EXPERI ME NTS WIT H HI G H-E NER GY NEUTRI N O BEA MS

Nobel Lect ure, Dece mber 8, 1988 b y J ACK STEI NBER GER CE R N, , S witzerland, and Scuola Nor male Superiore, Pisa, Italy

1. I NTR O D UCTI O N High- ne utrino bea ms have fo un d intensive an d varie d a p plication in p arti cl e p h ysi cs e x p eri m e nt ati o n i n t h e l ast d e c a d es. T his r e vi e w is c o n- str ai n e d t o a f e w of t h e m ost fr uitf ul e x a m pl es: t h e dis c o v er y of n e utr al c urrents, the meas ure ment of the Weinberg angle, the st u dy of weak c urre nts a n d t he co nse q ue nt test of t he electro wea k t heor y, t he st u d y of n ucleo n q uark str uct ure, an d the testing of quantu m chro mo dyna mics ( Q C D). Ot her st u dies s uc h as t he pro d uctio n of “ pro m pt” ne utri nos, t he s e ar c h f or fi nit e n e utri n o m ass es a n d n e utri n o os cill ati o ns, t h e s e ar c h f or hea vy le pto ns or ot her ne w particles, or t he meas ure me nt of proto n a n d ne utro n str uct ure f u nctio ns, elastic a n d pse u doelastic cross-sectio ns, a n d ot her excl usive processes, are not disc usse d here. Ne utri no ex peri me nts have bee n p urs ue d vigoro usly at t he Brook have n Natio nal Laboratory, at Fer milab, an d at C E R N. It is fair to say that they have ma de large contrib u- tions to o ur un derstan ding of .

2. NE UTRI N O BE A MS Present ne utrino bea ms are pro d uce d in fo ur ste ps: i) pro d uction of secon- dar y ha dro ns i n t he collisio n of hi g h-e ner g y proto ns o n a fixe d tar get; ii) mo ment u m (charge) selection an d foc using of the ha drons; iii) passage of t he bea m t hro ug h a n (e vac uate d) decay regio n, lo ng e no ug h to per mit a s ubstantial fraction of the ha drons to decay; iv) absor ption of the re maining h a dr o ns a n d t h e m u o ns t h at ar e pr o d u c e d al o n g wit h t h e ‘ n e utri n os i n a s hiel d of a de q uate t hic k ness. T he t wo-bo d y deca ys an d acc o u nt f or ~ 97 % of t he ne utri no fl ux i n prese nt bea ms. Positive ha drons pro d uce ne utrinos, negative ha drons pro d uce a nti ne utri nos. Fig ures la a n d lb gi ve a n i m pressio n of t he t wo ha dro n bea m-for ming options that are available, si de by si de, at C E R N: a conven- tional, so-calle d narro w-ban d bea m ( N B B), an d an achro matic, Van der Meer horn-foc use d, wi de-ban d bea m ( W B B). The ne utrino s pectra pro- d uce d b y t hese t w o bea ms are ver y differe nt, as s h o w n i n Fi g ure 2. T he 4 8 8 Physics 1988

Fi g ure 1 a Sketch of narro w-band and wide-band bea m layouts at C E R N, sho wing disposition of pri mary target, focusing ele ments, decay region, shielding, and monitoring de vices.

Fi g ur e 1 b Vie w of the neutrino bea m tunnel at the C E R N S P S in 1976, before operations began. T h e N B B li n e is s e e n i n t h e c e ntr e; o n t h e ri g ht is t h e p uls e tr a nsf or m er f or t h e W B B h or n, b ut t h e h or n its elf, d esti n e d f or t h e p e d est al o n t h e l eft, is n ot y et i nst all e d. At t h e f ar e n d, t h e 2. 5 m dia meter titaniu m windo w of the evacuated decay region can be seen. 4 8 9

Fi g u r e 2 Neutrino and antineutrino energy spectra, calculated for the horn-focused W B B and the more conventional N B B.

W B Bs are c haracterize d b y hi g h i nte nsit y, a stee p ( ge nerall y u n desira ble) energy fall-off, an d a s ubstantial conta mination of wrong-“sign” ne utrinos. T h e N B Bs h a v e l o w er i nt e nsit y, a fl at e n er g y d e p e n d e n c e i n t h e c o ntri b u- tion fro m each of the t wo decays, and s mall wrong-sign background. They also ha ve t he i m porta nt feat ure t hat t he e ner g y of t he ne utri no ca n be kno wn, s ubject to a t wofol d π - K dichoto my, if the decay angle is kno wn. In general this can be inferre d fro m the i m pact para meter of the event in the detect or.

3. DETE CT ORS The lo w cross-sections of ne utrinos are reflecte d in t wo general feat ures of ne utri n o detect ors: i) t hey are massi ve; ii) t he tar get ser ves also as detector. In the seventies, the most s uccessf ul detectors were large b ubble cha mbers. T h e m ost s pl e n di d of t h es e w er e t h e cr y o g e ni c d e vi c es b uilt at C E R N a n d Fer mila b, eac h wit h a vol u me of ~ 1 5 m 3 , i n l ar g e m a g n eti c fi el ds, a n d ca pa ble of o perati n g wit h li q ui d h y dro ge n, de uteri u m, or neo n. A pict ure of a ty pical ne utrino event in the C E R N cha mber is sho wn in Fig ure 3. It is a n exa m ple of t he “c harge d-c urre nt” ( C C) reactio n v + N → µ − + ha dro ns. Ho wever, one of the major discoveries at C E R N was ma de not in this but in a lar g e Fr e o n-fill e d b u b bl e c h a m b er, aff e cti o n at el y c all e d G ar g a m ell e. T h e a cti v e v ol u m e w as a c yli n d er 4. 8 m l o n g a n d 1. 9 m i n di a m et er, f or a v ol u m e of a b o ut 13 m 3 , i nsi d e a m a g n et pr o d u ci n g a fi el d of 2 T. Fi g ur e 4 gi v es so me i m pressio n of its size. The bubble cha mber has no w been largely replace d by detectors base d on electro nic detectio n met ho ds. As a n exa m ple, I me ntio n here t he C D HS P h ysics 1988

