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PreprintCC BY 4.0arXiv

Addressing the S-wave scalar f0(1500)-resonance in quasi-four-body FCNC rare Bs → f0(1500) (→ π+ π- ) ℓ+ ℓ- / νν̅ decays

  • Xue Zheng
  • Hai-Bing Fu
  • Dan-Dan Hu
  • Jing-Kai Yang
  • Jian-Qi Chen
  • Wan-Bing Luo
Open at sourcePDFDOICite

Abstract

The f0(1500) is a quite special resonance in the light scalar spectrum. Compared with other nearby resonance, it has an unexpectedly narrow decay width. Since its mass region overlaps strongly with f0(1370) and f0(980), physicists have long debated its internal structure. To explore this issue, this work adopted the conventional quark-antiquark qq̅ picture and investigated the behavior of the f0(1500)-resonance in quasi-four-body decay channels. Based on this, we constructed a twist-2 light-cone distribution amplitude(LCDA) schemes based on the light-cone harmonic oscillator model, and presented their moments ⟨ ξn 2;f0(1500) ⟩ |μ and Gegenbauer moments an;f0(1500)(μ) at μ0=1 GeV and μk= 3 GeV for n=1,3,5. Meanwhile, the Bs→ f0(1500) transition form factors (TFFs) are calculated by using the QCD light-cone sum rule. Then, we obtained the three TFFs at large recoil point, {\it i.e.,} f+ Bs f0(1500)(0)= 0.390−0.046 + 0.047, f-Bs f0(1500)(0)= −0.460−0.055 + 0.051, and fTBs f0(1500)(0)= 0.568 + 0.069−0.065. In addition, we extrapolated TFFs to the whole physical q2-region by using the simplified z(q2)-series expansion. Then we computed the branching fractions of the quasi-four-body rare decays Bs → f0(1500)(→ π+ π-)ℓ+ ℓ- and Bs → f0(1500)(→ π+ π-)νν̅. For comparison, we also present the results of the corresponding three-body decays obtained under the narrow-width approximation. Finally, we show the distribution of the double-differential decay width d2Γ/ds dq2 for the quasi-four-body decay Bs→ f0(1500)(→π+ π-)μ+ μ-. We hope that our predictions can provide a useful theoretical reference for future experimental measurements and phenomenological research.

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Cite

BibTeXRIS
BibTeX
@misc{zheng2026addressing,
  title = {{Addressing the $S$-wave scalar $f_0(1500)$-resonance in quasi-four-body FCNC rare $B_s \to f_0(1500) (\to π^+ π^- ) \ell^+ \ell^- / ν\bar ν$ decays}},
  author = {Xue Zheng and Hai-Bing Fu and Dan-Dan Hu and Jing-Kai Yang and Jian-Qi Chen and Wan-Bing Luo},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.18890},
  eprint = {2609.18890},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.18890},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Addressing the S-wave scalar f_0(1500)-resonance in quasi-four-body FCNC rare B_s → f_0(1500) (→ π^+ π^- ) ℓ^+ ℓ^- / νν̅ decays
AU  - Xue Zheng
AU  - Hai-Bing Fu
AU  - Dan-Dan Hu
AU  - Jing-Kai Yang
AU  - Jian-Qi Chen
AU  - Wan-Bing Luo
PY  - 2026
DA  - 2026/09/16
PB  - arXiv
DO  - 10.48550/arxiv.2609.18890
UR  - https://arxiv.org/abs/2609.18890
AB  - The f_0(1500) is a quite special resonance in the light scalar spectrum. Compared with other nearby resonance, it has an unexpectedly narrow decay width. Since its mass region overlaps strongly with f_0(1370) and f_0(980), physicists have long debated its internal structure. To explore this issue, this work adopted the conventional quark-antiquark qq̅ picture and investigated the behavior of the f_0(1500)-resonance in quasi-four-body decay channels. Based on this, we constructed a twist-2 light-cone distribution amplitude(LCDA) schemes based on the light-cone harmonic oscillator model, and presented their moments ⟨ ξ^n _2;f_0(1500) ⟩ |_μ and Gegenbauer moments a_n;f_0(1500)(μ) at μ_0=1 GeV and μ_k= 3 GeV for n=1,3,5. Meanwhile, the B_s→ f_0(1500) transition form factors (TFFs) are calculated by using the QCD light-cone sum rule. Then, we obtained the three TFFs at large recoil point, {\it i.e.,} f_+ ^B_s f_0(1500)(0)= 0.390_−0.046^ + 0.047, f_-^B_s f_0(1500)(0)= −0.460_−0.055^ + 0.051, and f_T^B_s f_0(1500)(0)= 0.568^ + 0.069_−0.065. In addition, we extrapolated TFFs to the whole physical q^2-region by using the simplified z(q^2)-series expansion. Then we computed the branching fractions of the quasi-four-body rare decays B_s → f_0(1500)(→ π^+ π^-)ℓ^+ ℓ^- and B_s → f_0(1500)(→ π^+ π^-)νν̅. For comparison, we also present the results of the corresponding three-body decays obtained under the narrow-width approximation. Finally, we show the distribution of the double-differential decay width d^2Γ/ds dq^2 for the quasi-four-body decay B_s→ f_0(1500)(→π^+ π^-)μ^+ μ^-. We hope that our predictions can provide a useful theoretical reference for future experimental measurements and phenomenological research.
ER  -