ANKARA UNIVERSITESI FEN FAKULTESI FIZIK BOLUMU


AU-HEP-00-01
February 2000





Three Remarks on the MSSM





S. Sultansoy


Deutsches Elektronen-Synchrotron DESY, Hamburg, Germany
Department of Physics, Faculty of Sciences, Ankara University, Turkey
Institute of Physics, Academy of Sciences, Baku, Azerbaijan





Abstract


First of all, "right" sneutrino can be the lightest supersymmetric particle. Then, the
flavor democracy favors large value of the tan. Finally, the huge number of free
parameters in the three families MSSM may be considered as an indication of SUSY at
arXiv: 28 Mar 2000 preonic level.





_______________


Electronic address: sultanov@mail.desy.de
sultan@science.ankara.edu.tr




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1. Introduction


The huge number of free parameters [1,2] in the three families MSSM leads to
consideration of some simplified versions, such as the constrained MSSM (see [3] and
references therein). In general, these simplifications ignore interfamily mixings and
possible existence of right-handed neutrinos, and consequently their super-partners. As
the result one avoid possible conflicts with experimental data on flavor violating
processes, but at the same time we also lose very interesting possible phenomenology.
Below we deal with the three families MSSM and do not consider possible R-parity
violation, as well as GUT and SUGRA extensions.



2. Parameter Inflation


The are a number of arguments favoring the existence of right-handed neutrinos. First
of all, in the framework of the SM R's are counterparts of the right-handed components
of the down-type quarks according to the quark-lepton symmetry. Then, almost all
extensions of the SM, with the SU(5) GUT as a possible exception, naturally contain
right-handed neutrinos. Moreover, observation of the neutrino oscillations provides the
experimental confirmation for R. For these reasons, we consider three families MSSM
including right-handed neutrinos. Therefore, we deal with the six species that constitute a
family, rather than five considered in [2] (below we follow the notations used in this
paper): q, d , u , l, e and v , where q and l denote weak iso-doublets and the rest are iso-
singlets.
The masses of the SM fermions and their super-partners are generated due to


L=Lscalar+LYukawa+Ltriscalar . (1)

The first term has the form

~
L 2 ~
scalar
= mAij i
A A j , (2)
A,i, j

where A labels above-mentioned six species, the tilde labels sparticle and i,j=1,2,3 are
family labels. Therefore, this part contain six 33 Hermitian mass matrices with six real
parameters and three phases each. The Yukawa part is derived from the superpotential


Yukawa
W = (qi uiju jHu + qi dijd jHd + li ij jHu + li eije jHd ) , (3)
i, j

where four Yukawa matrices are general 33 matrices with nine real parameters and
nine phases each. Finally, the triscalar part (in order to avoid confusion with the second
equation we introduce here the notations, which are slightly different from that in [2]) is
given by

~
~ ~ ~ ~ ~
L = q
~
( a u H
+ q~ a d H + l a H + l a e H ) M
triscalar i uij j u i dij j d i ij j u i eij j d , (4)
i, j




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where a are general 33 matrices and M is the some mass parameter. As the result we
have 108 real parameters (masses and mixing angles) and 90 phases. However, part of
them are unobservable because of [U(3)]6 symmetry of the gauge sector, so 18 angles and
34 phases can be rotated out and remaining two phases correspond to baryon number in
quark sector and general lepton number. Finally, matter sector of the MSSM
(fundamental fermions and their superpartners) contains 90 observable real parameters,
namely 36 masses and 54 mixing angles, and 56 phases.
It is clear that tremendous number of physical parameters, which makes meaningless
any general analysis, at the same time gives the opportunity to get the predictions up to
the experimental upper limits almost for all rare processes. For this reason, from the
viewpoint of the MSSM the investigation of charmed particles (oscillations, CP-violation
etc) becomes as interest as investigation of beauty particles, the search for  and
e is as important as the search for e etc.


