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Chapter 30: Problem 6

Three types of sigma baryons can be created in accelerator collisions. Their quark contents are given by uus, uds, and dds, respectively. What are the electric charges of each of these sigma particles, respectively?

Short Answer

Expert verified
Answer: The electric charges of the three sigma particles (uus, uds, and dds) are +1, 0, and -1, respectively.

Step by step solution

01

Know the electric charges of the quarks

To calculate the electric charge of the sigma particles, first, we need to know the electric charges of the quarks (u, d, and s). The up quark (u) has a charge of +2/3, the down quark (d) has a charge of -1/3, and the strange quark (s) also has a charge of -1/3 (all charges are in units of the electron charge).
02

Calculate the electric charge of the uus sigma particle

The first sigma particle has a quark content of uus. To find the electric charge, we simply add the charges of these quarks: Charge(uus) = Charge(u) + Charge(u) + Charge(s) = (+2/3) + (+2/3) + (-1/3) = +3/3 = +1.
03

Calculate the electric charge of the uds sigma particle

The second sigma particle has a quark content of uds. To find the electric charge, we add the charges of these quarks: Charge(uds) = Charge(u) + Charge(d) + Charge(s) = (+2/3) + (-1/3) + (-1/3) = 0.
04

Calculate the electric charge of the dds sigma particle

The third sigma particle has a quark content of dds. To find the electric charge, we add the charges of these quarks: Charge(dds) = Charge(d) + Charge(d) + Charge(s) = (-1/3) + (-1/3) + (-1/3) = -3/3 = -1.
05

State the electric charges of the sigma particles

Based on our calculations, the electric charges of the three sigma particles (uus, uds, and dds) are +1, 0, and -1, respectively.

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Most popular questions from this chapter

According to Figure \(30.2,\) higher energies correspond with times that are closer to the origin of the universe, so particle accelerators at higher energies probe conditions that existed shortly after the Big Bang. At Fermilab's Tevatron, protons and antiprotons are accelerated to kinetic energies of approximately 1 TeV. Estimate the time after the Big Bang that corresponds to protonantiproton collisions in the Tevatron.
The energy at which the fundamental forces are expected to unify is about \(10^{19}\) GeV. Find the mass (in kilograms) of a particle with rest energy \(10^{19} \mathrm{GeV}\).
A proton of mass \(0.938 \mathrm{GeV} / c^{2}\) and an antiproton, at rest relative to an observer, annihilate each other as described by \(\mathrm{p}+\overline{\mathrm{p}} \rightarrow \pi^{-}+\pi^{+} .\) What are the kinetic energies of the two pions, each of which has mass $0.14 \mathrm{GeV} / \mathrm{c}^{2} ?$
Two factors that can determine the distance over which a force can act are the mass of the exchange particle that carries the force and the Heisenberg uncertainty principle \([\mathrm{Eq} .(28-3)] .\) Assume that the uncertainty in the energy of an exchange particle is given by its rest energy and that the particle travels at nearly the speed of light. What is the range of the weak force carried by the \(\mathbf{Z}\) particle that has a mass of $92 \mathrm{GeV} / \mathrm{c}^{2} ?$ Compare this with the range of the weak force given in Table 30.3
Which fundamental force is responsible for each of the decays shown here? [Hint: In each case, one of the decay products reveals the interaction force.] (a) \(\pi^{+} \rightarrow\) \(\mu^{+}+v_{\mu},\) (b) $\pi^{0} \rightarrow \gamma+\gamma(\mathrm{c}) \mathrm{n} \rightarrow \mathrm{p}^{+}+\mathrm{e}^{-}+\bar{v}_{\mathrm{e}}$
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