L e = -1: Le in Java

Integrated Data Matrix in Java L e = -1: Le
L e = -1: Le
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e+ and P , e all other particles.
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(12.2)
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Similar assignments are made for Lp, and LT' Clearly, Lp, = 1 and L e = 0 for both the initial and final states of 1L - -'> e- PePp,' so this decay is consistent with the conservation of these quantum numbers; but 1L - -'> e - y is not. In fact, known reactions conserve these three lepton numbers separately (see Section 12.12 for a further discussion).
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Weak Interactions
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EXERCISE 12.1 Give the 7T+ and p,+ decay processes. List the possible decay modes of the 'T-Iepton (the 'T is the third lepton in the sequence e, p" 'T with a mass m = 1.8 GeV).
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The two examples of weak decays given in (12.1) involve neutrinos. Neutrinos are unique in that they can only interact by weak interactions. They are colorless and electrically neutral and, within experimental limits, also massless. Neutrinos are frequently found among the products of a weak decay, but not always. For example, a K + meson has the following weak decay modes:
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} semileptonic decays,
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K+~ 7T 0 p,+ Pp, , 7Toe+Pe
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(12.3)
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nonleptonic decays.
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The customary terminology is given on the right. The weak interaction is also responsible for the /3-decay of atomic nuclei, which involves the transformation of a proton to a neutron (or vice versa). Examples involving the emission of an e+ Pe lepton pair are lOC 14 0
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~lOB* ~14N*
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(12.4)
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Here, one of the protons in the nucleus transforms into a neutron via p
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(12.5)
For free protons, this is energetically impossible (check the particle masses), but the crossed reaction, the /3-decay process (12.6) is allowed and is the reason for the neutron's instability (mean life 920 sec). Without the weak interaction, the neutron would be as stable as the proton, which has a lifetime in excess of 1030 years. 12.1 Parity Violation and the V-A Form of the Weak Current
Fermi's explanation of /3-decay (1932) was inspired by the structure of the electromagnetic interaction. Recall that the invariant amplitude for electromagnetic electron-proton scattering (Fig. 12.1) is
(eupyp,u p )(
~21 )( -eueyp,u e),
(12.7)
see (6.8), where we have treated the proton as a structureless Dirac particle. 0lL is the product of the electron and proton electromagnetic currents, together with the propagator of the exchanged photon, see Section 6.2. To facilitate the comparison
Parity Violation and the V-A Fonn of the Weak Current
Fig. 12.1
Electron-proton (electromagnetic) scattering.
with weak interactions, we define, for example, an electron electromagnetic current of the form
ej;m
jti(O)
eu/y"u i ,
wherejti(x) is given by (6.6). Thus, the invariant amplitude, (12.7), becomes
0lL = -
e2 q
U;m) (jem,,) e.
The /3-decay process (12.5), or its crossed form
is shown in Fig. 12.2. By analogy with the current-current form of (12.7), Fermi proposed that the invariant amplitude for /3-decay be given by (12.8) where G is the weak coupling constant which remains to be determined by experiment; G is called the Fermi constant. Note the charge-raising or chargelowering structure of the weak current. We speak of these as the "charged weak currents." (The existence of a weak current that is electrically neutral, like the electromagnetic current, was not revealed until much later in 1973, see Section 12.9). Also note the absence of a propagator in (12.8). We return to this point in Section 12.2.
Fig. 12.2 The diagram for f3-decay, p showing the weak currents.
ne+"e'
Weak Interactions
Fermi's inspired guess of a vector-vector form of the weak amplitude 0lL is a very specific choice from among the various Lorentz invariant amplitudes that can in general be constructed using the bilinear covariants of (5.52). There is a priori no reason to use only vectors. The amplitude (12.8) explained the properties of some features of f3-decay, but not others. Over the following 25 years or so, attempts to unravel the true form of the weak interaction led to a whole series of ingenious f3-decay experiments, reaching a climax with the discovery of parity violation in 1956. Amazingly, the only essential change required in Fermi's original proposal was the replacement of y" by y"(l - y5). Fermi had not foreseen parity violation and had no reason to include a y5 y" contribution; a mixt~re of y" and y5 y" terms automatically violates parity conservation, see (5.67). In 1956, Lee and Yang made a critical survey of all the weak interaction data. A particular concern at the time was the observed nonleptonic decay modes of the kaon, K + ~ 2'17 and 3'17, in which the two final states have opposite parities. (People, in fact, believed that two different particles were needed to explain the two final states.) Lee and Yang argued persuasively that parity was not conserved in weak interactions. Experiments to check their assertion followed immediately. The first of these historic experiments serves as a good illustration of the effects of parity violation. The experiment studied f3-transitions of polarized cobalt nuclei:
The nuclear spins in a sample of 60Co were aligned by an external magnetic field, and an asymmetry in the direction of the emitted electrons was observed. The asymmetry was found to change sign upon reversal of the magnetic field such that electrons prefer to be emitted in a direction opposite to that of the nuclear spin. The essence of the argument is sketched in Fig. 12.3. The observed correlation between the nuclear spin and the electron momentum is explained if the required Jz = 1 is formed by a right-handed antineutrino, PR , and a left-handed electron, e L"