In these classic lectures, Feynman analyses the theoretical questions related to electron and photon interactions at high energies. These lectures are based on a special topics course taught by Feynman at Caltech in 1971 and 1972. The material is dealt with on an advanced level and includes discussions of vector meson dominance and deep inelastic scattering. The possible consequences of the parton model are also analyzed. ONTENTS......Page 12 EDITORS FOREWARD......Page 8 SPECIAL PREFACE......Page 10 VITA......Page 11 PREFACE......Page 17 15 GENERAL THEORETICAL BACKGROUND......Page 20 First Order Coupling......Page 22 Conservation of Current......Page 23 2nd Order Coupling......Page 24 Unitarity 2nd Order......Page 25 Proof......Page 27 End of Proof......Page 29 Research Problem......Page 30 Conservation of Current......Page 31 Remark......Page 32 Isotopic Spin, Strangeness, Generalized Currents......Page 33 Conservation of Generalized Currents......Page 35 Singularities on the Light Cone......Page 38 Vacuum Expectation of Vsub(μν)(1, 2)......Page 39 esup(+) + esup() → Any Hadrons......Page 40 Note: Annoying Point......Page 45 Commutator......Page 46 Problems......Page 47 Pion Photoproduction Low Energy (0 to 2GeV)......Page 48 Problem......Page 52 Note......Page 55 The Quark Model......Page 59 Note......Page 61 Problern......Page 66 CalcuIation of Matrix Elements......Page 67 Feynman, Kislinger and Ravndal, Phys. Rev. (1971)......Page 68 References......Page 77 tChannel Exchange Phenomena......Page 88 Comments......Page 92 sChannel Resonances......Page 93 Veneziano Fomula......Page 95 Estimates of Coupling Constants......Page 96 Electron Production of Vector Mesons......Page 99 Vector Meson Dominance Model......Page 106 φ as ss......Page 111 VDM and Photon Hadron Interactions......Page 113 Diffractive Production of ρ, ω, φ......Page 119 Other Tests of VDM......Page 125 Shadowing in Nuclei......Page 126 To Summarize the Position of VDM......Page 130 Nucleon......Page 131 In Lab......Page 132 Electromagnetic Form Factors (continued)......Page 133 Pion Form Factor......Page 135 Proton Form Factor for Positive qsup(2)......Page 138 Note......Page 139 Other Photon Processes for qsup(2)
This page intentionally left blank Andcl-son: Dasic Notions of Condcnsctl 1lqattc1-f3hysics, ARC ppl>k, lSBN 0-201-32830-9 Atiyah: K-'fheory, AB@ ppl~k,1SBK 0-201-40792-2 Rcthc: fntcr-mctliatc Quantum Mechanics, ABC pphk, ISRK 0-201-32831- Ciicmmoxtr: I3tctrocrt) namic s of Particles and Ptasrnas, ARC ppbk, 1SBX 0-20147986-9 Ilacitlscjn: Physics of Xanneutrat f31asn-ras, ABC pphk ISBK 0-201-57830- ctTf-,si~agnat: Corrcrptual 1.oundations (lua~ltumMtchanics, AKC ppbk, 1SBK 0-7382-0104 iieynn.ran: f3hoton-Haclran fntcr-actions, ARC pphk, XSBK 0-201- 36074-8 Iscynman: Quantum l:tcctrodynamics, ABC ppbk, ISBN Q- 201 - 36075-4 iieynn.ran: Statistical ~lqcchanics,ARC pphk, XSBK 0-201- 36076-4 I:cynman: * f i r o r >of 1.utrdanrcrrtal 1'1-occsscs, ABC ppbk, fSBK 0-201- 36077-2 iiorstc.r: l4ydrotljnamic X;tuctuations, Drokcn Symmcrry, and Correlation X;unctions, ARC pphk, ISRPU' 0-201-41049-4 Ccli-hfann/Xe'eman:'fhe kightfotct Way, AB@ pplk, 1SBK 0-7382-0299-1 Gon&icd: Quantun.r Mechanics, ARC pphk, ISRN 0-201-40633-0 Kactanoff/Bajm: Qr~a~rtrim Statistical Mechanics, AKC ppbk, ISBN 0-201-41i1.2-6-X KhaIarnikoc :An Intro to thc "Theory of Stipcr-Ruitlity, AARC pphk, ISRN 0-7382-0300-9 Ma: Modern'fheory of Criticat t%henomena, ABC ppbk, ISBN Q-"138-0301-7 Migtlal: Qualitatixcl Mellttods in Quantum Theory, AARC pphk, fSI3S 0-7382-0302-9 r\lcgclc/Orfand: Quantum Many- t%articlc Systems, ABC pplhk, lSBN Q-"138-0052-2 No/iei-cs/X'incs:'I'hcory of Qtianturn I,icluicls, ABC pphk, ISRK 0-7382-0229-0 Koziercs: