Fast decaying neutrinos and observable flavour violation in a new class of majoron models

V01ume 216, num6er 3,4

PHY51C5 L E 7 7 E R 5 8

12 January 1989

FA57 DECAY1N6 N E U 7 R 1 N 0 5 AND 0 8 5 E R V A 8 L E FLAV0UR V10LA710N 1N A NEW CLA55 0 F M A J 0 R 0 N M 0 D E L 5 M.C. 6 0 N 2 A L E 2 - 6 A R C 1 A and J.W.F. VALLE CERN, CH-1211 6eneva 23, 5w1t2er1and and Department de F151ca 7e6r1ca, Un1ver51tat de Va1enc1a, E-46100 8urja550t, Va1enc1a, 5pa1n Rece1ved 15 5eptem6er 1988

Neutr1n05 can have any ma55 (a110wed 6y 1a60rat0ry 11m1t5) w1th0ut v101at1n9 11m1t5 fr0m c05m0109y, a5tr0phy51c5 0r 1a60rat0ry 5earche5 f0r 1ept0n v101at10n phen0mena. We pre5ent a 51mp1e exten510n 0f the 5tandard the0ry where neutr1n05 decay d0m1nan11y 1nt0 1nv15161em0de5 1nv01v1n9 a maj0r0n a550c1ated w1th the 5p0ntane0u5 v101at10n 0 f 8 - L 5ymmetry due t0 phy51c5 at 0r 6e10w the e1ectr0weak 5ca1e. Mea5ura61e 6ranch1n95 f0r 1ept0n-f1av0ur-v101at1n9 pr0ce55e5 5uch a5 9 ~ e + y, and f0r n0n-5tandard 2 decay5 e,9. 2 ~ e + t , and 2 ~ 9 + ~ (p1u5 the1r c0nju9ate5) at LEP are p055161e w1th0ut unnatura1 f1ne-tun1n9 0 f t h e parameter5. Lept0n-num6er-v101at1n9 effect5 5uch a5 neutr1n01e55 [313decay may a150 6e pre5ent at a mea5ura61e 1eve1.

1.1ntr0duct10n 1f neutr1n05 are ma551ve they can decay. 7he 4ue5t10n 0f neutr1n0 5ta6111ty may have 1mp0rtant c05m01091ca1 and a5tr0phy51ca1 c0n5e4uence5. 1f 5ta61e, neutr1n05 w0u1d c0ntr16ute t00 much t0 the ener9y den51ty • t h e un1ver5e 1f [ 1 ] 60 eV < m,, < few 6 e V .

( 1)

7h15 ma55 ran9e may 6ec0me c05m01091ca11y a110wed, h0wever, 1fthere are new neutr1n0 decay and/ 0r ann1h11at10n channe15. 7he c05m01091ca1 den51ty c0n5tra1nt 0n the neutr1n0 decay 11fet1me f0r a m ~< 1 MeV neutr1n0 ~ < 1 . 5 X 107 ( k e V / m ) 2 y r

(2)

f0110w5 fr0m demand1n9 an ade4uate red5h1ft 0f the heavy neutr1n0 decay pr0duct5. 7he ava11a61e neutr1n0 decay m0de5 are, h0wever, very m0de1 dependent. W1th1n the 5tandard e1ectr0weak m0de1, w1th neutr1n0 ma55 1ntr0duced 1n the 51mp1e5t way, neutr1n05 w1th m~. ~<1 MeV w0u1d decay a5 v• - * v + 7 and v•-*v+7+7.7he f1r5t ha5 a very 10n911fet1me, due t0 the 61M mechan15m [2]. A1th0u9h the v• ~ v + 7 + 7 decay m0de av01d5 the 61M 5uppre5510n the 11fet1me 15 5t111t00 10n9 [ 3 ] t0 av01d the c05m01091ca1 60und. 1t ha5 6een n0ted 10n9 a90 [4,5], that, 1n the 5tan360

dard e1ectr0weak the0ry, the 51mu1tane0u5 pre5ence 0f D1rac and Maj0rana neutr1n0 ma55 term5 1n the 1a9ran91an a110w5 f0r the 1nv15161e ~ decay v•-. 3v t0 0ccur, med1ated 6y the neutra1 current w1th a 11fet1me r ( v ~ 3 v ) ~ 7.6X 10 m ( k e V / m ) 5 ( P ) - 2 y r

(3)

f0r a 9ener1c heavy neutr1n0 0f ma55 m, where P 15 the appr0pr1ate c0up11n9 parameter. C0mpar1n9 e4. (2) and e4. (3) 0ne 9et5 ( m / k e V ) 3 ( P 2) > 5X 103 ,

(4)

wh1ch 1ead5 t0 the c0nd1t10n m > 17 keV. 7he f1r5t c0ncern 15 that a 5h0rt 3v decay 11fet1me w0u1d 1mp1y e.9. a 1ar9e 9-~e+e-e - decay 6ranch1n9 rat10 (8R) 6ut 1n the 5tandard m0de1 th15 can pr06a61y 6e ade4uate1y 5uppre55ed 51nce th15 m0de w0u1d take p1ace 0n1y at 0ne 100p. H0wever, 1f rnv, <~ 1 MeV and the neutr1n0 ma55 f0110w5 fr0m a 5ee-5aw mechan15m we expect a t1ny va1ue f0r P < 10- 5 50 that the5e 11fet1me5 are, a9a1n, t00 10n9 t0 a110w f0r 5uff1c1ent red5h1ft 0f the heavy neutr1n0 decay pr0duct5, and thu5 f0r61dden 6y c05m0109y. 0 n the 0ther hand, f0r rnv. >~ 1 MeV ~ V1516h,decay5 are very c0n5tra1ned 6y a5tr0phy51c5 [6,7] and 1a60rat0ry. [8]. 1n c0ntra5t, h0wever, decay5 5uch a5 v• ~ 3 v are a1m05t unc0n5tra1ned, except fr0m the c05m01091ca1 den51ty ar9ument5.

