[MUSIC] In this 6th module, we are discussing weak interactions. And in this third video, we will go through the general properties of weak interactions, which are not quite like the others. After following this video, you will know about the nonconservation of parity for weak interactions. And the main vertices and charges which are relevant. Weak interactions, in fact, do not deserve their name. Their apparent weakness at low energy is due to the fact that they are transmitted by heavy particles, the neutral Z, and the charged W± bosons. Their propagator weakens the amplitude at low momentum transfer. Their coupling constant, g and g’, on the other hand, are of comparable magnitude as the electric charge e. Indeed, they are connected by the condition of electro-weak unification, which involves the Weinberg angle theta_W. Its value is close to 30 degrees. So instead of three coupling constants, there's only one and an angle. The tangent of this angle is the ratio between g’ and g. At the same time, it links the masses of the weak bosons by cos theta_W = M_W/M_Z. Feynman diagrams for typical charged and neutral weak interactions are shown in the two left graphs. Comparison with the corresponding photon exchange diagram shows that the structure of weak interactions is quite similar to that of electromagnetism. The neutral component of weak interactions can even interfere with electromagnetic interactions when it acts between charged particles. The charged weak interaction is the only force that can change the flavor of matter particles. It can even mediate between members of different generations at the same vertex. There are however other major differences between electromagnetic and weak interactions. The weak charge is a quantity with two components, in contrast with a single component for the electromagnetic charge, and three components for the color charge. The weak charge is called weak isospin by analogy to spin. One characterizes particles by their total weak isospin T and its third component T_3. They determine the coupling constants g and g’ together with the electromagnetic coupling e. The weak force is transmitted by vector bosons, similar to the photon and the gluon, but very heavy. The W± mass is of the order of 80 GeV, that of the Z of order 90 GeV. The two bosons carry themselves weak isospin, and can thus interact among themselves. In addition, charged bosons can obviously interact with the photon. Weak interactions also do not conserve parity. Thus, they produce polarization phenomena even from non-polarized initial states. This explains the first part of the small print at the bottom of this table. This non-conservation of parity is the most visible example of symmetries, which are respected by other interactions, but not by weak interactions. Weak interactions do not even respect the combined CP symmetry, and are therefore the only known interaction which distinguishes between matter and anti-matter. We will discuss this in video 6.8. At the same time, and maybe even for the same reason, they are the only interactions which connect particles from different generations at a single vertex. They can thus not conserve flavor. This fact is well established for quarks. And also has been observed for leptons as we will see in video 6.7 and 6.10, respectively. Now let us first discuss the discovery of parity nonconservation in charged weak interactions. In 1956, based on the study of experimental data obtained by C.S. Wu, Lee and Yang concluded that weak interactions are not invariant under the operation of parity. In order to investigate their behavior under this transformation, Wu and colleagues have designed an experiment that remains a classic of our discipline. It uses beta decay of neutrons n -> p e- nu_e-bar bound in Co-60 nuclei. At low temperature of the order of 0.01 Kelvin and in the presence of a magnetic field, the spin vectors of these nuclei with J=5 are strongly aligned with the magnetic field direction. Their decay, Co-60 with J=5 into Ni-60 with J=4 can lead to two spin configurations. p and E denote momentum and energy of the emitted electron, and sigma denotes a unit vector in the direction of the spin of the nucleus. In case a shown on top, the electron is emitted in the direction opposite to the Co-60 spin. In case B, it is emitted in the direction of the initial spin. Any combination of the two cases is allowed by conservation of angular momentum. The experiment showed the angular distribution of case a exclusively. It does not admit a contribution, however small, of configuration b. This corresponds to a maximum violation of parity. Indeed, conservation of parity would imply that the probabilities of the two configurations a and b are the same. This also means that charged weak interactions only admit a certain spin direction of participating fermions. In our example, the two spins of electron and neutrino must be aligned with that of the nucleus to conserve total angular momentum. In case a, the electron spin is antiparallel to its direction of motion. The antineutrino spin is parallel. So we find that the electron has negative helicity, it is left handed. The antilepton has positive helicity, it is right handed. This property of charged weak interactions can be generalized. As far as we know, the W only interacts with left-handed fermions, fermions of negative helicity. And right-handed antifermions, antifermions of positive helicity. Charged weak interactions thus violate parity to a maximum extent. Consequently, we assign left-handed leptons to doublets of weak isospin. Right-handed leptons to singlets. In this way, left-handed matter fields carry a weak charge and are coupled to W and Z. Right-handed matter fields do not. In the same manner, quarks are assigned to doublets and singlets according to their helicity. For antimatter fields, the opposite is true. Right-handed antileptons and antiquark carry weak isospin. Left-handed ones do not. The W and Z themselves belong to a triplet of weak isospin with T = 1. They can therefore interact among themselves. In addition, the W± obviously carries an electromagnetic charge and can interact with a photon. Weak interactions conserve weak isospin such that the fundamental weak interaction vertices with matter are shown on this graph. Here, l denotes a generic charged lepton. And nu_l a neutrino of the same flavor. q is an up-type quark. q’ is a down-type quark. The exact definitions we will reserve for later. W interactions change T_3 by one unit. So a charged lepton is transformed into a neutrino. An up-type quark is transformed into a down-type quark or vice versa. Attention, the emitted quarks and neutrinos do not necessarily belong to the same generation. The interaction of the Z boson keeps T_3 the same and conserves flavor. In the next video, we will present a prototype of W interactions, namely muon and tau lepton decay. [MUSIC]