COO - 2271 - 101
THEORETICAL HIGH ENERGY PHYSICS
Progress Report
for the Period
May 1, 1977-April 30, 1978
This report was prepared as an account of work sponsored by the United States Government. Neither the United States nor the United States Department of Energy, nor any of their employees, nor any of their contractors, subcontractors, or their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness or usefulness of any information, apparatus, product or process disclosed, or represents that its use would not infringe privately owned rights. Principal Investigator:
T. D. Lee
Department of Physics Columbia University New York/ N. Y. 10027 ,. BROOKHAVEN PATENT GROUP June 1978 -^/^-^7£ By C&Z Prepared for The U. S. Department of Energy under Contract EY-76-C-02-2271. DISTRIBUTION OF THIS DOCUMENT IS UNT.TWT*?ft DISCLAIMER This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency Thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. DISCLAIMER Portions of this document may be illegible in electronic image products. Images are produced from the best available original document. ' ' Notice - -- -: ,- = " i' ■* -—~ This report was prepared as* an account of work sponsored by the United States Government. Neither the United States nor the United States Department of Energy, nor any of their employees, nor any of their .contractors^ subcontractor or their employees, makes any warranty, express or implied, or assumes any lega liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product or process disclosed or represents that its use would not infringe privately owned rights. PUBLICATION LIST EY-76-C-02-2271 1. C. Bernard and E. J. Weinberg, "Interpretation of Pseudoparticles in Physical Gauges", Physical Review DJ_5, 3655 (1977). 2. C. Bernard, N. H. Christ, A. Guth and E. J. Weinberg, " Pseudoparticle Parameters for Arbitrary Gauge Groups", Physical Review D]6, 2967 (1977). 3. C. Bernard, A. Guth and E. J. Weinberg, "Note on the Atiyah-Singer Index Theorem", Physical Review D17, 1053 (1978). 4. C. Bernard, "Instanton Interactions at the One-Loop Level", to be published in -Physical Review D. 5. N. H. Christ, N. Stanton and E. J. Weinberg, "General Self-Dual Yang-Mills Solutions", submitted to Physical Review D. 6. B. Coffey and R. Friedberg, "Effect of Short-Range Coulomb Interaction on Cooperative Spontaneous Emission", Physical Review A17, 1033 (1978). 7. S. Cummins, "Confinement in Three Dimensions", to be published in Physical Review D. 8. A. Duncan, "Explicit Dimensional Renormalization of Quantum Field Theory in Curved Space-Time", Physical Review D^, 964 (1978). 9. A. Duncan, "Instanton Effects in Bound-State Dynamics", to be published in Physical Review D. 10. G. Feinberg, "Parity Nonconservation in Atoms", to be published in the Proceedings of the Ben Lee Memorial International Conference on Parity Nonconservation, Weak Neutral Currents and Gauge Theories, held at Fermilab in October 1977. 11. G. Feinberg, "Handedness of Atoms and Parity Nonconservation", Nature 271, 509 (1978). 12. G. Feinberg, "Lorentz Invariance of Tachyon Theories, Physical Review D17, 1651 (1978). 13. G. Feinberg, " Parity-Violating Electromagnetic Interactions of Nuclei", Transactions of the New York Academy of Sciences 38, 26 (1977). 14. G. Feinberg, M. Goldhaber and G. Steigman, "Multiplicative Baryon Conservation and the Oscillation of Hydrogen into Antihydrogen", to be published in Physical Review A. 2. 15. G. Feinberg, J. Hiller and J. Sucher, "New Techniques for Evaluating Parity Conserving and Parity Violating Contact Interactions", submitted to Physical Review A. 16. J. Finkelstein, "A Sum Rule for Kaon-Nucleon Scattering", to be published In Physical Review D. 17. J. Finkelstein, G. Chew, J.-P. Sursock and G. Weissman, "Ordered Hadron , S Matrix", submitted to Nuclear Physics. 18. R. Friedberg and T. D. Lee, "Fermion-Field Nontopological Solitons II. Models for Hadrons", Physical Review D16, 1016 (1977). 19. R. Friedberg and T. D. Lee, "QCD Corrections in a Soliton Model of Hadrons", to be published in Physical Review D. 20. Fl'Krausz, "Cancellations of Mass Singularities in Yang-Mills Theories", Nuclear Physics B]26, 340 (1977). 21. T. D. Lee, "Nontopological Solitons", in Proceedings of the Symposium on Frontier Problems in High Energy Physics, edited by L. Foa and L. A. Radicati, Scuola Normale Superiore, Pisa, 1976, p. 47. 22. T. D. Lee, "Nontopological Solitons and Applications to Hadrons", Comments on Nuclear and Particle Physics 7, 165 (1978). 23. T. D. Lee, "Solitons and Hadrons", in Problemes Theoriques Lie's Aux Nouvelles Particules, Centre National de la Recherche Scientifique, Montpellier, 1977, p. 413. 24. -T. D. Lee, "Recent Results on Nontopological Soliton Solutions", to be published in Science of Matter (Festschrift in honor of T. Y. Wu). 25. T. D. Lee, "Nontopological Solitons and Applications to Hadrons", to be published in the issue of Physica Scripta devoted to the Chalmers Symposium on Solitons, Gbteborg, Sweden, 1978. 26. E. Mottola, "Fermion Green's Functions in the Presence of Pseudoparticles", Physical Review D]7, 1103 (1978). 