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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

Estimate the magnetic field strength required at the LHC to make 7.0-TeV protons travel in a circle of circumference \(27 \mathrm{km}\). Start by deriving an expression, using Newton's second law, for the field strength \(B\) in terms of the particle's momentum \(p,\) its charge \(q,\) and the radius \(r\). Even though derived using classical physics, the expression is relativistically correct. (The estimate will come out much lower than the actual value of 8.33 T. In the LHC, the protons do not travel in a constant magnetic field; they move in straight-line segments between magnets.)
A sigma baryon at rest decays into a lambda baryon and a photon: $\Sigma^{0} \rightarrow \Lambda^{0}+\gamma .$ The rest energies of the baryons are given by \(\Sigma^{0}=1192 \mathrm{MeV}\) and \(\Lambda^{0}=1116 \mathrm{MeV} .\) What is the photon wavelength? [Hint: Use relativistic formulas and be sure momentum is conserved as well as energy.]
A neutral pion (mass \(0.135 \mathrm{GeV} / \mathrm{c}^{2}\) ) decays via the electromagnetic interaction into two photons: $\pi^{0} \rightarrow \gamma+\gamma$ What is the energy of each photon, assuming the pion was at rest?
In the Cornell Electron Storage Ring, electrons and positrons circulate in opposite directions with kinetic energies of 6.0 GeV each. When an electron collides with a positron and the two annihilate, one possible (though unlikely) outcome is the production of one or more proton-antiproton pairs. What is the maximum possible number of proton-antiproton pairs that could be formed?
A proton in Fermilab's Tevatron is accelerated through a potential difference of 2.5 MV during each revolution around the ring of radius \(1.0 \mathrm{km} .\) In order to reach an energy of 1 TeV, how many revolutions must the proton make? How far has it traveled?
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