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Unformatted text preview: arXiv:0904.1962v3 [hepph] 23 Jan 2010 Unparticle selfinteractions Howard Georgi, 1 Yevgeny Kats, 2 Center for the Fundamental Laws of Nature Jefferson Physical Laboratory Harvard University Cambridge, MA 02138 Abstract We develop techniques for studying the effects of selfinteractions in the conformal sector of an unparticle model. Their physics is encoded in the higher npoint functions of the conformal theory. We study inclusive processes and argue that the inclusive production of unparticle stuff in standard model processes due to the unparticle self interactions can be decomposed using the conformal partial wave expansion and its generalizations into a sum over contributions from the production of various kinds of unparticle stuff, corresponding to different primary conformal operators. Such processes typically involve the production of unparticle stuff associated with oper ators other than those to which the standard model couples directly. Thus just as interactions between particles allow scattering processes to produce new particles in the final state, so unparticle selfinteractions cause the production of various kinds of unparticle stuff. We discuss both inclusive and exclusive methods for computing these processes. The resulting picture, we believe, is a step towards understanding what unparticle stuff looks like because it is quite analogous to way we describe the production and scattering of ordinary particles in quantum field theory, with the primary conformal operators playing the role of particles and the coefficients in the conformal partial wave expansion (and its generalization to include more fields) play ing the role of amplitudes. We exemplify our methods in the 2D toy model that we discussed previously in which the BanksZaks theory is exactly solvable. 1 georgi@physics.harvard.edu 2 kats@physics.harvard.edu Contents 1 Introduction 3 2 Unparticle selfinteractions 8 3 2D toy model of unparticle physics 12 3.1 Sommerfield model of a BanksZaks sector . . . . . . . . . . . . . . . . . . . 12 3.2 Coupling to the standard model . . . . . . . . . . . . . . . . . . . . . . . . 14 4 Correlation functions of the unparticle operator 15 4.1 2point function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 4.2 Higher npoint functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 4.3 Momentum space and IR divergences . . . . . . . . . . . . . . . . . . . . . . 20 5 Disappearance process: + U 22 6 Missing charge process: + + + U 24 6.1 Inclusive treatment: general . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 6.2 Results for small a . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 6.3 Inclusive treatment: series expansion . . . . . . . . . . . . . . . . . . . . . . 28 6.4 Interpretation in terms of exclusive processes . . . . . . . . . . . . . . . . . . 30 6.5 Exclusive treatment: amputated 3point functions . . . . . . . . . . . . . . .Exclusive treatment: amputated 3point functions ....
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This note was uploaded on 02/04/2012 for the course PHY 253B taught by Professor Georgi during the Spring '10 term at Princeton.
 Spring '10
 GEORGI

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