0370-2693/89/$ 03.50 • E15ev1er 5c1ence Pu6115her5 8.V. (N0rth-H011and Phy51c5 Pu6115h1n9 D1v1510n)

v01ume 216, num6er 3,4

PHY51c5 LE77ER5 8

the 3v decay w0u1d a150 6e acc0mpan1ed 6y the v15161echanne1 v• - , e + e v. 7h15 w0u1d 1mp1y a150 a 3•-ray 6ur5t fr0m a 5upern0va exp10510n, where the ph0t0n5 ar15e fr0m 5u65e4uent ann1h11at10n a n d / 0 r 6rem55trah1un9 pr0ce55e5 [ 9 ]. 7he n0n-065ervat10n 0f 5uch a 6ur5t fr0m 5N1987 [9] make5 th15 p05516111ty n0w 5eem un11ke1y (a1th0u9h n0t 5tr1ct1y exc1uded). Can we have fa5ter decay5, w1th0ut v101at1n9 a5tr0phy51c5• 7he 5p0ntane0u5 v101at10n 0f 8 - L 5ymmetry 1n the 5tandard e1ectr0weak m0de1 9enerate5 a ma551e55 N a m 6 u - 6 0 1 d 5 t 0 n e 6050n - a maj0r0n - den0ted J. 1n the5e m0de15 a new 5ca1e 15 1ntr0duced character121n9 th15 5p0ntane0u5 v101at10n 0f t0ta1 1ept0n num6er 5ymmetry, e1ther 6e10w the e1ectr0weak 5ca1e [ 10 ] 0r a60ve [ 1 1 ]. 1t wa5 5u99e5ted that 1n th15 ca5e neutr1n05 w111decay very fa5t 1nt0 the 1nv15161e maj0r0n5 [10,11] v~-~v+J.

(5)

Deta11ed 1nve5t19at10n 5h0wed, h0wever, that there 15 a 5u6t1e cance11at10n wh1c11 5uppre55e5 the na1ve1y expected [ 1 1 ] 5tren9th 0f the 0ff-d1a90na1 c0up11n95 0f the maj0r0n t0 119ht neutr1n05 [ 5 ]. A5 a re5u1t fa5t decay5 0f 119ht neutr1n05 mv ~<0 ( 10-100 keV) d0 n0t happen 1n the5e m0de15 n0r 1n 51mp1e exten510n5 there0f [5]. F0r 1ar9er neutr1n0 ma55e5, 5uch a5 a110wed f0r v~ and, 1e55 11ke1y, f0r v~ (1f 1t5 ma55 happen5 t0 6e re1at1ve1y c105e t0 the pre5ent 1a60rat0ry 11m1t) there 15 5t111 an 0pen w1nd0w, a5 empha515ed recent1y 1n ref. [ 12]. 7here ha5 6een a 10t 0f 1ntere5t 1n the p055161e decay 0f 119ht neutr1n05 1n c0nnect10n w1th c05m0109y, a5tr0phy51c5 and part1c1e phy51c5 [ 13 ]. 7he5e decay5 have 50 far 0n1y 6een p055161e 1n the c0ntext 0f var1ant5 0f the maj0r0n that pr0m0te the 0r191na1 8 - L 5ymmetry t0 0ne wh1ch d1fferent1ate5 6etween 1ept0n fam111e5, add1n9 a150 a 5u1ta61y extended 5ca1ar 5ect0r. 7h15 way the fa5t decay 11fet1me make5 any va1ue 0f the neutr1n0 ma55 (c0n515tent w1th exper1ment) c05m01091ca11y a110wed a5 we11 [ 14 ]. We f1nd 1t 1ntere5t1n9 t0 exp10re h0w the phy51c5 0f the 51mp1e5t (15051n91et) maj0r0n depend5 0n deta115 0f the ferm10n repre5entat10n c0ntent 1n the 5 U ( 2 ) • U ( 1 ) the0ry. 8 y 5u1ta61y extend1n9 the ferm10n 5ect0r (rather than the 5ca1ar) we are a61e n0w t0 re55urrect the 1dea 0f 119ht 1nv15161ydecay1n9 neutr1n05 1n the framew0rk 0 f a 8 - L maj0r0n. 7he ad-

