ANKARA UNIVERSITESI FEN FAKULTESI FIZIK BOLUMU

AU-HEP-00-04
April 2000
Contributed paper to ICHEP2000





Why the Four SM Families





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


arXiv: 28 Apr 2000 The flavor democracy favors the existence of the nearly degenerate fourth SM family,
whereas the fifth SM family is disfavored both by the mass phenomenology and precision
tests of the Standard Model. The multi-hundreds GeV fourth family quarks will be
copiously produced at the LHC. However, the first indication of the fourth family may
come from the Higgs search at the upgraded Tevatron.





_______________


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




1


1. Introduction


Today, the mass and mixing patterns of the fundamental fermions are the most
mysterious aspects of the particle physics. Even the number of fermion generations does
not fixed by the Standard Model (SM). In this sense, SM may be treated as an effective
theory of fundamental interactions rather than fundamental particles. The statement of the
Flavor Democracy (or, in other words, the Democratic Mass Matrix approach) [1], which
is quite natural in the SM framework, may be considered as the interesting step in true
direction. It is intriguing, that Flavor Democracy favors the existence of the fourth SM
family [2, 3]. Moreover, Democratic Mass Matrix approach provide, in principle the
possibility to obtain the small masses [4, 5] for the first three neutrino species without
see-saw mechanism. The fourth family quarks, if exist, will be copiously produced at the
LHC [6]. Then, the fourth family leads to an essential increase [7, 8] of the Higgs boson
production cross section via gluon fusion at hadron colliders and this effect may be
observed soon at the Tevatron.
In this letter we consider the present status of the four family SM and the future
search for the fourth family fermions. The Flavor Democracy hypothesis is presented in
Section 2, where we also give some predictions for the fourth family phenomenology.
Arguments against the fifth SM family are listed in Section 3. In Section 4 possible
manifestations of the fourth family fermions at future colliders are considered. Possible
alternative scenarios such as additional Higgs doublets (the MSSM case) and exotic new
fermions (E6 phenomenology) are briefly discussed in Section 5. Finally, in Section 6 we
give some concluding remarks.



2. Flavor Democracy and the Standard Model


It is useful to consider three different bases:


- Standard Model basis {f0},
- Mass basis {fm} and
- Weak basis {fw}.


According to the three family SM, before the spontaneous symmetry breaking quarks are
grouped into following SU(2)U(1) multiplets:

 





   





 0  0 
0
 u
L  c t
, 0
u , 0
d ; L , 0
c , 0
d ;  L , 0
t , 0
b . (1)
 0  R R  0  R R
 0  R R
d L sL bLl

In one family case all bases are equal and for example, d-quark mass is obtained due to
Yukawa interaction


+

(d )
L = a ( )

 . . , (2)
 + =
Y d (u L d L ) d h c L d m dd
R m d
0




2


where m
d=ad , =<0>249 GeV. In the same manner mu=au , me=ae and me=ae
(if neutrino is Dirac particle). In n family case







n 







( ) 0 0 0
  + 
d d  0 0
 n
 d d d
L = . . , , (3)

 + = =
a u d d h c m d d m a
Y ij Li Li Rj ij i j ij ij
0
i, j =1 i, j =1


where d 0 0
1 denotes d0, d2 denotes s0 etc. The diagonalization of mass matrix of each type
of fermions, or in other words transition from SM basis to mass basis, is performed by
well-known bi-unitary transformation. Then, the transition from mass basis to weak basis
result in CKM matrix
u + d
U =
CKM U
( L ) U L ,

which contains 3(6) observable mixing angles and 1(3) observable CP-violating phases in
the case of three(four) SM families.
Before the spontaneous symmetry breaking all quarks are massless and there are no
differences between d0, s0 and b0. In other words fermions with the same quantum
numbers are indistinguishable. This leads us to the first assumption [1], namely, Yukawa
couplings are equal within each type of fermions:

d d u u l l
a a , a a , a a , a a .
ij ij ij ij (4)


The first assumption result in n-1 massless particles and one massive particle with
m=naF (F=u, d, l, ) for each type of the SM fermions.
Because there is only one Higgs doublet which gives Dirac masses to all four types of
fermions (up quarks, down quarks, charged leptons and neutrinos), it seems natural to
make the second assumption [2, 3], namely, Yukawa constants for different types of
fermions should be nearly equal:

ad
au al a a . (5)

Taking into account the mass values for the third generation, the second assumption leads
to the statement that according to the flavor democracy the fourth SM family should exist.
In terms of the mass matrix above arguments mean

 





 





1 1 1 1 0 0 0 0
 





 





1 1 1 1 0 0 0 0
0 m
 





M =
a M 4
a . (6)
 = 






1 1 1 1 0 0 0 0






 
1 1 1 1 0 0 0 1


Now, let us make the third assumption, namely, a is between e=gwsinW and gw/cosW.
Therefore, the fourth family fermions are almost degenerate, in good agreement with




3


experimental value =0.99980.0008 [9], and their common mass lies between 320 GeV
and 730 GeV. The last value is close to upper limit on heavy quark masses, m
Q 700
GeV, which follows from partial-wave unitarity at high energies [10]. It is interest that
with preferable value ag
w flavor democracy predicts m4 8mW 640 GeV.
The masses of the first three family fermions, as well as an observable interfamily
mixings, are generated due to the small deviations from the full flavor democracy [11,
12].



