A low right-handed scale in a supersymmetric context

Nuclear Physics B260 (1985) 391-401 © North-Holland Publishing Company

A LOW RIGHT-HANDED

SCALE IN A SUPERSYMMETRIC

CONTEXT

J. MAALAMPI*' ** and J. PULIDO***

Fakultdt fiir Physik, Universitdt Bielefeld, D-4800 Bielefeld, Federal Republic of Germany Received 18 April 1985

We investigate the prospects for a low right-handed scale M R in the context of locally supersymmetric SO(10), limiting ourselves to the most interesting case of a single breaking scale between the grand unified scale M x and the W-mass. It is found that supersymmetry seems to imply a unique solution as regards the Higgs content and the intermediate symmet~ group if a low right-handed scale (less than 10 4 GeV) exists at all. Apart from a minimal set of representations providing the symmetry breaking pattern, the Higgs sector consists of a pair of 16 and 16 spinor representations lying at scale M R and the residual symmet~ is SU(3), × U(1) R L × SU(2)~. × U(1)R.

1. Introduction T h e f e a t u r e s t h a t m a k e SO(10) g r a n d u n i f i e d t h e o r i e s a d v a n t a g e o u s o v e r S U ( 5 ) o n e s a r e w e l l k n o w n (for a r e v i e w see [1]). F e r m i o n s are a c c o m m o d a t e d in a single anomaly-free

spinor representation

16, w h i c h a c c o m p l i s h e s a full q u a r k - l e p t o n

u n i f i c a t i o n . S O ( 1 0 ) m o d e l s also o f f e r a n a t u r a l m e c h a n i s m for p r o d u c i n g a small b u t f i n i t e m a s s for n e u t r i n o s . F u r t h e r m o r e , t h e o r e t i c a l s c e n a r i o s a i m e d at a u n i f i c a t i o n o f f e r m i o n g e n e r a t i o n s w i t h i n large S O ( N ) g r o u p s e v i d e n t l y r e c o m m e n d SO(10) as a GUT symmetry. T h e m o s t r e m a r k a b l e d i f f e r e n c e b e t w e e n S U ( 5 ) a n d SO(10) m o d e l s is, h o w e v e r , t h a t t h e l a t t e r a l l o w s for an i n t e r m e d i a t e m a s s scale b e t w e e n the G U T scale ( M × ) a n d t h e e l e c t r o w e a k scale ( M w ) . T h i s is a c o n s e q u e n c e o f the fact that the r a n k of S O ( 1 0 ) is o n e u n i t larger t h a n that of SU(5). T h i s f e a t u r e of SO(10) m o d e l s will b e c o m e p a r t i c u l a r l y a t t r a c t i v e if a l o w - l y i n g i n t e r m e d i a t e scale n o t far f r o m M w is f o u n d c o m p a t i b l e w i t h m o d e l s satisfying the u p to n o w a v a i l a b l e e x p e r i m e n t a l data. T h i s n e w scale w i t h all the i n t e r e s t i n g n e w physics a s s o c i a t e d w i t h it c o u l d t h e n b e a c c e s s i b l e w i t h t h e n e x t g e n e r a t i o n of a c c e l e r a t o r s . * On leave of absence from Department of High Energy Physics, University of Helsinki, Finland. **Supported by Bundesministerium far Forschung und Technologie, Bonn, Federal Republic of Germany. *** Permanent address: CFMC, Av. Prof. Gama Pinto 2, 1699 Lisboa Codex, Portugal. 391

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J. Maalampi, J. Pulido / Low right-handed scale

