Bd,s0→f1f1 decays with f1(1285)−f1(1420) mixing in the perturbative QCD approach

Jiang, Zewen; Yao, De-Hua; Zou, Zhi-Tian; Liu, Xin; Li, Ying; Xiao, Zhen-Jun

doi:10.1103/PhysRevD.102.116015

$B_{d, s}^{0} \to f_{1} f_{1}$ decays with $f_{1} (1285) - f_{1} (1420)$ mixing in the perturbative QCD approach

Zewen Jiang (Department of Physics, Jiangsu Normal University, Xuzhou 221116, China) ; De-Hua Yao (Department of Physics, Jiangsu Normal University, Xuzhou 221116, China) ; Zhi-Tian Zou (Department of Physics, Yantai University, Yantai 264005, China) ; Xin Liu (Department of Physics, Jiangsu Normal University, Xuzhou 221116, China) ; Ying Li (Department of Physics, Yantai University, Yantai 264005, China) ; et al. - Show all 6 authors

We investigate the $B_{d, s}^{0} \to f_{1} f_{1}$ decays in the framework of perturbative QCD (PQCD) approach with a referenced value $ϕ_{f_{1}} \sim 24 °$ . Here, $f_{1}$ denotes the axial-vector mesons $f_{1} (1285)$ and $f_{1} (1420)$ with mixing angle $ϕ_{f_{1}}$ in the quark-flavor basis. The observables such as branching ratios, direct $C P$ violations, and polarization fractions of the $B_{s}^{0} \to f_{1} f_{1}$ decays are predicted for the first time. We find that (i) the almost pure penguin modes $B_{s}^{0} \to f_{1} f_{1}$ have large branching ratios in the order of $10^{- 6} \sim 10^{- 5}$ due to the Cabibbo-Kobayashi-Maskawa enhancement and generally constructive interferences between the amplitudes of $B_{s}^{0} \to f_{n} f_{s}$ and $B_{s}^{0} \to f_{s} f_{s}$ with $f_{n}$ and $f_{s}$ being the quark-flavor states of $f_{1}$ mesons. (ii) The observables receive important contributions from the weak annihilation diagrams in the PQCD approach. In particular, without the annihilation contributions, the $B_{s}^{0} \to f_{1} (1420) f_{1} (1420)$ branching ratio will decrease about 81% and its longitudinal polarization fraction will reduce around 43%. And (iii) the dependence of the $B_{d, s}^{0} \to f_{1} f_{1}$ decay rates on $ϕ_{f_{1}}$ exhibits some interesting line shapes, whose confirmations would be helpful to constrain the determination of $ϕ_{f_{1}}$ inversely. All the PQCD predictions await for the (near) future examinations at Large Hadron Collider beauty and/or Belle-II experiments to further understand the properties of the axial-vector mesons and the perturbative dynamics released from the considered decay modes.

