Semileptonic decays $D\to {\pi }^{+}{\pi }^{-}{e}^{+}{\nu }_e$ and $D_s\to {\pi }^{+}{\pi }^{-}{e}^{+}{\nu }_e$ as the probe of constituent quark-antiquark pairs in the light scalar mesons

Abstract

Decays $D\to {\pi }^{+}{\pi }^{-}{e}^{+}{\nu }_e$ and $D_s\to {\pi }^{+}{\pi }^{-}{e}^{+}{\nu }_e$ serve as probes that check the existence of constituent $q\bar{q}$ components in the wave functions of scalar mesons decaying into ${\pi }^{+}{\pi }^{-}$. There exists a great deal of concrete evidence in favor of the exotic four-quark nature of light scalars. At the same time, the further expansion of the area of the $q^2{\bar{q}}^2$ model validity for light scalars on ever new processes seems extremely interesting and important. We analyze the BESIII and CLEO data on the decays $D^{+}\to {\pi }^{+}{\pi }^{-}{e}^{+}{\nu }_e$ and $D_s^{+}\to {\pi }^{+}{\pi }^{-}{e}^{+}{\nu }_e$ and show that the results of these experiments together can be interpreted in favor of the four-quark nature of light scalar mesons $\sigma (500)$ and $f_0(980)$. Our approach can also be applied to the description of other similar decays involving light scalars.

8 pages, 8 figures; v2: published version, clarifications and references added

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• Amplitude analysis of e+e- => Y(nS)pi+pi- at sqrt(s)=10.865 GeV
• Lightest scalar in the SU_L(2)*SU_R(2) linear σmodel
• Isospin mixing in the nucleon and 4He and the nucleon strange electric form factor
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Cited by in corpus (14)

• Evidence of the four-quark nature of $f_0(980)$ and $f_0(500)$
• Hadronic three-body D decays mediated by scalar resonances
• Scalar resonances in the $D^{+}\to K^{-}{K}^{+}{K}^{+}$ decay
• Semileptonic decays $D\to \eta \pi e^{+}{\nu }_e$ in the $a_0(980)$ region
• Study of the $f_0(980)$ and $f_0(500)$ Scalar Mesons through the Decay $D_s^{+}\to {\pi }^{+}{\pi }^{-}{e}^{+}{\nu }_e$
• Study of light scalar mesons through $D_s^{+}\to {\pi }^0{\pi }^0{e}^{+}{\nu }_e$ and $K_S^0{K}_S^0{e}^{+}{\nu }_e$ decays
• Four-body Semileptonic Charm Decays $D\to P_1{P}_2{\ell }^{+}{\nu }_{\ell }$ Based on SU(3) Flavor Analysis
• Study of $a_0^0(980)$-$f_0(980)$ mixing from $a_0(1450)\to a_0^0(980)f_0(500)\to {\pi }^{+}{\pi }^{-}{f}_0(500)$
• Observation of $D^{+}\to f_0(500){\mu }^{+}{\nu }_{\mu }$ and study of $D^{+}\to {\pi }^{+}{\pi }^{-}{\ell }^{+}{\nu }_{\ell }$ decay dynamics
• Testing the light scalar meson as a non-$q\bar{q}$ state in semileptonic $D$ decays
• The $D_s^{+}\to K^{+}{\pi }^{+}{\pi }^{-}$ reaction and the scalar $f_0(500)$, $f_0(980)$ and $K_0^{\ast }(700)$ resonances
• Phenomenological description of the ${\pi }^{-}{\pi }^{+}$ $S$-waves in $D^{+}\to {\pi }^{-}{\pi }^{+}{\pi }^{+}$ and $D_s^{+}\to {\pi }^{-}{\pi }^{+}{\pi }^{+}$ decays: The problem of phases
• Study of the light scalar $a_0(980)$ through the decay $D^0\to a_0(980{)}^{-}{e}^{+}{\nu }_e$ with $a_0(980{)}^{-}\to \eta {\pi }^{-}$
• Transition form factors for $D/B$ to $a_0(980)$ from light-cone QCD sum rules