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Lecture 9 CPT Theorem and CP Violation

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Lecture 9 CPT Theorem and CP Violation Lecture 9 CPT theorem and CP violation Emmy Noether's theorem (proved 1915, published 1918) •Any differentiable symmetry of the action of a physical system has a corresponding conservation law. The action of a physical system is the integral over time of a Lagrangian function (which may or may not be an integral over space of a Lagrangian density function), from which the system’s behavior can be determined by the principle of least action. •Energy, momentum and angular momentum conservation laws are consequences of symmetries of space. eg, if a physical system behaves the same regardless of how it is oriented in space -> Lagrangian is rotationally symmetric -> angular momentum of the system must be conserved •We have seen that although both charge conjugation and parity are violated in weak interactions, the combination of the two CP turns left-handed antimuon onto right-handed muon, that is exactly observed in nature. •There is another symmetry in nature – time reversal T (winding the film backward). •Charge conjugation, C, together with parity inversion, P, and time reversal, T, are connected into the famous CPT theorem. •CPT theorem is one of the basic principles of quantum field theory. It states that all interactions are invariant under sequential application of C, P and T operations in any order. Any Lorentz invariant local quantum field theory with a Hermitian Hamiltonian must have CPT symmetry. •It is closely related to the interpretation that antiparticles can be treated mathematically as particles moving backward in time. Ernst Stueckelberg (1905-1984) Should have received several Noble prizes • 1934 - First developer of fully Lorentz-covariant theory for quantum field • 1935 - Developed vector boson exchange as theoretical explanation for nuclear forces. Rediscovered by Yukawa. • 1938 - Proposed a conservation of baryon number. • 1941- Recognized that electrodynamics with massive particles contain a hidden scalar. Rediscovered in 1964 by Higgs. • 1941- Proposed an interpretation of positron as a positive energy electron travelling backwards in time. • 1943 – Proposed renormalization method to deal with infinities in quantum electrodynamics (paper rejected by Physical Review) Spent substantial fraction of his time in later years dealing with mental problems. Most of his papers were written in very difficult German and published in small local journals in Switzerland. He did not like public talks and avoided crowd. Recognized only after his death à if you want to be famous – learn to talk and present your ideas. I have to give credit to Stueckelberg for the concept of antiparticle considered as particle travelling backward in time. In most of the Literature it is usually connected with Richard Feynman, who used it to introduce Feynman diagrams that vastly simplify QED calculations and are used as graphical illustration of particle level processes. Consider a Lorentz boost in a fixed direction z. This can be interpreted as a rotation of time axis into the z axis with an imaginary rotation parameter. If this rotation parameter were real, it would be possible for a 1800 rotation to reverse the direction of time and of z. Reversing the direction of one axis is a reflection of space in any number of dimensions. For a 3 dimensional space, it is equivalent to reflection of all the coordinates, because an additional rotation of 1800 in the x-y plane would be included. •Symmetry of time reversal is very difficult to test experimentally. One of its prediction is that some properties of particles and antiparticles should have the same magnitudes, e.g., mass, lifetime, magnetic moment. For most of the cases that has been verified to be true within measurement precision, but not always. •CPT theorem implies that the violation of CP invariance implies violation of time reversal symmetry T. •One of the most important unresolved questions today is the evolution of the universe. If it started with a Big Bang where all interactions had strength of strong forces – then there should be equal amount of matter and antimatter in the universe. CP violation allows for some preference of survival of matter over survival of antimatter, but so far we have not seen sufficient amount of CP violation to account for observations of the Cosmos. Insert Matt Stein –cosmic rays Cosmic Rays Matt Stein - SMU A long, long time ago… • 1785: France • Charles Coulomb shows that charged metallic bodies gradually lose charge when placed in air • There will be conflicting opinions on this claim, and its causes, for the next ~100 years • In 1895, J.J. Thompson would speak on “ions” in the atmosphere Charles-Augustin de Coulomb 9 Why is the atmosphere • Radium in the Earth ionized? • Tests conducted over seas by Arthur S. Eve, 1907 • 1901: Charles Thomson Rees Wilson conducted experiments in deep tunnels • Found no decrease in ionization no matter how much rock was overhead • “It is unlikely, therefore, that