27. A. H. Mueller, "Lectures on Hadron-Nucleus Collisions at High Energies", in Many Degrees of Freedom in Particle Theory, edited by H. Satz (Proceedings of the 1976 International Summer Institute of Theoretical Physics held at the University of Bielefeld) (New York, Plenum Press, 1978), p. 417. 28. A. H. Mueller, "Classical Euclidean Field Configurations and Charge Confinement", Physical Review D17, 1605 (1978). 3. 29. S. Sheth, "Effective Potential between Hard Spheres with an Attractive Tail", to be submitted to Physical Review. 30. A. Sinha, "Lorentz Transformations for Gauge Theory Monopole Solutions", Physical Review D]6, 1828 (1977). Dissertations A. S. Blaer, "Renormalization and the Elimination of Overlapping Divergences", 1977 A. Sinha, "On Gauge Theory Monopole Solutions", 1978. \ EY-76-C-02-2271 Percentages of Time Devoted to Project by Investigators November 1, 1977- October 31, 1978 Name % of Time Period Professors N. H. Christ 100 3 summer months -16 9 academic months G. Feinberg 100 3 summer months H. M. Foley 100 1^ summer months R. Friedberg 100 2 summer months T. D. Lee 100 3 summer months A. H. Mueller 100 3 summer months -15 9 academic months G. C. Wick 100 3 summer months Assistant Professors J. Finkelstein 100 3 summer months 50 9 academic months N. Stanton 100 1 summer month ' E. J. Weinberg 100 2\ summer months 50 9 academic months Research Associates C. Bernard 100 10 months S. Dimopoulos 100 2 months A. Duncan 100 12 months Note: During the academic year, the average teaching load for our faculty members is one course. A considerable amount of research (in addition to that specified above) Is performed by the several Investigators during those nine months. Progress Report Dr. Claude Bernard During the past year, Dr. Bernard has worked mainly on various aspects of "instanton" solutions to Yang-Mills field theory. In the summer and fall, he com• pleted work with Norman Christ, Alan Guth and Erick Weinberg which applied the mathematical tool of Atiyah-Singer index theory to the problem of counting the number of such solutions for arbitrary topological charge and gauge group. Most of their results appeared in Physical Review D16, 2967 (1977); a calculation of the Atiyah-Singer index for the case of interest will be published shortly in Physical Review D. More recently, Dr. Bernard has been studying the relation between exact multi-instanton solutions and linear superposition of single instantons in singular gauge. He has been able to establish a precise connection—keeping terms up to a fairly high order in the ratio of instanton size to separation—between the topological charge two exact solution (which is completely known) and the superposition of two instantons with arbitrary position, scale and orientation. Aside from elucidating the properties of the exact solution, this connection provides a parameterization of the exact solution which proves useful in discussing the lowest order quantum corrections. He expects to complete this work in the near future. Progress Report Professor Norman H. Christ During the past year Professor Christ's research has concentrated on the mathe• matical properties and physical applications of non-abelian gauge theories. In col• laboration with Claude Bernard, Alan Guth and Erick Weinberg, he produced an ex• haustive analysis of the number of parameters entering classical, self-dual, Yang-Mills solutions for all the compact, simple Lie groups. In all cases the number of parameters obtained was precisely that predicted by the simple physical picture that a self-dual solution with topological charge k is in a sense the superposition of k single instan• tons with arbitrary positions, scales and group orientations (Bernard, Christ, Guth and Weinberg, Phys.Rev. D]6, 2967 (1977)). Next, principally with Erick Weinberg and Nancy Stanton, in the Columbia Mathematics Department, Professor Christ undertook a detailed study of the method of Atiyah and Ward for the explicit construction of new self-dual solutions. This work produced a number of results, in particular: i) explicit formulae were obtained pro• ducing a self-dual vector potential given a rational function a(z) homogeneous of degree % in four complex variables z, ••• z* , ii) the singularities of the resulting gauge field were found in general to be 3 (9, odd) or 1 (% even) dimensional surfaces of infinite action density. However, before these conclusions were written up a new, more promising method for constructing the relevant mathematical objects was put forward by Atiyah, Hitchen, Drinfeld and Manin. Consequently, Professors Christ, Stanton and Weinberg turned their energies to this procedure with considerable success. First, specific algorithms were found reducing the construction of self-dual 2. solutions in O , SU and Sp to the problem of solving a quadratic matrix equa• tion. The number of parameters entering the solutions was determined and agreed for all k with the results obtained a year ago. The quadratic matrix equations were solved exactly for k = 1, 2 and 3 giving new k = 3 