Future Solar Neutrino Experiments and Neutrino Spin-Flavour Precession

Transcript

1 DFTT 75/93 Novmbr 993 Futur Solar Nutrino Exprimnts an Nutrino Spin-Flavour Prcssion S.M. Bilnky (a;b;c) an C. Giunti (b;c)? p-p/ Dc 993 (a) Joint Institut of Nuclar Rsarc, Dubna, Russia (b) INFN Torino, Via P. Giuria, I 025 Torino, Italy (c) Dipartimnto i Fisica Torica, Univrsità i Torino Abstract T main faturs of t obsrvabls in t SNO an Supr-Kamiokan solar nutrino xprimnts in t cas of nutrino spin an/or spin-flavour prcssion in t magntic fil of t sun ar iscuss. It is sown witout any mol pnnt assumption tat in t cas of Majorana transition magntic momnts t vnt rat N os not pn on tim an a masurmnt of N will allow to trmin t initial flux of nutrinos wit a tortical uncrtainty of a fw %. In t cas of Dirac magntic momnts t vnt rat will pn on tim an w obtain a mol inpnnt lowr boun for t transition probability of initial s into rigt-an stril nutrinos. BILENKY@TO.INFN.IT? GIUNTI@TO.INFN.IT

2 Introuction It was sown in rf.[, 2, 3] tat futur ral-tim solar nutrino xprimnts (SNO [4] an otrs), in wic ig-nrgy nutrinos from cay will b tct troug t obsrvation of iffrnt ractions, will allow to sparat t invstigation of nutrino proprtis (masss, mixing, tc.) from t invstigation of t cntral invisibl rgion of t sun in wic nrgy is gnrat. If only activ nutrinos ar prsnt in t solar nutrino flux on t art, t initial flux of nutrinos an t survival probability can b trmin irctly from t ata of futur solar nutrino xprimnts witout any assumption about t mcanism of transition of into an/or. In t gnral cas of nutrino mixing, solar s can transfr into activ nutrinos,, an into stril lft-an (anti)nutrinos (s rf.[5]). Diffrnt mol inpnnt rlations an inqualitis btwn obsrvabls, wic coul allow to rval wtr tr ar stril nutrinos in t flux of solar nutrinos on t art, wr riv in rf.[3]. In tis papr w will iscuss possibilitis of a mol inpnnt tratmnt of t ata from futur solar nutrino xprimnts in t cas of spin an/or spin-flavour prcssion of solar s u to anomalously larg nutrino magntic momnts. T ffcts of nutrino magntic momnts [6, 7] wr wily iscuss in last yars (s rf.[8]) in connction wit a possibl inication of t xistnc of an anticorrlation btwn t flux of solar s an t sunspot numbr [9]. T possibl transitions of nutrinos in t magntic fil of t sun pn on t natur of nutrinos. In t cas of Dirac nutrinos, solar s can b transform into stril rigt-an nutrinos `R (` = ; ; ), quanta of rigt-an fils. In t cas of Majorana nutrinos, transitions of solar s into activ rigt-an antinutrinos ` (` = ; ; ), quanta of lftan fils, coul tak plac. Notic tat irct transitions! ar forbin by CPT invarianc. Howvr, sizabl! transitions can occur unr spcial conitions if bot spin-flavour prcssion an t MSW or vacuum oscillations mcanisms ar oprating [0]. In t SNO xprimnt nutrinos (antinutrinos) from t sun will b tct troug obsrvation of t following procsss: +! + p + p (CC) () () +! () + p + n () (2) () +! () + () (3) It is also plann [3] to sarc for from t sun wit t lp of t raction +! + + n + n (4) T trsol for nutrino tction in tis xprimnt will b ratr ig ( & 5 MV for CC an, = 2:2 MV for an 4 MV for raction (4)). Tus SNO will tct Lt us notic tat t Mont Blanc collaboration as obtain t following uppr boun for t flux of in t nrgy rang 9 MV E 20 MV: < 8:2 04 cm 2 sc []. From t analysis of t backgroun in t Kamiokan xprimnt t following uppr boun for t flux of ig-nrgy wit E 0:6 MV was obtain: < 6: 04 cm 2 sc [2].