the ionization is due to radiation which has traversed our atmosphere; it seems to be a property of the air itself.” – Elster Geitel 10 1909 – Theodor Wulf • Ionization at different heights • Theorized that if Earth were the source of radiation, it should quickly diminish with increasing height • Took measurements from the base and top of the Eifel Tower (~300m) • Recorded 6 ions generated per cc per second at ground level, and 3.5 ions per cc per second on top • Expected to find ionization at the top to be ~1% that of the bottom 11 The Gold-leaf Electroscope • Charge is applied to metallic wires • The static charge causes repulsion between the wires and they spread to form a “v” shape • Separation between the wires is measured and 12 total charge on wires can be August 7, 1912 – Victor F. Hess • Most decisive results starting coming in by the 7th flight • Took off near Aussig, Austria and flight lasted 6 hours • Balloon elevation ~ 16,400ft (5 km) • Conclusively correlated increasing radiation with increasing altitude 13 14 Confirmation by Werner Kolhorster 15 The Millikan Doubts • Extraterrestrial origin of cosmic rays was difficult for some to believe • Robert Millikan would work for years in an attempt to disprove Hess’ claims • Sent balloons to over 50,000ft (15km) • “The results then… constitute definite proof that there exists no radiation of cosmic origin having such characteristics as we had assumed.” • Later conducted experiments at Lake Muir, Arrowhead Lake, Mt. Whitney, and Pikes Peak 16 17 1925 – Lake Muir and Arrowhead Lake • Submerged electroscopes to depths as deep as 20m • Readings decreased steadily to 15m • Compare where discharge rates are similar • Millikan confirms that this radiation definitely originates from outside the Earth’s atmosphere 18 “Cosmic Rays” • Millikan coins the term “Cosmic Rays” • After his 1923 Nobel Prize, he is already the most respected physicist in America • The New York Times names this 19 radiation “Millikan What are cosmic rays? • A large variety of particles including: • Electrons • Positrons • Protons • Muons • Other nuclei like carbon, oxygen, neon, magnesium, silicon, iron, nickel, and more. • Gamma rays (~0.1%) • Can be split into “Primary” and “Secondary” rays 20 Primary and Secondary Cosmic Rays • Primary rays are the first to interact with Earth’s atmosphere • They collide with air molecules and create an “air shower” of secondary particles • Can even convert 21 Nitrogen into Carbon-14 LHC 99.99999999999999999999951% c OMG! 22 23 How do we detect cosmic rays? • High energy cosmic rays can be detected from their air showers • Air Shower Arrays are created to detect particles and their direction • In general, there are more particles in the center of the air shower • Scintillator detectors and water Cherenkov detectors are used on Earth 24 Water Cherenkov Scintillator Detector Detector 25 Tibet Air Shower Experiment 26 Alpha Magnetic Spectrometer • Capable of detecting primary cosmic rays • 5 detectors onboard 27 Recent AMS Results • Positron fraction is higher than previously assumed • Two popular theories: • 1. Positrons generated by pulsars • 2. Positrons are generated by dark matter collisions 28 • Further data collection up to There’s an app for that! • http://wipac.wisc.edu/le arn 29 Sources of Cosmic Rays 30 Pierre Auger Observatory 31 32 Supernovae as sources 33 Cosmic Rays • First significant finding came in 1912 from Hess’ balloon flight • Cosmic rays are a variety of very high energy particles; the highest known to exist • Air showers form when primary cosmic rays interact with the upper atmosphere • Detecting these primary particles can be done in space, as in the case of the AMS • Charged particles are difficult to determine the source unless at the very highest energy levels • Most cosmic rays probably originate within ~160,000 light years • Sources are supernovae for low energy cosmic rays, and AGN for high energy cosmic rays 34 Resources • Abraham, J., et al. "Correlation of the Highest-Energy Cosmic Rays with Nearby Extragalactic Objects." Science 318.5852 (2007): 938-43. • Ackermann, M. et al. "Detection of the Characteristic Pion-Decay Signature in Supernova Remnants." Science 339.6121 (2013): 807-11. • Amenomori, M., et al. "Tibet Air Shower Array: Results and Future Plan." Journal of Physics: Conference Series 120.6 (2008): 062024. • Bauleo, Pablo M., and Julio Rodríguez Martino. "The Dawn of the Particle Astronomy Era in Ultra-high-energy Cosmic Rays." Nature 458.7240 (2009): 847-51. • Carroll, Bradley W., and Dale A. Ostlie. An Introduction to Modern Astrophysics. 2nd ed. San Francisco: Pearson Addison-Wesley, 2007. Print. • Cronin, James W., Thomas K. Gaisser, and Simon P. Swordy. "Cosmic Rays at the Energy Frontier." Scientific American 276.1 (1997): 44-49. • Griffiths, David J. Introduction to Elementary Particles. 2nd ed. Weinheim: Wiley-VCH, 2008. Print. • Matthiae, Giorgio. "The Cosmic Ray Energy Spectrum as Measured Using the Pierre Auger Observatory." New Journal of Physics 12.7 (2010): 075009. • Xu, Qiaozhen.
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