Study of the $B_s$ $\to$ $\varphi f_0(980)$ $\to$ $\varphi {\pi }^{+}{\pi }^{-}$ decay with perturbative QCD approach

Abstract

The rare cascade $B_s$ $\to$ $\varphi f_0(980)$ $\to$ $\varphi {\pi }^{+}{\pi }^{-}$ decay is studied with the perturbative QCD approach based on the formula for the quasi two-body decay, where the two-pion pair originates from the $S$-wave resonant $f_0(980)$ state. It is found that with the introduction of the nonperturbative two-pion distribution amplitudes and the Flatté parameterization of the scalar form factor for the $f_0(980)$ resonance, the branching ratio in the mass range 400 MeV $<$ $m({\pi }^{+}{\pi }^{-})$ $<$ 1600 MeV is ${\mathcal{B}}_{\mathrm{theo}}(B_s^0\to \varphi f_0(980)\to \varphi {\pi }^{+}{\pi }^{-})$ $=$ $[1.31_{-0.31}^{+0.40}(a_{\pi \pi }){}_{-0.16}^{+0.19}(m_b){}_{-0.09}^{+0.10}(\text{CKM})]\times 10^{-6}$, where the uncertainties come from the parameter $a_{\pi \pi }$ of the two-pion distribution amplitudes, the $b$ quark mass $m_b$, the Cabibbo-Kobayashi-Maskawa (CKM) factors, respectively. This result agrees with the recent LHCb measurement within uncertainties, ${\mathcal{B}}_{\exp }(B_s^0\to \varphi f_0(980)\to \varphi {\pi }^{+}{\pi }^{-})$ $=$ $(1.12\pm 0.16_{-0.08}^{+0.09}\pm 0.11)\times 10^{-6}$, where the errors are statistical, systematic and from the normalization, respectively.

arXiv comment27 pages, 2 figures

References in corpus (99)

