Parity violation

In physics, parity violation describes the fact, discovered in 1956, that there are physical processes that take place differently in a mirror-inverted world than in a mirror image of the normal world. In other words, such a parity-violating process observed in the mirror differs from the process that actually takes place in a mirror-inverted but otherwise identically structured test arrangement.

The name parity violation more precisely means violation of the maintenance of parity . The quantity parity is defined in quantum mechanics in order to describe the symmetry character of a wave function compared to spatial reflection . This “spatial reflection” is also meant when one speaks in this context of the fact that physical laws or processes are “mirror-symmetrical”.

Processes that violate parity are known only in the weak interaction . The other basic forces of physics ( gravitation , electromagnetic interaction , strong interaction ) are parity-preserving . But these three basic forces determine the processes of daily life; therefore it is not easy to observe parity violations. For a long time, it was the scientific doctrine that nature is governed exclusively by mirror-symmetrical laws. A parity violation was considered impossible until the middle of the 20th century. The opposite was proven in 1956 by the groups around CS Wu using the example of - radioactivity and, almost at the same time, around Leon Max Lederman using the example of the decay of polarized muons. ${\displaystyle \beta }$

The only eigenvalues ​​of quantum mechanical parity are the quantum numbers +1 ( symmetrical ) and −1 ( antisymmetrical ). The energy levels of atoms, molecules etc. almost always have a certain parity (+1 or −1) to a very good approximation, but some of the wave functions that are often used (e.g. the plane wave ) do not. As long as the weak interaction is not involved in a process, the symmetry character is retained as it was at the beginning ( preservation of parity of the wave function of the entire system ). If z. If, for example, an excited atom generates a light quantum through electromagnetic interaction, which has parity −1 for itself, then the atom in its final state must have opposite parity to the initial state (parity selection rule ). Light quantum and atom taken together then have the same parity in the final state as the initial state. In processes of the weak interaction, however, (eg. - radioactivity , weak decay of unstable elementary particles) is produced from an initial state with pure parity a final state with equal proportions of both parities, so maximum mixture. Therefore, the parity violation from the weak interaction is said to be maximum . ${\displaystyle \beta }$

Discovery of the parity violation

→ Main article : Wu experiment

Principle of the proof of parity violation in the Wu experiment

The parity violation was discovered and correctly published in 1928, but was regarded as a measurement error because it did not fit the doctrine of parity maintenance at the time. For the same reason, the description of electrons (and neutrinos) in the form of the 2-component spinor proposed by Hermann Weyl and used today was rejected.

In 1956, Tsung-Dao Lee and Chen Ning Yang published the conjecture that the “τ-θ puzzle” in the case of the disintegration of the kaon could be explained by the fact that in the weak interaction , in contrast to gravity , the strong and electromagnetic interaction , the parity is not preserved. They pointed out (unaware of the 1928 work by Cox et al.) That this question had never been carefully examined and were able to suggest several specific experiments for it. For this they received the Nobel Prize in Physics as early as 1957, after Chien-Shiung Wu had confirmed this assumption in a groundbreaking experiment: the angular distribution of the rays (electrons) in a mirror-inverted apparatus does not actually have the same shape as in the mirror image of the original structure. ${\displaystyle \beta }$

The principle of the Wu experiment is explained with the help of the figure: In the original setup (left in the figure) a radioactive ⁶⁰ Co source is observed from above with a detector that counts the electrons of the radiation flying upwards . The source is located in an electromagnet whose coil is traversed by electrons from bottom to top. To the right of it is a level mirror. In the mirror image, the detector counts just as many electrons as in the real apparatus on the left. When choosing the mirror plane (perpendicular and perpendicular to the plane of the drawing), the direction from bottom to top is also from bottom to top in the mirror image. The current direction in the supply cables, the position of the detector and the flight direction of the counted electrons are therefore the same in the mirror image as in the apparatus to the left of the mirror. A second, mirror-inverted apparatus is now built and operated exactly as the mirror image indicates (on the right in the illustration). If parity is maintained, the process in it would have to run exactly as the mirror image of the original process shows. The detector of the mirror-inverted device counts significantly fewer electrons. As a result, parity conservation is violated. ${\displaystyle \beta }$ ${\displaystyle \beta }$ ${\displaystyle \beta }$ ${\displaystyle \beta }$