3 s an nutrinos (an antinutrinos) originating from tm. T nrgy spctrum of t initial s is givn by (E) = (E) (5) wr (E) is a known function (t pas spac factor of t cay! ) an is t total initial flux (trmin by t cntral tmpratur of t sun, t cross sctions of iffrnt ractions of t pp an CNO cycls, tc.). In t Supr-Kamiokan (S-K) xprimnt [4] ig nrgy solar nutrinos ( & 5 MV) will b tct troug t obsrvation of procss (3). A masurmnt of t CC vnt rat as a function of nutrino nrgy E will allow to obtain t flux on t art (E) an to trmin t survival probability up to a constant. If it will occur tat t CC vnt rat pns on tim prioically, it will b an vinc tat nutrinos av larg magntic momnts an tir ffcts ar important. In tis papr w iscuss wic aitional informations can b xtract from a masurmnt of t an vnt rats troug t obsrvation of t procsss (2) an (3), rspctivly. In particular, w will sow tat troug t obsrvation of t an ractions it will b possibl to istinguis Dirac from Majorana magntic momnts. 2 Nutral Currnt Lt us consir first t procss (2). In t cas of Majorana nutrino magntic momnts t intgral vnt rat is givn by N = (E) ; `(E) E + (E) ; `(E) E (6) wr (E) an (E) ar t cross sctions of t procsss! pn an! pn, `(E) an `(E) ar t fluxs of all typs of nutrinos an antinutrinos on t ; ; art. Taking into account tat ; from Eq.(5) an Eq.(6) w obtain `(E) + ; `(E) = (E) (7) N = + I (8) wr I " (E) 2 (E) # (E) 2 ; [P!`(E) P!`(E)] E (9)

4 Hr ; P!`(E) ; (antinutrinos) of all typs an P!`(E) A is t transition probability of solar s into nutrinos ( ) + 2 () (0) (E) (E) E () T cross sctions of t procsss! np an! np wr calculat by svral groups an rviw in rf.[5]. Using t rsults prsnt in rf.[5], w obtain 2 = 4: cm 2 (2) = 4: cm 2 (3) It is asy to s tat t valu of t intgral I is vry small. In fact, for t absolut valu of tis intgral w av t following uppr boun: I + ' (4) T uppr boun of t intgral I is so small bcaus t cross sctions of t procsss! np an! np ar vry clos to ac otr in t nrgy rgion nar t trsol. T argumnt in favour of tis fact is ratr gnral: from symmtry consirations it follows tat nar t trsol (if only t s-stat of t final nuclons is takn into account) t vctor currnt os not contribut to t matrix lmnts of t procsss! np an! np an t cross sctions an ar qual. T corrctions u to igr stats ar small in t rlvant nrgy rgion (s rf.[5] an rfrncs trin). Tus, t trm I in Eq.(8) can b safly nglct an, in t cas of Majorana magntic momnts, w com to t following conclusions:. T vnt rat os not pn on tim (witin lss tan 2%). 2. T flux of t initial s is givn by ' N (5) an trfor can b trmin irctly from t xprimntal ata 3. 2 W us t valus of t function (E) givn in rf.[6]. 3 Notic tat t xprssion (5) for 8 B coincis wit tat obtain in rf.[2] for t cas of transitions of solar s only into an/or u to usual nutrino mixing. 3

5 3. It is possibl to obtain t survival probability irctly from masurabl quantitis: P! (E) = P!`(E) P!`(E) wr ; = (E) (E) N (6) wr (E) is t flux of on t art, wic can b trmin from t CC vnt rat. Consir now t cas of Dirac nutrino magntic momnts. In tis cas ; N = (E) ; `(E) E (7) `(E) = (E) S (E) an S (E) is t flux of stril rigt-an nutrinos on t art. It is clar tat in t Dirac cas N will pn on tim. Hnc, a tim pnnc of t CC an vnt rats will b a signal tat nutrinos av larg Dirac magntic momnts. For t avrag transition probability of solar s into stril stats w obtain t following mol inpnnt lowr boun: * ; P!`R (E) + N (E) (E) ( =) max ; P!`R (E) E wr ( =) max inicats t maximum valu of (E)=(E), wic can b obtain from t ata on t CC vnt rat. Lt us strss tat, unlik t cas consir in rf.[3], in t cas of spin an/or spin-flavour transitions u to Dirac magntic momnts t lowr boun (8) will pn on tim. (8) 3 Elastic Scattring Lt us consir now t procss (3). Using Eq.(5), in t cas of Majorana nutrinos w av wr Et = + I N (E) (E) (E) E i (E) (E) (E) E ; Et i (9) (20) 4

