N eu trino ()scilla tion

Transcription

1 N u trino ()scilla tion Siddhshwar Lal Oscillation as a quantum mchanical phnomnon btwn a nutral particl and its anti particl was first nvisagd in 1955 to undrstand th KO - KO problm. In th study of nuclar intractions producd by high nrgy particls, coming from outr spac in th form of cosmic rays, as wll as thos producd through acclrators in th laboratory, many nw unstabl particls lik pions, muons, kaons tc., wr discovrd. Positiv,.ngativ and nutral chargd K-msons wr also found. Th nutral K-mson is producd through th following typs of ractions: Th strangnss quantum numbr S is zro for pions, nuclons (protons -nutrons), -1 for A and + 1 for 1(+. Consrvation of strangnss, thn dmands S == + 1 for 1( in (1) and -1 for KO in (2). ThKOwithS == -1 is writtn as KOand calld antiparticl of KO. In such a cas on could form stats with linar combinations of th two: (1) (2) Siddhswar Lal aftr working in TIFR, Mumbai for about 20 yars, joind Univrsity srvic in Madhya Pradsh and rtird in Jun H has bn associatd with Intr Univrsity Consortium for DAE Facilitis. His filds of intrst ar high nrgy physics and rlatd problms in astrophysics using cosmic rays and nutrino physics. == _1 (IKo> + KO».J2 == 12 (I 1( > - I 1( > ). Th 1( and K ar distinguishd by thir mod of production, whras th Kl and 1(2 ar distinguishd by thir mod of d~cay. Kl dcays into two pions with a liftim of 0.9 x10- lo sc. andk 2 dcays into thr pions with a liftim of 0.5 x 10-7 sc. Ths dcays hav bn obsrvd xprimntally. Such a scnario would lad to th procss of rgnration. This mans, a pur bam of ](0 particls, aftr travlling partly through vacuum and partly through mattr will contain a mixtur of KO and K 0..~AnA~.~ RESONANCE I Dcmbr 1998 'V V V V v 13

2 1 S Anjon S Joshipuro, Missing Nutrinos from th Sun. Rsonanc, Vo1.2, No.8, This was obsrvd xprimntally also and th phnomna wr trmd oscillations btwn KO - K o. N cutrino i Th bta dcay of nucli at rst visually lookd lik a 2-body dcay consisting of th mittd lctron and th daughtr nuclus in th final stat whras th continuous nrgy spctrum of th mittd lctrons and considrations of spin and statistics indicatd it as a 3-body dcay. Pauli, in a dsprat attmpt to xplain this apparnt anomaly, suggstd th xistnc of a nw nutral particl with almost zro mass which could b mittd along with th lctron to mak it a 3-body dcay. Frmi who workd out th thory for th bta dcay christnd this particl nutrino. Nutrinos ar mittd along with lctrons and muons and hnc a subscript is addd to indicat this lik v and vj-i' Similarly, nutrinos mittd with positivly chargd particls ar writtn simply as u whras thos with ngativly chargd particls ar calld anti-nutrino and writtn as v Rins and Cowan [1] in a bautiful xprimnt carrid out first at Hanford ractor and latr at th Savannah Rivr ractor confirmd th xistnc of v (anti-lctron nutrino). Davis [1] through anothr bautiful xprimnt showd that v (associatd with lctrons) is not th sam as v (associatd with positron). Pontcorvo thn argud [2] that thr could b possibl oscillations btwn v and v. In 1962, Danby and othrs [3] dmonstratd clarly that v -:t:. v that is nutrinos associatd J-I with lctrons ar not th sam as thos associatd with muons. Solar Nutrino Enrgy production in th sun taks plac through p-p and CNO chain of fusion ractions, which occur at a high tmpratur of about 1.7 x 10 7 K insid th sun. In both th chains protons fus to form H, through various intrmdiat nuclar ractions, which. produc high-nrgy photons and v' For th last thr dcads scintists hav bn dtcting ths so-calld solar nutrinos. It is found that in all th xprimnts th obsrvd ~ RE-S-O-N-A-N-C-E--I-D--c-m-b--r S

