January 11, 2001 Physics 841 1 Cross-Sections and Decay Rates • There are three types of measurements one can make – static properties of particles (mass, charge, etc.) – decay rates (lifetimes/line-widths, branching ratios) – cross-sections (inclusive, semi-inclusive, exclusive) • We will focus our attention on the dynamical properties of particles (decay rates and cross- sections), not because they are intrinsically more interesting than the static properties (mass, charge, etc.) but, rather, because they are more directly related to understanding CP violation. • Understanding the masses of particles, and the patterns of masses, is a key problem in particle physics, and we will address it, in part, next quarter.
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January 11, 2001Physics 8411 Cross-Sections and Decay Rates There are three types of measurements one can make –static properties of particles (mass, charge,
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January 11, 2001 Physics 841 1
Cross-Sections and Decay Rates
• There are three types of measurements one can make– static properties of particles (mass, charge, etc.)– decay rates (lifetimes/line-widths, branching
• We will focus our attention on the dynamical properties of particles (decay rates and cross-sections), not because they are intrinsically more interesting than the static properties (mass, charge, etc.) but, rather, because they are more directly related to understanding CP violation.
• Understanding the masses of particles, and the patterns of masses, is a key problem in particle physics, and we will address it, in part, next quarter.
January 11, 2001 Physics 841 2
Differential Cross-Sections
• Classically, scattering from a point-like object, or a spherically symmetric potential, can be described in terms of the impact parameter of the incident particle with respect to the target and the (asymptotic) scattering angle. If the impact parameter is known, and the potential is known, the scattering angle is unique. While this is not true in the quantum mechanical world, understanding the classical picture is useful in developing intuition.
• Cross-sections measure the strengths of interactions. We expect that– “larger” objects should have larger cross-
sections– “stronger” potentials (or their equivalent)
should have larger cross-sections
January 11, 2001 Physics 841 3
Classical Scattering
January 11, 2001 Physics 841 4
Hard Sphere Scattering
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R
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α
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January 11, 2001 Physics 841 5
Classical Rutherford Scattering
January 11, 2001 Physics 841 6
More Rutherford Scattering
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January 11, 2001 Physics 841 7
Fermi’s Golden Rule for Scattering
nota bene:
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h=1
January 11, 2001 Physics 841 8
Lorentz Invariant Phase Space
January 11, 2001 Physics 841 9
Lorentz Invariant Phase Space, Continued
January 11, 2001 Physics 841 10
Transition Matrix Elements in Perturbation Theory - I
January 11, 2001 Physics 841 11
Transition Matrix Elements in Perturbation Theory - II
January 11, 2001 Physics 841 12
Transition Matrix Elements in Perturbation Theory - III
January 11, 2001 Physics 841 13
nota bene:
Transition Matrix Elements in Perturbation Theory - IV