Testing the light scalar meson as a non-$$ q\overline{q} $$ state in semileptonic D decays

A bstract While the light scalar mesons ( S 0 ) are considered to be either ordinary $$ q\overline{q} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>q</mml:mi> <mml:mover> <mml:mi>q</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> or exotic tetraquark states, we investigate the semileptonic decays D → S 0 e + ν e , by taking into account the resonant effects of S 0 → M 1 M 2 , where S 0 = a 0 (980), f 0 (980), and f 0 (500)/ σ 0 , and M 1(2) represents a pseudoscalar meson. For the first time, the D → S 0 form factors in the two quark structures are both presented. Subsequently, we calculate $$ \mathcal{B} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>B</mml:mi> </mml:math> ( $$ {D}_s^{+} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>D</mml:mi> <mml:mi>s</mml:mi> <mml:mo>+</mml:mo> </mml:msubsup> </mml:math> → σ 0 e + ν e , σ 0 → π + π − ) = (20.3 ± 1.8 ± 0.5) × 10 − 4 in the $$ q\overline{q} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>q</mml:mi> <mml:mover> <mml:mi>q</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> structure, showing significant 9 σ deviations from the experimental upper limit of 3.3 × 10 − 4 . In contrast, $$ \mathcal{B} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>B</mml:mi> </mml:math> ( $$ {D}_s^{+} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>D</mml:mi> <mml:mi>s</mml:mi> <mml:mo>+</mml:mo> </mml:msubsup> </mml:math> → σ 0 e + ν e , σ 0 → π + π − ) = ( $$ {0.58}_{-0.57}^{+1.43} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mn>0.58</mml:mn> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.57</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>1.43</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> ± 0.01) × 10 − 4 in the $$ {q}^2{\overline{q}}^2 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>q</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:msup> <mml:mover> <mml:mi>q</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mn>2</mml:mn> </mml:msup> </mml:math> structure is within the allowed experimental range. Clearly, the light scalar meson is tested as a non- $$ q\overline{q} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>q</mml:mi> <mml:mover> <mml:mi>q</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> state. We hence demonstrate a highly sensitive new approach for exploring the true nature of scalar mesons, which can be extended to non-leptonic D decays as well as B meson decays.