12 January 1989

d1t10na1 weak 15051n91et ferm10n5 u5ed 1n 0ur m0de1 may ar15e 1n var10u5 attempt5 t0 un1fy 4uark5 and 1ept0n5 1n a 5uper5tr1n9 framew0rk ~2 [ 16,1 7 ]. 1n an appr0pr1ate ran9e 0f parameter5 0ur m0de1 ha5 the f0110w1n9 feature5: ( 1 ) A11 neutr1n0 ma55e5 f0r 60th v, and v~ are p055161e, 6ecau5e 0f the pre5ence 0f fa5t 1nv15161e decay m0de5 (f19. 1 ). (2) 7he pr0ce55 9 ~ e + 3• can 0ccur w1th a 1ar9e 8 R a5 a re5u1t 0f effect1ve neutr1n0 n0n-0rth090na11ty 1rre5pect1ve 0fneutr1n0 ma55 [ 18]. (3) 7he c0rre5p0nd1n9 9 - , e +•{ 8 R f0r the ca5e 0f n0n2er0 neutr1n0 ma5515 a150 5u65tant1a11y enhanced and can 1ead t0 a mea5ura61e 519na1 (f195. 2,3) f0r va1ue5 0f the neutr1n0 parameter5 wh1ch are c0n515tent w1th 1a60rat0ry, c05m0109y and a5tr0phy51c5. (4) 51m11ar1y, there can 6e 065erva61e 1ept0n-f1av0ur-v101at1n9 519nature5 1n the decay5 0f the 2 1nt0 ~5 at LEP [ 18 ]. Neutr1n01e551313 may 6e 065erved 1n the near future.

2 . 7 h e m0de1 We u5e the f0110w1n9 5et 0f (1eft-handed) 1ept0n5 (repeated 0ver 9enerat10n 1ndex, 1): (v~) e, ~ e ~ v ~ 5~

(6)

wh11e the 4uark 5ect0r 15 the 5tandard 0ne. 1n add1t10n t0 r19ht-handed neutr1n05 there are an e4ua1 num6er 0f9au9e 51n91et 1ept0n5 51 ~5.7he5e extra ferm10n5 ar15e 1n 50me m0de15 1n5p1red 6y the 5uper5tr1n9, where 0ften 0ne 15 1ed t0 a ma55 matr1x (1n the 6a515 v, v c, 5) 0f the f0rm [ 15,16 ] 7

0 M7

M p

.

(7)

7he 2er0e5 0f the5e entr1e5 can ar15e 1n 50me 0fthe5e m0de15 6ecau5e e.9. there are n0 H1995 f1e1d5 t0 pr0v1de the u5ua1 Maj0rana ma55 term5 needed 1n the 5ee-5aw mechan15m [ 15-17 ]. We c0n51der e4. (7) t0 ,2 F0r a rev1ew5ee ref. [ 15 ]. ~37he num6er 0f 51n91etferm10n5 that can 6e added t0 the 5tandard e1ectr0weak the0ry 15 ar61trary 51nce they d0 n0t carry any an0ma1y [ 19]. 361

V01ume 216, num6er 3,4

PHY51C5 LE77ER5 8

6e 1ntere5t1n9 1n 1t5 0wn r19ht and 1nve5t19ate 1t5 phy51c5 c0n5e4uence5 w1th1n the framew0rk 0f the 5tandard the0ry. 7he matr1x D5j 15 the D1rac ma55 term f0r the three r19ht-handed neutr1n05, M1j 15 an 15051n91et 6are ma55. 1f p ~ 0 , e4. (7) ac4u1re5 three ma551e55 ma55-e19en5tate5, c0rre5p0nd1n9 t0 the u5ua1 neutr1n05.7he 0ther 51x neutra1 Wey1 1ept0n5 c0m61ne 1nt0 three heavy D1rac ferm10n5. A11 1ept0n char9e5 w0u1d 6e c0n5erved 1f 1t were n0t f0r the ar61trary Yukawa c0up11n9 0r191nat1n9 the char9ed 1ept0n ma55e5.7hu5 the the0ry ha5 0n1y a net t0ta1 L c0n5ervat10n, th15 6e1n9 the (9106a1) 5ymmetry re5p0n5161e f0r keep1n9 neutr1n05 ma551e55. We n0w d15cu55 the phy51c5 a550c1ated w1th t0ta11ept0n-num6er v101at10n 1ntr0duced thr0u9h a 5ma11 P51. 0 n c e th15 15 added, n0n-2er0 Maj0rana neutr1n0 ma55e5 are 9enerated fr0m ML = D M - 1 ~ t M 7 - 1 D 7 .

(8)

F0r C0ntra5t We Wr1te the C0rre5p0nd1n9 neutr1n0 ma55 1n the 5ee-5aW m0de1 [20 ] M ~ ..... = D M ~ 1 D 7 ,

(9)

Where M~ 15 the Maj0rana ma55 f0r the r19ht-handed neutr1n05. 1n 0rder t0 9enerate t0ta1-1ept0n-nUm6er V101at10n 1n a 5p0ntane0U5 Way We 1nC1Ude a 9aU9e 51n91et H1995 ~ (Carry1n9 -- 2 Un1t5 0f 1ept0n nUm6er) 1n add1t10n t0 the 5tandard H1995 d0u61et 0 re5p0n5161e f0r 4uark and char9ed 1ept0n ma55e5: P1J = 2 , (46) .

(10)

Neutr1n0 ma55e5 are n0w acc0mpan1ed 6y the ex15tence 0 f a ma551e55 maj0r0n J = 1m 46 ~4.7he maj0r0n f0110w1n9 fr0m e4. (10) 15 6a51ca11y the 5ame a5 1n ref. [ 1 1 ]. H0wever, f0r 5ma11 p the phen0men0109y 0f f1av0ur v101at10n f0110w1n9 fr0m e4. (8) 15 marked1y m0re exc1t1n9 than that 0f e4. (9) [ 5ee e4. (2 3 ) 6e10w ].