6 N is t intgral vnt rat, `(E) ( `(E)) is t total cross sction of t procss `! ` (`! `) wit ` = ;, an I " # (E) (E) (E) [P!`(E) P!`(E)] E (2) 2 wr + 2 ( ) ; (22) ( )(E) (E) E (23) T valus of t cross sctions `(E) an `(E) (` = ; ) wit a 5 MV trsol kintic nrgy for lctron tction ar pict in Fig. in t nrgy rang rlvant for solar nutrino xprimnts. W us g V = 0:036 an g A = 0:505 [7]. For an w obtain t following valus: = 2: cm 2 (24) = 2: cm 2 (25) Using ts valus, w av t following uppr boun for t absolut valu of t intgral I : Lt us notic tat t ral valu of I ' 0:2 (26) + I can b significantly smallr tan t uppr boun givn in Eq.(26). W calculat t intgral I in t simplst mol wit two non-mix massiv Majorana nutrinos an a larg transition magntic momnt. In rf.[8] it was sown tat t xisting solar nutrino ata can b scrib by tis mol wit ' 0 B unr spcific assumptions for t magntic fil of t sun. For t avrag valu of m 2 foun in rf.[8] (m 2 = 0 8 V 2 ) w obtain tat 7:6 0 2 I 9:3 0 3, wr t lowr an uppr bouns corrspon to ig an low solar activity, rspctivly. T tim pnnc of t quantity is trmin by t intgral I, wic is lss tan ' 0%. Nglcting I in Eq.(9), w obtain t following approximat xprssion for t initial flux of nutrinos: ' (27) Tus, in t cas of Majorana magntic momnts, t initial flux of nutrinos can b trmin in two inpnnt ways: from t vnt rat (s Eq.(5)) an from t an CC vnt rats (s Eq.(27)). Trfor, inpnntly from t valu of t initial nutrino flux, w av t following approximat rlation btwn masurabl quantitis: N ' 5 (28)

7 Tis rlation is a gnralization of an analogous rlation tat was obtain in rf.[2] for t cas in wic only activ nutrinos,, ar prsnt in t flux of solar nutrinos on t art (in tat cas t rlation is xact). Lt us notic tat, in t cas of Majorana magntic momnts, t vnt rat will pn on tim. Tis tim pnnc is trmin by t tim pnnc of t CC vnt rat. Lt us consir now t cas of Dirac nutrino magntic momnts. In tis cas w av = (E) (E) E t ; P!`R (E) E (29) wr N (E) (E) (E) E (30) Et In t cas unr consiration t quantity will pn on tim. From Eq.(29), w obtain t following lowr boun for t avrag transition probability of solar s into all possibl rigt-an stril stats: * ; P!`R (E) + Et (E) (E) ( =) max ; In t cas of Dirac magntic momnts, insta of rlation (28) w av P!`R (E) E (3) N = + (32) wr = (E) S (E) E (E) S (E) E (33) E t Lt us assum tat is not obsrv. If t rlation (28) is violat an pns on tim, w will av an aitional argumnt in favour of Dirac magntic momnts. Notic, owvr, tat, accoring to our mol calculations, t two trms in t rigt-an si of Eq.(33) coul cancl ac otr. 4 On t transition probability of into an/or Lt us consir t cas of Majorana magntic momnts (t CC vnt rat pns on tim but t vnt rat is constant). As w av sn in Sc.2, from t ata on t CC an ractions (an t procss (4)) it will b possibl to trmin t sum of t probabilitis of 6

8 t transitions of initial s into,,, (s Eq.(6)). In tis sction w will iscuss possibilitis to obtain from t SNO an S-K ata an information about t transition probability P!`(E). Wit t lp of Eq.(5) w obtain N ' I (34) wr Et N (E) (E) (E) E i (E) (E) (E) E Et i (35) an I i (E) (E) (E) Et P!`(E) E (36) It is asy to s tat 0 I = 0:2 (37) Hnc, in orr to obtain an information about t transition probability P!`(E), it is ncssary to know t masurabl quantity =N wit an accuracy bttr tan ' 20%. If tis accuracy will b aciv, t avrag probability of t transition of solar s into an/or can b trmin irctly from t xprimntal ata: * P!`(E) + 5 Conclusions ' i (E) (E) (E) Et N P!`(E) E A (38) In SNO, Supr-Kamiokan an otr futur solar nutrino xprimnts ig nrgy solar nutrinos will b tct troug t obsrvation of CC, an (- lastic scattring) ractions. If nutrinos av larg (Majorana or Dirac) magntic momnts, solar nutrinos can unrgo spin an/or spin-flavour prcssions in t magntic fil of t sun. In tis cas t CC vnt rat will manifst a prioical tim pnnc. W av sown tat in t cas of Majorana nutrino magntic momnts t vnt rat in t SNO xprimnt (N ) will not pn on tim an a masurmnt of N will allow to 7