Recently a new approach [2] has appeared in which a low-lying left-right symmetric SU(3)c × U(1) × SU(2)L × SU(2)R intermediate stage in non-supersymmetric SO(10) is possible. It postulates the decoupling of parity and SU(2)a breaking scales, thereby introducing one extra intermediate scale which appears as a free parameter. Lately an alternative scheme [3] has been proposed by us, also within a non-supersymmetric context, which uses mass split fermion multiplets. We did not consider, however, what possible mechanisms could generate these mass splittings nor did we analyse their stability against radiative corrections. Furthermore, the models derived suffer from some arbitrariness, namely the predicted mass of the right-handed gauge boson depends on the set of fermion fields inserted into the intermediate or lower scale and the intermediate symmetry group is not fixed uniquely. In the present paper we investigate the prospects for a light W R and Z R within the context of supersymmetric SO(10) [4]. We will limit ourselves to the most interesting case of one intermediate mass scale. We explore our previous idea of mass split representations, finding, however, that their existence is no longer essential. Apart from the well-known stability of certain mass relations and hierarchies against radiative corrections, a substantial improvement is found, relative to the non-supersymmetric cases, in the sense that the arbitrariness of both the Higgs content of the model and the intermediate symmetry group is naturally removed. In fact, we recover the result one of us has pointed out [5] that left-right symmetric groups within SO(10) cannot survive as intermediate symmetries at least if M R < 1015 GeV. The intermediate group [SU(3)~ × U(1) R ~ × SU(2)L × U(1)a ] and Higgs content are now unique if we are to have a light ( > O (200 GeV)) intermediate scale. Only a Z R gauge boson (and its superpartner) is therefore predicted at this scale. For our present discussion the Pati Salam SU(4)c × SU(2)L × SU(2)R intermediate symmetry is uninteresting since it imposes the breaking to occur at energies >~ 105 GeV from the bound on leptoquark decay [6]. In the following section we first analyse the constraints to left-right symmetric models from the recently measured value of sin20w at the SPS experiments [7]. Next we present our main discussion starting with supersymmetric SU(3)~ × U(1)n t. × SU(2) L × SU(2)Rusing a minimal Higgs content and then consider a smaller group with SU(2)R replaced by U(1)R. In sect. 3 we summarize our main conclusions.

2. Low right-handed scale in SO(10) As is well known [8] in the conventional SO(10) models left-right symmetry can be restored at low energies provided the weak mixing angle is in the range sin20w = 0.27 - 0 . 2 8 . This is in agreement with the low-energy neutral current data, since an SU(2)L × SU(2)R × U(1)8 t~ fit to this data gives [9] sin:0 w= 0 . 2 5 - 0.31. One should now ask whether these numbers are consistent with the UA1 result [7] sinZ0w = 0.226 + 0.011 based on the measured values of gauge boson masses. Let us consider therefore the conventional SU(2)L × SU(2)~ × U ( 1 ) , ~ model with the

393

J. Maalampi, J. Pulido / Low right-handed scale

s t a n d a r d Higgs content consisting of a scalar triplet A R(1, 3, 1) and a set of doublets q,(2, 2, 0). T h e v a c u u m expectation values of higgses,

0 0

= (k0 k0,) '

(1)

b r e a k S U ( 2 ) R × U ( 1 ) B L and S U ( 2 ) L × U ( 1 ) r, respectively. A straightforward calculation for the gauge boson masses leads us to the following relation between the light mass eigenstates:

( M~Z )2 = COS20w + Zl(k,k',v),

(2)

where to first order in (k 2 + k ' 2 ) / v 2 we have

A(k,k,,v)=g4(g2+2g '2) k2+k '2 (g2 + g , 2 ) 3

-

-

v2

k 2 + k '2 -

O ( 0 . 7 ) -

U2

(3)

H e r e g and g' are the SU(2)L and U ( 1 ) y coupling constants and we are neglecting W L / W R mixing which is known to be very small. On the other hand, the UA1 result is extracted from the standard model relation (M2w/M2z)= coS?0w . The correction term A in eq. (3) indicates the difference between the definitions of the weak angle in the two models and decreases with increasing v. The difference between the neutral current result sin20w = 0 . 2 5 - 0.31 and the UA1 result [7] sin20,v = 0.226 +_ 0.011 can be entirely due to the correction A if obviously 0.25 - 0.237 < A ~< 0.31 0.215 or 2.7mwL < mWR __<7.3mw, .

(4)

Hence, although these bounds might be too strict, the predictions of ref. [9] are certainly not to be ruled out, as they refer to a range 150 GeV _< m w , < 240 GeV. In order that the difference A between the two definitions m a y be ignored, a possible criterion is to require it to lie within the experimental uncertainty 0.011 of sin20,~,. This implies from eq. (3) row, >_ BrawL.

