ELECTRON-NEUTRINOS, v e. G. R. Kalbfleisch Brookhaven National Laboratory ABSTRACT

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1 -1- SS ELECTRON-NEUTRINOS, v G. R. Kalbflisch Brookhavn National Laboratory ABSTRACT Elctron (rathr than muon) nutrino intractions ar proprly th ons to us in comparing rsults with -p intractions. Elctron-nutrino fluxs from muons as wll as kaons ar crudly stimatd. Th muonic lctron -nutrinos ar mor numrous than th kaonic ons but pak at a lowr nrgy of cours. Typical runs in th 25-foot (H or D) bubbl chambr should yild svral thousand v intractions ovr th rang -50 GV in th currnt Nzrick bam. Idntification of ths vnts (lctron track) should b asir than th corrsponding muonic ons with a suitabl plat array or track-snsitiv targt (N-H 2 or N-D in th chambr. Som possibilitis for gratr v yilds in th futur ar 2) indicatd which will allow dtaild studis of xotic procsss (such as v + - v + I also. I. INTRODUCTION Proprtis of th wak intraction ar bing xplord with vn intractions. Th copious high -nrgy v sourc yilds mainly muon nutrinos. Elctron -nutrino intractions ar also dsird. Th ssntial diffrnc btwn lctrons and muons has not yt bn found. This diffrnc may b found in th comparison of vn and v jj.n intractions. In addition, vn, rathr than vn data, is most proprly compard with (xtnsiv) N data. Exinsiv N data should xist latr to proprly compar with th mor copious vn data. Also, th xpctd (and assumd) dcay mods of th muon and + + tj- - vvjj.j - v v can b dirctly xprimntally vrifid if a bam of muonically producd lctron nutrinos is availabl. A crud stimation of lctron nutrinos in th currnt Nzrick bam is mad in -4

2 -2- SS-121 this papr. Th muonic sourc (considrd hr apparntly for th first tim) givs th dominant portion. Th K± - Tfo±v raction givs th highr nrgy lctron nutrinos as considrd by BNL and CERN in thir arly xprimnts. Th o ± :;: ± + K - Tf fl v fl and Tf V fluxs hav not bn don yt. L II. BRIEF SUMMARY Only an outlin of this (crud) stimation is givn hr. A dtaild computr calculation should b undrtakn sinc a rasonably usful flux is xpctd. Th numrical rsults ar workd out in Tabl I. Th pion-muon SOurcs ar shown schmatically in Fig. 1. Figur 2 givs th rsults as a ratio R vrsus momntum p v ' This R is th factor to b applid to th calculatd v 1T spctrum to obtain th v spcfl trum. In addition thr is a contribution for K dcays. This factor has bn ap plid to Nzrick's spctrum (s Fig. 4) and yilds Fig.. Th vnt yilds for a run in th 25-foot bubbl chambr ar givn latr. III. v FROM MUON DECAY IN boo-meter 1T DRIFT SPACE For vry 1T dcay, on obtains a fl as wll as a v fl' For vry such fl which dcays, on obtains an, v vfl'.g., ' + + ". - I-L v fl L+v v fl Th dcay rat of muons, howvr, is about 0.01 of that for pions of th sam momntum. Thus a fraction of on prcnt might yild v into th v fl bam. Lt us calculat th ratio btwn v and v ; call this ratio R. fl Considr th avrag angls for 1T and dcay, th avrag dcay paths for rr and fl, and th rlativ solid angl subtndd by th dtctor for v's from pion and muon dcay. Ths considrations yild th valu of R. will b dnotd by x. Avrags of a quantity x Th lab angl L of a particl having a c. m. angl " and vlocity 1" from a dcaying systm travling with vlocity i is sin fi" A rough avrag angl in th lab systm corrsponds to fi'" = 90, i... fl L 1''ril. For a masslss particl (,\, or v) w s that this is fl (m =0) = 1/Yj. Thus th muon L angl from 1T dcay is (j11 = 1 "'I TJ = m Ip (p ':'/m). Th avrag momntum is rr I-L Tl' rr TT JJ. about /4 p (m 1m )p (sinc p rangs from -112 p to P, as is wll-known). TT f-l'" 'IT f-l 1T ".