3. Weak 9au9e current5

1n the pre5ence 0f neutra1 heavy 1ept0n5 ( N H L ) , e.9. r19ht-handed neutr1n05, the m05t 9enera1 1ept0n ~4 Maj0r0n em15510n15n0t expected t0 c0ntr16ute exce551ve1y10 5te11arener9y 105551nceth15 maj0r0n 1550 weak1yc0up1edthat 1t w111n0t 6e c0p10u51ypr0duced 1n 5tar5 [21 ]. 362

12 January 1989

m1x1n9 matr1x de5cr161n9 the char9ed current (CC) weak 1nteract10n 1n the 5tandard 5U ( 2 ) • U ( 1 ) the0ry 15 91ven 6y a rectan9u1ar matr1x [4]. F0r n 9enerat10n5 e4. (6) 1mp11e5 that n ( 5 n - 1 ) parameter5 are needed t0 5pec1fy the CC 1n 0ur m0de1.7h15 1nc1ude5 the new CP-v101at1n9 pha5e5 character15t1c 0f Maj0rana neutr1n05 [4,22] 6ut exc1ude5 n0n-phy51ca1 pha5e5 that can 6e e11m1nated 6y appr0pr1ate redef1n1t10n5 0f the char9ed 1ept0n5.70 the extent that L 15 a 900d 5ymmetry ( p - , 0 ) , h0wever, th15 num6er reduce5 further 6ecau5e the c0rre5p0nd1n9 matr1x K c011ap5e5 t0 3 × 6, and can 6e c0nven1ent1y wr1tten a5 K=(KL, K.)=(UD1VL,

UDADHVn),

(11)

where DA and DH are d1a90na1 matr1ce5 re1ated 6y D a2 -•( 1 - D ~ D ~ j ) and U, VL and V, are ar61trary un1tary matr1ce5 ar151n9 fr0m the d1a90na112at10n 0f the var10u5 ma55 matr1ce5.1f we treat the new N H L a5 D1rac part1c1e5 (5tr1ct1y 5peak1n9 they are Qua51D1rac [ 2 3 ] ) , there are add1t10na1 a110wed pha5e tran5f0rmat10n5 0n the heavy neutr1n05 that rem0ve 0ther pha5e5 fr0m K a n d thu5 51mp11fy the f0rm 0fthe CC 1nteract10n. F0r 51mp11c1tywe a55ume 1n what f0110w5 CP c0n5ervat10n, 50 the matr1ce51n e4. ( 1 1 ) are a11 rea1, up t0 fact0r5 0f1 that ar15e when expre551n9 a D1rac neutr1n0 a5 a 5um 0 f t w 0 Wey1 part1c1e5 [24]. 7hen, f0r the 51mp1e ca5e 0f tw0 9enerat10n5 f1ve parameter51n t0ta1 are needed t0 de5cr16e the weak current5, 06 0H, 0~5, h~, h2 ar151n9 fr0m ~ , VH, U and Dm re5pect1ve1y. F0r DA¢ 1 the CC 1nteract10n5 0f the phy51ca1 ma55 e19en5tate 119ht neutr1n05 are effect1ve1y de5cr16ed 6y a m1x1n9 matr1x KL wh1ch 15 n0nun1taty [4]. Hence the neutr1n05 that can 6e k1nemat1ca11y pr0duced 1n 10w ener9y weak decay pr0ce55e5, are effect1ve1y n0n-0rth0n6rma1.7h15 1ead5 t0 the remarka61e p05516111ty0f1ept0n-f1av0ur v101at10n even 1fthe neutr1n05 are ma551e55 (p--,0) and 1~-~ 1. When 1ept0n-num6er v101at10n 15 turned 0n, th15 1ept0n-f1av0ur v101at10n 6ec0me5 re1ated t0 mv 6ut the re5u1t1n9 effect5 are marked1y 1ar9er than what w0u1d 6e expected 1n the 5ee-5aw m0de1 (5ee 6e10w). 7he neutra1 current 1n the neutr1n0 5ect0r a150 6ec0me5 n0n-d1a90na1 when expre55ed 1n term5 0f ma55 e19en5tate neutr1n05 [4 ] 7 9 P.1, = [ VLDA VL]a1,•

(12)

51nCe the d1a90na1 matr1X DA 151n 9enera1 n0n-de9en-

V01ume 216, num6er 3,4

PHY51C5 LE77ER5 8

12 January 1989

erate, the c0up11n9 1n e4. (12) 15 1n 9enera1 n0n-d1a90na1 [4].

9~ =~ ~2hj h2 c05 20c.