solutions and solved iteratively in an expansion about the dilute gas limit for arbitrary k . Finally, explicit forms for the propagators of I = 5 and 1 particles in the fields of a general self-dual SU« solution were found (Columbia preprint No. CU-TP-119). It is hoped that these results may be useful for explicit calculation of multi-instanton effects and may provide an additional step in the gradual unfolding of the surprising mathematical simplicity of the Yang-Mills theory. In collaboration with two of his students Professor Christ has addressed two somewhat more physical problems. Mr. Mottola has examined the relationship between the U, problem and instantons in the color Yang-Mills field. So far he has justified the use of 'tHooft's effective Lagrangian to arbitrary order in a dilute gas expansion . (Phys.Rev. D17, 1103 (1978)) and resolved a paradox raised by Crewther about such an application. Mr. Han is beginning to work on a new theory of CP violation in which a large 6FF term in the weak gauge theory violates CP and contributes, through the axial anomaly, to a AS = 2 transition providing a possible model of superweak CP -8 IT /a violation whose small size is the e characteristic of weak instanton effects. Finally, Mr. Mottola has analysed the hypothesis of Olive and Motoyon that the Georgi- Glashow model has a dual version in which the roles of t Hooft-Polyakov monopoles and the Yang-Mills quanta are exchanged. In particular he has found all the zero-frequency modes in the Prasad-Sommerfeld limit in terms of which the single-monopole Fock space n™ 3. can be analysed. The result appears to be negative—the threefold degeneracy required for a spin 1 monopole does not exist, spoiling the hypothesized duality. This result is now being written up. Progress Report Dr. Anthony Duncan Since his arrival at Columbia in September 1977, Dr. Duncan has been engaged in research on (a) quantum field theories in curved space-time and (b) instanton effects in gauge field theories of the strong interactions. With regard to the first topic, he was able to complete some investigations (begun at the Aspen Center for Physics) on the dimensional renormalization of a certain class of curved space quantum field theories. This work demonstrated, both in a general context and with reference to some specific solvable models (one of which is directly relevant to the radiation-dominated early universe), the usefulness of the method of continuation in the number of space-time dimensions for regularizing and renormalizing curved-space field theories (Physical Review D17, 964 (1978)). More recently, Dr. Duncan has been studying the effects of instantons on bound states in nonabelian gauge field theories. A systematic method was developed for computing the effects of instanton configurations on binding energies of threshold bound states. Specifically, mesonic (quark-antiquark) bound states were considered, although the formalism can be trivially extended to baryons. Interactions of exchanged quantum gluons with the background instanton fields (not previously considered in the literature) were found to lead to binding energies of the same order in the strong coup• ling a as direct interaction of the quarks with the background fields, and furthermore to lead to a linear static kernel in the dilute gas limit. It remains to be seen whether this (naively, confirming!) behavior persists or is damped out by multi-instanton effects should one attempt to iterate this kernel (Columbia CU-TP-116). Progress Report Professor Gerald Feinberg In the past year Professor Feinberg's research has concentrated in three areas: 1. Parity nonconservation in atoms - In this field, he has surveyed the various approaches to the calculation of the amount of optical rotation to be expected for linearly polarized light passing through Bismuth vapor. As a result of this survey, he has written two review articles on the subject (Proceedings of the B. Lee Memorial Conference, to be published; Nature 271, 509 (1978)). 2. Lorentz invariance of tachyon theories - Professor Feinberg has written a paper with a proof that under certain reasonable assumptions, a theory of tachyons interacting with ordinary particles will have transition rates that are Lorentz invariant in the pas• sive sense. This paper has been published in Physical Review D17, 1651 (1978). 3. In collaboration with M. Goldhaber and G. Steigman, Professor Feinberg has studied the constraints from astrophysical and other observations on a form of baryon number nonconservation in which two baryons change into two leptons. They have shown that 21 the upper limit for the strength of such an interaction is 10 times smaller than the weak interaction. Progress Report Assistant Professor Jerome Finkelstein During the past year, Professor Finkelstein has been engaged on the following projects: 1) The application of sum rules derived previously to an analysis of some recently acquired data on kaon-nucleon scattering. Using these sum rules, he has shown that the cross section for the process K p -» K n should be twice that for the process K p-»K A , even if the usually assumed exchange degeneracy is not valid in these processes. This production is quite well borne out by the data, except perhaps in the extreme forward direction; this result may indicate an anomalous behavior for the spin-non-flip amplitude. This work has been reported in a paper to be published in Physical Review. 