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      "value": "We investigate the <math><mrow><msubsup><mrow><mi>B</mi></mrow><mrow><mi>d</mi><mo>,</mo><mi>s</mi></mrow><mrow><mn>0</mn></mrow></msubsup><mo>\u2192</mo><msub><mrow><mi>f</mi></mrow><mrow><mn>1</mn></mrow></msub><msub><mrow><mi>f</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></math> decays in the framework of perturbative QCD (PQCD) approach with a referenced value <math><mrow><msub><mrow><mi>\u03d5</mi></mrow><mrow><msub><mrow><mi>f</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></msub><mo>\u223c</mo><mn>24</mn><mi>\u00b0</mi></mrow></math>. Here, <math><msub><mi>f</mi><mn>1</mn></msub></math> denotes the axial-vector mesons <math><mrow><msub><mrow><mi>f</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><mn>1285</mn><mo>)</mo></mrow></math> and <math><mrow><msub><mrow><mi>f</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><mn>1420</mn><mo>)</mo></mrow></math> with mixing angle <math><mrow><msub><mrow><mi>\u03d5</mi></mrow><mrow><msub><mrow><mi>f</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></msub></mrow></math> in the quark-flavor basis. The observables such as branching ratios, direct <math><mrow><mi>C</mi><mi>P</mi></mrow></math> violations, and polarization fractions of the <math><mrow><msubsup><mrow><mi>B</mi></mrow><mrow><mi>s</mi></mrow><mrow><mn>0</mn></mrow></msubsup><mo>\u2192</mo><msub><mrow><mi>f</mi></mrow><mrow><mn>1</mn></mrow></msub><msub><mrow><mi>f</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></math> decays are predicted for the first time. We find that (i) the almost pure penguin modes <math><mrow><msubsup><mrow><mi>B</mi></mrow><mrow><mi>s</mi></mrow><mrow><mn>0</mn></mrow></msubsup><mo>\u2192</mo><msub><mrow><mi>f</mi></mrow><mrow><mn>1</mn></mrow></msub><msub><mrow><mi>f</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></math> have large branching ratios in the order of <math><mrow><msup><mrow><mn>10</mn></mrow><mrow><mo>\u2212</mo><mn>6</mn></mrow></msup><mo>\u223c</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>\u2212</mo><mn>5</mn></mrow></msup></mrow></math> due to the Cabibbo-Kobayashi-Maskawa enhancement and generally constructive interferences between the amplitudes of <math><mrow><msubsup><mrow><mi>B</mi></mrow><mrow><mi>s</mi></mrow><mrow><mn>0</mn></mrow></msubsup><mo>\u2192</mo><msub><mrow><mi>f</mi></mrow><mrow><mi>n</mi></mrow></msub><msub><mrow><mi>f</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow></math> and <math><mrow><msubsup><mrow><mi>B</mi></mrow><mrow><mi>s</mi></mrow><mrow><mn>0</mn></mrow></msubsup><mo>\u2192</mo><msub><mrow><mi>f</mi></mrow><mrow><mi>s</mi></mrow></msub><msub><mrow><mi>f</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow></math> with <math><msub><mi>f</mi><mi>n</mi></msub></math> and <math><msub><mi>f</mi><mi>s</mi></msub></math> being the quark-flavor states of <math><msub><mi>f</mi><mn>1</mn></msub></math> mesons. (ii) The observables receive important contributions from the weak annihilation diagrams in the PQCD approach. In particular, without the annihilation contributions, the <math><mrow><msubsup><mrow><mi>B</mi></mrow><mrow><mi>s</mi></mrow><mrow><mn>0</mn></mrow></msubsup><mo>\u2192</mo><msub><mrow><mi>f</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><mn>1420</mn><mo>)</mo><msub><mrow><mi>f</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><mn>1420</mn><mo>)</mo></mrow></math> branching ratio will decrease about 81% and its longitudinal polarization fraction will reduce around 43%. And (iii) the dependence of the <math><mrow><msubsup><mrow><mi>B</mi></mrow><mrow><mi>d</mi><mo>,</mo><mi>s</mi></mrow><mrow><mn>0</mn></mrow></msubsup><mo>\u2192</mo><msub><mrow><mi>f</mi></mrow><mrow><mn>1</mn></mrow></msub><msub><mrow><mi>f</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></math> decay rates on <math><msub><mi>\u03d5</mi><msub><mi>f</mi><mn>1</mn></msub></msub></math> exhibits some interesting line shapes, whose confirmations would be helpful to constrain the determination of <math><msub><mi>\u03d5</mi><msub><mi>f</mi><mn>1</mn></msub></msub></math> inversely. All the PQCD predictions await for the (near) future examinations at Large Hadron Collider beauty and/or Belle-II experiments to further understand the properties of the axial-vector mesons and the perturbative dynamics released from the considered decay modes."
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Published on:: 21 December 2020
Publisher:: APS
Published in:: Physical Review D , Volume 102 (2020)
Issue 11
DOI:: https://doi.org/10.1103/PhysRevD.102.116015
arXiv:: 2008.05366
Copyrights:: Published by the American Physical Society
Licence:: CC-BY-4.0

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