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14Phys129-Lect7-CP,N Physics 129 LECTURE 7 January 28, 2014 ● Newly Discovered Pulsar System Allows New Test of the Einstein Equivalence Principle ● Running Coupling Constants ● Grand Unification and Proton Decay (Perkins Ch 4) ● CP Violation n In Neutral K Mesons n In the CKM Matrix n In the Strong Interactions, Avoided with Axions n In Physics Beyond the Standard Model ● Neutrino Masses and Oscillations ● Supersymmetry Tuesday, January 28, 14 Science 10 January 2014: 343, pp. 126-127 Rare Celestial Trio to Put Einstein's Theory to the Test Adrian Cho In a cosmic coup, astronomers have found a celestial beacon known as a pulsar in orbit with two other stars. The first-of-its-kind trio could soon be used to put Einstein's theory of gravity to an unprecedented test. "It's a wonderful laboratory that nature has given us," says Paulo Freire, a radio astronomer at the Max Planck Institute for Radio A pulsar (left) and one star (center) Astronomy in Bonn, Germany, who was not involved are orbited by a more distant star (right). in the work. "It's almost made to order." A pulsar consists of a neutron star, the leftover core of a massive star that has exploded in a supernova. The core's intense gravity squeezes atomic nuclei into a single sphere of neutrons. The spinning neutron star also emits a beam of radio waves that sweeps the sky as steadily as the ticking of an atomic clock. Tiny variations in the flashing can reveal whether the pulsar is in orbit with another object: As the pulsar cycles toward and away from Earth, the pulse frequency oscillates. Roughly 80% of the more than 300 fast-spinning "millisecond" pulsars have a partner. But a single partner couldn't explain the peculiar warbles in the frequency of pulsar PSR J0337+1715, which Scott Ransom, an astronomer at the National Radio Astronomy Observatory in Charlottesville, Virginia, and colleagues discovered in 2007 with the Robert C. Byrd Green Bank Telescope in West Virginia. Training other radio telescopes on the object, Ransom and colleagues monitored it almost constantly for a year and a half. Eventually, Anne Archibald, a graduate student at McGill University in Montreal, Canada, figured out exactly what's going on. The pulsar, which has 1.4 times the sun's mass and spins 366 times a second, is in a tight orbit lasting 1.6 days with a white dwarf star only 20% as massive as the sun. A second white dwarf that weighs 41% as much as the sun orbits the inner pair every 327 days, Ransom and colleagues reported this week in Nature. "We think that there are not more than 100 of these [trios] in our galaxy," Ransom says. "They really are one-in-a-billion objects." Tuesday, January 28, 14 Rare Celestial Trio to Put Einstein's Theory to the Test (continued) The distinctive new system opens the way for testing a concept behind Einstein's theory of gravity, or general relativity. Called the equivalence principle, it relates two diferent conceptions of mass: inertial mass, which quantifies how an object resists accelerating when it's pushed or pulled, and gravitational mass, which determines how much a gravitational field pulls on it. The simplest version of the principle says inertial mass and gravitational mass are equal. It explains why ordinary objects like baseballs and bricks fall to Earth at the same rate regardless of their mass. The strong equivalence principle takes things an important step further. According to Einstein's famous equation, E = mc2, energy equals mass. So energy in an object's own gravitational field can contribute to its mass. The strong equivalence principle states that even if one includes mass generated through such "self-gravitation," gravitational and inertial mass are still equal. The strong equivalence principle holds in Einstein's general theory of relativity but not in most alternative theories, says Thibault Damour, a theoretical physicist at the Institute for Advanced Scientific Studies in Bures-sur-Yvette, France. So poking a pin in the principle would prove that general relativity is not the final word on gravity. Researchers have tried to test the strong equivalence principle by scrutinizing how the moon and Earth orbit in the gravitational field of the sun and how pulsar–white dwarf pairs cavort in the gravitational field of the galaxy. But Earth's self-gravitation is tiny, and the galaxy's gravity is weak. So such tests have yielded a precision of only parts per thousand, Damour says. The new pulsar system opens the way to a much more stringent test by combining the powerful self-gravitation of the pulsar with the strong gravitational field of the outer white dwarf. By tracking whether either the inner white dwarf or the pulsar falls faster toward the outer white dwarf, Ransom and colleagues should be able to test strong equivalence about 100 times as precisely as before, Damour says. If strong equivalence falters, Freire says, the result would mark "a complete revolution" in physics. Ransom says his team should be able to test the principle within a year. Tuesday, January 28, 14 Running Coupling Constants In the Standard Model of particle physics, the gauge theory SU(2)xU(1) describes the Electroweak interaction, and “color” SU(3) describes the Strong interaction. It turns out to be possible to calculate the values of the effective couplings of these gauge fields as a function of the momentum transfer q2 through the interaction. To first order in terms that are logarithmic in q2 (called “leading log approximation”), the electromagnetic coupling, which is α ≈ 1/137 at low q2, becomes This relates the coupling at one momentum transfer µ2 to that at another q2. Note that as q2 increases, the effective electro- magetic coupling constant α(q2) increases. This is because higher q2 corresponds to shorter distances and greater penetration + − of the cloud of e e pairs that shields the Cartoon Feynman Diagram bare charge at larger distances. Perkins’ Example 3.3 uses the above formula to calculate the value of 1/α(q2) at two values of q2, the electroweak scale q ~ 100 GeV, where 1/α ~ 129, and a grand unified theory (GUT) scale q ~ 3x1014 GeV, where 1/α ~ 111. (Homework 3 problem 1 is about running couplings.) Tuesday, January 28, 14 Perkins, D. H.. Particle Astrophysics (2nd Edition). : Oxford University Press, . p 95 http://site.ebrary.com/id/10288472?ppg=95 Copyright © Oxford University Press. All rights reserved. May not be reproduced in any form without permission from the publisher, except fair uses permitted under U.S. or applicable copyright law. Perkins, D. H.. Particle Astrophysics (2nd Edition). : Oxford University Press, . p 95 http://site.ebrary.com/id/10288472?ppg=95 Copyright © Oxford University Press. All rights reserved. May not be reproduced in any form without permission from the publisher, except fair uses permitted under U.S. or applicable copyright law. Running Coupling Constants In the Standard Model of particle physics, for the gauge theories SU(2) and “color” SU(3), the effective couplings of these nonabelian gauge fields decrease as a function of the momentum transfer q2, unlike for the abelian U(1) electromagnetic case. The reason is that the photon interacts only with electrically charged particles but not with itself since it is uncharged, while in the nonabelian theories the gauge particles interact with themselves. The diagrams below are examples of how gluons interact with quarks (b) but also with themselves (c). The leading log approximation is shown at right for the “running” of the Strong coupling 2 2 αS(q ), which decreases as q increases. This behaviour is known as “asymptotic freedom”. The effective Weak coupling also decreases as q2 increases. Experiments have abundantly confirmed these predictions of the Standard Model, as discussed in Perkins Section 3.12. Tuesday, January 28, 14 Perkins, D. H.. Particle Astrophysics (2nd Edition). : Oxford University Press, . p 96 http://site.ebrary.com/id/10288472?ppg=96 Copyright © Oxford University Press. All rights reserved. May not be reproduced in any form without permission from the publisher, except fair uses permitted under U.S. or applicable copyright law. Perkins, D. H.. Particle Astrophysics (2nd Edition). Perkins, D. H.. Particle Astrophysics (2nd Edition). : Oxford University Press, . p 96 : Oxford University Press, . p 96 http://site.ebrary.com/id/10288472?ppg=96 http://site.ebrary.com/id/10288472?ppg=96Perkins, D. H.. Particle AstrophysicsCopyright (2nd Edition).© Oxford University Press. All rights reserved. Copyright © Oxford University Press.: Oxford . All rights University reserved. Press, . p 96May not be reproduced in any form without permission from the publisher, May not be reproduced in any formhttp://site.ebrary.com/id/10288472?ppg=96 without permission from the publisher,except fair uses permitted under U.S. or applicable copyright law. except fair uses permitted under U.S. or applicable copyright law. Copyright © Oxford University Press. All rights reserved. May not be reproduced in any form without permission from the publisher, except fair uses permitted under U.S. or applicable copyright law. Grand Unified Theories (GUTs) If the Electromagnetic, Weak and Strong interactions are “grand unified”, then they will all meet at some value of q2 when we run the coupling constants. The dashed lines at right show what happens in the Standard Model: they do not all meet. The solid lines show what happens in a supersymmetric version of the same model: they all meet at about q = 1016 GeV. In this figure, α1 is the U(1) Electro- Perkins Fig. 4.6 weak coupling, α2 the Weak coupling, and α3 the Strong coupling. In GUTs there are, besides the Standard Model gauge bosons (photon, W±, Z0, and gluons), there are additional leptoquark gauge bosons X and Y that transform leptons into quarks and vice versa.
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