3 flux of solar nutrinos is only SO - 60% of th flux xpctd on th basis of standard solar modl (SSM? Sinc th par~mtrs usd for SSM hav bn found satisfactory from othr considrations,,it was imprativ to look for diffrnt rasons for this dficincy in th flux of obsrvd solar nutrinos. On suggstion was th xistnc of a nw kind of wakly intracting massiv particl (WIMP) which could affct th SSM, lowring th tmpratur in th rgions insid th sun. Th low tmpratur will slow down th rat of nuclar ractions and hnc flux of nutrinos mittd by th sun may b lss thn xpctd. Sinc thr ar no othr indications for th xistnc of WIMP, thy hav not bn takn sriously. This lft th possibility of oscillations btwn v and vp as a possibl solution to th dficit in th obsrvd flux of solar nutrinos. Th nutrinos mittd in th fusion ractions insid th sun ar all v typ and th dtctors basd on th arth ar dsignd to dtct v only. Pontcorvo [4] suggstd that sinc th v mittd by th sun has to travl vry larg distanc bfor bing dtctd in th ground basd dtctors, som of thm may turn into v through oscillation phnomna. Ths Ii V)J will b missd by th ground-basd dtctors.(which only dtct v ). 2 S B N Dwivdl, Unruly Sun Emrgs from Solar Spac Obsrvatory, SOHO, Rsonanc, Vol.2, No.9, 1997 and Ashok Ambastha, Probing th Solar Intrior, Rsonanc, Vol.3, No.3, N u trino Oscillations Lt us calculat th probability for oscillation whr a nutrino of on typ (flavour) changs into a nutrino of anothr typ. On ssntial condition for th oscillation to tak plac is that diffrnt typs of nutrinos hav diffrnt masss. As of now, w know thr typs of nutrinos - lctron, muon and tau nutrinos, along with thir distinct anti particls. Existnc of lctron and muon nutrino has bn stablishd xprimntally but th xistnc of tau nutrino is surmisd from th kinmatical considrations in th raction: + +- ~'t++ 't- I ~ )1+ + VIJ + V r ~I.. C+ v)j+ vr If lpton flavour is not consrvd and nutrinos hav finit ~AAAAA~ RESONANCE I Dcmbr 1998 'V V V V V v~ 15

4 masss, thn mixing may occur btwn th nutrinos of diffrnt flavour. For simplicity w considr only two of thm, viz., v and v. Lt I v > and I v > indicat stats which hav flavour ~ ~ but do not hav dfinit masss. And lt Iv 1 > and I v 2 > rprsnt mass ignstats which do not hav dfinit flavour. W can writ th flavour stat as a combination of th two mass ignstats through th unitary transformation ( V) (cos sin J (VI) V Ii = - sin () cos (} V 2 whr () is th mixing angl with maximal valu as tr/4. W start with a bam of I v > at tim t = 0 propagating with momntum p. W can writ (3) I v ' t = 0> = I VI' t = 0 > cos() + I V 2 ' t =0 > sin() Lt th stat volv in vacuum up to tim t whn w will hav (using natural units whr c = h = 1) I v,t = t > = -iel t I VI' t = 0 > cos() + -iezt I V 2 ' t = 0 > sin() (4) whr Sinc w ar considring spatial cohrnc, th stats I VI (t) > and I V 2 (t) > will hav sam momntum P = PI = P2' Th stats I v (t) > and I v~ (t) > ar ignstats of th momntum but not of th mass. Using th invrs of (3) th R.H.S. of (4) can b writtn as: I V ~ > sin()) cos() -iel t (I v > cos() - + -iezt (I v > sin() + I v~ > cos()) sin() = I v >- [-iel t cos 2 () + -iezt sin 2 ()] + I V > [--iel t + -iezt] sino cos(). Ii Hnc th amplitud for I V > ~ I V~ > will b givn by sino cos() (-iel t - riel'). W can, thrfor, writ th probability ~ R-E-S-O-N-A-N-C-E-I-D--c-m--b-r S