Figure 3 A typical neutrino event as ob- Fi g ure 4 Pre parati o n of t he i nteri or of t he served in the Big European Bubble Cha m- 1 3 m 3 bubble cha mber Garga melle, later to b er ( B E B C) fill e d wit h n e o n at t h e C E R N b e fill e d wit h Fr e o n. It is wit h t his d et e ct or 450 Ge V Super (SPS) that the neutral currents were discovered. accelerator. The can be seen on the left. It has been tagged by an external muon identifier. The many-particle sho wer is t o t h e ri g ht.

( CE R N- Dort mund- Heidelberg-Saclay Collaboration) detector used at C E R N fro m 1977 to 1985. It co nsists of 19 mo d ules ma de of iro n plates 3.75 m in dia meter, each with total iron thickness of 75 c m an d a weight of ~ 6 5 t. T h e ir o n is t or oi d all y m a g n eti z e d t o a fi el d of 1. 7 T b y m e a ns of c oils t hat pass t hro ug h a hole i n t he ce ntre.

I nt erl e a v e d wit h t h e 5 c m t hi c k ir o n pl at es ar e s ci ntill at or stri ps, w hi c h serve to meas ure t he e nergy of t he seco n dary ha dro ns by sa m pli ng t he ionization. The typical ha dron sho wer is ~ 25 c m in ra di us an d ~ 1 m long, so t he s ho wer di me nsio ns are very s mall co m pare d wit h t he size of t he detector. T he m uo n mo me nta are deter mi ne d o n t he basis of c ur vat ure i n t he ma g netic fiel d, wit h t he hel p of drift c ha m bers i nserte d bet wee n t he iro n mo d ules. T hese meas ure t he positio ns of tra versi ng tracks i n t hree pr oj e cti o ns. T h e us ef ul t ar g et w ei g ht is ~ 8 0 0 t. Fi g ur e 5 s h o ws t h e C D H S experi ment an d Figure 6 a typical event of the sa me type as that sho wn in Fi g ur e 3. J. St ei n b er g er

Figure 5 Vie w along the 19 modules of the C D H S electronic at the S P S. The black light-guides and phototubes, which are used to measure the hadron energy, can be seen sticking out of the magnetized iron modules. The hexagonal alu miniu m structures are the drift cha mbers that measure the muon trajectories

Figure 6 Co mputer reconstruction of a typi- c al e v e nt of t h e r e a cti o n v + + X. F o ur vi e ws ar e s h o w n, wit h t h e h ori z o nt al a xis al o n g t h e b e a m dir e cti o n. T h e t o p vi e w s h o ws t h e s ci ntill at or p uls e h ei g ht, or h a d- r o n e n er g y, a n d its distri b uti o n al o n g t h e d et e ct or. T h e n e xt vi e w s h o ws t h e s ci ntill a- t ar hits as w ell as t h e h ori z o nt al wir e hits and the reconstructed track in the x projec- ti o n. T h e ot h er t w o vi e ws s h o w t h e wir e hits a n d t h e r e c o n str u ct e d tr a c k f or t h e ± 6 0º pr oj e cti o ns. 4 9 2 f’ h ysics 1988

4. NE UTR AL C URRE NTS 4. 1 Discovery T he evol utio n of t he electro weak u nifie d ga uge t heory i n t he late sixties a n d early seventies was a miraculous achieve ment, but one that ha d no i m me di- at e i m p a ct o n t h e m aj orit y of p arti cl e p h ysi cists - c ert ai nl y n ot o n m e - per ha ps beca use it was a t heoretical co nstr uct w hic h left t he existi ng ex peri- me ntal do mai n i ntact. Ho wever, it pre dicte d so me e ntirely ne w p he no- m e n a, a n d of t h es e t h e n e utr al w e a k c urr e nts w er e t h e first t o b e dis c o v- ere d. T he verificatio n of ne utral c urre nts ( N Cs) establis he d t he t heory over nig ht, a n d s ubseq ue nt ex peri me nts o n t heir detaile d str uct ure rei n- force d t his. T his observatio n 1 of neutral weak currents at CE R N in 1973 by the Garga melle group was the first great discovery made at CE R N. It was follo we d 10 years later b y t he seco n d-also a pre dictio n of t he sa me t h e or y - t h e i nt er m e di at e b os o n.

