The standard model and particle interactions

Which particle is a lepton?

The charges of the up, down and strange quarks are +2/3 e, −1/3 e and −1/3 e.
Which combination of quarks forms a baryon with a charge of −1 e?

Which quantity is not always conserved in particle interactions?

A muon has a rest mass of 1.88 × 10⁻²⁸ kg.

Particles in the standard model can be grouped as baryons, mesons, leptons and photons. The charges of the up and down quarks are +2/3 e and −1/3 e.

Lepton numbers: electron, muon and neutrino +1; positron, antimuon and antineutrino −1; all other particles in this question 0. Baryon numbers: proton and neutron +1; antiproton −1; pions 0.
For each interaction below, state whether it is possible, giving a reason based on conservation laws.

The charges of the up, down and strange quarks are +2/3 e, −1/3 e and −1/3 e. Figure 1 shows the quark content of four particles W, X, Y and Z.
Which particle is a meson with zero charge?

Figure 1 shows the pattern of fundamental particles known before the top quark was discovered. The symmetry of the pattern led physicists to predict a particle to fill the box marked ?.
Which describes the predicted particle?

Figure 1 shows the tracks of five particles that enter a uniform magnetic field at the same speed. Track P is made by a proton.
Which track could be made by an antiproton?

Figure 1 shows the charges of the up, down and strange quarks and of their antiquarks.

Figure 1 is a chart used to classify particles. P, Q and R are three groups of particles.

A particle has a mass of 1.00 GeV/c².
What is this mass in kilograms?

Mass of electron = 9.11 × 10⁻³¹ kg.
What is the minimum energy of a photon that can produce an electron–positron pair?

The positive pion π⁺ consists of an up quark and an anti-down quark (ud̄).
What is the quark composition of its antiparticle?

Muons are produced about 12 km above the Earth's surface and travel downwards at a speed close to c. Their mean lifetime at rest is 2.2 µs, in which time they would travel less than 1 km. Large numbers of muons are detected at sea level.
Which statement explains this?

The top quark was predicted many years before it was first detected.
Which reason led physicists to predict it?

In a hospital scanner, a radioactive tracer emits positrons inside the patient's body. Each positron slows down and then annihilates with an electron. Assume both particles are at rest when they annihilate. Mass of electron = 9.11 × 10⁻³¹ kg.

A student places a source of positrons next to a gamma-ray detector. The positrons annihilate with electrons in the surrounding material, almost at rest. The detector records a sharp peak in the number of photons at an energy of 0.511 MeV. The uncertainty in this energy reading is ±0.004 MeV.

A detector on a mountain, 2500 m above sea level, counts 600 muons per minute arriving vertically. An identical detector at sea level counts 410 per minute. Assume all these muons travel vertically at 0.995c and that no muons are produced between the two heights. For muons at rest, half of any sample decays every 1.52 µs.

A free neutron decays into a proton, an electron and an antineutrino. Lepton numbers: electron, muon and neutrino +1; positron, antimuon and antineutrino −1; all other particles in this question 0. Rest energies: neutron 939.57 MeV; proton 938.27 MeV; electron 0.511 MeV; the antineutrino's rest energy is negligible.

Figure 1 shows the rest energies of five particles. A gamma photon of energy 250 MeV passes close to a nucleus, which takes negligible energy.
Which is the most massive particle that this photon can create together with its antiparticle?

Photons of different energies produce pairs of a particle X and its antiparticle near nuclei, which take negligible energy. Figure 1 shows the total kinetic energy of X and its antiparticle against the energy of the photon.
What is the rest mass of X?

Figure 1 shows how the kinetic energy of protons varies with distance along a linear accelerator.
What is the kinetic energy gained by a proton between 20 m and 50 m from the start?

Figure 1 shows the tracks in a magnetic field when a negative kaon K⁻ (a meson) comes to rest and decays into a negative muon μ⁻ and a neutral particle X, which leaves no track. Lepton numbers: electron, muon and neutrino +1; positron, antimuon and antineutrino −1; all other particles in this question 0.
Which particle is X?