3. Flavor Democracy


Let me remind you the main assumptions of the flavor democracy or, in other words,
democratic mass matrix hypothesis (in the frameworks of the n family SM):
i) Before the spontaneous symmetry breaking fermions with the same quantum
numbers are indistinguishable. Therefore [4], Yukawa couplings are equal within each
type of fermions: uij=u , dij=d , lij=l and ij= .
ii) There is only one Higgs doublet, which gives Dirac masses to all four types of
fermions. Therefore [5], Yukawa constants for different types of fermions should be
nearly equal:
u d l .
The first statement result in n-1 massless particles and one massive particle with
m=nF (F=u, d, l, ) for each type of the SM fermions. The masses of the first n-1
families, as well as observable interfamily mixings, are generated due to a small
deviation from the full flavor democracy [6]. Taking into account the mass values for the
third generation, the second statement leads to the assumption that the fourth SM family
should exist. Alternatively, masses of up and down type fermions should be generated by
the interaction with different Higgs doublets, as it takes place in the MSSM.
Finally, flavor democracy provides the opportunity to get the massless states as the
superposition of initially massive particles. This property may be useful for the preonic
models because, in general, the masses of composite objects are expected to be of the
order of compositness scale.



4. Sneutrino as the LSP


It is straightforward to apply flavor democracy to the MSSM. For example, according
the flavor democracy sneutrino mass matrix has the form





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2 2 2 2 2 2
mLL mLL mLL mLR mLR mLR
2 2 2 2 2 2
m m m m m m
LL LL LL LR LR LR
2 2 2 2 2 2
m m m m m m
LL LL LL LR LR LR
. (5)
2 2 2 2 2 2
mRL mRL mRL mRR mRR mRR
2 2 2 2 2 2
mRL mRL mRL mRR mRR mRR
2 2 2 2 2 2
mRL mRL mRL mRR mRR mRR

As the result we deal with four massless sneutrinos and two sneutrinos have the masses

2 3 2 2 2 2 2 2 2
m ,
3 6 = mLL + m m (
RR mLL - m )
RR + 4mLRmRL . (6)
2

The (small) masses of the rest four species can be generated due to violation of flavor
democracy and/or radiatively. Including F- and D-term contributions, the elements of the
matrix (5) have the following form [3]:


1
2 2
m = m + ( v )2 2
+ m cos 2,
LL u Z
l 2
2 2
m = m = a (Mv - v ),
LR RL u d
2 2
m = m + ( v )2,
RR u


where vu and vd are vacuum expectation values of the Higgs fields Hu and Hd, tan=vu/vd
and  is the supersymmetry-conserving Higgs mass parameter.
In the recent paper [7] it is shown that LEP1 data leads to lower bound 44.6 GeV on
the sneutrino masses and, consequently, in the framework of the constrained MSSM
sneutrino cannot be the LSP. Let me present some notes on this statement. First one is
rather technical. Presented lower bound is valid for the case of degenerated superpartners
of left-handed neutrinos. For non-degenerate case it should be change to 43.6 GeV for
lightest one. Then, according flavor democracy the constrained MSSM seems not to be so
natural at all. The most important note is following: LEP1 data does not essentially
constrain the masses of superpartners of the right-handed neutrinos if the LR mixings are
sufficiently small. Indeed, the contribution of the "right" sneutrino to the invisible Z
width is given by

2 3 / 2

m~
2 2
inv = 0.5   1 - 

, (7)
mZ

where denotes the "left" sneutrino fraction due to corresponding mixings and =167
MeV. Therefore, the experimental value
inv 2.0 MeV leads to ||0.155 for
sufficiently light "right" sneutrino. If there are two light species one obtain
| |2+| |2
1 2 0.024. Therefore, "right" sneutrino still can be considered as the LSP both in




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constrained and unconstrained MSSM. This scenario may lead to very interesting
phenomenology, however, this is beyond the scope of the present paper.



5. Flavor Democracy and tan

According to the first assumption of the flavor democracy, in the framework of the
three families MSSM the masses of t- and b-quarks are as follows:

= 3  , = 3
t
m 
t vu b
m b vd . (8)

Application of the second assumption, namely
t b, immediately leads to relation


v m
u t
tan = . (9)
vd b
m

With m
t 174 GeV and mb 4.3 GeV [8] we obtain tan40. More conservatively (taking
into account the "running" of the quark masses etc.), flavor democracy favors the region
of 30<tan<50 and lower values can be interpreted as an indication of the fourth MSSM
family. In the last case one has


u
m
tan 4
1 (10)
md4

in order to satisfy exp=0.99980.0008 [8].