Monte Carlo calculation for induced background

Figure 7 A “ muonless” event in Garga melle. Fi g ur e 8 Distri b uti o n of t h e ori gi n of m u o n- All tr a c ks st o p or i nt er a ct i n t h e c h a m b er. less events along the bea m direction in Gar- None could be a muon. The neutrino pro- ga melle. Neutrino events are expected to be duces one K + and one K 0 . The K + unifor mly distributed, whereas neutron m es o n i nt er a cts i n t h e li q ui d a n d t h e n d e- events should decrease with distance be- c a ys. T h e i n visi bl e K 0 meson decays to t wo cause of their absorption in the Freon. The pi o ns. nuclear mean free path in Freon is about 80 c m. The expected and observed distribu- tions of neutron interactions are sho wn in the botto m t wo histogra ms. The muonless events are consistent with neutrino and in- c o nsist e nt wit h n e utr o n ori gi n ( R ef. 1). J. Stei nberger 4 9 3

T he b ubble c ha mber, b uilt u n der t he directio n of A. Lagarrig ue at t he École Polytechniq ue in Paris, was ex pose d to ne utrino an d antine utrino W B Bs at t he C E R N 24 Ge V proto n accelerator. T he nor mal C C reactio ns,

were fo un d as us ual, b ut N C “ m uonless” reactions,

w hic h ha d har dly bee n looke d for before-a n d t herefore ha d not bee n fo u n d- were t here as well. S uc h a n e ve nt is s ho w n i n Fig ure 7. T hese e ve nts were selecte d o n t he basis of no m uo n ca n di date a mo ng t he observe d particles. The main ex peri mental challenge was to sho w that they were not d u e t o str a y n e utr o ns i n t h e b e a m. I m ys elf w as a s c e pti c f or a l o n g ti m e, a n d I lost a bottle or t wo of goo d wi ne o n t his matter. Ho we ver, t he ne utro n backgro un d wo ul d be ex pecte d to decrease ex ponentially along the length of t he c ha mber, ro ug hly wit h t he ne utro n mea n free pat h i n Freo n. I nstea d, t he e ve nt distri b utio n was flat, as ex pecte d for ne utri no e ve nts (see Fi g. 8.). I ha ve ne ver e njoye d payi ng u p a debt more t ha n at t he di n ner we ga ve for the winners, very goo d frien ds, Jacq ues Prentki, John Ilio po ulos an d Henri E pstei n. T he rati os of t he cr oss-secti o ns

are gi ve n i n t he electro weak t heory i n ter ms of t he Wei nberg a ngle q w :

a n d

w here r is, t he rati o of a nti ne utri n o t o ne utri n o, C C t otal cr oss-secti o ns: r = 0. 4 8 0 . 0 2 ex peri me ntall y. O n t he basis of t hese rati os,

2 t he ex peri me nt yiel de d a first meas ure of si n q w , t hat was n ot ver y differe nt fro m prese nt, more precise deter mi natio ns. I n t he sa me ex pos ure a bea uti- f ul exa m ple of a not her N C process, t he scatteri ng of a n a nti ne utri no o n a n electro n, was also fo u n d*.

4.2 Precisio n meas ure me nt of a nd right-ha nded ne utral c urre nts T he hig her e nergies t hat beca me available a fe w years later at Fer milab a n d C E R N ma de the st u dy of N C processes m uch easier. The m uons of the C C background had no w a greater penetration po wer, which per mitted cleaner se paratio n of N C a n d C C e ve nts. Also, wit h t he a d ve nt of t he hig her e nergies, t he a d va ntage i n t he st u dy of i ncl usi ve ne utri no scatteri ng ha d s hifte d to electro nic detectio n tec h ni q ues. I n t he perio d 1977 to 1985, ha dronic N C ne utrino scattering was st u die d extensively by the C D HS 4 9 4 Physics 1988

e v e nt le n gt h. T h e p e a k at s m all e v e nt lengths is d ue to N C events. The long tail is I d ue to m uo nic e ve nts, w hic h m ust be s ub- tr a ct e d u n d er t h e p e a k t o gi v e t h e N C r at e ( R ef. 3).

Collaboratio n at C E R N i n or der to get a more precise val ue for a n d t o c heck t he pre dictio n of t he electro weak t heory for t he ratio of rig ht- ha n de d to left-han de d N Cs 4 . T he N C e ve nts are selecte d o n t he basis of s hort e ve nt le ngt h, i.e. t he s hort pe netratio n of t he ha dro nic s ho wer co m pare d wit h t hat of t he m u o n of C C e ve nts. T his is ill ustrate d i n Fi g ure 9. A 15 % backgro un d of C C events is s ubtracte d. The ne utrino N C-to- C C ratio yiel de d t he most precise val ue of t he wea k mixi n g a n gle a vaila ble at prese nt, = 0. 2 2 7 0.006. O nce i s k n o w n , t h e a n t i n e u t r i n o r a t i o follo ws fro m E q. (2). Its meas ure me nt pro vi de d a se nsiti ve test of t he electro wea k t heor y, a n d co nfir me d it i n its si m plest for m. T he prese nce of right-han de d N Cs ( C Cs are p urely left-han de d) in the a mo unt pre dicte d by t he t heory co ul d be de mo nstrate d by co m pari ng t he ha dro n e nergy distri- b utio ns of t he N C a n d C C processes. T he res ult is s ho w n i n Fig ure 10.

Fi g ure 1 0 Str e n gt hs of t h e left- a n d ri g ht- - ha n de d ne utral c urre nts. If t he N C were p urely left- ha n de d, as is t he case for t he C C, the ex peri mental point wo ul d be ex pecte d t o f all o n t h e V- A li n e. T h e e x p eri m e nt sho ws a right-han de d co m ponent, which is

( W ei n b er g- S al a m m o d el) ( R ef. 4).