5 GENERAL \ ARTlClE for th stat I U > at tim t = 0 to b in th stat I up > at t = t as P(t) = sin 2 8 cos 2 8 l-ielt - -iei 12 v ~v p = 1/4 sin 2 (28 )[1 + l-zr (+iel t -iei)] = 1/2 sin 2 (28) [1-cos(E 1 -E 2 ) t]. Assuming E =p > > m 1, m z ' w gt W can thn writ P (t) = 1/2 sin z sin z ( t funz 14E). v ~v p Th xprssion insid th brackt for sin 2 should b a dimnsionlss quantity for numrical calculations. Not that th trms xpo (-iel t) and xpo (-iezt) in (4) should hav bn xpo (-ieltlli ) and xpo (-ie2tlli ); similarly, th trms m 1 and m 2 should hav bn m C 1 z and m z C z in rg units. Using natural units w had put c = Ii = 1. Hnc w gt sin 2 (t fun2 14E Ii ) whr fun 2 is in V2 ande is in V. W also writ Ii in V and thn th xprssion bcoms sin 2 (t fun2 x x 10-1Z ) I (4E x X ) whr fun2 is in V2, E is in V. W now wri t t = Li whr L is th distanc travlld by u with nrgy E and vlocity c. Furthr, lt us xprss L in mtrs and E in MV and thn th xprssion bcoms sin 2 (1.267 fun 2 LIE). W thn writ th probability P (L) for a u with nrgy E MV to chang into v du to oscillation in travlling distanc L J1.AA~AA" RESONANCE I Dcmbr 1998 v V V V V v..

6 Nutrino nrgy E &n 2 = m 2 _m (V) (V)Z (V)Z (V)Z IMV 10MV IGV 100 GV L osc. 10m 100 m 10km 10 3 km 10 km 100 km 10 4 km 10 6 km d ff 1 AU Tabl 1. mtrs as u ~u J1, whr &n 2 is in V2,E is in MV andl is in mtrs. For convninc w introduc L = 4 1f E/ &n 2 as th oscillation lngth. osc. Envisagd valus for Losc. for diffrnte and &n 2 ar takn from Mossbaur [5] and givn in Tabl 1 whrd ff == 10 8 m == ffctiv diamtr of th solar fusion cor; on astronomical unit = 1 AU = man distanc btwn sun and arth. In xprimnts to dtct nutrino oscillation, valus of E and L ar usually prdtrmind. On thn plots th stimatd valus for th probability P (L) in th paramtric spac covrd by &n 2 and sin 2 2B. Exprimntal Obsrvations Exprimnts to look for nutrino oscillations hav bn in progrss for quit som tim using (i) sun (ii) cosmic rays and (iii) ractors and acclrators in th laboratory as nutrino sourcs. Rang for th mass paramtr,&n 2, for diffrnt nutrino sourcs [5] is givn in th Figur 1. Figur 1. Mass paramtr rang!l.m2 of nutrino oscillation xprimnts for.diffrnt typ of nutrino sourcs. Acclrator Ractor Sun ~ R-E-S-O-N-A-N-C-E--I-D--c-m-b--r S

7 (i) Solar nutrinos: As mntiond arlir fusion ractions throughp-p and CNO chains in th sun produc v. Thr ar thr on going xprimnts, which dtct solar nutrinos through th radiochmical tchniqu. Th flux of solar nutrinos dtctd in th xprimnts is compard with th xpctd flux on th basis of SSM. Th dficit in th flux is attributd to disapparanc of solar v into othr flavours du to oscillation during thir journy from th sun to th dtctors. In th Homstak Gold Mins in South Dakota, USA, th dtctor consisting of615 tons of prchlorothyln is kpt 1500 m blow ground. Th v intracts with th chlorin nucli to produc radioactiv Ar, which is collctd and countd and from this data flux of v mittd from tli sun is stimatd. Th ida of accuracy involvd can b imagind from th fact that only on of th incidnt solar nutrinos ractd vry fw days with a singl nuclus of chlorin to produc Ar through th raction 37Cl + v Ar + - Th thrshold nrgy Ev~ 0.8 MV. Th GALLEX xprimnt in th GRANSASSO mountain rang in Italy has 30 tons of gallium dissolvd as a chlorid solution. Th v from th sun intracts via 7lGa + v -4 71G + - and has a thrshold nrgy E ~ v MV. Hr th counting of activatd 7lG nucli involvs furthr chmical tratmnt bfor its dcay into 71Ga can b countd in a spcial low-activity proportional countr. Finally, th flux of 7lG so dtrmind givs th flux of solar nutrinos. Th SAGE xprimnt (Sovit Amrican Gallium Exprimnt) is bing don in th Caucasian Mountains in Russia whr th dtctor consists of 57 tons of mtallic gallium. Th background in SAGE is lowr than in GALLEX. Th Supr-Kamiokand xprimnt is a collaboration btwn USA and Japan. Hr th dtctor is 50,000 tons of ultrapur watr in a tank kpt 1000 mtrs blow ground in Cntral Japan. Th nutrinos produc chargd particls lik j1/, which in turn produc Crnkov radiation, which is dtctd. Th Crnkov radiation also indicats th dirction of th incoming particl. In thir latst rsult [6] th authors claim vidnc for nutrino oscillations and hnc for nonzro masss for nutrinos. This ~ RESONANCE I Dcmbr