A particle Y and its antiparticle, both at rest, annihilate and produce two photons. Figure 1 shows the energy spectrum recorded by a photon detector; the sharp peak is caused by these annihilations.
What is the mass of particle Y?

An antiproton slows down in a detector and annihilates with a proton at rest. The detector is in a uniform magnetic field directed into the page. Figure 1 shows the tracks. Three pions are produced; product 3 leaves no track and is shown dashed. Rest energies: proton 938 MeV; charged pion 140 MeV; neutral pion 135 MeV.

A student plots the rest energy of four particles against their mass (Figure 1). The masses are: muon 1.88 × 10⁻²⁸ kg, positive pion 2.49 × 10⁻²⁸ kg, positive kaon 8.80 × 10⁻²⁸ kg and proton 16.7 × 10⁻²⁸ kg.

In a storage ring, muons circulate at 0.9994c. Detectors record the electrons produced when the muons decay; the count rate is proportional to the number of muons remaining. Figure 1 shows how the count rate varies with time, measured in the laboratory. The half-life of muons at rest is 1.52 µs.

A beam of positive pions strikes protons at rest in a detector placed in a uniform magnetic field directed into the page. Figure 1 shows the tracks from one collision. Baryon numbers: proton +1, pions 0.

Figure 1 shows the charge and baryon number of several particles. J and Y are not named. Quark charges: u +2/3 e, d −1/3 e, s −1/3 e.

Lepton numbers: electron, muon and neutrino +1; positron, antimuon and antineutrino −1; all other particles in this question 0.
Which interaction is possible?

A charged lepton has a rest mass of 1.78 GeV/c². It annihilates with its antiparticle when both are at rest, producing two photons.
What is the wavelength of each photon?

A gamma photon of energy 3.20 MeV passes close to a lead nucleus in a detector and produces an electron–positron pair. The detector is in a uniform magnetic field directed into the page. Mass of electron = 9.11 × 10⁻³¹ kg.

A neutral particle X, at rest, decays into a proton and a negative pion: X → p + π⁻. Rest masses: X 1116 MeV/c²; proton 938 MeV/c²; π⁻ 140 MeV/c²; neutron 940 MeV/c². Quark charges: u +2/3 e, d −1/3 e, s −1/3 e.

Muons are produced when cosmic rays strike nuclei about 15 km above sea level. They travel towards the ground at 0.998c. The mean lifetime of a muon at rest is 2.2 µs. A detector at sea level records large numbers of these muons.

Figure 1 shows how the mean lifetime of charged pions, measured in a laboratory, depends on their speed. A beam of pions travels through the laboratory at 0.80c.
What is the mean distance a pion travels before it decays, as measured in the laboratory?

Figure 1 shows the tracks produced when an antiproton collides with a proton at rest in a uniform magnetic field. The particles labelled π⁺ and π⁻ are pions; particle X is not identified. Lepton numbers: electron, muon and neutrino +1; positron, antimuon and antineutrino −1; all other particles in this question 0. Baryon numbers: proton +1, antiproton −1, pions and leptons 0.
Which particle could X be?

A gamma photon passes close to a nucleus and produces a positive pion and a negative pion. The nucleus takes negligible energy. Figure 1 shows how the energy of the photon is shared after the event.

A positive pion π⁺ comes to rest at A in a detector and decays into a positive muon μ⁺ and a neutral particle X, which leaves no track. The muon stops at B and decays into a positron and two neutral particles. Figure 1 shows the tracks in a magnetic field. Lepton numbers: electron, muon and neutrino +1; positron, antimuon and antineutrino −1; all other particles in this question 0. Rest energies: π⁺ 139.6 MeV; μ⁺ 105.7 MeV; the rest energies of neutrinos are negligible.

Figure 1 shows a collider in which electrons and positrons travel in opposite directions and collide head-on; the beam energies are shown. In some collisions the electron and positron annihilate and produce a meson M and its antiparticle, each of rest mass 5.28 GeV/c².