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particle physics

Questions and Answers of Particle Physics

Show that mesons with the quantum numbers (7.8) are forbidden in the simple quark model.Equation 7.8B = Q = S = C = B̃ = 0
Table 5.3 lists the allowed combinations of strangeness S and isospin I for mesons composed of light quarks u, d, s in the simple quark model. What are the allowed combinations for tetraquarks
Draw two quark diagrams corresponding to the decay sequence (7.10b), given that the b quark couples to lighter quarks almost exclusively via the vertex bcW analogous to the udW vertex of Figure
Draw quark diagrams for the decay sequence (7.10c), assuming P+c is the charmonium–pentaquark state P+c = uudcc̅.Equation 7.10cΛ0b → K− + P+c ; P+c → J/ψ + p
Estimate the cross-section ratio R, defined by (7.18), at total centreof- mass energies ECM= 2.8, 5 and 15 GeV, assuming that there are no resonance peaks at these energies and that (7.22) remains
Perform the angular integration in (8.5) and use the result (a) To show that GE (q2) is a function of q2 only (b) To derive (8.9) for the root-mean-square charge radius rE.
Show that the scattering variable ν defined by (8.28) reduces to (8.30) in the rest frame of the proton. Hence show that the scaling variable (8.29) lies in the range 0 ≤ x ≤ 1 if the lepton
A cylindrical proportional chamber has a central anode wire of radius 0.02 mm and an outer cathode of radius 10mm with a voltage of 500 volts applied between them. What is the electric field at the
Estimate the minimum length of a gas Ċerenkov counter that could be used in the threshold mode to distinguish between pions and kaons with momentum 20 GeV/c. Assume that 200 photons need to be
Two particles of masses m1 and m2, and common momentum p, travel between two scintillation counters that are a distance L apart. Show that the difference in their flight times decreases like p−2
Assuming the Bethe–Bloch formula is valid for low energies, show that the rate of ionisation has a maximum (the Bragg peak) and find the kinetic energy of protons in iron for which this maximum
Derive the result of Equation (4.12) for the range R. dE M -F(ß;), q?ne d3 R = = - dr
An electron with an initial energy of 2 GeV traverses 10 cm of water with a radiation length of 36.1 cm. Calculate its final energy. How would the energy loss change if the particle were a muon
A positron with laboratory energy 50 GeV interacts with the atomic electrons in a lead target to produce μ+μ− pairs. If the cross-section for this process is given by σ =
Estimate the thickness of iron through which a beam of neutrinos with energy 200 GeV must travel if 1 in 109 of them is to interact. Assume that at high energies the neutrino–nucleon total
Charged pions with momentum 50 GeV/c are deflected through a collimator slit 3mm wide by a bending magnet 2m long that produces a uniform field of 1.5 T. Calculate how far from the magnet the slit
A liquid hydrogen target of volume 125 cm3 and density 0.071 g/cm3 is bombarded with a mono energetic beam of negative pions with a flux 2 × 107/m2 s and the reaction π− + p → π0 + n observed
An e+e− collider has a diameter of 8km and produces beams of energy 45 GeV. Each beam consists of 12 bunches each containing 3 × 1011 particles. The bunches have a cross-sectional area of 0.02mm2.
At a collider, two high-energy particles A and B with energies EA and EB, which are much greater than either of the masses, collide at a crossing angle θ. Show that the total centre-of-mass energy
Show that the momentum p in GeV/c for a relativistic particle of charge e moving in a circular orbit of radius ρ metres in a magnetic field of magnitude B = |B| tesla is given by p = 0.3B ρ.
What is the length L of the longest drift tube in a linac, which, operating at a frequency f = 50 MHz, is capable of accelerating protons to a maximum energy of E = 300 MeV?
Which of the following possible hadronic states with quantum numbers (Q,B, S,C, B̃) = (1, 0, 0, 1, 1), (−1, 1,−2, 0,−1), (0, 0, 1, 0, 1) and (−1, 1, 0, 1,−1) are compatible with the simple
Derive the allowed combinations of charm C and electric charge Q for mesons and baryons in the simple quark model.
Draw the quark diagram for: (a) The decay Δ++ → π+ + p of the Δ(1232) resonance discussed in Section 3.5 and (b) The two corresponding diagrams for the process π−p → Δ0 → π0n.
Draw a lowest-order Feynman diagram at the quark level for each of the following decays:(a) D− → K0 + π−; (b) Λ → p + e− + ν̅e.
The Σ+(1189) = uus decays almost entirely to states composed solely of hadrons. Identify these states and make a rough estimate of the particle lifetime.
Apart from the p, n and Λ described in the text, the only baryon lighter than the Σ0(1193) = uds is its charged companion Σ+(1189) = uus. Use this fact to identify the dominant decay mode of the