8 might hav baring on th 'missing mass' in th univrs. Complt dtails of th rsults ar not yt availabl. Th Sudbury Nutrino Obsrvatory (SNO) is a collaboration btwn Canada, UK and USA and is locatd 2070m blow th ground in a nickl min in Ontario. This xprimnt uss havy watr and is xpctd to giv rsults by Havy watr as a dtctor is xpctd to tll th diffrnc btwn v and th othr two flavours (v and v) through th brak-up ractions of th J.1. T dutrium nucli in th havy watr. Two typs of ractions ar possibl by th v in h~vy watr, (i) d + v ~ p + p + - (ii) d + v ~ p + n + v Th first raction is a chargd currnt intraction and can b causd only by th v. Th scond is through a nutral currnt and can b causd by nutrinos of all flavours. From th products dtctd, on can gt v flux and th total v flux. This can giv dfinit info.rmation about nutrino oscillation. Krastv and Ptcov [7] had analysd th data availabl upto 1992 and found that a small rgion of valus of th two paramtrs charactrising th oscillations, flm,2 == ( ) x V 2 and sin 2 28 == was allowd. Latr on thy hav analysd [8] th data from Homstak, GALLEX and Kamiokand and find that thir arlir rsults on th allowd rgions of th paramtrs flm,2 and sin 2 28 ar ruld out as a solution to th solar nutrino problm in trms of two nutrino oscillations in vacuum. (ii) Cosmic ray nutrinos: Strongly intracting particls of cosmic rays, in thir intractions with th atmosphric nucli, produc pions, muons and kaons among othr particls. Ths, in thir dcays, produc v and v. Th xpctd ratio of J.1. (v + v )/ (v + v ) is about 2. Howvr, obsrvations show J.1. J.1. this ratio to b narly 1. Rcnt data by th Kamiokand group [9] rports znith angl dpndnc of this ratio which maks nutrino oscillations a strong candidat to undrstand this ~ RE-S-O-N-A-N-C-E--I-D--c-m-b--r a

