Erschienen:
Springer Science and Business Media LLC, 2021
Erschienen in:The European Physical Journal C
Sprache:
Englisch
DOI:
10.1140/epjc/s10052-021-09820-3
ISSN:
1434-6044;
1434-6052
Entstehung:
Anmerkungen:
Beschreibung:
<jats:title>Abstract</jats:title><jats:p>We perform a study of the <jats:inline-formula><jats:alternatives><jats:tex-math>$$D_s^+ \rightarrow a_0(980)(f_0(980)) e^+ \nu _e$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
<mml:mrow>
<mml:msubsup>
<mml:mi>D</mml:mi>
<mml:mi>s</mml:mi>
<mml:mo>+</mml:mo>
</mml:msubsup>
<mml:mo>→</mml:mo>
<mml:msub>
<mml:mi>a</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mn>980</mml:mn>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:msub>
<mml:mi>f</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mn>980</mml:mn>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:msup>
<mml:mi>e</mml:mi>
<mml:mo>+</mml:mo>
</mml:msup>
<mml:msub>
<mml:mi>ν</mml:mi>
<mml:mi>e</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math></jats:alternatives></jats:inline-formula> reactions investigating the different sources of isospin violation which make the production of the <jats:inline-formula><jats:alternatives><jats:tex-math>$$a_0(980)$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
<mml:mrow>
<mml:msub>
<mml:mi>a</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mn>980</mml:mn>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math></jats:alternatives></jats:inline-formula> possible. We find that loops involving kaons in the production mechanism provide a source of isospin violation since they do not cancel due to the different mass of charged and neutral kaons, but we also find that the main source comes from the breaking of isospin in the meson-meson transition <jats:italic>T</jats:italic> matrices, which contain information on the nature of the low lying scalar mesons. The reaction is thus very sensitive to the nature of the <jats:inline-formula><jats:alternatives><jats:tex-math>$$a_0(980)$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
<mml:mrow>
<mml:msub>
<mml:mi>a</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mn>980</mml:mn>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math></jats:alternatives></jats:inline-formula> and <jats:inline-formula><jats:alternatives><jats:tex-math>$$f_0(980)$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
<mml:mrow>
<mml:msub>
<mml:mi>f</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mn>980</mml:mn>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math></jats:alternatives></jats:inline-formula> resonances. Our results are consistent with the present upper bound for <jats:inline-formula><jats:alternatives><jats:tex-math>$$a_0(980)$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
<mml:mrow>
<mml:msub>
<mml:mi>a</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mn>980</mml:mn>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math></jats:alternatives></jats:inline-formula> production and only a factor three smaller, indicating that future runs with more statistics should find actual numbers for this reaction from where we can learn more about the origin of the scalar resonances and their nature.</jats:p>