4. Fa5t neutr1n0 decay5

F0r 5ma11 m1x1n95 we 0n1y keep the 5ec0nd term. A 51mp1e e5t1mate may 6e 06ta1ned 6y rep1ac1n9 an ar61trary matr1x e1ement/t110r M v 6 y / t and M, re5pect1ve1y. 1n add1t10n 5ett1n9 (h~)2~ (h~)2~m2/1t and c~2~1~/Mwe have ~5

E4. (12) 1ead5 t0 the p055161e 1nv15161e decay e4. (3). 7h15 can 6e an eff1c1ent decay m0de f0r v~ heav1er than 1 MeV 0r 50, 6ut th15 p05516111ty 15 a 61t un11ke1y 1n v1ew 0f the n0n-065ervat10n 0f a y-ray 6ur5t f0110w1n9 the 5N 1987 exp10510n [ 9 ]. F0r rn ~< 1 MeV, there c0u1d 5t111 6e a 5ma11 a110wed w1nd0w 1n 0ur m0de1 f0r neutr1n05 decay1n9 v1a the neutra1 current [e4. (4) ] 1n c0ntra5t t0 the 5ee-5aw m0de1 where the re4u1red va1ue5 f0r the n0n-d1a90na1 P matr1x e1ement5 are 1nc0n515tent w1th the neutr1n0 ma55e5 determ1ned fr0m e4. (9). H0wever, 1nv15161e neutr1n0 decay5 6ec0me much m0re 5pectacu1ar even f0r the 1ntere5t1n9 ca5e 0f119ht neutr1n051fa maj0r0n 15 1ntr0duced, e4. (10). U51n9 the meth0d deve10ped 1n ref. [5] we have determ1ned the c0up11n95 0f 0ur maj0r0n t0 119ht neutr1n05 a5 9,,/,=(46)

~[rn,,+m1,]P~,,~,,

a~6,

(13)

where m, den0te the f19ht neutr1n0 ma55e5 and P• 15 91ven 6y

P~=V7DM7-11tM 1M7-1f1]1/1-1D7V~,

(14)

V~ 6e1n9 the matr1x that d1a90na112e5 the 119ht neutr1n0 ma55 matr1x, e4. (8). 7h15 can 6e rewr1tten a5 P• = V7 DH~2DH ~ ,

(15)

where we have def1ned E2 = 8 U ~ 1 t M - ~ [ M - ~ ] v1tU787, H~=D[M-1]

7,

H=87Du8.

F0r the 51mp1e ca5e 0f tw0 fam111e5 the n0n-d1a90na1 c0up11n9 re5p0n5161e f0r the decay 0f a neutr1n0 0f ma55 m21nt0 a ma551e55 neutr1n0 p1u5 a maj0r0n may 6e parameter12ed a5 9,2 = m 2 < 0 ) -•(95 + 9 ~ ) ,

(16)

where

~ = ~ ( e 2 , ~ h ~ - e ~ , h ~ ) 51n 20L, and

912 ~ m ~ / M 2 .

(18)

(19)

7 h e neutr1n0 decay 11fet1me 6ec0me5 ~(V2-+ V1 + J ) 1.3× 105 ( k e V / m 2 ) 5 ( M / 6 e V ) 4 5 .

(20)

7he C0rre5p0nd1n911fet1me e5t1mated 1n the 5ee-5aW m0de115 f0rma11y 06ta1ned 6y tak1n9 e22 = e~ ~= 1 and e~2=0 1n e4. (17) and 1n e4. (18). Var10U5 exper1menta1 11m1t5 0n neutr1n0 phy51c5 1nc1ud1n9 [3130vdecay, etc. 5u99e5t that m05t 11ke1y mt 15 5ma11 and neutr1n05 are weak1y m1xed. 1n the appr0x1mat10n where rn~ << m2 we have 51n20c ~ m~/m2 50 the re5u1t1n9 11fet1me 15 ~"........ (V2--~ V1 + J ) 1.3× 1011 ( k e V / m 2 ) 4 ( M R / 6 e V ) 4 ( e V / r n ~ ) 5 .

(21) 7h15151n a9reement w1th the 9enera1 re5u1t5 06ta1ned 6y the 0r191na1 ana1y515 0f the 4ue5t10n 0f neutr1n0 5ta6111ty 1n maj0r0n m0de15 91ven 1n ref. [ 5 ]. 8arr1n9 acc1denta1 cance11at10n5, the n0n-065ervat10n 0f [3130,, decay 1mp11e5 m1 < 5 eV. 7he5e 11fet1me5 1n e4. (20) and 1n e4. (21) are p10tted 1n f19. 1 . 7 h e d1fference 6etween 0ur m0de1 and the 5ee-5aw m0de1 pred1ct10n5 1n the 5ma11 m1x1n9 appr0x1mat10n f0110w5 fr0m the 10wer N H L ma55 natura1 1n 0ur m0de1 6ut n0t 1n the 5ee-5aw m0de1.

5. Enhanced 1ept0n-f1av0ur v101at10n E45. ( 1 1 ) and (12) 1ead t0 the p05516111ty 0 f h a v 1n9 1nd1v1dua1 f1av0ur v101at10n effect5 1n the 5tandard e1ectr0weak the0D•, even 1f neutr1n05 are 5tr1ct1y

(17) ~5 We a55umed the Yukawa c0up11n99enerat1n9 1t t0 6e 0f0rder un1ty. 363

V01ume 216, num6er 3,4

PHY51C5 LE77ER5 8

0f 0rth090na1 neutr1n05, we can 5t1111nduce 1ar9e f1av0ur v101at10n due t0 neutr1n0 ma55 6ecau5e 0f (a) the h19her neutr1n0 ma55e5 n0w a110wed 6y the 1nv15161e decay and (6) the enhanced N H L adm1xture n0w a110wed 6y e4. (7). 7h15 1ead5 t0 enhanced rate5 f0r p . ~ e + y ar151n9 fr0m N H L exchan9e. 7he c0rre5p0nd1n9 8 R can 6e 91ven a5 [27 ]

