{"ID":22964812,"CreatedAt":"2026-09-17T02:29:35.102872001Z","UpdatedAt":"2026-09-17T02:29:35.102872001Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2609.18890","arxiv_id":"2609.18890","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","abstract":"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 $q\\bar{q}$ 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 $\\langle ξ^n _{2;f_0(1500)} \\rangle |_μ$ and Gegenbauer moments $a_{n;f_0(1500)}(μ)$ at $μ_0=1~\\mathrm{GeV}$ and $μ_k= 3~\\mathrm{GeV}$ for $n=1,3,5$. Meanwhile, the $B_s\\to f_0(1500)$ 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 $f_{\\rm T}^{B_s f_0(1500)}(0)= 0.568^{ + 0.069}_{-0.065}$. 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 $B_s \\to f_0(1500)(\\to π^ + π^-)\\ell^ + \\ell^-$ and $B_s \\to f_0(1500)(\\to π^ + π^-)ν\\barν$. 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 $B_s\\to f_0(1500)(\\toπ^ + π^-)μ^ + μ^-$. We hope that our predictions can provide a useful theoretical reference for future experimental measurements and phenomenological research.","short_abstract":"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 adopt...","url_abs":"https://arxiv.org/abs/2609.18890","url_pdf":"https://arxiv.org/pdf/2609.18890v1","authors":"[\"Xue Zheng\",\"Hai-Bing Fu\",\"Dan-Dan Hu\",\"Jing-Kai Yang\",\"Jian-Qi Chen\",\"Wan-Bing Luo\"]","published":"2026-09-16T16:22:32Z","proceeding":"hep-ph","tasks":"[\"hep-ph\"]","methods":"[]","has_code":false}