91Ó°ÊÓ

Mesons are hadronic subatomic particles made up of an equal number of quarks and antiquarks, generally one of each, and linked together by strong interactions in particle physics.

A quark is a basic matter ingredient and an elementary particle.

Anti-quarks are the antiparticles that correspond to each flavour of quark.

Find the quark compositions for\({{\rm{D}}^{\rm{ + }}}\)given that all its quantum numbers as follows –

Now, find its quark configuration –

Since \({{\rm{D}}^{\rm{ + }}}\) is a meson. Thus, it consists of quark and anti-quark.

\({D^ + } = \left( {q\bar q} \right)\)

Since it has a charm of \(c = + 1\). Therefore, the quark is the charmed \({\rm{c}}\).

\({D^ + } = \left( {c\bar q} \right)\)

Since its charge is \({\rm{ + 1}}\) and the charge of the charm quark is \({\rm{ + 2/3}}\). Thus, an anti-quark with charge \({\rm{ + 1/3}}\) is needed. The options available are – \({\rm{\bar d,\bar s,}}\) and \({\rm{\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\leftarrow$}} \over b} }}\).

Since its strangeness and bottomness are zero. Therefore,\({\rm{\bar s,}}\)and \({\rm{\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\leftarrow$}} \over b} }}\) cannot be considered.

Hence, the quark configuration for the \({\rm{D}}\)-meson \({{\rm{D}}^{\rm{ + }}}\) is –

\({D^ + } = \left( {c\bar d} \right)\)

Therefore, the quark configuration is obtained as \({D^ + } = \left( {c\bar d} \right)\).