The quark contents of the following charmed particles are:...

The quark contents of the following charmed particles are: the hyperon $A_c$ is $u d c$, the $D^{+}$meson is $c \bar{d}$ and the $D^{-}$meson is $\bar{c} d$. Which of the following reactions are allowed? (a) $\pi^{+} p \rightarrow D^{+} p$, (b) $\pi^{+} p \rightarrow D^{-} \Lambda_c \pi^{+} \pi^{+}$, (c) $\pi^{+} p \rightarrow D^{+} \Lambda_c$, (d) $\pi^{+} p \rightarrow D^{-} \Lambda_c$.

Key Concepts

Quark Composition

In particle physics, understanding the quark composition of hadrons is essential because the properties of baryons and mesons, such as their electric charge, baryon number, and flavor quantum numbers (e.g., charm), are determined by the types of quarks that constitute them. This composition is used to analyze whether a reaction can be allowed based on how quarks rearrange or pair up in the final state.

Conservation Laws

Reactions in particle physics are governed by several fundamental conservation laws, including the conservation of electric charge, baryon number, and flavor quantum numbers like charm. In processes mediated by the strong interaction, these quantities must remain unchanged from the initial to the final state, which restricts the set of possible reactions that can occur.

Charm Quantum Number and its Conservation

The charm quantum number is an important flavor quantum number that must be conserved in strong interactions. Since charm is carried by specific quarks, any reaction creating or annihilating charmed particles has to ensure that charm is balanced on both sides of the reaction equation, often leading to the simultaneous production of charm and anti-charm quarks.

Transcript

00:01 Now in the first part of this question, we want to show that these two reactions actually have obey the conservation of quarks.

00:11 So the quarks are conserved on the left -hand side to the right -hand side of these two reactions.

00:19 So to show that we have to break the, break down the particles into their constituent quads.

00:28 Alright, so for the pion, it's made up of one up and one anti -down.

00:40 For the proton, it is up, up, down.

00:47 The k -on is made of one up and one string, and one anti -strange.

01:01 And then is the sigma baron, is up -up -up strange.

01:10 So looking at the various quarks, first of all looking at the up quark.

01:16 On the left we have total of three up quarks.

01:21 On the right hand side we have again three up quarks.

01:25 So this is conserved.

01:27 For the down quarks, on the left we have one anti -down and one down.

01:32 So they kind of cancel each other off and we get zero.

01:35 On the right hand side we have no down quarks.

01:38 So this is conserved.

01:41 For the strange quark, on the left we have zero, and on the right we have one anti -strange and one strange.

01:48 So they will cancel out each other again, leaving us with zero strange quarks.

01:54 So this is all conserved.

01:59 Looking at the second reaction, break it down again into its constituent quarks.

02:05 So there's anti -up and strange.

02:10 Proton is up, up, down.

02:15 The positive k -on is anti -strange and up, neutral k -on is strange and down, and then finally the omega barion is strange, strange quarks.

02:33 So first off the up -clock, we have one anti -up and two ups, so one will get cancelled out and we are left with only one up -cork on the left.

02:44 On the right side we indeed only have one up quark.

02:48 So this is conserved...

Please give Ace some feedback