Abnormal isospin violation and $a_0-f_0$ mixing in the $D_s^{+}\to {\pi }^{+}{\pi }^0{a}_0(980)(f_0(980))$ reactions

Abstract

We have chosen the reactions $D_s^{+}\to {\pi }^{+}{\pi }^0{a}_0(980)(f_0(980))$ investigating the isospin violating channel $D_s^{+}\to {\pi }^{+}{\pi }^0{f}_0(980)$. The reaction was chosen because by varying the ${\pi }^0{a}_0(980)(f_0(980))$ invariant mass one goes through the peak of a triangle singularity emerging from $D_s^{+}\to {\pi }^{+}{\bar{K}}^{\ast }K$, followed by ${\bar{K}}^{\ast }\to \bar{K}{\pi }^0$ and the further merging of $K\bar{K}$ to produce the $a_0(980)$ or $f_0(980)$. We found that the amount of isospin violation had its peak precisely at the value of the ${\pi }^0{a}_0(980)(f_0(980))$ invariant mass where the singularity has its maximum, stressing the role of the triangle singularities as a factor to enhance the mixing of the $f_0(980)$ and $a_0(980)$ resonances. We calculate absolute rates for the reactions and show that they are within present measurable range. The measurement of these reactions would bring further information into the role of triangle singularities in isospin violation and the $a_0-f_0$ mixing in particular and shed further light into the nature of the low energy scalar mesons.

9pages, 6figures

References in corpus (16)

• A Discussion on Triangle Singularities in the ${\Lambda }_b\to J/\psi K^{-}p$ Reaction
• $B^0$ and $B_s^0$ decays into $J/\psi$ $f_0(980)$ and $J/\psi$ $f_0(500)$ and the nature of the scalar resonances
• On the nature of $a_1(1420)$
• $B_s\to f_0(980)$ form factors and $B_s$ decays into $f_0(980)$
• The low lying scalar resonances in the $D^0$ decays into $K_s^0$ and $f_0(500)$, $f_0(980)$, $a_0(980)$
• The "$a_1(1420)$" peak as the $\pi f_0(980)$ decay mode of the $a_1(1260)$
• $f_1(1285)$ decays into $a_0(980){\pi }^0$, $f_0(980){\pi }^0$ and isospin breaking
• Possibility of measuring a0(980)-f0(980) mixing from J/psi -> phi a0
• Investigation of a0-f0 mixing
• Role of a triangle singularity in the $\gamma p\to K^{+}\Lambda (1405)$ reaction
• Amplitude analysis of the ${\chi }_{c1}\to \eta {\pi }^{+}{\pi }^{-}$ decays
• Study a0(980)-f0(980) mixing from a0(980) -> f0(980) transition
• Predictions for ${\eta }_c\to \eta {\pi }^{+}{\pi }^{-}$ producing $f_0(500)$, $f_0(980)$ and $a_0(980)$
• Revising the $f_1(1420)$ resonance
• Triangle singularities in $B^{-}\to D^{\ast 0}{\pi }^{-}{\pi }^0\eta$ and $B^{-}\to D^{\ast 0}{\pi }^{-}{\pi }^{+}{\pi }^{-}$
• $f_2(1810)$ as a triangle singularity

Cited by in corpus (12)

• Triangle singularity in the $J/\psi \to K^{+}{K}^{-}{f}_0(980)(a_0(980))$ decays
• Triangle singularity in the $B^{-}\to K^{-}{\pi }^{0}X(3872)$ reaction and sensitivity to the $X(3872)$ mass
• Theoretical study of the $D^0\to K^{-}{\pi }^{+}\eta$ reaction
• Scalar resonances in the $D^{+}\to K^{-}{K}^{+}{K}^{+}$ decay
• The $D_s^{+}\to a_0(980)e^{+}{\nu }_e$ reaction and the $a_0(980)-f_0(980)$ mixing
• Strong isospin symmetry breaking in light scalar meson production
• Role of the triangle mechanism in the ${\Lambda }_b\to {\Lambda }_c{\pi }^{-}{f}_0(980)$ reaction
• Study of $a_0^0(980)$-$f_0(980)$ mixing from $a_0(1450)\to a_0^0(980)f_0(500)\to {\pi }^{+}{\pi }^{-}{f}_0(500)$
• The role of meson interactions in the $D_s^{+}\to {\pi }^{+}{\pi }^{+}{\pi }^{-}\eta$ decay
• The $D_s^{+}\to K^{+}{\pi }^{+}{\pi }^{-}$ reaction and the scalar $f_0(500)$, $f_0(980)$ and $K_0^{\ast }(700)$ resonances
• The role of triangle singularity in the decay process $D^0\to {\pi }^{+}{\pi }^{-}{f}_0(980),f_0\to {\pi }^{+}{\pi }^{-}$
• Triangle mechanism in the decay process $B_0\to J/\psi K^0{f}_0(980)(a_0(980))$