(5)

2.1. THE SU(3), × U(1) B t. × SU(2)L × SU(2)R SUPERSYMMETRIC MODEL W e use the one-loop renormalization group equations for the three gauge couplings of the standard SU(3),.x SU(2)L × U ( 1 ) v symmetry, which for the inter-

J. Maalampi, J. Pulido f Low right-handedscale

394

mediate group SU(3),, x U(1)B L × SU(2)L

1

1

Ot3

Ot(i

b; MR 2~ In ~t

b3+ In Mx 2~r M R

0( 2

1 c~c;

b2> MR ~ In #

b2k In ~ 2~"

1 5 1 aI 3 aG

5b I M R 327r In tt

)< S U ( 2 ) R

read at energy #

'

sin20w a

51(2

3 )

Mx

32qr -~b~,~+ ~bzR l n ~ R -

COS 20w

a

(6)

Here a(; is the grand unified coupling and the weak mixing angle is given by

al(/~) sin20,~(#) = 0~1(~) _~_of2 (~)

e~(g) g2 (~t)

(7)

Since we are considering supersymmetry, the coefficients of the fl-functions are given for S U ( N ) by

bN=3N-2Nc,-2nRT(R )

(R,N>

1),

(s)

where N o is the number of generations, n R is the number of R-dimensional representations and T(R) is the appropriate Casimir invariant. For the U(1)r generator b~ = - ~ , S ( R ) ,

(9)

where T(R) is now the square of the Y-eigenvalue of representation R. From the first two equations (6) one can extract an equation for M x as a function of MR: In

b+-

I( si0w) 2~r

0:3

-

+ (b~ - b2t )ln ~

_.

(10)

and, upon elimination of ln(MR//z), we get from (6) B OL(~[.t) Jr- O~(jLt) [ 5 ( b 1 - b2L ) sin20w (/~ ) = - -1 { 3 1 +B + a3(~) 16Tr

(lla) with

B=

5bz+L-- 3b2R -- 2bl, 8(b] - b2+L)

(llb)

J. Maalampi, J. Pulido / Low right-handed scale

395

We will use q)(16), q,(16) instead of F(126), F(126) to break the intermediate group since the latter may otherwise be problematic from the point of view of proton decay [5]. F, F will be used to generate the so-called doublet/triplet splitting inducing a high mass ( - M x ) to the SU(3)c colour triplets in the (6,1,1) component of H(10) while leaving the corresponding weak doublets (1, 2, 2) light*. This is done through a coupling T F H [10] where T is a 210 acquiring a VEV for its Pati Salam singlet component. The breaking of SO(10) is performed by the VEV of an adjoint Z(45) along its (1,0,1,1) component under our intermediate group, included in the (15,1, 1) under Pati Salam. Thus the couplings ,Y,T T and Z F F in the superpotential will generate a mass - M x to all components of the T, F and F chiral supermultiplets. Our minimal collection of chiral superfields is thus T, F, T', Z, H ( 6 , 1 , 1 ) with mass M x , ~, ~ with mass M R , three matter generations q~r, H ( 1 , 2 , 2) with mass/,.

(12)

We have then the following superpotential: m

m

(p(p W = ~,TT + ,~FF + T Y H + A~,'¢ + Aq, q,' + m#,'¢' + ~pq~f+f + ~TH q~e+r.

(13)

Here we have added a singlet A and a pair of extraheavy ~'(16),~'(16) with zero VEVs to ensure a mass contribution to ~ and ~ and the vanishing of all F-terms in the vacuum. This superpotential satisfies the vacuum condition I W[ ~< m wMp. The last two terms in (13) produce the Majorana mass for the right-handed neutrino and the other fermion masses [5,10]. Using (8) and (9), we obtain for the b-coefficients b; =-1, b2R = --

b3 = 3 , 5,

bl,.= - 10,

b~L=--5, b 1_

bzL=--l, 335,

(14)

where the superscripts ( + ) and ( - ) refer to representations above and below the intermediate scale respectively. Using the values a(kt)= 0.00784 and c~3(bt) = 0.101 and plotting sin20w against M R in the range 103 GeV ~< M R ~< 1015 GeV we obtain the graph shown in fig. 1 with M x decreasing linearly. It is seen that in this case the values of sinZ0w are far too high to be consistent with the data and no low M a scale is possible. In the absence of any other clear indication we take the common sense view of choosing the simplest scheme that overcomes this situation. The simplest SO(10) * For reasons of compactness we use the Pati Salam SU(4)c × SU(2)L X SU(2)R assignments for the representations. Decomposition with respect to the appropriate subgroup should be understood.

396

J. Maalampi, J. Pulido / Low right handed scale sin 2 0 .. 0.300W ~ x = 1 . g Ox 10z] GeV

0'280 1 o.26o 1

o..o 1

. . . .

103

107

,'--..,.x:,4x 1011

1015

MR

Fig. 1. The values of sin20~ against MR for the minimal model in an SU(3),. × U(1)~ SU(2) R supersymmetric scenario.