6. SUSY and Preons


The huge number of arbitrary parameters naturally leads to assumption that SUSY
should be realized at more fundamental, preonic or even pre-preonic level. Indeed, three
families MSSM with Dirac neutrinos contains 160 observable parameters (146 from
quark-squark and lepton-slepton sectors and the rest from gauge couplings etc [3]) which
should be compared with 26 observable parameters in SM case. Today, there is not any
realistic way to decrease essentially this number. The statements about a few parameters
in the SUGRA express rather our wishes, because they practically ignore interfamily
mixings. In principle, CKM-like mixings (rather than family replication) can be
considered as the serious indication of the compositness, because the superposition of
fundamental objects with different masses is forbidden in the framework of the quantum
field theory. Besides, the proposition [9] about similarity of CKM mixings and squared
mass differences in quark and squark sectors for explanation of experimental data on
flavor violating processes seems quite natural if MSSM matter fields are composite. On
the other hand, there is not any realistic preonic model, also. However, one can made
some general predictions for preonic SUSY without consideration of specific models.





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Composite models of leptons and quarks can be divided into two classes: fermion-
scalar models and three-fermion models. In the first class SM fermions are composites of
scalar preons, denoted by S, and fermion preons, denoted by F. In minimal variant
q,l={FS} and each SM fermion (FS) with m0 has three partners:

~
scalar ( S
F ) with m M ,
SUSY
~
scalar ( S
F ) with m M ,
SUSY
~~
fermion ( S
F ) with m 2M ,
SUSY


where MSUSY denotes the SUSY scale. In the second class SM fermions are composites of
three fermions, q,l= (F1F2F3), and each of them has seven partners:

~ ~ ~
three scalars (F F F ), (F F F ) and (F F F ) with m M ,
1 2 3 1 2 3 1 2 3 SUSY
~ ~ ~ ~ ~ ~
three fermions (F F F ), (F F F ) and (F F F ) with m 2M ,
1 2 3 1 2 3 1 2 3 SUSY
~ ~ ~
scalar (F F F ) with m 3M .
1 2 3 SUSY


Of course, mixings between quarks (leptons, squarks, sleptons) can drastically change the
simple mass relations given above. Therefore, it is quite possible that the search for
SUSY at future colliders will give rather surprising results.
Finally, let me note that even one family MSSM contains two observable mixing
angles and two phases both in quark-squark [1] and lepton-slepton sectors. This fact may
be useful for construction of the supersymmetric preonic models.



7. Conclusion


Today, the mass and mixing patterns of the MSSM, as well as the SM itself, are the
most mysterious aspects of the particle physics. It seems that the general tendency is
toward the idea of A. Salam and collaborators on pre-preonic SUSY model [10]. Let me
finish by two notes on the rare processes mentioned in the Section 2:
i) a huge number of charmed particles which will be produced at HERA-B [11]
provide the strong tool for detailed investigation of charm physics, and
ii) an operation of the TESLA at Z-resonance (TESLA-Z [12]) will give opportunity
to improve by an orders the upper limits on the Br() and Br(e).

Acknowledgements
I am grateful to I. Ginzburg, M. Spira and P. Zerwas for useful discussions and
valuable remarks. This work was made during my sabbatical visit to DESY. I would like
to express my gratitude to DESY Directorate for invitation and hospitality.


P.S. According to the recent classification of H.E. Haber [13], the three family MSSM
should be denoted as "MSSM>160" and the four family MSSM as the "MSSM>272".
The meaning of the symbol ">" will be explained in forthcoming paper [14].




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P.P.S. Professor P. Zerwas drew my attention to the paper [15], which contains the
statement similar to (9). Unfortunately, their approach based on minimal S0(10) model is
excluded by the recent experimental values of s and mt [8].

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