc. Sci. LATTICE2023 (2024) 055 [arXiv:2312.01078].
M.-L. Du, F.-K. Guo, C. Hanhart, B. Kubis, and U.-G. Meißner, Where is the lightest charmed scalar meson?, Phys. Rev. Lett. 126, 192001 (2021).
R. Aaij et al. (LHCb Collaboration), Amplitude analysis of $B^{-} \to D^{+} π^{-} π^{-}$ decays, Phys. Rev. D 94, 072001 (2016).
A. Le Yaouanc, J.-P. Leroy, and P. Roudeau, Model for nonleptonic and semileptonic decays by ${\bar{B}}^{0} \to D^{* *}$ transitions with $BR (j = 1 / 2) ≪ BR (j = 3 / 2)$ using the Leibovich-Ligeti-Stewart-Wise scheme, Phys. Rev. D 105, 013004 (2022).
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. Meißner, $B_{l 4}$ decays and the extraction of $| V_{u b} |$ , Phys. Rev. D 89, 053015 (2014).
M. Wirbel, B. Stech, and M. Bauer, Exclusive semileptonic decays of heavy mesons, Z. Phys. C 29, 637 (1985).
R. Mandal, Angular analysis of $\bar{B} \to D_{2}^{*} (\to D π) ℓ \bar{ν}$ decay and new physics, Phys. Rev. D 101, 033007 (2020).
See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevD.110.L091502 for an extended discussion of the technical details.
J. Grigo, J. Hoff, P. Marquard, and M. Steinhauser, Moments of heavy quark correlators with two masses: Exact mass dependence to three loops, Nucl. Phys. B864, 580 (2012).
G. Martinelli, S. Simula, and L. Vittorio, Constraints for the semileptonic $B \to D (*)$ form factors from lattice QCD simulations of two-point correlation functions, Phys. Rev. D 104, 094512 (2021).
A. Melis, F. Sanfilippo, and S. Simula, Hadronic susceptibilities for b to c transitions from two point correlation functions, Proc. Sci. LATTICE2023 (2024) 243 [arXiv:2401.03920].
K. M. Watson, Some general relations between the photoproduction and scattering of pi mesons, Phys. Rev. 95, 228 (1954).
A. B. Migdal, Bremsstrahlung and pair production in condensed media at high-energies, Phys. Rev. 103, 1811 (1956).
Y.-J. Shi, C.-Y. Seng, F.-K. Guo, B. Kubis, U.-G. Meißner, and W. Wang, Two-meson form factors in unitarized chiral perturbation theory, J. High Energy Phys. 04 (2021) 086.
U.-G. Meißner and W. Wang, Generalized heavy-to-light form factors in light-cone sum rules, Phys. Lett. B 730, 336 (2014).
L. Leskovec, S. Meinel, M. Petschlies, J. Negele, S. Paul, A. Pochinsky, and G. Rendon, A lattice QCD study of the $B \to π π ℓ \bar{ν}$ transition, Proc. Sci. LATTICE2022 (2023) 416 [arXiv:2212.08833].
C. G. Boyd, B. Grinstein, and R. F. Lebed, Model independent extraction of —V(cb)— using dispersion relations, Phys. Lett. B 353, 306 (1995).
C. G. Boyd, B. Grinstein, and R. F. Lebed, Model independent determinations of anti-B— $>$ D (lepton), D* (lepton) anti-neutrino form-factors, Nucl. Phys. B461, 493 (1996).
C. G. Boyd, B. Grinstein, and R. F. Lebed, Precision corrections to dispersive bounds on form-factors, Phys. Rev. D 56, 6895 (1997).
N. Gubernari, D. van Dyk, and J. Virto, Non-local matrix elements in $B_{(s)} \to {K^{(*)} . ϕ} ℓ^{+} ℓ^{-}$ , J. High Energy Phys. 02 (2021) 088.
N. Gubernari, M. Reboud, D. van Dyk, and J. Virto, Improved theory predictions and global analysis of exclusive $b \to s μ^{+} μ^{-}$ processes, J. High Energy Phys. 09 (2022) 133.
T. Blake, S. Meinel, M. Rahimi, and D. van Dyk, Dispersive bounds for local form factors in $Λ b \to Λ$ transitions, Phys. Rev. D 108, 094509 (2023).
J. M. Flynn, A. Jüttner, and J. T. Tsang, Bayesian inference for form-factor fits regulated by unitarity and analyticity, J. High Energy Phys. 12 (2023) 175.
W. Rudin, Real and Complex Analysis, 3rd ed., McGraw-Hill Series in Higher Mathematics (McGraw-Hill, New York, NY, 1987).
R. Omnes, On the solution of certain singular integral equations of quantum field theory, Nuovo Cimento 8, 316 (1958).
N. I. Muskhelishvili, Singular Integral Equations: Boundary Problems of Function Theory and Their Application to Mathematical Physics (Wolters-Noordhoff, Groningen, 1953).