~ 10 ~

~

10 10 t

•••

•

10 7

N

8 , ~c+v- 32~r {[K1-,FK*H]1212 ,

N

-1

,

10 -~

,

1 ,,1,,1

1

1

a

•

•,•,•1

1

10

•

~'~111[

1

r

1(~

F19. 1. Neutr1n0 decay 11fet1me5 e5t1mated 1n the m0de1 de5cr16ed 1n the text and 1n the 5ee-5aw m0de1.1n 60th ca5e5 the decay 11fet1me 15 determ1ned, f0r 5ma11 m1x1n9, 6y the NHL ma55. L1ne A c0rre5p0nd5 t0 the 5ee-5aw m0de1 pred1ct10n f0r MR= 50 6 e V wh11e 11ne 8 c0rre5p0nd5 t0 0ur pred1ct10n f0r M = 10 6eV. L1ne C c0rre5p0nd5 t0 the c05m01091ca1 ma55 den51ty c0n5tra1nt. Fa5ter 1nv15161e 119ht neutr1n0 decay5 are natura11y atta1na61e 0n1y 1n the new m0de1.

ma551e55 [ 18 ] ~6.1n the 51mp1e5t 5tandard m0de1 w1th ma551ve D1rac neutr1n05 the 6 1 M mechan15m 5uppre55e5 f1av0ur-v101at1n9 pr0ce55e5 50 neutr1n0 ma55e5 can 0n1y affect neutr1n0 pr0pa9at10n pr0pert1e5. A1th0u9h the 6 1 M mechan15m 15 105t 1n the 5ee-5aw m0de1 [4] the rate5 f0r f1av0ur v101at1n9 pr0ce55e5 e.9. ~--+e+7 are 5t111 t00 10w t0 6e mea5ured exper1menta11y 51nce the character15t1c 5tren9th 0f the5e pr0ce55e5 15 c0n5tra1ned 6y c05m01091ca111m1t5 0n the neutr1n0 ma55.7h15 15 true even 1f neutr1n0 ma55e5 are pu5hed c105e t0 the1r 1a60rat0ry 11m1t5 (wh1ch 15 c05m01091ca11y p055161e 0n1y 1f a maj0r0n 15 1ntr0duced). 51nce, h0wever, 1ept0n-f1av0ur v101at10n can 0ccur unre1ated t0 the neutr1n0 ma55 1t can 6e 1ar9e [ 18 ], the n0ve1 effect5 6e1n9 a550c1ated w1th neutr1n0 n0n0rth090na11ty. 7 h e fact that the5e f1av0ur v101at10n effect5 can 6e mea5ura61e 1n the a65ence 0f 065erva61e neutr1n0 ma55 effect5, wa5 0r191na11y n0ted 1n ref. [ 18] and m0re recent1y 5tre55ed 1n ref. [26]. 1n the ca5e 0f 0ur pre5ent 1ntere5t, even 1f we take the 11m1t ~6 F0r a re1ated d15cu5510n, 1n the c0ntext 0f a 1eft-r19ht m0de1 where a 5pec1a1 d15crete 5ymmetry wa5 5u99e5ted t0 keep neutr1n05 ma551e55, 5ee ref. [25 ].

364

30L

-.

~° 5

10

12 January 1989

(22)

where the f0rm fact0r F 15 p10tted 1n f19. 2 a5 a funct10n 0f the N H L ma55.7he 5tren9th 0f the pr0ce55 15 c0n5tra1ned 6y 1a60rat0ry 11m1t5 0n the adm1xture 0f N H L 1n the CC. H0wever, 5tr0n9er c0n5tra1nt5 h01d 1n 0ur m0de1, fr0m the 1mp11ed re1at10n 6etween th15 adm1xture and the neutr1n0 ma55 06ta1ned fr0m e4. (8) ~7. We then re-expre55 0ur re5u1t f0r 8~ .~+v a5 a funct10n 0f the neutr1n0 ma55, f0r a typ1ca1 va1ue 0fthe re1evant f0rm fact0r d1fference enter1n91n e4. (22). We f1nd e.9. f0r A F ~ 0.5, 51n 0H~ 1: 8 , , e + v ~ 5 X 10 -5 [ m 2 / / L ] 2 .

(23)

7h15 15 p10tted 1n f19. 3. 7he5e 6ranch1n9 rat105 are w1th1n reach 0f the pr0p05ed M E 0 A exper1ment at L05 A1am05. A9a1n 0ne can 5ee that the 5ee-5aw ex~7 Certa1n1y the c0rre5p0nd1n9 c0n5tra1nt5 1n the 5ee-5aw e4. (9) m0de1 w0u1d 6e m0re 5tr1n9ent and w0u1d n0t a110w any 512ea61e f1av0ur-v101at1n9 effect 0f the type we are c0n51der1n9. h•

0

-0.25

-0.5

-0.75

--1

-1.25

-1.5

-~.75

-2

1

100

200

,

,

,

]

300

,

1

,

,

1

,

,

,

,

400 M n (6 eV~°°

F19. 2.8ehav10ur 0f the f0rm fact0r f0r 11~ e + y p10tted a5 a funct10n 0fthe NHL ma55.