4.3 Ne utri no-electro n scatteri ng T he elastic-scatteri ng reactio ns of ne utri nos o n ato mic electro ns

a n d procee d via N Cs. T hey are c haracterize d by s mall cross - sectio ns-s maller t ha n t heir ha dro nic co u nter parts by t he mass ratio beca use of t he s maller c. m. e nergies - a n d, for t he sa me reaso n, by s mall electro n pro d uc- J. Stei n berger 4 9 5 ti o n a n gles, U ntil n o w, t h es e a n gl es h a v e n ot b e e n r es ol v e d b y t he ex peri me nts, so o nly total cross-sectio ns have bee n meas ure d. T he ex pectations in the electro weak theory are:

a n d

T h es e r e a cti o ns c a n als o s er v e t o test t his t h e or y, a n d h a v e t h e a d v a nt a g e that strongly interacting particles are not involve d, so that the un derstan d- i n g of str o n g-i nteracti o n c orrecti o ns is n ot necessar y i n t he i nter pretati o n. They have the experi mental disa dvantage of lo w rates an d consequent large bac k gro u n d. T he best res ults at prese nt are fro m a B N L ex peri me nt 5 usi n g relatively lo w e nergy ne utri nos, E 1. 5 G e V, a n d a 1 4 0 t d et e ct or e ntir el y co m pose d of ma ny layers of plastic sci ntillator a n d drift c ha mbers. T he backgro un d is s ubtracte d on the basis of the distrib ution in the pro d uction a n gle of t he electro n s ho wer (see Fi g ure 11). I nstea d of co m pari n g t he ne utri n o a n d a nti ne utri n o cr oss-secti o ns directl y wit h t he t he or y, t he a u- t h ors f or m t h e r ati o of t h e t w o, w hi c h is less s e nsiti v e t o s o m e s yst e m ati c err ors. Fr o m t his t h e y fi n d t h e r es ult = 0.209 ± 0.032. A C E R N gr o u p r e p orts a si mil ar r es ult, wit h = 0. 2 1 1 ± 0. 0 3 7. T h e a gr e e m e nt with other metho ds of obtaining this angle is an i m portant confir mation of t he t heory. A massive ex peri me nt to i m prove t he precisio n is c urre ntly under way at CE R N.

Figure 11 Identification of neutrino-elec- tr o n e v e nts o n t h e b asis of t h eir s m all a n gl e wit h r es p e ct t o t h e b e a m i n t h e e x p eri m e nt of A hr e ns et al. “. T h e p e a k at s m all a n gl es i n the t wo top graphs is due to neutrino-elec- tron scattering. The botto m graphs sho w the flat distribution observed if photons rather than are detected. This sho ws the angular distribution of ground events.

5. NE UTRI N O- N UCLE O N I NCL USIVE SC ATTERI N G A N D T HE Q U ARK STR UCT URE OF H A DR O NS 5.1 Pheno menology W e c o nsi d er t h e C C r e a cti o ns, v + + ha drons a n d + ha drons, in de pen dently of the final ha dron config uration. This is calle d the incl usive pr o c ess. It is ass u m e d t h at t h e l e pt o n v ert e x is d es cri b e d b y t h e v e ct or- 4 9 6 P h ysics 1988 axial vector c urre nt of t he electro weak t heory. Let k be t he i nitial a n d k’ t he final energy- mo mentu m four vectors, p that of the inci dent , a n d p’ t hat of t he fi nal ha dro n state:

Defi ne t he ki ne matic variables:

Q 2 ( k- k’) 2 = 4 E E ’ s i n 2 θ / 2 , 2 V p. Q / m p = E h , - m p , E h (t h e e n er g y of t h e fi n al-st at e h a dr o ns i n t h e l a b or at or y s ys- t e m), 2 X Q / 2 m p v, 0 < x < 1, v / E E / E, 0 < y < 1, Y h w h er e E a n d E’ ar e t h e e n er gi es of t h e i niti al n e utri n o a n d fi n al m u o n, r es p e cti v el y, a n d θ is t he a ngle bet wee n t hese, all i n t he laboratory syste m. The cross-sections can be written in ter ms of three str uct ure f unctions, each a f u n cti o n of t h e v ari a bl es x a n d Q 2 t hat c haracterize t he ha dro nic vertex:

2 2 2 T he f u nctio ns F 2 (x, Q ), x F 3 (x, Q ), a n d F L (x, Q ) are t he t hree str uct ure f u nctio ns t hat ex press w hat ha p pe ns at t he ha dro n vertex. T he s u m of ne utri no a n d a nti ne utri no cross-sectio ns has t he sa me str uct ure-f u nctio n de pen dence as does the cross-section for charge d le ptons:

5.2 Q uark str uct ure of t he n ucleo n In 1969, at the ne wly co m plete d S- mile linear accelerator at S L A C, it was discovere d’ t hat i n electro n- proto n collisio ns, at hig h mo me nt u m transfer, the for m factors were in depen dent of Q 2 . T his s o- c all e d “s c ali n g ” be ha vi o ur is c haracteristic of “ p oi nt”, or str uct ureless, particles. T he i nter- pretatio n i n ter ms of a co m posite str uct ure of t he proto ns - t hat is, proto ns c o m p os e d of p oi nt-li k e q u ar ks - w as gi v e n b y Bj or k e n 8 and Feyn man 9 . Ne utri n os are pr ojectiles p ar excelle nce f or i n v esti g ati n g t his str u ct ur e, i n part beca use of t he hea v y mass of t he i nter me diate boso n, a n d i n part beca use q uarks an d antiq uarks are scattere d differently by ne utrinos o wing t o t he V- A c haracter of t he wea k c urre nts; t he y ca n t heref ore be disti n- J. Stei nberger 4 9 7 g uis he d i n ne utri no scatteri ng, w hereas i n c harge d-le pto n scatteri ng t his is not possible. T he q uark mo del makes defi nite pre dictio ns for ne utri no- ha dron scattering, which are bea utif ully confir me d ex peri mentally. Many of t he pre dictio ns rest o n t he fact t hat no w t he ki ne matical variable x ta kes o n a p hysical mea ni ng: it ca n be i nter prete d as t he fractio n of t he n ucleo n mo me nt u m or mass carrie d by t he q uark o n w hic h t he scatteri ng takes place. T he ne utri no ex peri me nts we revie w here have pri marily use d iro n as t he target material. Iro n has ro ug hly eq ual n u mbers of proto ns a n d ne u- tr o ns. F or s uc h n uclei, t he cr oss-secti o ns ca n be ex presse d i n ter ms of t he t otal q uar k a n d t otal a nti q uar k distri b uti o ns i n t he pr ot o n. Let u(x), d(x), s(x), c(x), etc., be t he u p, do w n, stra n ge, c har m, etc., q uar k distri b utio ns i n the proton. The proton contains three “valence” q uarks: t wo u p-q uarks an d o ne do w n-q uark. I n a d ditio n, it co ntai ns a “sea” of virt ual q uark-a ntiq uark pairs. T he u p vale nce- q uar k distrib utio n is u(x) a n d t he do w n va- le nce- q uar k distri b utio n is d(x) - The sea q uarks an d antiq uarks have necessaril y i de ntical distri b uti o ns, s o t hat s(x) = c( x) = et c. F or t h e ne utro n, u a n d d c ha n ge roles, b ut s a n d c are t he sa me. Let a n d be t he total q uar k a n d a nti q uar k distrib utio ns of t he proto n, res pecti vel y. For s pi n-l /2 q uarks i nteracti ng accor di ng to t he Sta n dar d Mo del, for a target with eq ual n u mbers of an d ne utrons, an d for

a n d

Co m pariso n wit h t he ex pressio n for t he cross-sectio n i n ter ms of str uct ure f u nctio ns t he n gives t hese f u nctio ns i n ter ms of q uark distrib utio ns:

Fro m t hese si m ple ex pressio ns for t he cross-sectio ns, i n ter ms of q uar k str uct ure, several tests of t he q uark mo del are derive d. For t he ex peri me n- tal co mparisons, we take the C D HS experi ments 1 0 . It s h o ul d be n ote d t hat the meas ure ments in the detector, i.e. the ha dron energy an d the m uon mo me nt u m, are j ust s ufficie nt to defi ne t he i ncl usive process. 4 9 8 P h ysics 1988

1 2 T ot al n e utri n o a n d a nti n e utri n o cr o s s- s e cti o n s p er n u cl e o n di vi d e d b y n e utri n o energy. The flat ‘scaling’ behaviour is a consequence of the point-like interaction of the c o nstit u e nts ( R ef.

Figure 13 The average of y (the fraction of t h e n e utri n o e n er g y tr a ns mitt e d t o t h e fi n al h a dr o n st at e) as a f u n cti o n of t h e n e utri n o energy, for and antineutrinos. The unifor mity is a consequence of scaling, which in turn is a consequence of the point- li k e i nt er a cti o n of t h e q u ar k ( R ef. 1 0).

1) S c ali n g. T he i n de pe n de nce of t he differe ntial cr oss-secti o ns wit h res pect t o Q 2 is e vi de nt e ver y w here, o ver a lar ge do mai n i n Q 2 . As o ne exa m ple, Fig ure 12 s ho ws t he li nearity of t he total cross-sectio ns wit h ne utri no energy; as another, Fig ure 13 sho ws the unifor mity of the average of y with res pect to ne utri no e nergy; bot h exa m ples are co nseq ue nces of scali ng. S mall deviations fro m scaling are observe d in the str uct ure f unctions, as we will see later, b ut t hese have t heir ex pla natio n i n t he stro ng i nteractio ns of t he q uarks. J. Stei nberger 4 9 9

2) The y-depe nde nce of the cross-sectio ns. We ex pect

a n d

T he agree me nt wit h t his ex pectatio n is q uite goo d, as ca n be see n fro m

Fi g ure. 14. A c or ollar y of t his a gree me nt is t hat F L ( x) is s m all. It is f o u n d t h at 0.1. Agai n, t his de viatio n fro m t he si m ple q uark pict ure is u n derst o o d i n ter ms of t he str o n g i nteracti o ns of t he q uar ks, as w e will s e e l at er.

I I I

Fi g ure 1 4 T he y- de pe n de nce of t he s u m a n d t he differe nce of ne utri no a n d a nti ne utri no cross- s e cti o ns. q uarks are ex pecte d to ha ve y- de pe n de nces 1 + (1-y) 2 f or t h e s u m a n d 1 - ( 1- y) 2 f or t he differe nce ( Ref. 10).

3) Correspo nde nce bet wee n B ot h are pr o p orti o nal t o q(x) + q(x), a n d so are ex pecte d to ha ve t he sa me x- de pe n de nce i n t he si m ple q uark mo del. T hey are relate d by t he factor

H er e a n d are t he u p- a n d do w n- q uar k electric c har ges, res pec- tively. T he agree me nt i n s ha pe a n d mag nit u de, s ho w n i n Fig ure 15, not o nly s u p ports t he q uark pict ure, b ut also de mo nstrates t he t hir d i ntegral q uark electric c har ges. 5 0 0 Physics 1988