• Weak Decays Beyond Leading Logarithms
• QCD Factorization for $B\to \pi \pi$ Decays: Strong Phases and CP Violation in the Heavy Quark Limit
• QCD factorization for exclusive, non-leptonic B meson decays: General arguments and the case of heavy-light final states
• QCD Factorization in B -> pi K, pi pi Decays and Extraction of Wolfenstein Parameters
• Penguin Enhancement and $B\to K\pi$ decays in perturbative QCD
• Fat penguins and imaginary penguins in perturbative QCD
• Branching Ratio and CP Violation of B to pi pi Decays in Perturbative QCD Approach
• Leading-power contributions to $B\to \pi ,\rho$ transition form factors
• Branching fractions, polarisation and asymmetries of B -> VV decays
• Hard exclusive electroproduction of two pions and their resonances
• Broken SU(3) Symmetry in Two-Body B Decays
• $B\to \pi \rho$, $\pi \omega$ Decays in Perturbative QCD Approach
• Factorization theorems, effective field theory, and nonleptonic heavy meson decays
• Three-Scale Factorization Theorem and Effective Field Theory
• Charmless Three-body Decays of B Mesons
• SU(3) Relations and the CP Asymmetries in B Decays to ${\eta }^{\prime }{K}_S$, $\varphi K_S$ and $K^{+}{K}^{-}{K}_S$
• Measurement of resonant and $CP$ components in ${\overline{B}}_s^0\to J/\psi {\pi }^{+}{\pi }^{-}$ decays
• CP violation and kaon-pion interactions in B --> K pi+ pi- decays
• Three-Body Non-Leptonic B Decays and QCD Factorization
• Branching Fractions and Direct CP Violation in Charmless Three-body Decays of B Mesons
• Three-body nonleptonic B decays in perturbative QCD
• Applicability of Perturbative QCD to $B\to D$ Decays
• Analysis of the resonant components in Bs->J/ψπ+π-
• Measurement of the resonant and CP components in ${\overline{B}}^0\to J/\psi {\pi }^{+}{\pi }^{-}$ decays
• QCD factorization for B -> PP
• Analysis of the resonant components in B0->J/ψpi+pi-
• Direct CP Violation in Charmless Three-body Decays of $B$ Mesons
• $S$-wave resonance contributions to the $B_{(s)}^0\to J/\psi {\pi }^{+}{\pi }^{-}$ and $B_s\to {\pi }^{+}{\pi }^{-}{\mu }^{+}{\mu }^{-}$ decays
• Quasi-two-body decays $B\to K\rho \to K\pi \pi$ in perturbative QCD approach
• Rescattering and chiral dynamics in B\to ρπdecay
• CP violation in $B^{\pm }\to {\pi }^{\pm }{\pi }^{+}{\pi }^{-}$ in the region with low invariant mass of one ${\pi }^{+}{\pi }^{-}$ pair
• CP-violating asymmetries in B^0 decays to K^+K^-K_{S(L)}^0 and K_S^0K_S^0K_{S(L)}^0
• A model-independent analysis of final-state interactions in \bar B_{d/s}^0 --> J/psi pi pi
• Interference between f0(980) and rho(770) resonances in B --> pion-pion-kaon decays
• Charmless Three-Body Baryonic B Decays
• CP asymmetries in three-body B+- decays to charged pions and kaons
• Direct CP asymmetries of three-body $B$ decays in perturbative QCD
• Nonresonant Three-body Decays of D and B Mesons
• Long-distance effects and final state interactions in B to pion pion K and B to K anti-K K decays
• Analysis of the Decays B-> ππand πK with QCD Factorization in the Heavy Quark Limit
• Quasi-two-body decays $B_{(s)}\to P\rho \to P\pi \pi$ in perturbative QCD approach
• Symmetry relations in charmless B->PPP decays
• I-spin, U-spin, and penguin dominance in $B\to KK\bar{K}$
• Vector-pseudoscalar two-meson distribution amplitudes in three-body $B$ meson decays
• U-spin breaking in CP asymmetries in B decays
• New Bounds On The CKM Matrix From B -> K pi pi Dalitz Plot Analyses
• S-, P- and D-wave final state interactions and CP violation in B+- --> pi+- pi-+ pi+- decays
• SU(3) Breaking in Charmless B Decays
• Comprehensive Study of ${\overline{B}}^0\to K^0({\overline{K}}^0)K^{\mp }{\pi }^{\pm }$ Decays in the Factorization Approach
• U-spin analysis of CP violation in $B^{-}$ decays into three charged light pseudoscalar mesons
• Understanding $B\to D^{\ast -}N\bar{N}$ and Its Implications
• Improved method for CKM constraints in charmless three-body B and B_s decays
• B->rho pi decays, resonant and nonresonant contributions
• CP Violation in Multibody $B$ Decays from QCD Factorization
• Parametrizations of three-body hadronic $B$- and $D$-decay amplitudes in terms of analytic and unitary meson-meson form factors
• Charmless Three-body Decays of B_s Mesons
• The S-wave resonance contributions in the $B_s^0$ decays into $\psi (2S,3S)$ plus pion pair
• NLO corrections and contribution of a tensor gluon operator to the process ${\gamma }^{\ast }\gamma \to \pi \pi$
• The Nonresonant Cabibbo Suppressed Decay $B^{\pm }\to {\pi }^{+}{\pi }^{-}{\pi }^{\pm }$ and Signal for CP Violation