V01ume 216, num6er 3,4

PHY51C5 LE77ER5 8

,9• v

-10 10 -11 10

D

/

10 -15 10

1

.

10 10

1

..

1

-16 10 10 10 -19 10 -20

" F 1 "

10 10_ 1

~

10

10~

12 January 1989

5U (2) • U ( 1 ) the0ry. F1r5t, 065erva61e f1av0ur-v101at10n effect5 may 6e a man1fe5tat10n 0f the n0n-0rth090na11ty 0f the f1av0ur neutr1n05 (rather than 0f neutr1n0 ma55e5) due t0 the p055161e adm1xture 0f N H L 1n the CC weak 1nteract10n. F1av0ur v101at10n a550c1ated w1th n0n-2er0 neutr1n0 ma55e5 may a150 6e much 1ar9er than the 5tandard 5 U ( 2 ) • U ( 1 ) the0ry w0u1d 5u99e5t. F1na11y, neutr1n0 ma55e5 them5e1ve5 can 6e a51ar9e a5 the1r pre5ent 1a60rat0ry 11m1t5 due t0 the pre5ence 0f neutr1n0 1nv15161edecay m0de5. We have 5u99e5ted a p1au5161e 5cenar10 f0r th15 phy51c5 6y ana1y51n9 a m0de1 where the mechan15m 1ead1n9 t0119ht neutr1n0 ma55e515 marked1y d1fferent fr0m the u5ua1 5ee-5aw mechan15m.

m(~v)

F19. 3. 8R(1a-,e+7) ver5u5 neutr1n0 ma55 1n the m0de1 de5cr16ed 1n the text and 1n the 5ee-5awm0de1, f0r a typ1ca1 va1ue 0f the f0rm fact0r c0rre5p0nd1n9t0 NHL ma55e50f 5ay, 20 6eV and 60 6eV. L1ne5fr0m A t0 D c0rre5p0nd t0 d1fferentMLv va1ue5 where MLv den0te5 9ener1ca11ythe 5ca1echaracter121n9 t0ta1 1ept0n num6er v101at10n 1n each 0f the tw0 m0de15 de5cr16ed: MLv-~,tt [e4. (8)] f0r the new m0de1 and Mt.v=MR [e4. (9)] f0r the 5ee-5awm0de1.7he c0rre5p0ndence15A (50 6eV ), 8 ( 10 6eV), C (1 6eV) and D (0.1 6eV). H19her 6ranch1n9 rat105 re4u1re 10wer Mkv va1ue5wh1ch are natura11yatta1na61e0n1y1n the new m0de1.

Ackn0w1ed9ement 7h15 w0rk wa5 part1a11y 5upp0rted 6y C1CY7 under 9rant n u m 6 e r AE-88-0021-04. J.V. thank5 the C E R N 7he0ry D1v1510n f0r the h05p1ta11ty. 7 h e w0rk 0 f M . C . 6 . - 6 . ha5 6een 5upp0rted 6y a fe110w5h1p fr0m the 5pan15h M1n15try 0f 5c1ence.

N0te added pectat10n5 f0r a neutr1n0 0f the 5ame ma55, even f0r the m05t fav0ura61e ca5e, 11e5 5evera1 0rder5 0f ma9n1tude 6e10w 0ur re5u1t. 51m11ar1y (we n0w c0n51der the three-fam11y ca5e) ~8 0ur m0de1 0pen5 up the n0ve1 p05516111ty 0f 065erv1n9 n0n-5tandard decay5 5uch a5 2 - - , e + ~ , 2-~ 1a+2 and the1r c0nju9ate5, at the 2 peak w1th the 1um1n051t1e5 expected at LEP [18]. 7 h e 6ranch1n9 rat105 were ca1cu1ated 1n ref. [18] f0r the ca5e 0f ma551e55 n0n-0rth090na1 neutr1n05. A9a1n, even 1f we a55ume neutr1n0 0rth090na11ty, the 5ame rea50n1n9 a60ve a150 1ead5 t0 8 R f0r the5e an0ma10u5 2 decay5 wh1ch c0u1d 6e 065erved exper1menta11y, f0r c05m01091ca11y a110wed neutr1n0 ma55 va1ue5.

6. C0nc1u510n5 Neutr1n0 ma55 and f1av0ur-v101at10n effect5 may 6e much 1ar9er than expected 1n the 5tandard ~8 A mea5ura61e2-~1a+~ decay rate w0u1dv101ateexper1menta1 11m1t50n 80 ~e+y.

Re9ard1e55 0f 5uper5tr1n9 c0n51derat10n5, the 0n1y 2er0 1n e4. (7) that d0e5 n0t f0110w fr0m 1ept0n n u m 6er and 5 U ( 2 ) • U ( 1 ) 9au9e 1nvar1ance 15 the Maj0rana ma55 term f0r the r19ht-handed neutr1n0, ar151n9 fr0m a c0up11n9 vcvc~ *, ana1090u5 t0 55~. We have n0t 1nc1uded 5uch term 51nce the c0rre5p0nd1n9 Yukawa c0up11n915 f0r61dden 6y 5uper5ymmetry, 0 u r re5u1t5 f0r 1a-,e +•/ne91ect h0wever the p055161e ex15tence 0f 5uper5ymmetr1c c0ntr16ut10n5.

