First measurements of the absolute branching fraction of ${\Lambda }_{c}\left(2625{\right)}^{+}\to {\Lambda }_{c}^{+}{\pi }^{+}{\pi }^{-}$ and upper limit on ${\Lambda }_{c}\left(2595{\right)}^{+}\to {\Lambda }_{c}^{+}{\pi }^{+}{\pi }^{-}$

The absolute branching fraction of the decay ${\Lambda }_{c}\left(2625{\right)}^{+}\to {\Lambda }_{c}^{+}{\pi }^{+}{\pi }^{-}$ is measured for the first time to be $\left(50.2±{5.7}_{\mathrm{stat}}±{3.5}_{\mathrm{syst}}\right)%$ with $368.48\text{}\text{}{\mathrm{pb}}^{-1}$ of ${e}^{+}{e}^{-}$ collision data collected by the BESIII detector at the center-of-mass energies of $\sqrt{s}=4.918$ and 4.950 GeV. Although the central value of the result is lower than the theoretical prediction of 67%, obtained from isospin symmetry, they are consistent taking the uncertainties into account. This is the first absolute branching fraction measurement for ${\Lambda }_{c}\left(2625{\right)}^{+}$ since it was found. This measurement is necessary to obtain the coupling constants for the transitions between $s$-wave and $p$-wave charmed baryons in heavy hadron chiral perturbation theory. In addition, we search for the decay ${\Lambda }_{c}\left(2595{\right)}^{+}\to {\Lambda }_{c}^{+}{\pi }^{+}{\pi }^{-}$. No significant signal is observed, and the upper limit on its branching fraction is determined to be 85.0% at the 90% confidence level.