As a control, the detector is also used to observe the radiation that is generated by the (parity-maintaining) electromagnetic interaction. Here the observation in the mirror-inverted apparatus corresponds exactly to the mirror image (and the original apparatus). (Formulas can be found below) ${\displaystyle \gamma }$

In the real experiment, Wu did not reproduce the mirror-inverted apparatus, but simply reversed the direction of the current in the original apparatus and thus the magnetic field in which the radiation source was located. The mere polarity reversal means the same as the mirror-inverted replica, because the only physical difference between the two structures is that the mirrored magnet coil has the opposite screw direction and therefore generates the opposite magnetic field with the same current. The observed parity violation can therefore also be expressed solely with the help of the two directions of movement of the electrons in the supply cables of the coil or in the preferred direction of the rays: In the original structure they are parallel and in its mirror image therefore also, in reality the mirror-inverted apparatus but opposite. ${\displaystyle \beta }$

Further details are dealt with under Wu experiment . Inspired by the Wu experiment, Richard L. Garwin, Leon M. Lederman and Marcel Weinrich succeeded within a month later with a much simpler proof of the parity violation due to the weak interaction, this time on the basis of the non-mirror-symmetrical angular distribution of the electrons that arise when polarized muons decay . They were even finished with the elaboration sooner than the group around CS Wu, but let it go ahead with the publication.

Explanation of the parity violation

Problem of perception

The parity violation contradicts the immediate perception, because a mechanical device, which in a mirror-image replica would not function exactly as the original, is beyond our imagination. Rather, these are in harmony with all practical experiences in the macroscopic world, which are completely determined by the parity-maintaining interactions of gravity and electromagnetism.

Chirality

The physical explanation of parity violation is based on chirality ; H. the possibility of identifying a right-handed and a left-handed part of every fermion (such as electron, proton, neutron, neutrino) according to Dirac's theory . The parity violation is explained by the fact that the weak interaction of the fermions does not apply equally to both parts, but only to the left-chiral (with antifermions only to the right-chiral). Since a spatial reflection of the particles and the antiparticles interchanges these two chiral components, a weak interaction that is also reflected would now start on the other component (for particles on the right-handed, for antiparticles on the left-handed), the real weak interaction in the mirror-inverted experiment but not. A process in the mirror-inverted replica can therefore differ from the mirror image of the original process.

For fermions with (almost) the speed of light , the chirality is (almost) identical to the helicity . This is also called longitudinal polarization , because it measures the degree of alignment of the spin along the direction of flight: When the spin is in the direction of flight, when it is opposite. In general, a chiral right-handed particle has helicity at speed , a chiral left- handed particle . Every particle that does not move at the speed of light consists of both chiral components. At both parts are equal, at one goes to zero, the other to 1. As a consequence, z. B. high-energy electrons with the "spin forward" (positive helicity) only a small left-chiral component with which they can participate in the weak interaction. ${\displaystyle c}$ ${\displaystyle h}$ ${\displaystyle h=+1}$ ${\displaystyle h=-1}$ ${\displaystyle v}$ ${\displaystyle h=+{\tfrac {v}{c}}}$ ${\displaystyle h=-{\tfrac {v}{c}}}$ ${\displaystyle {\tfrac {1}{2}}(1\pm {\tfrac {v}{c}})}$ ${\displaystyle v=0}$ ${\displaystyle v\rightarrow c}$

Chirality in beta radioactivity

The beta-minus decay of an atomic nucleus is based on the conversion of a neutron into a proton, which creates an electron and an antineutrino . The left-handed part of a neutron emits a virtual W ^- boson , making it a proton, while the W ^- boson immediately radiates into a left-handed electron and a right-handed antineutrino . Since the antineutrino is practically only emitted at the speed of light, it always has maximum longitudinal polarization . Measurements of the polarization of electrons and neutrinos from the radioactivity have confirmed this picture (see e.g. the Goldhaber experiment ). ${\displaystyle {\overline {\nu }}_{e}}$ ${\displaystyle {\overline {\nu }}_{e}}$ ${\displaystyle h=+1}$ ${\displaystyle \beta }$

Chirality in the decay of the charged pion π ^-

A negatively charged pion decays almost exclusively into a muon and a muon antineutrino

${\displaystyle \pi ^{-}\rightarrow \mu ^{-}+{\overline {\nu }}_{\mu }\ \ (+29\,\mathrm {MeV} )}$,

and only 0.0123% in an electron and an electron antineutrino

${\displaystyle \pi ^{-}\rightarrow e^{-}+{\overline {\nu }}_{e}\ \ (+135\,\mathrm {MeV} )}$,

although this second path of decay should be more likely than the first because of the higher kinetic energy of the electron and antineutrino alone.