Df"hcoryof interacting Iscrmi Systems, AB@ ~ j p l ~ kISBN , 0-201- 32824-0 X'arisi: Statistical I.:iejd 'I'hcory, ABC pphk, ISRK 0-7382-0051-4I'iincs: Etcmcntary I k c i ~ t i o r r sin Solids, ABC ppbk, fSBN 0-7382-01 5-4 1'incs:'I'hc 1Wanj-Body X'robtcm, ABC pphk, ISRK 0-201-32834-8 Q u i g : Garrgc*Ibcaricsof the Strong, Weak, and I:lccti-omagnctic fnteractiorrs, ABC pplzk, ISWK 0-0-201-32832-1 Richartison: Fxpcrin-tcntal'lkchniyues in Condensed Martcr X'hysics at I ow 'fempcratnrcs, ABC pphk lSRS 0-201 - 36078-El 12ohrlich: Classical Chargcs t%articlcs, ABC ppbk ISBN 0-201-48 300-9 Schi-iegcr: Theory of Supcrconducti~ity, ARC jq"fhk fSI3S 0-7382-0120-0 "ihwingcr: t%articlcs, "iourccs, and Ficfdr Vol 1, I"IBC plibii ISB?; Q-"182-0053-0 Schwingcr: Particles, Sources, and Fictds Vol 2, ABC: ppEA ISBX 0-7382 -0054-9 Schwingcr: Particles, Sctui-ccs, and Ficlcts'riol 3, ABC pphk ISRX 0-7382-0055-7 "ihwingcr: Quantum Kinematics and Dynamics, I"IBC plibii, ISBK 0-"182-030 3- "Thorn: Structura! Stability and 1Worphogcnesis,ARC ppbk, ISB?; 0-201-40685-3 Whyld: Mathematical Mcthods for 13hhysics,ABC pppbk, ISBN 0-"138-0125-1 NTERACTIONS RICHARD P FEYNMAN late, California Institute of Technology " L i / * ~*q% Addvnnccd Book Pmgnm, i - , /' A Member af the Xlcrseus Books Group Libmry of Congress Catalogixlgin~Pu'Et1ica;tion Data Feynman, Richard PhiHips Photon-hadron tnteracrrions I Richard Feynman p cm - (Advanced book cfassics series) Originally published : Reading, Mass : W A Benjamin, Advanced Book Program, 2912 (Frontiers in physics) Includes index, Photon-hadron mteract-ions Hadron interacdons Title XI, Series QC/93,S,IE)428F49 1989 539.1Y544~19 89-30697 XSBN 0-201-36014-8 (paperback) Copyright O 1912, 1998 All: rights reserved No part of this publication may be reproduced, stored in a renieval system, or transmitted, in any form or by any meatas, electronic, mechanical, photocopying, recording, or otherwise, without the prior written pemission of the publisher Printed in the United States of America, Westview Prcss 1s a Mcmhcr of the Perscus Books Group Cover design by Suzanne Weiser 2345678910 First printing, February 1998 Find us on the World Wide Web at htt~:www.we~ieli~~ress.com Editor's Foreword Addison-Wesley's F~ontiersin Physics series has, since 1961, made it possible for leading physicists to communicate in coherent fashion their views of recent developments in the most exciting and active fields of physics-without having to devote the time and energy required to prepare a formal review or monograph Indeed, throughout its nearly forty-year existence, the series has emphasized informality in both style and content, as well as pedagogical clarity Over time, it was expected that these informal accounts would be replaced by more formal counterparts-tex tbooks or monographs-as the cutting-edge topics they treated gradually became integrated into the body of physics knowledge and reader interest dwindled However, this has not proven to be the case for a nurnber of the volumes in the series: Marry works have remained in prim on an on-demand bmis, while others have such intrinsic value that the physics community has urged us to extend their life span The Aduanced Book Classics series has been designed to meet this demand It will keep in print those volumes in Frontiers in Physics or its sister series, Lecturre Notes ~ n Supipkments d in Physics, that continue to provide a unique account of a topic of lasting interest And through a sizable printing, these cIassics will he made available at a comparatively modest cost to the reader These notes on Richard Feynman's lectures at Caltech on the topic of photon-hadron interactions, in which he developed his theory of partons, were first