2) In collaboration with G. Chew, J.-P. Sursock and G. Weissman of Berkeley, Professor Finkelstein has succeeded in generalizing the concept of the 'planar1 approx• imation to the topological expansion that had previously been restricted to amplitudes involving only ordinary mesons. They have constructed amplitudes (which they called 'ordered amplitudes') that accommodate an arbitrary number of 'neighbors' for each particle, and so are appropriate for processes involving ordinary mesons and baryons, as well as states containing larger numbers of quarks. Two of the features of these amplitudes are zero trivality for all allowed states (i.e., quark confinement) and the suppression of the couplings of baryonium to mesons relative to its couplings to baryons. This work has been reported in a paper submitted to Nuclear Physics. Progress Report Professor Henry M. Foley Professor Foley has been working on the following projects: a) "Cascade" in exotic H atoms (with his student, D. Chang). Calculations of transition downwards by inelastic heavy particle collisions of H - N atoms, where N ranges from muon to £ masses, have been completed, and the cascading phenomenon itself is being worked out. b) Short-range atomic perturbations (with his student, Y. Lee). Some progress has been made in finding a general method of describing interactions such as fine struc• ture, hyperfine structure, and other nuclear interactions, which includes "automatically" the inner electron curve distortion. A quasi-particle description of the valence electron may be feasible. Progress Report Professor Richard Friedberg Professor Friedberg has been working on the following problems: i) With Professor Lee he has continued to study baglike models for hadrons. They have explored the possibility that the scalar field producing the bag is only a phenom- enological average effect of an underlying vector gauge field theory, perhaps QCD. The direct exchange of vector particles with a coupling constant —5 could then account for mass splittings among low-lying hadrons. The residual discrepancy of about 20% is of the right order of magnitude for second order effects. The mass of rj' receives a contribution from an annihilation diagram which we observe contains a large factor due to the multiplicity of colors and flavors. ii) With Brian Coffey he has finished a paper dealing with radiation from two and three atoms. They are now performing a calculation of radiation from a completely inverted large sample of twor-level atoms, in the one-dimensional approximation but taking into account the quantum effects that begin the process, the spatial depen• dence of excitation, and the interaction of two waves going in opposite directions. iii) With another student, Sunil Sheth, Professor Friedberg has been working on the properties of helium at low temperature. At present they are completing a paper on the effective potential (ladder approximation) between two atoms interacting via an infinitely repulsive core and an attractive square well. Progress Report Professor T. D. Lee During this past year Professor Lee has worked in the following areas: 1. Solitons The study of nontopological soliton solutions that began about two years ago has been further extended [T. D. Lee, Physics Reports 23C, 254 (1976); R. Friedberg, T. D. Lee and A. Sirlin, Physical Review D]3, 2739 (1976), Nuclear Physics B115, 1, 32 (1976); T. D. Lee, Proceedings of the Symposium on Frontier Problems in High Energy Physics, edited by L. Foa and L. A. Radicati, Scuola Normale Superiore, Pisa, 1976, p. 47; R. Friedberg and T. D. Lee, Physical Review D]5, 1694 (1977); T. D. Lee, Comments on Nuclear and Particle Physics 7, 165(1978) J. A review article on this subject is being prepared, which will be published in the Review of Modern Physics. 2. QCD and Applications to Hadrons In a recent paper, Professor Lee (CU-TP-118 written with Professor Friedberg) has examined the relation between QCD and the soliton solutions. By starting from QCD in a finite volume and then taking the infinite volume limit, they,showed that under rather general assumptions there is a "phase transition" phenomenon, which implies the existence of a long-range order in the vacuum for an infinite volume. This long-range order is rep• resented by Lorentz scalars, because of relativistic invariance; such Lorentz scalars can in turn be identified with the phenomenological scalar fields used in a soliton model of hadrons. In the phenomenological appraoch, a permanent quark confinement can be simply viewed as the vacuum of an infinite volume being a perfect "dia-electric" 2. substance, with its dielectric constant K -* 0 , while the "vacuum" inside a hadron is normal (« = 1), which may be identified as that of QCD for a finite volume. Inside the hadron, exchanges of gauge quanta between quarks give the QCD corrections to the soliton model. Spectroscopy of light quark hadrons is then examined by expanding the hadron masses M in powers of the "fine structure constant" a of QCD: 2 M = M. + a M. + a M~ + .... The near-zero mass of the pion is correlated with the existence of a critical value a in the mass formula, and the r\ ~ r)1 anomaly is 2 associated with a large enhancement factor in the 0(a ) quark-antiquark annihila• tion diagrams, due to coherence in the various color and flavor degrees of freedom. 