:. ×

SU(2)k ×

representations that provide all possible and desirable alterations to the scenario a b o v e are the 10 and 16. Our objective is clear from fig. 1: we look for a reduction of the sin20w values in the low M R region. This is achieved by two classes of representations: a light (mass - / ~ ) (6,1, 1) from a split 10 a n d / o r a light (4, 1, 2) f r o m a split 16 with, of course, their counterparts (1, 2, 2) and (4, 2, 1), respectively, lying at M x. In table 1 we briefly list these effects. F i n d i n g mechanisms to provide these mass splittings is certainly possible: in fact a light (6,1, 1) with a heavy (1, 2, 2) in H'(10) can be generated through a VEV from an extra adjoint representation 27'(45) with a VEV along the (1, 1, 3) direction. In the superpotential we would then have a coupling Z'(1, 1,3)H'(1, 2, 2)H'(1,2, 2) providing the desired heavy mass. The 27(45) should of course not couple to the 10 representation responsible for SU(2)L × U ( 1 ) y breaking. This 10 would still undergo the n o r m a l d o u b l e t / t r i p l e t splitting, i.e. its (1,2,2) c o m p o n e n t light and coloured triplets (6, 1, 1) heavy. On the other hand, the splitting of the 16 can also be done t h r o u g h the doublet/singlet splitting mechanism [5] which we review below. However, both mechanisms break the SU(2)R group preserving only the U(1)R symmetry. We are thus lead to consider the symmetry group SU(3), × U(1)R i. × SU(2)L

TABLE 1 The effects o n sin20,~ a n d M x of a d d i n g one r e p r e s e n t a t i o n t r a n s f o r m i n g as (6, 1,1) or one t r a n s f o r m i n g

as (J,, 1,2) under the Pati Salam group at mass/a - Mw~ to the minimal model in an SU(3)~ × U(1)B /. × SU(2)L X S U ( 2 ) R supersymmetric scenario

MR

Minimal model (MM) sin20~ Mx

MM + (6, 1, l). sin20w Mx

MM + (4, 1,2)u sin20,, Mx

103 104 105

0.300 0.295 0.290

0.272 0.267 0.263

0.244 0.240 0.236

Units are in GeV.

1.9 × 1021 7.0 × 1020 2.7 × 102~

3.6 X 10 24 9.4 × 1023 3.1 × 1023

1.9 X 10 21 7.2 × 102° 2.7 × 102°

J. Maalarnpi, J. Pulido / Low right-handed scale

397

× U(1)R where the situation is changed and the requirements for a low M R scale are totally different as we will see below.

2.2. T H E SU(3), × U(1)B L × SU(2)L × U(1)R SUPERSYMMETRIC MODEL

Up to now we have relaxed the extended survival hypothesis [8,10]: only the Higgs representations that break the symmetry at some energy scale should be left massless down to that scale. The present group allows us to apply it strictly by raising the masses of the unnecessary light SU(2)L doublets in ~(16) and q~(16) to mass - M x in the previous model (see (12)) while their SU(2)L singlets remain light. This could be readily done by the doublet/singlet splitting mechanism [5] which we briefly review here. It operates through a coupling T~q, with a VEV ( - M x) of the T-representation in the (15,1,1) and the (15,1, 3) directions under the Pati Salam group. This also provides the breaking of SO(10) into the group SU(3)c × U(1)e t. x SU(2)L × U(1)R. So in the superpotential we would have a mass term like ( T ( 1 5 , 1 , 1 ) ) ~ ( 4 , 2,1) q~(4, 2, 1) + [(T(15, 1,1)) + {T(15, 1,3))] ~ ( 4 , 1 , 2 ) ~ ( 4 , 1,2),

(15) giving a large mass contribution to the SU(2) t doublets and a vanishing contribution to the singlets, provided (T(15,1,1)) = - (T(15,1,3)).