4) = 3. Si n c e = x[ q( x) x i n t he q uar k m o del a n d q ( x ) - is t he vale nce- q uar k distri b utio n, t his s u m r ule states t hat t here are three valence q uarks in the n ucleon. The ex peri mental de monstration is not wit ho ut proble ms, beca use t he v a n d cr oss-secti o ns are fi nite as x 0, a n d t h e diff er e n c e, w hi c h is has a c o nse q ue nt lar ge err or at s mall x, w hi c h is di vi d e d b y x as x 0. H o we ver, all ex peri me nts gi ve a val ue near 3, wit h t y pical u ncertai nties of 1 0 %. Together with the charge d-le pton incl usive scattering ex peri ments, the ne utri no ex peri me nts leave no do ubt abo ut t he vali dity of t he q uark pict ure of n ucleo n str uct ure. I n a d ditio n, t he ne utri no ex peri me nts are u niq ue i n offering the possibility of meas uring in de pen dently the q uark an d antiq uark distrib utio ns i n t he n ucleo n, s ho w n i n Fig ure 15. If t he q uarks were t he sole n ucleo n co nstit ue nts, we wo ul d ex pect d x = x[ q(x) + q(x)] dx t o be e q ual t o 1. Ex peri me ntall y, d x = 0. 4 8 0.02. We s ho ul d have ex pecte d t hat so me of t he n ucleo n mo me nt u m is carrie d by t he gl uo ns, t he meso ns t hat bi n d t he q uarks. T he ex peri me ntal res ult is t herefore i nter prete d to mea n t hat gl uo ns acco u nt for abo ut half of the nucleon mo mentu m (or mass). 5 0 1

5. 3 Neutrino scattering and quantu m chro modyna mics ( Q C D) Q C D is t he elega nt ne w ga uge t heory of t he i nteractio n of q uarks a n d gl uo ns, w hic h describes t he bi n di ng of q uarks i nto t he ha dro ns. Dee p- i nelastic le pt o n scatteri n g pr o vi de d a mea ns of testi n g t he pre dicti o ns of t his i m p ort a nt t h e or y a n d g a v e it its first e x p eri m e nt al s u p p ort. S o f ar, n o one has succeeded in calculating lo w-energy hadronic pheno mena such as t he wa ve f u nctio ns of q uarks i n ha dro ns, beca use of t he large co u pli ng co nsta nt t hat fr ustrates pert urbatio n met ho ds at lo w e nergy. At hig h Q 2 , h o w e v er, t h e eff e cti v e c o u pli n g c o nst a nt b e c o m es l o g arit h mi c all y s m all er, an d pert urbation calc ulations beco me cre dible. The theory pre dicts ‘scaling vi ol ati o ns’ i n t h e f or m of a ‘s hri n ki n g’ of t h e str u ct ur e f u n cti o ns t o w ar ds s m all er x as Q 2 gets larger. This is observe d ex peri mentally, as can be seen fr o m Fi g ur e 1 6. I n t h e t h e or y, t h e ‘s hri n ki n g’ is t h e c o ns e q u e n c e of t h e

Figure 16 Scaling is only approxi mately true for the structure functions. Early measure-

me nts of F 2 (X ) in three different energy do- m ai ns e x hi bit s hri n ki n g, as e x p e ct e d i n t h e Q C D t h e or y. e missi o n of gl u o ns i n t he scatteri n g pr ocess. T his e missi o n ca n be calc u- late d. T he Q 2 e v ol uti o n at s ufficie ntl y hi g h Q 2 is t herefore q ua ntitati vely pr e di ct e d b y t h e t h e or y. I n n e utri n o e x p eri m e nts, t his Q 2 evol utio n co ul d be meas ure d, a n d t hese meas ure me nts co nfir me d t he t heory a n d co ntri- b ute d to its acce pta nce. I n t he case of xF 3 , t h e t h e or eti c al pr e di cti o ns h a v e 2 o nl y o n e fr e e p ar a m et er, t h e c o u pli n g c o nst a nt I n t he case of F 2 , t h e Q evol ution is co u ple d to the gl uon distrib ution G(x, Q 2 ). T h e e x p eri m e nt al Q 2 e v ol uti o ns of x F 3 a n d F 2 in the latest C D HS experi ment are sho wn, together wit h t heir Q C D fits, i n Fig ure 17 a n d 18. T he t heory fits t he data a deq uate- 5 0 2 P h ysics 1988 l y. T hese fits gi ve a val ue for t he para meter A i n t he r u n ni n g stro n g- co u pli ng co nsta nt,

2 2 Figure 18 Variation of F ( x, Q 2 ) wit h I n Q 2 . Figure 17 Variation of x F 3 ( x, Q ) wit h I n Q 2 in different x bins. The Q 2 e v ol uti o n pr e di c- T h e Q C D fit is als o s h o w n. tions of Q C D with A = 128 Me V are also s h o w n ( R ef. 1 0).

where N f = nu mber of excite d flavours ( N f 4 i n t his ex peri me nt), A 100 Me V. T he y also gi ve t he gl uo n distrib utio n s ho w n i n Fi g ure 19. T hese Q C D co m pariso ns s uffer so me w hat fro m t he fact t hat Q 2 is still t o o lo w to re d uce no n- pert urbative effects to a negligible level, b ut t he calc ula- ble pert urbati ve effects do mi nate a n d are co nfir me d by t he ex peri me nts. Pert urbati ve Q C D also pre dicts a no n-zero lo n git u di nal str uct ure f u nctio n 2 F L ( x, Q ) as a n ot h er c o ns e q u e n c e of t h e e missi o n of gl u o ns. T his pr e di cti o n is c o m p ar e d wit h t h e C D H S e x p eri m e nt al r es ults i n Fi g ur e 2 0. A g ai n, t h e experi ment len ds s upport to the theory. J. Stei n berger 5 0 3

Figure 19 The distribution G(x) derived Fi g ur e 2 0 T h e str u ct ur e f u n cti o n F L ( x) ass o- 2 fr o m t h e Q C D fits t o F 2 ( x, Q ), a n d ci at e d wit h l o n git u di n all y p ol ari z e d i nt er m e- 2 x F 3 ( x, Q ) ( R ef. 1 0). di at e b os o m, a n d t h e Q C D pr e di cti o ns. I n

t h e si m pl e q u ar k m o d el, F L is z er o ( R ef. 1 0).