The simplest way of explaining this branching relationship is based on the parity violation. The pion has spin  0, so the spins of the muon (or electron) and antineutrino must be opposite. As a right-handed antiparticle , the almost massless antineutrino has its spin practically parallel to the direction of flight. Since the directions of flight of both particles are opposite due to the conservation of momentum , the spin of the muon (or electron) must also be directed parallel to its direction of flight, i.e. positive helicity must be present. In the case of positive helicity, however, the left-chiral component tends to zero the closer the speed of the particle comes to the speed of light. Now, because of its low mass, the kinetic energy of the electron is many times higher than its rest energy , so, unlike the muon, it is almost the speed of light. As a result, the left-chiral part of the electron, on which its generation by the weak interaction depends, is suppressed by about five orders of magnitude. This explains the observed frequency ratio of both types of decay. ${\displaystyle {\overline {\nu }}_{\mu }}$ ${\displaystyle m_{e}\ll m_{\mu }}$ ${\displaystyle m_{e}c^{2}\,{\mathord {\approx }}\,0{,}5\,\mathrm {MeV} }$

This argument, reproduced in many textbooks, is criticized to the effect that it is not the parity violation caused by the weak interaction that is responsible for the branching ratio, but rather its character of being a vector interaction. Assuming that the weak interaction would not only produce particles and antiparticles as left or right chiral, but equally often in the opposite sense, then it would receive parity, but due to its vector character still a particle together with an antiparticle only with opposite ones Can generate chiralities. As before, however, the conservation of momentum and angular momentum prescribe the same helicities for the particles and antiparticles produced during decay; there is therefore in any case the same hindrance as described above for the decay path to the electron. The vector character of the weak interaction in turn follows from its construction in the form of a gauge theory . There are two possible vectorial subtypes which have vectorial (V) and axial vectorial ( A) character (see VA theory ). The parity violation comes about through a certain interaction of both in the weak interaction. In contrast to this, the electromagnetic interaction and the strong interaction , which are also formulated as gauge theory and consequently also have vector character, are based only on the vector component. Therefore, parity is preserved for these two. What is also remarkable about the vector character is that of the five forms of interaction possible in principle within the framework of the Dirac theory, only the two vector forms can lead to a parity violation. ${\displaystyle \pi ^{-}}$

Chirality in the decay of the muon μ

Muons , which are formed when a pion decays , are completely polarized in the direction of flight due to the parity violation caused by the weak interaction (see previous section). If they (after complete braking in matter) according to

${\displaystyle \mu ^{-}\rightarrow e^{-}+\nu _{\mu }+{\overline {\nu }}_{e}\ \ (+105\,\mathrm {MeV} )}$

decay, the weak interaction causes an asymmetrical angular distribution of the electrons . For example, high energy electrons are preferentially emitted in the opposite direction to the direction of the muon spin. This can be explained by the fact that an electron of high energy can only be created if the other two particles fly in parallel in the opposite direction to the electron in order to maintain the total momentum. Since they have opposite helicities as neutrinos and antineutrinos, their two angular momenta are also opposite and thus add up to zero. The direction of the electron spin is thus fixed, it is the original angular momentum of the muon. Since the weak interaction only creates the chiral left-handed component of the electron when it decays, it is most likely to generate the electrons that are emitted opposite to their spin, i.e. opposite to the original direction of flight of the muon. The same phenomenon occurs with the opposite sign when the positive pion decays , followed by . Here the positrons fly primarily in the direction of the spin of the , which in turn is opposite to its original direction of flight. ${\displaystyle e^{-}}$ ${\displaystyle \pi ^{+}\rightarrow \mu ^{+}+{\nu }_{\mu }}$ ${\displaystyle \mu ^{+}\rightarrow e^{+}+{\overline {\nu }}_{\mu }+{\nu }_{e}}$ ${\displaystyle \mu ^{+}}$