published some twenty-five years ago As is the case with all of Feynman's lectures, the presentation in this work reflects his deep physical insight, the freshness and originality of his approach to understanding physics, and his overall pedagogical wizardq As a result, this volume will always be of fundamental importance to anyone interested in understanding the development of quantum chromodynamics (QCD) the theory of quarks and gluons which explains hadron-hadron interactions at high energies David Pines Urbana, Illinois December 1991 Preface Many of us wem first in~dtlcecito the concepts of the p m n model from this b k At h t lllme the eompting view ww one in which there were no elemenm pheles, E v e ~ p d c l e was suppsd tn, be a campsite of evey other pdcle The ideas and conmpts in &isbook h v e helpd pave &e way far our undersmding of the constituentname of trra&ons which evennially led ts the Quantum Chmnndynamic (WD)&wq of qu&s and gluo'ns, & is m e of most of Feynmank b b s , the maximum bnefit is o b ~ n e ifd one has previowly studied the subjeer in some d e ~ fFcynmank unique:p r s p t i v e can br;be a p ~ w i a t d by rwdws with a mlid b ~ k g o m din the subject Although this book is dmost l8 yms otd, it still is an excellent referace, It a m a s on the raomntenkd rmding fistof &I thecmmtwD b k s , Tke bkprovidcs a g d undersmdingof ltfte m d d from rheman who invenkd it In the "pre-QGW or "'naive" "on m d e i tfie constituents within ha&ons were assume8 u> b hunded in the transvers dlr~tion,The pmbability of finding a pmon wifftin a high momentm ha&on wi& a lmge msverrze momentum was assumed to fd1 like a Gaussian or an expnential W D ells us that this is not exactfy &rueand givesa p w e r law fall-off in the transverg momentum, Beeause of this, many ""nve" "on mode8 e x p t a ~ o nare s mabifid (in an inzportant way) by Xogarlrhmic faem, Feynmru?used t;s laugh when his pmon mdeI was refened to as "n&ve,'"and he wollld say, ""At l m t X got it ~ g hup t to lag;&&rns." We all miss Feynman v e q much a d it is through books like this hat his id= live on, Photon-Hadran Interaetiom 268 A %&er of t h e deciroet: 4, h a s a s w f l e r probability of having a quark near x = than does t h e o c t e t f a r t o t a l c r o s s sections, We have already discussed t h e i a p l i c a t i o n s X t has i q l i c a t i o n s f o r products a l s o , of course klcz a l s o a s s u m t h a t i f a s t a t e i s a pure quark t o t h e l e f t i t has an m l i t l x d e t o be a b a q o n t o the l e f t with z n e a r l y which is proportional the the chance t h e baryan contains a f a s t quark near m e r e a r e them w a y implleations Eor products X = Z of the s a w kind, - and we have ~ t i o n e dso= t h a t came from u(x) being 1arlger than a l l t h e o t h e r s a s x -+ I, There a r e o t h e r s , of another type, f o r e x a q l e (Claneroa, p r i v a t e comunication) i n eke 4" e e - -c hrrdrons s i n e e 5u haa four times t h e p r o b a b i l i t y of ad the chance o f producing a proton with x n e a r l ( i n t h e c e n t e r of =ss) and anything, e l s e is f o u r times the probabi l i t y of producing a neutron, I f &S 5s c o r r e c t we shauld l i k e t o a s s u w solnething analogous f o r t h e The analogoos a s s m p t i o n Fa t h a t when one quark takes m e t of the =ems mwatufn i t i s of a type t h a t t h e low e n e r m quark =del t o be m b e o f Cbe t h e r e f o r e (Zn agreemeat with Zisneros) aserne: ( f o r t h e charge conjugate i t i a it8 Q supposes t h e meon @ near x = l and the remainder We have b u i l t a very t a l l house of cards asking s o m a y weakly-based eonJectures one upon t h e o t h e r and a g r e a t d e a l