9 trmin in a mol inpnnt way t total flux of initial nutrinos (s Eq.(5)) an t survival probability (s Eq.(6)). In t cas of Majorana nutrino magntic momnts t vnt rats will pn on tim. W av sown, owvr, tat a combination of an CC vnt rats (, s Eq.(20)) can av only a minor tim pnnc. W av also sown tat, in t cas of Majorana nutrino magntic momnts, tr is a rlation btwn t, CC an vnt rats (Eq.(28)). In t cas of Dirac nutrino magntic momnts t vnt rat in t SNO xprimnt, as wll as t CC an vnt rats, will pn on tim. W av sown tat a masurmnt of t (or ) an CC vnt rats will allow to trmin a (tim pnnt) lowr boun for t avrag transition probability of solar s into all possibl rigt-an stril stats (s Eq.(8) an Eq.(3)). Finally, for t cas of Majorana magntic momnts w av riv an xprssion tat allows to obtain t avrag probability of t transition of initial s into an/or from masurabl quantitis (s Eq.(38)). T trmination of tis avrag probability will rquir a masurmnt of t vnt rats wit ratr ig accuracy. Acknowlgmnts It is a plasur for us to xprss our gratitu to Wana Albrico for vry usful iscussions. Rfrncs [] H.H. Cn, Pys. Rv. Ltt. 55 (985) 534; R.S. Ragavan, S. Pakvasa an B.A. Brown, Pys. Rv. Ltt. 57 (986) 80; J.N. Bacall, M. Balo-Colin, D.B. Clin an C. Rubbia, Pys. Ltt. B 78 (986) 324; S. Winbrg, Int. J. Mo. Pys. A 2 (987) 30; C. Rubbia, CERN-PPE/93-08; G. Fiorntini t al., INFNFE [2] S.M. Bilnky an C. Giunti, Pys. Ltt. B 3 (993) 79. [3] S.M. Bilnky an C. Giunti, DFTT 62/93, to b publis in Pys. Ltt. B. [4] T Subury Nutrino Obsrvatory Collaboration, Pys. Ltt. B 94 (987) 32; H.H. Cn, Nucl. Instr. Mt. A 264 (988) 48; G.T. Ewan, Procings of t 4 t Intrnational Worksop on Nutrino Tlscops, Vnzia, Marc 992. [5] S.M. Bilnky an B. Pontcorvo, Pys. Rp. 4 (978) 225; S.M. Bilnky an S.T. Ptcov, Rv. Mo. Pys. 59 (987) 67. [6] A. Cisnros, Astropys. Spac. Sci. 0 (970) 87; M.B. Volosin, M.I. Vysotsky an L.B. Okun,. Eksp. Tor. Fiz. 9 (986) 754 [ Sov. Pys. JETP 64 (986) 446]. [7] C.S. Lim an W.J. Marciano, Pys. Rv. D 37 (988) 368; E.K. Akmov, Pys. Ltt. B 23 (988) 64. 8

10 [8] P.B. Pal, Int. J. Mo. Pys. A 7 (992) [9] R. Davis Jr., Intrn. Symp. on Nutrino Astropys., Takayama/Kamioka, Japan, 992. [0] E.K. Akmov, Sov. Pys. JETP 68 (989) 690; C.S. Lim t al., Pys. Ltt. B 243 (990) 389; E.K. Akmov, Pys. Ltt. B 255 (99) 84; E.K. Akmov, S.T Ptcov an A.Yu. Smirnov, Procings of t 5 t Intrnational Worksop on Nutrino Tlscops, Vnzia, Marc 993; H. Nunokawa an H. Minakata, Pys. Ltt. B 34 (993) 37. [] M. Aglitta t al., Astropart. Pys. (992). [2] R. Barbiri t al., Pys. Ltt. B 259 (99) 9. [3] H.H. Cn, Nucl. Instr. Mt. A 264 (988) 48. [4] A. Suzuki, Proc. of t Worksop on Elmntary Particl Pictur of t Univrs, KEK, Japan, 987; Y. Totsuka, ICRR-rport (990); C.B. Bratton t al., "Proposal to Participat in t Supr-Kamiokan Projct", Dc [5] K. Kubora an S. Nozawa, USC(NT)-93-6, nucl-t/ [6] J.N. Bacall an R. Ulric, Rv. Mo. Pys. 60 (988) 297; J.N. Bacall, Nutrino Pysics an Astropysics, Cambrig Univrsity Prss, 989. [7] P. Langackr, Lcturs prsnt at TASI-92, Boulr, Jun 992. [8] E.K. Akmov, A. Lanza an S.T Ptcov, Pys. Ltt. B 303 (993) 85. 9

11 00 σ / E (0-46 cm 2 /MV) 0 ν - ν - ν µ - ν µ E (MV) Figur : Valus of t cross sctions (E), (E), (E), (E) in t nrgy rang rlvant for solar nutrino xprimnts, wit a 5 MV trsol kintic nrgy for lctron tction. W us g V = 0:036 an g A = 0:505 [7]. 0