See also

• CP violation

literature

• Theo Mayer-Kuckuk: The broken mirror: symmetry. Symmetry breaking and order in nature. Birkhäuser, Basel 1989.
• Jörn Bleck-Neuhaus: Elementary Particles. Modern physics from the atoms to the standard model . Springer, Heidelberg 2010, ISBN 978-3-540-85299-5 , chap. 12.2, 7.2.
• James Bjorken , Sidney Drell : Relativistic Quantum Mechanics . Bibliographisches Institut, Mannheim 1990, ISBN 3-411-00098-8 (BI university pocket books; 98 / 98a) engl. Original edition: Relativistic Quantum Mechanics . McGraw-Hill, New York 1964, ISBN 0-07-005493-2 .
• Walter Greiner : Relativistic Quantum Mechanics. Wave equations. Volume 6, ISBN 3-8171-1022-7 .
• Walter Greiner , Berndt Müller : Calibration theory of the weak interaction . 2nd Edition. Harri Deutsch, 1995, ISBN 3-8171-1427-3 , p. 272

Remarks

1. ↑ The formulas for the angular distribution are:

   Electrons: ${\displaystyle W\!_{\beta }(\theta )=1+A_{\beta }\cdot \cos \theta }$

   Photons: ${\displaystyle W\!_{\gamma }(\theta )=1+A_{\gamma }\cdot \cos ^{2}\theta }$

   The coefficient is given by the degree of polarization of the nuclear spins, i.e. H. by a sum of the magnetic quantum numbers weighted with the occupation numbers . Furthermore, the electron speed, A is a constant ( independent of), the nuclear spin. In contrast, the coefficient does not reflect the polarization, but the alignment , i.e. H. a sum of the squares weighted with the occupation numbers . For the mirrored direction ( ) remains the same, no. Sources: O. Koefoed-Hansen, in Handbuch der Physik (S. Flügge. Ed., 1962) Vol. 41/2, Formula (15.1); S. Devons, L. Goldfarb, in Handbuch der Physik (S. Flügge. Ed., 1957) Vol. 42 . ${\displaystyle A_{\beta }=A{\tfrac {v}{c}}{\tfrac {\langle I_{z}\rangle }{I}}}$ ${\displaystyle {\tfrac {\langle I_{z}\rangle }{I}}}$ ${\displaystyle m_{z}}$ ${\displaystyle v}$ ${\displaystyle v}$ ${\displaystyle I}$ ${\displaystyle A_{\gamma }}$ ${\displaystyle m_{z}^{2}}$ ${\displaystyle \theta \rightarrow 180^{\circ }\!-\theta }$ ${\displaystyle W_{\gamma }}$ ${\displaystyle W_{\beta }}$
2. ↑ For example, one should be able to imagine what happens between the thread and the wood in a normal wood screw if it violates parity, i.e. comes out when turning it in .

credentials

1. ↑ This is not just the reversal of the coordinate on the mirror normal , as in the plane mirror , but of all three coordinate axes and is also called point reflection . Both reflections only differ by a 180 ° rotation around the z-axis. ${\displaystyle z\rightarrow -z}$ ${\displaystyle (x,y,z)\rightarrow (-x,-y,-z)}$
2. ^ ^{A b} C. S. Wu, E. Ambler, RW Hayward, DD Hoppes, RP Hudson: Experimental Test of Parity Conservation in Beta Decay . In: Physical Review . 105, 1957, pp. 1413-1415. doi : 10.1103 / PhysRev.105.1413 .
3. ^ ^{A b} Richard L. Garwin, Leon M. Lederman, Marcel Weinrich: Observations of the Failure of Conservation of Parity and Charge Conjugation in Meson Decays: the Magnetic Moment of the Free Muon . In: Physical Review . 105, 1957, pp. 1415-1417. doi : 10.1103 / PhysRev.105.1415 .
4. ^ RT Cox, CG McIlwraith, B. Kurrelmeyer: Apparent evidence of polarization in a beam of β-rays , Proc. Natl. Acad. Sci USA, Vol. 14 (No. 7), p. 544 (1928)
5. ↑ TD Lee, CN Yang: Question of Parity Conservation in Weak Interactions . In: Physical Review . 104, 1956, pp. 254-258. doi : 10.1103 / PhysRev.104.254 .
6. ↑ Jörn Bleck-Neuhaus: Elementary Particles. From the atoms to the Standard Model to the Higgs boson (Section 12.2) . 2nd Edition. Springer, Heidelberg 2013, ISBN 978-3-642-32578-6 .