anay be wrong (Probably - s a m p l a t e a u f o r gap and hadron - b u t i f i t were wrong i t does not a l t e r t h e t h r w t of any of t h e o t h e r s - j u s t i n t h e operator expreesions the weakest is C6 we s h a l l have t o be c a r e f u l t o u l ~ et h e rgght plateauh),] tdevertheless t h i a is the b e s t guess I can riitaake ROW - and we- can t r y t o use them has warking hypotheses Probably t h e g r e a t e s t challenge t o e x p e r i w n t and theory is t o get soracr, evidence o f quark qumurturn n u d e r s i n high-energy collisions, The low-energy quark ausdel, good a s i t is, i a n o t enough, t h e r e i s always l i n g e r i n g doubt that: the r e g u l a r i t i e s observed have so= e n t i r e l y d i f f e r e n t bask8 o r arc?, i n part, accidental, The establSshment of evidence f o r the quark model ( m d we have i n d i c a t e d very nrany ways - both i n the l a s t few l e c t u r e s a s w e l l a s e a r l i e r -(Llewellyn S ~ t ' sh sum r u l e (Equation 33.61, t h e s p i n sum r u l e f o r glp-gIn e t c ) by high energy e n p e r i m n t s would c o n f i w a t once the r e a l i t y of the r e g u l a r i t i e s i n t e r p r e t e d by the low energy quark aaotlel This would m k e f i r m a e m j e c t u r e of deepest s i g n i f i c a n c e t o understanding high energy physics - t h e intgortance of quark q u a a t m n m b e r s Supposing f o r a m m n t t h i s i s done, t h a t h e next s e r i o u s question w i l l become t h e o r e t i c a l - what e x a c t l y is t h e r e l a t i o n of t h e quark q u a l i t i e s a t high energy and, t h a s e a t low e n e r m "I"heW"prtans a s q u a r b " "del does not iarply t h e low energy model ( i e why a r e the wave f m c t i o n s n o t m r e c o q l i c a t e d involving quark antiquark p a i r s ) n o r v i c e versa would n o t b e understood courage - you mi&t confirmed, A t present t h e i r relation To s t a r t working on t h i s n m w i l l take a l i t t l e waste your time - mybe partons a s quarks w i l l not be I f you s t a r t , p o s s i b l y one place t o s t a r t might be t o t h i n k about low energy m a t r i x eferoents l i k e d -c p +y i n a fahit m v i n g systetn i n which a l l ( o r some) m m n t a a r e of t h e o r d e r P s o parton wave f m c t i o n s can be used, (We have one r e l a t i o n of t h i s kind i n Bjorken" sslun r u l e f a r g, Equation 3 - ) F i n a l l y i t should be noted t h a t even i f our house of cards s u r v i v e s and proves t o be r i g h t , we have n o t thereby proved t h e e x i s t e n c e a f partons 'Ilhe final, r e s u l t of o u r c o n s i d e r a t i o n s has been t o d a a c r i b e ehe r e s u l t of t h e - operation of a c u r r e n t on a proton s t a t e I /p> ( f o r l a r g e v , -q2 ZMur) a s U a l i n e a r corobination of o p e r a t o r s l i k e D ~ E ~ ( ~ - ~ , ~ ~ M /c Yr eAact i,n g f i n a l outgoing hadron s t a t e s only, It might be wise t o follow t h i s o u t f o m a l l y without mentioning partons (analogous t o t h e way Gel1-Mann and F r i t z s c h d e s c r i b e parton r e s u l t s f o r t o t a l i n c l u s i v e c r o s s s e c t i o n s i n tevma of c a r n u t a t i o n r u l e s f o r q u a n t i t i e s , c u r r e n t s , defined i n general whether partans ""exist" o r r o t ) From t h f s p o i n t a f view t h e partons would appear as an unnecessary s c a f f o l d i n g t h a t was used i n b u i l d i n g our house of cards On t h e o t h e r hand, t h e partons would have been a u s e f u l psychological guide a s t o what r e l a t i o n s t a expect - and i f they continued t o s e r v e t h i s 270 PIZO~OB-R~TOP~ Intemctioll~ way