Can we understand the decay width of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:msubsup><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi><mml:mi>c</mml:mi></mml:mrow><mml:mrow><mml:mo linebreak="badbreak" linebreakstyle="after">+</mml:mo></mml:mrow></mml:msubsup></mml:math> state?

Inspired by the recent discovery of a doubly charmed tetraquark state $T_{cc}^+$ LHCb Collaboration, we employ effective Lagrangian approach to investigate decay width $T_{cc}^{+}\to D^{+} D^{0}\pi^{0}/D^{0} D^{0}\pi^{+}$ and D^{0}D^{+}\gamma$ with assumption that $T_{cc}^{+}$ is an isoscalar $DD^{\ast}$ molecule. We show both $T_{cc}\to D D\pi$ DD\gamma$ modes contribute $T_{cc}$, former being dominant. The resulting total about $\Gamma=63$ keV smaller than experimental obtained from Breit-Wigner fit data, $\Gamma=410\pm 165\pm 43^{+18}_{-38}$ keV, while close number alternative unitary analysis, $\Gamma=48\pm 2^{+0}_{-14}$ which supports molecular nature $T_{cc}$.