The Weak Force

1. The Weak Force so named because unlike the PROMPT processes  qg e+ e- _ rg e+ e-  qr which seem instantaneous    or the electromagnetic decay: which involves a 10-17 sec lifetime path length (gap) in photographic emulsions mere nm! weak decays are “SLOW” processes…the particles involved: , ±,  are nearly “stable.” 10-6 sec 700 m pathlengths 887 sec 10-8 sec +++ 7 m pathlengths and their inverse processes: scattering or neutrino capture are rare small probability of occurrence (small rates…small cross sections!).

2. Such “small cross section” seemed to suggest a SHORT RANGE force…weaker with distance compared to the infinite range of the Coulomb force or powerful confinement of the color force This seems at odds with the predictions of ordinary gauge theory in which the VECTOR PARTICLES introduced to mediate the forces like photons and gluons are massless. This means the symmetry cannot be exact. The symmetry is BROKEN. This does not mean we’re giving up. There is a mathematically prescribe way to HIDE SYMMETRIES or restrict certain states from exhibiting the full symmetry of their Lagrangian

3. Spontaneous Symmetry Breaking Englert & Brout, 1964 Higgs 1964, 1966 Guralnick, Hagen & Kibble 1964 Kibble 1967 The Higg’s Mechanism The Lagrangian& derived equations of motion for a system possess symmetries which simply do NOT hold for a specific ground state of the system. (The full symmetry MAY be re-stored at higher energies.) • (1) A flexible rod under • longitudinal compression. • Lagrangian symmetric with respect • to rotations about the rod’s axis • once force exceeds some critical value • it must buckle sideways forming an • arc in SOME arbitrary direction • Although one direction is chosen, the • complete set of all possible final shapes • DOES show the full symmetry.

4. (2) IRON SAMPLE • in absence of external magnetic field • no preferred orientationof atomic • magnetic moments • macroscopic samples • showno net magnetization • rotationally & translationally invariant • yet through random fluctuations it settles • into domains destroying (on a microscopic scale) • its spatial invariance. • (3) FERROMAGNETIC MATERIALS • Anymacroscopic sample, at high temperature •  zero net magnetization • but below the curie temperature atomic magnetic • moments all align in an arbitrary direction (chosen • randomly by quantum mechanic fluctuations) • The ground state is NOT rotational & translationally symmetric • but mathematically • the set of ALL POSSIBLE solutions still IS!

5. What is the GROUND STATE? lowest energy state What does GROUND STATE mean in Quantum Field Theory? Shouldn’t that just be the vacuum state?|0  which has an compared to 0. Fields are fluctuations about the GROUND STATE. Virtual particles are created from the VACUUM. The field configuration of MINIMUM ENERGY is usually just the obvious  0 (e.g. out of  away from a particle’s location)