to produce other valjid expectations they would of course b e d n to becclr~e "'real'" pposiibly as real as any other thczoretjlcal structure invented to bscrjlbe lature A t any rate we shall see to, It is good to have sowthing to look forvard Appendix A The sospin of Quark Fragmentatior Products The dfseussion (Lecture 56) Leading t o the idea t h a t a d d i t i v e quark quantum n d e r s could appear a s mean t o t a l quantum n d e r s of p r ~ d u c t sm v i n g i n one d i r e c t i o n i s s u r p r i s i n g - e s p e c i a l l y when i t is noted t h a t what holds f o r 3-isospin holds a l s o f o r any o t h e r c o q o n e a t such a s l-isospin o r 2-isospin (although of course i n p r a c t i c e they a r e nearly inrpossible t o measure) It looks l i k e m isaospin 112 o b j e c t could be represented by a group a f i s o s p i n l obJects (e.g pions) which a t f i r s t s e e m irapossible - except - t h a t we have an i n d e f i n i t e n m b e r of such o b j e c t s , It i s t h e r e f o r e of i n t e r e s t t o make a very simgle s p e c i a l =the- m t i c a l -del, t o show t h a t indeed such things can be done i n p r i n c i p l e This i s e s p e c i a l l y i a p a r t a n t when i t is r e a l i z e d t h a t our previous attempts a t m a t h e m t i c a l f o m u l a t i o n cannot be copletcr; and m w t be looked a t a s mere m e m n i c s (see note i n Iazeture SS on the D and E operators) This l i t t l e ntodel may h e l p by its exalngle t o l e a d t o c o r r e c t pososfble formal expressians of our ideas I n t h i s model suppose quarks c a r r y only fsospfn 112 m d hadrons a r e 271 only pions of isospin - made of quark antiquark p a i r s Zmgine t h a t we s t a r t with some current a n n i h i l a t i o n (analogous t o eie- but i n more general isospin d i r e c t i o n ) i n i t i a l l y d i s i n t e g r a t i n g i n t o a p a i r of quarks Qa, GB (a,@ a r e SU2 i n d i c e s fixed i n t h i s problem I a e d i a t e l y a f t e r interaction: -P P Q@ N quark p a i r s i n s i n g l e t s t a t e a f t e r M m i l t m i a n operates; m k e s hirdrons o f type Next the a c t i o n of the Wamiltonian f s t o produce p a i r s of quarks i n a s i n g l e t s t a t e uniformly spaced i n y space - a t y p i c a l one i s qihi The number o f such p a i r s M is then proportional d on a l l I, equally t o Rn2P whlch we take t o be very l a r g e , ( h e could a l s o ass- the n u d e l : d i s t r i b u t e d v i a Poisson with a man M e t c , but we avoid compli- - choose N cations which only serve t o confuse our point fixed.) Next t h i s row of: quarks is a a s m d t a convert t o pions by a simple Thus ( i n r u l e , each pion is f o ~ by d a p a i r adjacent i n t h e y space figure) I f the f i r s t new s h g l e t p a i r had index 1, the next f i r et n e t c the f o m d front an antiqmrtr index fl and a quark, index f ; igi next by an antiquark index 1, and a qusrk index 3; - the - etc ? To describe the i s o s p i n a t a t e of a n we we an isospin 3-vector + Thus i f the s is a n e u t r a l pion wo we have V with only a z cowoneat, (0,0,1) 4- For a a we have ?=(l,f,O) 42- etc antiquark of index y and a quark of index fom a vector if The amplitude t h a t an 7~ characterized by i s then proportianal t a the yd m t r i x element of the two- by-rwo ~ o a t r i xoeif where U a r e the Pauli m t r i c e s , m i t e t h i s a s (WE! work i n r e l a t i v e m p l i t u d e e and p r o b a b i l i t i e s l a v i n g overall n o m l i z a t i m r o the end ) Bus t h e t o t a l amplitude t o f i n d t h e n ' s i n d i r e c t i o n s ?l$2 qH i s Amp = ~ * ? ~ l o,>the < ~ / o l ? ~ ie>i j l ~ = ~ 1, For s t a t e p@ /o%