The Σ+(1189), Σ0(1193) and Σ−(1197) baryons have the quark compositions uus, uds and dds, respectively. Which of the following reactions are allowed and which are forbidden in strong
Six observed hadrons have the quantum numbers (Q, B, S, C, B̃) = (2, 1, 0, 1, 0), (0, 1,−2, 1, 0), (0, 0, 1, 0,−1), (0,−1, 1, 0, 0), (0, 1,−1, 1, 0) and (−1, 1,−3, 0, 0), respectively.
The particles X0(1193) and Yˆ’(1321) can be produced in the strong interaction processes Kˆ’+ p †’ Ï€0+ X0and Kˆ’+ p †’ K++
A large number of stopped K+(494) mesons are observed to decay to the π+π0 final state. Calculate the mean distance travel-led by the π+ mesons before they decay, in the approximations that both
Classify the following experimentally observed processes into strong, electromagnetic and weak reactions by considering the particles involved and the appropriate selection rules.(a) π− → π0 +
Which of the following reactions are allowed and which are forbidden by the conservation laws appropriate to weak interactions?(a) Λ → π+ + e− + ν̅e; (b) K+ → π+ + e− + ¯ ν̅e
If the Sun is assumed to be a uniform spherical plasma consisting of nucleons, with radius 7 × 105 km and total mass 2 × 1030 kg, calculate the mean free path λ = 1/nσ of solar neutrinos from the
A hypothetical KamLAND-type experiment detects v̅e neutrinos at a distance of 300 m from a nuclear reactor and finds that the flux is (90 ± 10)% of that expected if there were no oscillations.
Calculate the oscillation lengths L13, L12 associated with ν1 → ν3 and ν1 → ν2 oscillations for electron antineutrinos of energy 3MeV. Why is a two-component mixing model a good first
An electron antineutrino is produced at the center of the Sun. Somewhere on its journey to the surface it passes through a region where the density is such that matter effects lead to a resonant
In the KamLAND experiment, anti neutrinos are detected via the reaction ν̅e + p → e+ + n, where the target protons are at rest. Show that for incident anti neutrinos of energy Eν = 3MeV, the
Show that the oscillation length in (2.30h) may he written L0 = E/(1.27∆m2ij), where L0 is expressed in km, E in GeV and in ∆m2ij in (eV/c2)2.
In Section 2.3.1 it is stated that electron neutrinos interact with electrons in a different way from muon and tauon neutrinos. Justify this remark by considering the lowest-order Feynman diagrams
Draw the two fourth-order Feynman diagrams for the weak reactione− + μ+ → νe + ν̅μ.
Draw the lowest-order Feynman diagram for νeνμ elastic scattering.
Figure 2.5 shows one of the time-ordered diagrams for muon decay Î¼ˆ’†’ eˆ’ Î½Ì…eÎ½Î¼. What are the
Which of the following reactions are allowed, and which are forbidden, by the conservation laws appropriate to weak interactions?(a) νμ + p → μ+ + n,(b) νe + p → e− + π + + p,(c) ντ +
(a) The classical radius of an electron is defined as rc = e2/4πε0me in natural units. What is its value in fm?(b) A simple classical model of the electron is to regard it as a sphere of
For total centre-of-mass energies of a few GeV, the cross-section for the reaction νμ + e− → μ− + νμ is given by σ = G2F E2/π in natural units, where GF is the Fermi coupling constant
Parapositronium is an unstable bound state of an electron and a positron. Its lifetime is given in natural units by τ = 2/mα5, where m is the mass of the electron and α is the fine structure
In lowest order, the process e++ e-†’ Î¼++ Î¼-is given by the Feynman diagram of Figure 1.16. Estimate the typical distance between the vertices at energies much
In lowest order, the process e+ + e- †’ Î³ + Î³ is given by the Feynman diagrams of Figure 1.9. Show that for electrons and positrons almost at rest, the
Verify by explicit integration that substituting the Yukawa potential (1.30) into (1.32) leads to (1.35) for the corresponding scattering amplitude.Equation 1.30Equation 1.32Equation 1.35 g² -r/R V
Show that the Yukawa potential of Equation (1.30) is the only spherically symmetric solution of the static Klein€“Gordon equation (1.28) that vanishes as r goes to infinity.Equation
Draw one fourth-order diagram for each of the reactions(a) γ + e− → γ + e− and (b) e+ + e− → e+ + e−.
The matrices Î±i(i = 1, 2, 3) and Î² in the Dirac equation (1.8) can be chosen to have the explicit formswhere 1 and 0 are the 2 Ã— 2 unit matrix and null matrix,
Write down equations in symbol form that describe the following interactions:(a) The elastic scattering of an electron anti neutrino and a positron;(b) The elastic scattering of proton and a
Draw the topologically distinct Feynman diagrams that contribute to the following process in lowest order:(a) γ + e− → γ + e−;(b) e+ + e− → e+ + e−;(c) VeV̅e elastic scattering.

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