9 anomaly bcaus th chang in th flux can b rlatd to diffrnt travl lngths for diffrnt znith angls for th atmosphric nutrinos bfor thy rach th ground basd dtctors. Ths rsults again giv a possibl rang of valus for th pair of paramtrs viz., sin 2 2{) and /).m2 to fit th obsrvd data. (iii) Ractor/Acclrator nutrinos: Nuclar fission ractors produc ij (antilctron nutrinos) with nrgy up to about 8 MV. Evn if oscillation taks plac, th nrgy availabl is not sufficint to produc chargd lptons, which can b obsrvd. Hnc in such xprimnts on only masurs th dcras in th intnsity of th nutrinos of a givn flavour. A bam of U of known flux from th ractors is allowd to travl a crtain distanc and thn thir intnsity is masurd. Ths v ar dtctd through th raction. U + P ~ n + - An anomalous bhaviour in th spctrum of th nutrinos as a function of distanc L and nrgy E would b indicativ of nutrino oscillations. So far no xprimnt has rportd a positiv vidnc for nutrino oscillations from ractor xprimnts. Th nutrinos availabl from th acclrators ar of much highr nrgy and hnc capabl of producing chargd lptons, which can b dtctd. Th liquid scintillation nutrino dtctor (LSND) uss th Los Alamos mson physics facility (LAMPF). Hr acclratd protons produc ;r+ msons which dcay via th raction;r+ ~ J.1+ v followd by J.1+ ~+ v V. Thissupp- Jl Jl lis U with a maximum nrgy of52.8 MV which ar incidnt Jl on a tank filld with 167 mtric tons of dilut liquid scintillator locatd 30m from th nutrino sourc. If th v Jl produc v du to oscillations, th v will produc+ andn through th raction v P ~ +n. Th nutron is capturd producing a photon of 2.2 MV through np ~ dy. Thus th signatur for an oscillation vnt is th dtction of + followd by a 2.2 MV photon corrlatd with + signal in spac as wll as tim. Th background vnts originatd by v ar supprssd by kinmatical constraints. Th LSND xprimnt [10] is consistrit with oscillations at sin 2 2 f:) = 10-2 and b.m 2 ~lv2. Th authors hav givn a valu Suggstd Rading [1] (i)f Rins and C L Cowan. Phys. Rv , (ii)r Davis. Phys. Rv ,1956. [2] B Pontcorvo. Sov. Phys. JETP ,1958. [3] G Danby t al. Phys. Rv. Ltt , [4] B Pontcorvo. Sov. Phys. JETP , [5] R L Mossbaur. Proc. of Indian National Scinc Acadmy (PINSA). Part A, , [6] XVIII Intrnational Confrnc on Nutrino Astrophysics and Astrophysics hld in Japan in Jun [7] P I Krastv and S T Ptcov. Phys. Rv. Ltt. B , and ,1993. [8] PI Krastv and S T Ptcov. Phys.Rv.Ltt ,1994. [9] Y Fukuda t a1. Phys. Ltt. B ,1994. [10]C Athanassopoulos t a!. Phys.Rv.Ltt ,1996. [11] A Romosantal. Phys.Rv. Ltt , [12]Siddhshwar Lal. Nutrino - A Rviw (Forthcoming issu of Physics Education, Pun). [13] R N Mohapatra and P B Pal. Massiv N utnnos in Physics and Astrophysics, World Scintific, [1411 N Bahcall. Nutrino Astrophysics, Cambridg Univrsity Prss, R-ES-O-N-A-N--C-E-I-D--c--m-b--r ~

10 of (0.31 ± 0.l %) for th probability for v p - oscillation with th nrgy of v J1 bing tip to 52.8 MV in a path lngth of 30 m. Romosan t al [11] hav don a dtaild statistical analysis of th data collctd by th CCFR collaboration xprimnt don with Frmi lab, Tvatron. Th CCFR dtctor consists of 18 m long 690 ton total absorption targt calorimtr with a man dnsity of 4.2 gm/cm 3 followd by a 10m long toroidal spctromtr. Th nutrino sourc is locatd 1.4Km. bfor th nutrino. dtctor and producs v, v,v and v with nrgy btwn P J GVwith a man valuof140 GV. Flight lngth for Vp varis btwn 0.9 and 1.4 km. Th rsults of this analysis xclud oscillations in th rgion of sin 2 28> 1.8 x with ~2 > 1000 V2 and sin 2 28 = 1 with ~2 > 1.6 Vl. Th authors claim that thir rsult is th most stringnt limit to dat for ~2 > 25 V2 and xcluds th high ~2 oscillation rgion favourd by th LSND xprimnt. v Addrss for Corrspondnc Siddhswar Lal Intr-Univrsity Consortium for D A E Facilitis Univrsity Campus Khandwa Road Indor 452 OOl,lndia. On may, thrfor, say that so far thr is no confirmd vidnc for nutrino oscillations using ractor and acclrator xprimnts. Cosmic ray nutrinos do indicat possibility of nutrino oscillations. Rsults from som othr xprimnts including KARMEN at th Ruthrford Laboratory in UK ar xpctd in th nar futur. Th two xprimnts plannd with acclrators, CERN and Frmi Laboratory, allow th nutrinos to travl hundrds ofkms of path lngth bfor hitting th dtctor. On thrfor, hops that by 1999 w may hav mor xciting rsults. W hav considrd nutrino oscillations in vacuum only. On may also anticipat nutrino oscillations in mattr originating from MSW (Mikhyv-Smirnov-Wolfnstin) ffct. This bcoms rlvant whn on considrs that nutrinos producd insid th sun hav to travl through dns mattr bfor thy rach th surfac of th sun and scap. But discussion of MSW ffct is byond th scop of this articl ~ RE-S-O-N-A-N-C-E--I-D--c-m-b--r S