3 -: t2t Th avrag v angls ar v t/.,., and v t/n (nglcting small ffct of O); i.,, rr --- rr " m m v ~ m P ~ m p" rr That is, th solid angls subtndd at th dtctor diffr only in that th muon dcays occur somwhat closr to th dtctor. Th pion dcay path is calculatd from th pion momntum in th usual way, bing th smallr of av. p" ::: Tl CT ::: - CT or 6 00 mtrs, rr it it m IT " whras th muon dcay lngth IS givn ssntially by th smallr of 0 r/o or.',, I /2 mtrs, whr r is th pion dcay drift tunnl r adius " and 600 mtrs is " th drift tunnl lngth, Finally, th pv from" dcay of momntum p" is rr [or dcays into I)L 0 a to I)v." (pv ovr all angls z t/4 P,,), Ths quantitis ar valuatd in Tabl I giving finally valus of r (last column I as a function of p, Ths ar plottd in Fig. 2, A largr v tunnl radius r':' 0 D/2 0 u z dtctor diamtr would nhanc low nd by a factor of, but th v spctrum cuts off so fast blow GV /c that this is ffctivly of no valu. No chang in tunnl radius is rquird for v ' A similar calculation can b mad [or muons arising from K2 dcays, Th * A wightd avrag -w RI-l. ovr th dcay path and forward pakd (lab) solid angl givs a rsult within to%, This wightd avrag T W is 2 I) + J1)2 - (~J r r T W - + in E.. : _ o - J ( 0 2 fj j L 2 t o L 2:..> t O. L t whr 0 O~ and L 0 distanc from man" dcay point to nd of drift spac (s t Fig. t),

4 -4- SS -121 valu of r K is about a factor of tn down from th valus of r 1T' This is du to th shortr muon dcay path. sinc th man muon angl from K... is about tn tims 2 largr than that for 1T... Thus r contributs ngligibly rlativ to r at low mo 2. K 1T mntum whn th K/1T ratio is also takn into account. At high momntum. r con K tributs ngligibly compard to "copious" v from K dcay (s Sc. V blow). IV. MUON DECAYS 1N THE 00-METER F SHIELD Th high -nrgy muons hav an apprciabl path lngth in th F shild, allowing a contribution to th v flux. For F. de/dx = a = tt.6 MV/cm = 1.16 GV/m. ~ / Th dcay path... of a muon of momntum Pi (Pi> 5 GV c) slowd down to pcut = 5 GV/c (p t/ p - 2 GV/c, corrsponding to cutoff on v spctrum) is about v F Pi - Pcut... " a Th probability. P, for dcay of such a muon is m _... act... compard to 6 x to -4 from drift spac dcay (s Tabl O. is not 75 GV/c, it is Howvr, th avrag p... sinc p = Pi - ax. For dcays of 20-tOO GV/c...'s, th probability of dcay is F tims th to valu allowd by th... if th muon wr not slowd down. In par 4 ticular, a 75 GVIc muon (from too GV/c 1T) would giv xto- dcay probability m dx _... CT... n - Pi ) ( Pcut which is - 27 GV/c yilding a p - 9 cv l «. Th rlativ rat of such low-nrgy v -4 v's is much highr (Tabl I) 60xtO vn xcluding th incras of v... spctrum at lowr p, Thus dcays in th F shilding can b nglctd. V. v FROM K: DECAY Th problm hr is simplr. Th branching fractions ± ± K -... v /0 K±-rro±v 5%

5 -5- SS -121 giv v I v in ratio 5/64 = 0.08 into th sam solid angl (diffrnt mod of sam mo mntum K± and ~ = 1IJ']K)' Howvr, th avrag pv is diffrn,~ for t~,~~:o mods, sinc on is a two-body and th othr a thr-body dcay. Th Pv (or Pv ) for both mods is = 0.2 GV/c. For th thr-body mod, th P: spctrum is approximatly linar from 0 to p",max, i.., P~ 2/ p,:,max = 0.15 GV/c. For o to 0.9 PK so that v ---v = 0 5 p PK. K K) Thus N(v at p is 0.08 of N(v K) at 2 p, i,.. v v and ± K± N K (p 0.08 N (2p ). v v v v o 0 ± VI. v FROM K - rr v DECAY L Th branching ratios ar: o 0 ± K L - 'IT v 28% 8% rspctivly. Th solid angl and momntum spctra ar almost th sam for both v and v hr sinc p~,max for ach mod is approximatly th sam (0.22 GV/c). Thus th v spctrum for K~ dcays is 0.7 that of v ' Th unfocusd K~ - v spctrum has not bn calculatd by Nzrick. W will for now ignor th v contribution corrsponding to that sourc, although it may b = 10% of all v ' vn. FLUX Th v flux from + and K+ ar givn in Fig. using th rsults of Scs. III and V and th Nzrick v spctrum of Fig. 4. Th total v spctrum gos from about to 50 GV Ic with 800/0 rsulting from th muonic dcay. -47