6. NE UTRI N O I NTER ACTI O NS, T HE GI M WE A K C URRE NT, A N D T HE STR A N GE Q U ARK I N T HE N UCLE O N A mong the most beautiful results obtained with neutrino bea m experi ments are t hose co ncer ni n g t he o p posite-si g n ` di m uo ns’ first o bser ve d at Fer mi- l a b 1 1 a n d st u die d i n detail i n t he C D HS ex peri me nts 1 2 . T hese reactio ns o c c ur wit h r o u g hl y l / 1 0 0 of t h e r at e of t h e d o mi n a nt si n gl e- m u o n e v e nts. The experi ments are interesting, on the one han d because they confir m the do ublet str uct ure of t he q uark weak c urre nt pro pose d so me years ago by Glas ho w, Ilio po ulos a n d Maia ni 1 3 , a n d w hic h is f u n da me ntal to t he electro weak theory, and on the other hand because they give such a vivid co nfir matio n of t he n ucleo n q uar k str uct ure alto get her. The origin of the extra muon was quickly un derstoo d as being due to the pro d uctio n of c har me d q uarks a n d t heir s ubseq ue nt m uo nic decay. I n t he GI M mo del, t he c har m- pro d uci ng reactio ns are

a n d Physics 1988

Fig ure 21 The x-distributions of opposite-sign di muon events. a) For antineutrinos. The do mi- na nt pr ocess is + T h e o bs er v e d x- distri b uti o n is t h er ef or e t h at of t h e str a n g e s e a i n t h e n u cl e o n. b) F or ne utri n os. T he pr ocess is v + s or d - µ - + c. T h e s h a p e all o ws t h e d et er mi n ati o n of t h e r el ati v e c o ntri b uti o ns of s a n d d q u ar ks, a n d t h er ef or e t h e r el ati v e c o u pli n g c o nst a nt. T his confir med the GI M prediction ( Ref. 12).

i) o p posite-sign m uons are pro d uce d, like-sign ones are not; ii) i n ge neral, t he extra m uo n has little e nergy; iii) t he extra m u o n is c orrelate d, as ex pecte d, t o t he directi o n of t he ha dron sho wer, of which the char me d particle is a part. The GI M pa per 1 3 prece de d t he ex peri me ntal disco very of c har m by fi ve years. It was pro pose d beca use of t he t heoretical attracti ve ness of t he d o u blet str uct ure of t he wea k c urre nts. T he pre dicti o ns were precise. T he cross-sectio ns are pro portio nal to f or d a n d q u ar ks a n d t o f or s a n d q uarks. T he Cabibbo a ngle was previo usly k no w n, wit h = 0. 9 7, cl os e t o 1, a n d = 0.05, very m uch s maller. Reactions (3) an d (4), or (5) a n d (6), are n ot ex peri me ntall y se para ble si nce t he tar get n ucle o n c o nt ai ns b ot h s a n d d q u ar ks, a n d t h e fi n al st at e is t h e s a m e. I n t h e a nti n e utri n o case, reactio n (6) do mi nates (5) beca use is s o s m all. F or e a c h e v e nt, x an d y are meas ure d as for single- m uon events. Therefore, the x- distrib ution for a nti ne utri no di m uo n pro d uctio n, s ho w n i n Fig ure 21a, meas ures t he a mo unt an d the sha pe of the strange sea s(x). I n t h e n e utri n o r e a cti o ns, t h e s m all n ess of f or r e a cti o n ( 3) is v er y closely co m pe nsate d by t he fact t hat d(x), co ntai ni ng also vale nce q uarks, is m uc h greater t ha n s(x) of reactio n (4). By fitti ng, it ca n be see n t hat t he x- distri b uti o n i n Fi g ur e 2 1 b is a r o u g hl y e q u al mi xt ur e of s( x) as o bt ai n e d wit h t he a nti ne utri nos a n d d(x), previo usly k no w n fro m t he nor mal C C reactio ns. The ratio of the t wo contrib utions is a meas ure of as it e nters t he c har m pro d uction reaction. The Cabibbo angle obtaine d in this way is fo un d to be e q u al, wit hi n err ors, t o meas ure d i n stra n ge deca ys, as pr o p ose d i n t he J. Stei nberger 5 0 5

Fi g ure 22 T he y- distri b uti o n of di m uo ns. T he acce pta nce over t he y- do mai n is u nfort u nately very no n- u nifor m, beca use of t he 5 Ge V mi ni m u m e nergy req uire d of eac h m uo n. T he obser ve d y- distrib utio n agrees wit h a n acce pta nce-correcte d flat y- distrib utio n as pr e di ct e d b y t h e GI M c urr e nt, b ut diff ers stri ki n gl y fr o m t h e ( 1- y) 2 distrib utio n c haracteristic of t he si n gle- m u o n a nti ne utri n o cr oss-secti o n ( Ref. 12).