B. Moussallam, N(f) dependence of the quark condensate from a chiral sum rule, Eur. Phys. J. C 14, 111 (2000).
F.-K. Guo, C. Hanhart, and U.-G. Meissner, Interactions between heavy mesons and Goldstone bosons from chiral dynamics, Eur. Phys. J. A 40, 171 (2009).
L. Liu, K. Orginos, F.-K. Guo, C. Hanhart, and U.-G. Meissner, Interactions of charmed mesons with light pseudoscalar mesons from lattice QCD and implications on the nature of the $D_{s 0}^{*} (2317)$ , Phys. Rev. D 87, 014508 (2013).
D. Liventsev et al. (Belle Collaboration), Study of B– $>$ D**lnu with full reconstruction tagging, Phys. Rev. D 77, 091503 (2008).
G. P. Lepage, B. Clark, C. T. H. Davies, K. Hornbostel, P. B. Mackenzie, C. Morningstar, and H. Trottier (HPQCD Collaboration), Constrained curve fitting, Nucl. Phys. B, Proc. Suppl. 106, 12 (2002).
K. Hornbostel, G. P. Lepage, C. T. H. Davies, R. J. Dowdall, H. Na, and J. Shigemitsu, Fast fits for lattice QCD correlators, Phys. Rev. D 85, 031504 (2012).
M. Albaladejo (private communication).
A. Bazavov et al. (Fermilab Lattice, MILC, Fermilab Lattice, MILC Collaborations), Semileptonic form factors for $B \to D^{*} ℓ ν$ at nonzero recoil from $2 + 1$ -flavor lattice QCD: Fermilab Lattice and MILC Collaborations, Eur. Phys. J. C 82, 1141 (2022); 83, 21(E) (2023).
D. Bigi and P. Gambino, Revisiting $B \to D ℓ ν$ , Phys. Rev. D 94, 094008 (2016).
D. Bigi, P. Gambino, and S. Schacht, A fresh look at the determination of $| V_{c b} |$ from $B \to D^{*} ℓ ν$ , Phys. Lett. B 769, 441 (2017).
F. Meier et al. (Belle Collaboration), First observation of $B \to {\bar{D}}_{1} (\to \bar{D} π^{+} π^{-}) ℓ^{+} ν_{ℓ}$ and measurement of the $B \to {\bar{D}}^{(*)} π ℓ^{+} ν_{ℓ}$ and $B \to {\bar{D}}^{(*)} π^{+} π^{-} ℓ^{+} ν_{ℓ}$ branching fractions with hadronic tagging at Belle, Phys. Rev. D 107, 092003 (2023).
A. Le Yaouanc, J.-P. Leroy, and P. Roudeau, Large off-shell effects in the ${\bar{D}}^{*}$ contribution to $B \to \bar{D} π π$ and $B \to \bar{D} π \bar{ℓ} ν_{ℓ}$ decays., Phys. Rev. D 99, 073010 (2019).
J. M. Blatt and V. F. Weisskopf, Theoretical Nuclear Physics (Springer, New York, 1952).
F. Von Hippel and C. Quigg, Centrifugal-barrier effects in resonance partial decay widths, shapes, and production amplitudes, Phys. Rev. D 5, 624 (1972).
T. D. Cohen, H. Lamm, and R. F. Lebed, Precision model-independent bounds from global analysis of $b \to c ℓ ν$ form factors, Phys. Rev. D 100, 094503 (2019).
F. Abudinén et al. (Belle-II Collaboration), Reconstruction of $B \to ρ ℓ ν_{ℓ}$ decays identified using hadronic decays of the recoil $B$ meson in 2019–2021 Belle II data, arXiv:2211.15270.
B. Aubert et al. (BABAR Collaboration), A measurement of the branching fractions of exclusive $\bar{B} \to D^{(*)}$ ( $π$ ) $ℓ^{-} {\bar{ν}}_{ℓ}$ decays in events with a fully reconstructed $B$ meson, Phys. Rev. Lett. 100, 151802 (2008).
N. Gubernari, A. Khodjamirian, R. Mandal, and T. Mannel, $B \to D_{0}^{*}$ and $B_{s} \to D_{s 0}^{*}$ form factors from QCD light-cone sum rules, J. High Energy Phys. 12 (2023) 015.
S. Acharya et al. (ALICE Collaboration), First study of the two-body scattering involving charm hadrons, Phys. Rev. D 106, 052010 (2022).
M. Albaladejo, J. Nieves, and E. Ruiz-Arriola, Femtoscopic signatures of the lightest S-wave scalar open-charm mesons, Phys. Rev. D 108, 014020 (2023).

Phys. Rev. D 110, L091502– Published 18 November, 2024

Vol. 110, Iss. 9 — 1 November 2024

Received 20 December 2023
Accepted 18 October 2024

DOI: https://doi.org/10.1103/PhysRevD.110.L091502

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

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Model-independent description of $B \to D π ℓ ν$ decays

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Model-independent description of B→Dπℓν decays

Abstract

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (77)

Model-independent description of $B \to D π ℓ ν$ decays