6 -6- SS-121 VIII. v EVENT RATES 6 Ro's assumptions for a 10 pictur run of th 25-fo01 bubbl chambr with 21 foot dutrium lngth was usd for this stimation. Using v -8 2 (Jtot E X 10 cm G V 6 as an stirnat, Ro obtains about 10 total v N intractions, and w shall also obtain about 6,000 v N intractions of all kinds (similar to v ractions, rplacing out with ). About 2,200 will b from -10 GV/c, 2,200 from GV/c and 1,600 from GV/c. Also 65'10 driv from muonic v and th 50/0 balanc from kaonic v Also, sinc 1h v spc1rum is about on -third of v spc1rum, on will obtain similarly about 2,000 v N intractions whn 1und for 1T- antinutr-mos. Thus substantial v N physics can b don vn in th cur-r-nt nutr-ino propo sals. For th futur, Palmr quots X 10 fluxs on low-nrgy nutrinos at BNL-AGS and x100 for low-nrgy NAL 25-foot runs. "Muon focusing" in th drift spac may allow for dsigning yt anothr X1 0 factor. 1 shall think about this in th coming months. At this lvl, th comparison of v and v should b vry good. Th "focusd muon" bam might b arrangd so as to hav a ngligibl pionic v back + _ ground. Thn sinc th muonic v and v (for, and convrsly for ) spctra ar + + th sam, th dirct xprimntal tst of th assumption - Vv indicatd arlir can b mad. In addition, xotic ractions, lik "diagonal" v - v will giv substantial rats for many intrsting rsults. IX. ANALYSIS OF v EVENTS Although only - 0.6'10 of th v intractions ar v th analysis should b rla' tivly as asy as th muon analysis if on uss a doubl chambr (D and N-D or 2 2) a suitabl plat array to idntify th lctrons by thir showrs. Tabl 1. Pion - Muon - Elctron-Nutrino Dcay (S Fig. 1). p (GV/c) " (rad) I (m) T (m ) p (GV/c) a I-'(Dcay R(vl-'lv 1T) 1T 1T 1T _1-' v B Fraction) b 0. T 4.5X10 4.5X10- b b b 4.5X10-4.5X10- b b b X10- b 5.4X b. b X X10 b X10-5.4X X10 1.2X X10-0.6X10' X10-0.X10- a B I 2 = [(largr of D 2 or 1T y 1T)1 (largr of DI 2 or y 1-'11 0 (6.'J v)1 (6.0 v ) whr DI 2 b = 2.5 m and y 1Tand y distanc s ofman 1Tand I-' dcay points from nd ofsliild (s Fig. 1). For largr tunnl (radius" D/2 or taprd to this siz at shild jth fluxs for P1T =1,2,5, 10 GV I c ar incrasd by factors of,,,1. 5 rspctivly. -48

7 -7- SS Dtctor P v (GV/c) 2 v XfL 5 v XfL 10 v XfL I ~15 v f--- X_fLI~----:-:I li yj----.j dnots <Iv> from Targt x dnots (tv) + +(,fl) from Targt Fig. 1. Avrag dcay positions of pions and muons in th nutrino tunnl (s Tabl l). Distancs ar masurd from th targt nd. -49

8 -8 - SS-121 Rgion of Ngligibl 'VfL Flux -4 10,......_...---I.---I...~~ 'O'----"' 10 Nutrino Momntum(GVlc) ""'""'-I...a..l~ Fig. 2. Spctrum of th ratio of lctron to muon nutrinos, R 0 N]v (pl]/n[vtt(pij. fl

9 -9 - SS -12 t - ~ 10-1 o... o ~ Q. (D o <, C\I ~ -2 o 10 " > Q) <.!> LO <, Nutrino Momntum (GVlc) Fig.. Spctra of lctron nutrinos.

10 c -CD "0 "g 10 1 U> o ~O EIO... > CD ~ II) g -I.~ 10 -::;, CD Z O!--.-I'-----=!-.",.-...L.-~,..._...Jo-...",..".-...-~-..L.--~---I Fig. 4. Nutrino spctra usd to calculat spctra of Fig.. -52

Radiation Physics Laboratory - Complementary Exercise Set MeBiom 2016/2017

Radiation Physics Laboratory - Complementary Exercise Set MeBiom 2016/2017 Th following qustions ar to b answrd individually. Usful information such as tabls with dtctor charactristics and graphs with th proprtis of matrials ar availabl in th cours wb sit: http://www.lip.pt/~patricia/fisicadaradiacao.