3. Abnormal Nuclear States Work connected with the possible existence of a new form of matter at high density suggested by Lee and Wick [ Physical Review D9, 2291 (1974)] is being con• tinued. Their recent paper £to be published in Mesons in Nuclei, edited by M. Rho and D. Wilkinson (North-Holland) J gives a thorough survey of the field. This field is now quite active, especially in connection with the new BEVALAC-SUPERHILAC project at Berkeley. Professor Lee is in close contact with the experimental develop• ments. He participated in the January meeting of the Dense Nuclear Matter Review Group (organized by Lawrence Laboratory). He will also attend the Summer Study Group on High Energy Nuclear Collisions in Berkeley this July. Progress Report Professor Alfred H. Mueller Professor Mueller has spent the last year studying properties of the classical vacuum in Yang-Mills theories. The main motivation for this is to see if and how classical Euclidean solutions, equivalent to semiclassical Minkowski configurations, relate to confinement of quarks. In a completed piece of work, published in Physical Review Dl 7,11605 (1978), it was concluded that confinement cannot come about from configurations which are exact classical solutions in the long wavelength region. At the,moment Professor Mueller is finishing a calculation of the long wavelength behavior of fixed density multi-instanton solutions in the infinite volume limit. Progress Report Assistant Professor Erick J. Weinberg During the past year Professor Weinberg's research has been concerned with the classical Yang-Mills theory in four-dimensional Euclidean space. His main interest has been in the self-dual, or "instanton", solutions which are believed to have great significance for the quantum mechanical treatment of gauge theories. For SU(2), the most general solution which had previously been known was the (5k + 4)-parameter solution of Jackiw, Nohl and Rebbi; it was known that this was not the general solution.- For other groups, the only known solutions were those obtained by embedding SU(2) solutions into larger groups; it was not known whether there existed instanton solutions which were not essentially SU(2) in nature. * A first step in understanding the nature of the general self-dual solutions is to determine how many physical parameters are needed to specify it. In collaboration with Claude Bernard, Norman Christ and Alan Guth, Professor Weinberg determined this number for arbitrary gauge groups. Further, they were able to show that for topo• logical charge R the number is precisely that required to specify the position, scale and relative group orientation of k independent solutions each with topological charge 1 . A paper describing this work has appeared in Physical Review D. An important tool for determining the number of parameters in these solutions is the Atiyah-Singer index theorem. In collaboration with Claude Bernard and Alan Guth, Professor Weinberg developed a simple derivation of the form which the index theorem takes in this application. A paper describing this work has appeared in Physical Review D. 2 » " Finally, in collaboration with Norman Christ and Nancy Stanton (of the ■* j Columbia Mathematics Department) and using results obtained by Atiyah and Manin, Professor Weinberg studied the general selfdual solutions. They were able to obtain the form of the solution corresponding to the case of widely separated instantons. For the more general case, the nonlinear differential equations are reduced to a set of non linear algebraic equations, which they show take essentially the same form for all gauge groups. They are at present preparing a paper describing this work. Progress Report Professor Gian Carlo Wick As stated in last year's research proposal, Professor Wick's attention has been devoted mainly to gauge-field theories, in particular to the study of classical solutions (solitons, instantons). There are two rather different approaches to this subject being pursued at this moment. One approach has been adopted mostly by physicists, the other one by mathematicians. Professor Wick's effort has been to develop a description that would be understandable to both sides. He thinks there is a real need for this, and although he has not yet managed to write a satisfactory account on the subject, he is working on it. In this endeavor, the time he has spent learning the language employed by mathematicians would, he hopes, yield some rewards.