GI M hy pot hesis. F urt her s u p port of t he GI M c urre nt is pro vi de d by t he y- distri b uti o ns. T he y reflect t he relati ve helicities of t he ne utri n o a n d t he str uc k q uar k: if t he t w o helicities are t he sa me, as is t he case f or all f o ur c har m- pro d uci ng reactio ns, t he ex pecte d y- distrib utio n is flat; if t hey are o p p osite, as is t he case f or i nsta nce f or v + a n d + q, t he ex pecte d distri b uti o n is ( 1 - y) 2 . Bot h ne utri no a n d a nti ne utri no si ngle- m uo n reac- ti o ns are mixt ures of t he t w o, as we sa w i n Fi g ure 14. T he c o ntrast is es pecially stro ng for a nti ne utri nos, w here t he ex peri me ntal si ngle- m uo n y- distri b uti o n is d o mi n at e d b y ( 1 - y) 2 , w hereas t he di m uo n distrib utio n is flat, as sho wn in Fig ure 22, again confir ming the GI M pict ure.

7. C O NCL U DI N G RE M ARKS I have give n so me exa m ples to ill ustrate t he i m pact of hig h-e nergy ne utri no researc h o n t he particle p h ysics pro gress of t he past years, bot h i n t he fiel d of t he weak i nteractio ns a n d i n t hat of n ucleo n str uct ure. Ho w will t his de velo p i n t he f ut ure ? I d o n ot k n o w, of c o urse. T he i ncrease of pr ot o n accelerator e nergies i nto t he 10 Te V ra nge will certai nly per mit better Q C D tests t ha n t hose cite d a bo ve. I n ge neral, ho we ver, it ca n be ex pecte d t hat progress i n particle p hysics will de pe n d more a n d more o n colli ders, be- 5 0 6 P h ysics 1988 ca use of t heir hig her ce ntre-of- mass e nergies. Hig h-e nergy e- p mac hi nes, s u c h as H E R A, will p er mit e x pl or ati o n of i n cl usi v e s c att eri n g t o hi g h er Q 2 do mains than will be possible with fixe d-target ne utrino bea ms. Ho wever, t he fasci natio n wit h ne utri nos a n d t he u na ns were d q uestio ns c o ncer ni n g t he m - s uc h as t heir masses - are m oti vati n g a br oa d li ne of researc h i n astro p h ysics, accelerator p h ysics, a n d n uclear p h ysics. O ne of t he first a n d most i m porta nt res ults ex pecte d fro m t he t wo large e + e - c olli d ers j ust c o mi n g i nt o o p er ati o n, t h e St a nf or d Li n e ar C olli d er a n d t h e C E R N L E P, w hi c h will pr o d u c e l ots of Z 0 m es o ns, is t h e d et er mi n ati o n of ho w many fa milies of le ptons an d q uarks there really are. Are there others besi des t he t hree alrea dy k no w n ? T his f u n d a m e nt al q u esti o n will b e a n- s were d by deter mi ni ng ho w ofte n t he Z 0 d e c a ys t o n e utri n os, e v e n if t h e masses of the other me mbers of possible a d ditional fa milies are too large to p er mit t h eir pr o d u cti o n at t h es e e n er gi es.

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1. F. J. H as ert et al., P h ys. L ett. 4 6 B ( 1 9 7 3) 1 3 8. 2. F. J. H as ert et al., P h ys. L ett. 4 6 B ( 1 9 7 3) 1 2 1. 3. M. H ol d er et al., P h ys. L ett. 7 1 B (1977) 222. H. A bra m o wicz et al., Z. P h ys. C28 (1985) 51 a n d P h ys. Re v. Lett. 57 (1986) 2 9 8. 4. H. H ol d er et al., P h ys. L ett. 7 2 B (1977) 254. 5. L. H. A hre ns et al., P h ys. Re v. Lett. 54 (1985) 18. 6. J. Dore nbosc h et al., Ex peri me ntal res ults o n electro n- ne utri no scatteri ng, s ub mitte d to Zeitsc hrift f ur P hysik C. 7. E. D. Bl o o m et al., P h ys. Re v. Lett. 23 (1969) 930. M. L. Breite n bac h et al., P h ys. Re v. Lett. 23 (1969) 935. E. D. Bl o o m et al., Rece nt res ults i n i nelastic electr o n scatteri n g, Sta nf or d preprint S L A C-P U B 796 (1970), p a p e r 7 b-17 s u b mitte d t o t he 15t h I nt. Conf. on High- Energy Physics, Kiev, 1970. [ See i n Pr oc. tal k b y R. Wils o n ( Naukova Du mka, Kiev, 1972), p. 238.1 8. J. D. Bjor ke n, P h ys. Re v. 179 (1969) 1547. 9. R. P. Feyn man, Photon-ha dron interactions ( Benja min, Ne w York, 1972). 1 0. J. G. H. D e Gr o ot et al., Z. P h y s. Cl ( 1 9 7 9) 1 4 3. H. A br a m o wi c z et al., Z. P h ys. Cl 2 (1982) 289 a n d Cl 7 (1983) 283. H. Abra mo wicz et al., A meas ure me nt of differe ntial cross-sectio ns a n d n u- cleo n str uct ure f u nctio ns i n c harge d-c urre nt ne utri no i nteractio ns o n iro n, to be s ub mitte d to Zeitsc hrift f ur P hysik C. 1 1. A. Be n ve n uti et al., P h ys. Re v. Lett. 34 (1975) 419. 1 2. M. H ol d er et al., P h ys. L ett. 6 9 B (1977) 377. H. A br a m o wi c z et al., Z. P h ys. C 1 5 ( 1 9 8 2) 1 9. 1 3. S. L. Gl as h o w, J. Ili o p o ul os a n d L. M ai a ni, P h ys. R e v. D 2 (1970) 1285.