(16)

The relation (16) arises from global supersymmetry preservation due to the vanishing of the F-term FF(15,2,2 ) in the vacuum [10] and is protected from supersymmetry breaking effects provided the breaking scale Msusy<~O[Mw(Mp/Mx) 1/2] [5]. Furthermore, the doublet/triplet splitting can operate through a similar mechanism. In fact the coupling TFH contains in this case the terms (T(15,1,1)>

[/'(6,1,1) H(6,1,1)

+ / ' ( 1 5 , 2 , 2) H(1,2, 2)]

+(T(15,1,3))[F(~,l,3)H(6,1,1)+F(15,2,2)H(1,2,2)],

(17)

which give a large mass to the colour triplets and protects the mass of the weak doublets, again, provided (16) as satisfied. The mass of the T(210) can arise from a coupling ATT', where A is a singlet and T' is a superheavy 210 plet with ( T ' ) = 0, with no need for an adjoint as before. We are thus lead to the following collection of chiral superfields: T, T',/', F, H(6, 1,1), ~(4, 2, 1), ~(4, 2, 1) with mass M x , q~(4,1, 2), ~(4, 1, 2) with mass M R , three matter generations +f, H(1, 2, 2) with mass ~t,

(18)

398

.1. Maalampi. J. Pulido / Low right-handed scale sin z 0 w 0.220 0.200

0.1BO

0.160

x t

10 3

J 107

10lsGeV

.... '

i

i

1011

i

1015

MR

Fig. 2. The values of sin20,, against M R for the minimal model in an SU(3), x U(I) n U(1 ) ~ supersymmetric scenario.

/. X S U ( 2 ) I X

and the superpotential of the model is W = A TT' + MtFF +

+ A 4 ~ ' + Ad?'~ + M2~'qS' + Td?'q~+ T~qS'

TFH D / T splitting

+

~

D / S splitting

TH

(191

Here M~. 2 - M x and the three terms M 2 ~ ' ~ ' + T~'~ + T e ~ ' with ¢~(16),~'(~') having zero VEV were introduced to account for the vanishing of the F.r~5,~,h and F r(15,1,3~ in the vacuum (see eq. (15)). The equations for the coupling constants are the same as before (6) with the obvious replacement b2R ---, bit ¢. For the " m i n i m a l " model (18) we obtain the following b-coefficients:

b; =1, bl,

- 8

=3, b 1

b2L =b;L= - 1 , 33

bLR= --11, (20)

In fig. 2 we plot sin20w against Mg. A low M R scenario requires now an increase in sinZ0w . We have the reverse situation to our former example so, restricting ourselves to the split 10 and 16 representations of SO(10), we should insert at low scale ~ the c o u n t e r p a r t s of the (6,1, 1) in 10 a n d / o r (5,1,2) in 16. Their effects are shown in table 2. It is seen that the (1,2, 2) lowers the value of M x, so that two of these at low or even intermediate scale are illegal. As for the (4, 2, 1) one insertion at mass /~ is clearly not enough to allow for a relatively low intermediate scale and two is too much. On the other hand the mechanisms available for the mass splittings in 16 (e.g. eqs. (16) and (17)) imply that these representations should always come in pairs (16, 16), so that the possibility of having a (4,2, 1 ) + (1, 2, 2) at low scale, although providing permissible values for sin20,~ and M x, is certainly ruled out. Furthermore, the insertion of (4, 2, 1) + (,~, 2, 1) at the intermediate scale provides, as can be readily inferred f r o m table 2, correct values for these quantities being compatible with a low

J. Maalampi, J. Pulido / Low right-handed scale

399

TABLE 2 The effects on sin20w and M x of adding one representation transforming as (1, 2, 2) or one transforming as (4, 2,1) under the Pati Salam group at mass ~ - M E to the minimal model in an SO(3)c X U(1)B_ I_ X SU(2)L X U(I)R supersymmetric scenario Minimal model (MM)

MM + (1,2, 2)~,

MM + (4, 2,1)~,

MR

sin20,~

Mx

sin20w

Mx

sin20w

Mx

103 104 105

0.163 0.169 0.175

6.2 × 1015 6.2 × 10 ls 6.2 × 10 Is

0.191 0.197 0.203

3.5 × 1014 3.5 × 1014 3.5 × 1014

0.202 0.208 0.214

6.26 × 1015 6.45 × 1015 6.64 × 1015

Units are in GeV.