• Charmless B -> PPP Decays: the Fully-Symmetric Final State
• Infrared Divergence and Twist-3 Distribution Amplitudes in QCD Factorization For $B\to PP$
• The CP violating asymmetry in $B^{\pm }\to M\bar{M}{\pi }^{\pm }$ decays
• The penguin operators in nonresonant $B^{-}\to M\bar{M}{\pi }^{-}$ $(M={\pi }^{-},K^{-},K^0)$ decays
• Quasi-two-body decays $B_{(s)}\to K^{\ast }(892)h\to K\pi h$ in perturbative QCD approach
• Large SU(3) breaking effects and CP violation in $B^{+}$ decays into three charged SU(3) octet pseudoscalar mesons
• Quasi-two-body decays $B_{(s)}\to P{\rho }^{\prime }(1450),P{\rho }^{\prime \prime }(1700)\to P\pi \pi$ in the perturbative QCD approach
• Study of $B_c^{-}$ $\to$ $J/\psi {\pi }^{-}$, ${\eta }_c{\pi }^{-}$ Decays with QCD Factorization
• The $S$-wave resonance contributions to the three-body decays $B_{(s)}^0\to {\eta }_c{f}_0(X)\to {\eta }_c{\pi }^{+}{\pi }^{-}$ in perturbative QCD approach
• Diagrammatic Analysis of Charmless Three-Body B Decays
• Observation of the decay $B_s^0\to \varphi {\pi }^{+}{\pi }^{-}$ and evidence for $B^0\to \varphi {\pi }^{+}{\pi }^{-}$
• Measuring B -> rho pi decays and the unitarity angle alpha
• Final state interactions in B+- to K+ K- K+- decays
• The quasi-two-body decays $B_{(s)}\to (D_{(s)},{\bar{D}}_{(s)})\rho \to (D_{(s)},{\bar{D}}_{(s)})\pi \pi$ in the perturbative QCD factorization approach
• CP violation in the partial width asymmetries for B^- -> pi^+ pi^- K^- and B^- -> K^+ K^- K^- decays
• Quasi-two-body decays $B_{(s)}\to P{f}_2(1270)\to P\pi \pi$ in the perturbative QCD approach
• Direct CP Violation in $B\to {\pi }^{+}{\pi }^{-}\pi$: Determination of $\alpha$ without discrete ambiguity
• Evidence for Factorization in Three-body B --> D(*) K- K0 Decays
• Measuring gamma with B -> K pi pi and B -> K K Kbar Decays
• K* resonance effects on direct CP violation in B -> pi pi K
• Extraction of the CP-violating phase $\gamma$ using $B\to K\pi \pi$ and $B\to KK\bar{K}$ decays
• Measuring gamma in B -> K pi pi Decays
• Quasi-two-body decays $B\to {\eta }_c(1S,2S)[\rho (770),\rho (1450),\rho (1700)\to ]\pi \pi$ in the perturbative QCD approach
• Direct CP violation for ${\bar{B}}_s^0\to K^0{\pi }^{+}{\pi }^{-}$ decay in QCD factorization
• Study of ${\rm Y}(nS)$ $\to$ $B_{c}P$ decays with perturbative QCD approach
• Direct CP Violation, Branching Ratios and Form Factors $B\to \pi$, $B\to K$ in $B$ Decays
• Weak Phase gamma Using Isospin Analysis and Time Dependent Asymmetry in B_d -> K_s pi^+ pi^-
• CP violating phase $\gamma$ and the partial widths asymmetry in $B^{-}\to {\pi }^{+}{\pi }^{-}{K}^{-}$ and $B^{-}\to K^{+}{K}^{-}{K}^{-}$ decays
• Dalitz-plot dependence of CP asymmetry in B+- --> K+- K+ K- decays
• ${\rm Y}(1S)$ $\to$ $B_c\pi$, $B_{c}K$ decays with perturbative QCD approach
• Final state hadronic interactions and non-resonant $B^{\pm }\to K^{\pm }{\pi }^{+}{\pi }^{-}$ decays
• $CP$ violation induced by the double resonance for pure annihilation decay process in Perturbative QCD
• Analysis of the nonleptonic charmonium modes $B_s^0\to J/\psi f_2^{\prime }(1525)$ and $B_s^0\to J/\psi K^{+}{K}^{-}$
• Charmless 3-body B Decays: Resonant and Nonresonant Contributions
• $CP$ violation for $B_c^{+}\to D_{(s)}^{+}{\pi }^{+}{\pi }^{-}$ in Perturbative QCD
• The B^- -> phi phi K^- decay rate with phi phi invariant mass below charm treshold
• Evidence for Factorization in Three-body $\bar{B}\to D^{(\ast )}{K}^{-}{K}^0$ Decays
• Extraction of Axial Form Factors from Bbar0 --> D+ K- K{*0} Decay
• Study of the ${\bar{B}}_q^{\ast }$ $\to$ $DM$ decays with perturbative QCD approach
• Three-Body $B_{(s)}^0$ to $\varphi {\pi }^{+}{\pi }^{-}$ Decays

Cited by in corpus (8)

• Four-body decays $B_{(s)}\to (K\pi {)}_{S/P}(K\pi {)}_{S/P}$ in the perturbative QCD approach
• Study of $B_{(s)}\to (\pi \pi )(K\pi )$ decays in the perturbative QCD approach
• Quasi-two-body $B_{(s)}\to V\pi \pi$ Decays with Resonance $f_0(980)$ in PQCD Approach
• Study of $B_{u,d,s}\to K_0^{\ast }(1430)P$ and $K_0^{\ast }(1430)V$ decays within QCD factorization
• Global determination of two-meson distribution amplitudes from three-body $B$ decays in the perturbative QCD approach
• Resonant contributions to three-body $B_{(s)}\to [D^{(\ast )},{\bar{D}}^{(\ast )}]K^{+}{K}^{-}$ decays in the perturbative QCD approach
• Investigating $B_s$ three-body decays to scalar mesons in perturbative QCD approach
• Study $B_{(s)}^0$ decays into $\varphi$ and a scalar or vector meson