Reference5 [11R. C0w51kand 3. McC1e11and,Phy5. Rev. Lett. 29 (1972) 669; 8.W. Lee and 5. We1n6er9,Phy5. Rev. Len. 39 (1977) 165. [2] P. Pa1 andL. W01fen5te1n,Phy5. Rev. D25 (1982) 766. [31J.12. N1eve5,Phy5. Rev. D 28 (1983) 1664. [4 ] J. 5chechter and J.W.F. Va11e,Phy5. Rev. D 22 (1980) 2227. [5] J. 5chechter and J.W.F. Va11e,Phy5. Rev. D 25 (1982) 774. [6] M. 7akahara and H. 5at0, Phy5. Lett. 8 174 (1986) 373; M0d. Phy5. Lett. A 2 (1987) 293; A. Daret a1, Phy5. Rev, Lett. 58 (1987) 2146. 365

V01Ume 216, num6er 3,4

PHY51C5 LE77ER5 8

[ 7 ] 5.5arkar and A.M. C00per, Phy5. Lett. 8 148 (1984) 347. [ 8 ] L. 06erauer et a1., Phy5. Lett. 8 198 ( 1987 ) 113. [9] A. Dar and A. Dad0, Phy5. Rev. Lett. 59 (1987) 2368; de R051er et a1., Phy5. Rev. Lett. 59 ( 1987 ) 1868. [ 10] 6.6e1m1n1 and M. R0ncade111, Phy5. Lett. 8 99 ( 1981 ) 411. [ 11 ] Y. Ch1ka5h19e, R. M0hapatra and R. Pecce1, Phy5. Rev. Lett. 45 (1980) 1926; Phy5. Lett. 8 9 8 (1981) 265. [ 12] 5.61a5h0w, Phy5. Lett. 8 187 (1987) 367. [13] 6. 6e1m1n1, D. 5chramm and J.W.F. Va11e, Phy5. Lett. 8 146 (1984) 311: J.W.F. Va11e, Phy5. Lett. 8 159 (1985) 49; J. 8ahca11, 5. Petc0v, 5.705hev and J.W.F. Va11e, Phy5. Lett. 8 181 (1986) 369; 5. Nu551n0v, Phy5. Lett. 8 185 (1987) 171; J. Fr1eman, H. Ha6er and K. Free5e, Phy5. Lett. 8 200 (1988) 115. [14] J.W.F. Va11e, Phy5. Lett. 8 131 (1983) 87; 6.6e1m1n1 and J.W.F. Va11e, Phy5. Lett. 8 142 (1984) 181. [ 15 ] J.W.F. Va11e, 1n: Weak and e1ectr0ma9net1c 1nteract10n5 1n nuc1e1 (He1de16er9, 1986), ed. H. K1apd0r (5pr1n9er, 8er11n ) p. 927. [16] R. M0hapatra and J.W.F. Va11e, Phy5. Rev. D 34 (1986) 1642; 1. Ant0n1ad15 et a1., Phy5. Lett. 8 208 (1988) 209. [ 17 ] J.P. Derend1n9er et a1., NUC1. Phy5. 8 267 (1986) 365; F. de1 A9U11a et a1., NUC1, Phy5.8 272 (1986 ) 413;

366

12 JanUary 1989

R. M0hapatra and J.W.F. Va11e, Phy5. Lett. 8 177 (1986) 47;8 186 ( 1 9 8 7 ) 7 3 ; 8 196 (1987) 157. [ 18] J. 8erna6eu, A. 5antamar1a, J. V1da1, A, Mende2 and J.W.F. Va11e, Phy5. Lett. 8 187 (1987) 303. [ 19] J. 5chechter and J.W.F. Va11e, Phy5. Rev. D 21 (1980) 309. [20] M. 6c11-Mann, P. Ram0nd and R. 51an5ky, 1n: 5uper9rav1ty, ed5. D. Freedman et a1. (N0rth-H011and, Am5terdam, 1979 ); 7. Yana91da, KEK 1ecture5, ed5.0. 5awada et a1. ( 1979 ); R. M0hapatra and 6.5enjan0v1c, Phy5. Rev. Lett. 44 (1980) 912; Phy5. Rev. D 23 (1981) 196. [21 ] D. Dear60rn et a1., Phy5. Rev. Lett. 56 (1986) 26; M, Fuku91ta et a1., Phy5. Rev. Lett. 48 (1982) 1522; Phy5. Rev. D 26 (1982) 1841. [ 22 ] J. 5chechter and J.W.F. Va11e, Phy5. Rev. D 23 ( 1981 1666. [23] L. W01fen5te1n, Nuc1. Phy5.8 186 ( 1981 ) 147; 5. Petc0v, Phy5. Lett. 8 110 (1982) 245; J.W.F. Va11e, Phy5. Rev. D 27 (1983) 1672; J.W.F. Va11e and M. 51n9er, Phy5. Rev. D 28 ( 1983 ) 540. [ 24 ] J. 5chechter and J.W.F. Va11e, Phy5. Rev. D 24 ( 1981 ) 1883; D25 (1982) 283. [ 25 ] D. Wy1er and L. W01fen5te1n, Nuc1. Phy5. 8 218 ( 1983 ) 205. [26] P. Lan9acker and D. L0nd0n, prepr1nt DE5Y 88-044 (1988). [27] E, Ma and A. Pramud1ta, Phy5. Rev. D 24 ( 1981 ) 1410.