From the above discussion it immediately turns out that this is the only possible scenario, if we are to find M a up to the few TeV region. It is a remarkable fact that the slopes of sin20w and M x are in this case zero as a function of M R. The constant values of sin20w and M x are M R.

sin20w = 0.236,

M x = 6.3 × 1015 GeV

(for any MR),

(21)

with b coefficients given by bf=

-1,

bl~.= - 1 0 ,

b; =3, b 1-

b?L=-l,

b~>=-5,

335 "

blR=--ll, (22)

The unified coupling a o ranges from 0.17 ( M R = 500 GeV) to 0.045 ( M R = 1014 GeV). We recall at this point the structure of spinor representations we are using: we have a qq(16) and a qh(16) performing the breaking of the intermediate group whose SU(2)> doublets are heavy ( - M x ) and singlets light ( - MR). Moreover, we have another pair ~b2(16),~2(16) whose masses are split in opposite direction providing the possibility of a light M a mass. It is possible to find mechanisms compatible with the symmetry breaking pattern that generate these doublet/singlet (eqs. (15), (16)) and "reverse" doublet/singlet splittings and keep them protected against radiative corrections [5]. For the "reverse" doublet/singlet splitting we can use, as seen from (15), the VEV of T2(210 ) under its (15,1, 3) direction. So only the mass term (T2 (15,1,3))~2 (4,1,2) ~2 (4,1,2)

(23)

would be present. We can now summarize the structure to which we have been lead: assume two extra-heavy (mass - M x ) representations T1 and T2 transforming as 210 with (Tt) = (Tl(15, 1,1)) + ( T l ( 1 5 , 1 , 3 ) ) ,


(24)

J. Maalampi, J. Pulido / Low right handed scale

400

such that T 1 provides the doublet/triplet and doublet/singlet splittings when coupled to F H and (~lq)l respectively and T2 gives the "reverse" doublet/singlet splitting when coupled to ~2~2- Another extraheavy F(126) coupling to F(126) through a mass term must, of course, also be present. At this stage it is essential to make a few comments about the scheme we have been developing: we started by using the extended survival hypothesis and, with the help of the doublet/singlet splitting mechanism, raised the masses of the 01(16), 01(16) doublets while keeping the singlets at mass M R. Next we introduced the second pair 01(16), 02(16) whose masses were split in the reverse way. This model looks phenomenologically the same as if instead it used a single non-split 16, 16 pair at mass M R, in which case also the predictions for sin20,,., M x and M R would be unaltered. One could therefore consider the simpler model with T, T ' F , F, H(6, 1, 1) with mass M x ,

(/,, 0 with mass M R , three matter generations ~f, H(1,2, 2) with mass/*,

(25)

and a superpotential O0

TH

JVl p

lVl p

(26)

The doublet/triplet splitting acts as in (17). No doublet/singlet splitting is needed. One should emphasize, however, that this simpler model disregards the extended survival hypothesis which, as we have seen, is compatible with an SU(3), × SU(2)L x U(1)B L X U(1)R intermediate symmetry and can be taken into account in a natural way. Furthermore, it might be hard to justify the existence of a complete 16-plet at scale M R while the other 16-plets containing the ordinary fermions are much lighter. Let us finally remark that in all our analysis we have assumed that splitting occurs between the SU(4)c× SU(2)L X SU(2)R components of representations. In fact, although further mass splittings within this group could lead to slight shifts in our main results, no naturally simple mechanisms providing these splittings seems to exist. Finally, as sinZ0w is very stable under two-loop corrections [11], we do not see a reason for considering them.

3. Summary We have shown that, provided the W R mass is sufficiently low, there may be no discrepancy between the prediction for sinZ0w from the conventional left-right symmetric model and its experimental value as taken from the W / Z mass ratio.

J, Maalampi, J. Pulido / Low right-handed scale

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As to the main point of our work, we have analysed the prospects for a low-lying intermediate scale compatible with supersymmetric SO(10) unification. For simplicity, we have limited ourselves to the cases where no other scale exists between M x and the W-mass and to the analysis of the effects of the 10- and 16-dimensional representations of SO(10). If, as becoming increasingly accepted, we are to believe in supersymmetry, then the possibility that an intermediate scale lies accessible in the near future seems to imply, as a unique scenario, the intermediate symmetry group SU(3)~. × U(1) B /~ × SU(2)L × U(1)R*. From the phenomenological analysis [13] it is found that the ZR-like gauge boson associated to this group could lie in mass as low as 200 GeV. Further, the 16,16 set of fields predicted by us at this scale, mix with each other: they are therefore vector-like and thus distinguishable from the ordinary-type fermions. If the intermediate scale lies at a higher level (>/105 GeV), then more scenarios with Higgs contents and different intermediate symmetries are equally possible. One of us (J.P.) is grateful to D A A D (Deutscher Akademischer Austauschdienst) for financial support. The other (J.M.) wishes to acknowledge a discussion with K. Mursula. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [101 [11] [12] [13]

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* Some aspects of an SO(10) supergravity model with this intermediate group have been recently analysed in [12].