3. Arguments Against the Fifth SM Family


The first argument disfavoring the fifth SM family is the large value of m
t 175 GeV.
Indeed, partial-wave unitarity leads to m
Q 700 GeV 4mt and in general we expect that
m << <<
t m4 m5. Then, neutrino counting at LEP results in fact that there are only three
"light" (2m < mZ) non-sterile neutrinos, whereas in the case of five SM families four
"light" neutrinos are expected.
The main restrictions on the new SM families come from experimental data on the
parameters and S (see [9] and references therein). The first one is sensitive to mass
splitting of the up and down fermions, which is negligible according to the second
assumption of the flavor democracy. The second one needs more detailed consideration.
The contribution to S from heavy degenerate SM family is equal to 2/3 (0.21), which
should be compared with experimentally allowed value S=-0.160.14 [9]. At the first
glance, the fourth and fifth SM families are excluded at 2.5 and 4.1, respectively.
However, both the negative central value and comparatively small errors are caused
mainly by asymmetries and R ratios measured at the Z pole and a number of them differ
essentially from the SM predictions. For example, ALR deviation is 2.4, Ab is 2.5
below the Standard model prediction et cetera (for details, see [9] and references therein).
It would be useful to reanalyze experimental data excluding the mentioned observables.
The rough estimations show that in this case the fourth SM family is allowed at 2 and
the fifth SM family is excluded at 3.5 level. An enlargement of Higgs sector and/or the
inclusion of Majorana mass terms for right-handed neutrinos may further improve the
situation, but this is beyond the scope of present letter. Finally, the recent paper [13]
which show that precision electroweak data allows the existence of a few extra families,
if one allows neutral leptons to have masses close to 50 GeV, may be considered as an
indication of the fact that the situation on the subject is far from clearness.


4. A Search for the Fourth SM Family


4.1. LHC
The fourth SM family quarks will be copiously produced at the LHC via gluon-gluon
fusion (see [6] and references therein). The expected cross section is about 10(0.25) pb
for a quark mass of 400(800) GeV. The fourth generation up-type quark, u4, would
predominantly decay via u
4 Wb, therefore, the expected event topologies are similar to
those for t-quark pair production. The best channel for observing will be [14]:





4


u u
4 4 WWbb (l )( jj b
) b ,


where one W decays leptonically and the other hadronically. The mass resolution is
estimated to be 20(40) GeV for m4 = 320(640) GeV. The situation is much more
complicate for down-type quark because the dominant decay mode is d
4 Wt and the
final state contains four W bosons:

- + + - - +
d d
4 4 tW W
t bW W W
b W .


The small inter-family mixings [12] leads to the formation of the fourth family
quarkonia. The most promising candidate for LHC is the pseudo-scalar quarkonium state,
4, which will be produced resonantly via gluon-gluon fusion. Especially the decay
channel
4 ZH is the matter of interest [15].


4.2. Future Lepton and Photon Colliders
The future lepton colliders will give opportunity to look for the fourth family leptons,
which will hardly seen at hadron machines. Also, the number of different fourth family
quarkonium states can be produced resonantly at lepton machines. Moreover, in
difference from the LHC, states formed by up and down type quarks can be investigated
separately even if their mass difference is small. The fourth family fermions, except of 4,
and various quarkonium states will be copiously produced at photon colliders.


4.3. Upgraded Tevatron
If the mass of the Higgs boson does not essentially exceed 200 GeV, the first
indication of the fourth family may come soon from the Tevatron [7]. Indeed, the cross
section of the Higgs boson production via gluon fusion is essentially enhanced due to
extra heavy quarks [16]. For 100GeV< m <
H 200GeV the fourth SM family quarks with
300GeV< m <
4 700GeV lead to the enhancement factor k8 [8]. If the fifth SM family
exist, this factor becomes k22. Therefore, the search for the Higgs boson at the upgraded
Tevatron can simultaneously result in the first indication of the fourth SM family.
For illustration let me consider the process


p
p gg H W W
* * ljj and ll

which was analyzed in [17]. Using the Figure 3 from this paper one can estimate the
integrated luminosity values needed to reach:
a) 3 statistical significance for discovery of the Higgs boson in three family case,
b) 3 statistical significance for manifestation of the fourth family,
c) 5 statistical significance for exclusion of the fifth family,
at different values of the Higgs mass, which are presented in Table 1. Therefore, if
mH=165GeV, the existence of the fifth SM family can be excluded at 5 level by the
recent Tevatron data.
In my opinion, the subject is sufficiently important in order to initiate the detailed
studies, including different decay modes and detector aspects. For example, the search for




5


H + - channel will give an indication of the fourth family [7] and/or exclude the fifth
family if 105GeV< m <
H 135GeV.


Table 1.
mH, GeV 120 135 150 165 180 195
a) Lint, fb-1 100 30 12 10 30 90
b) Lint, fb-1 12 4 1.5 1.2 4 11
c) Lint, fb-1 14 3.5 1.5 1 3.5 11



5. Alternatives


5.1. Two and More Higgs Doublets
In the framework of the Flavor Democracy hypothesis if there are only three SM
families the large value of the t-quark mass to b-quark mass ratio (m
t /mb 40) may be
natural if the masses of the up- and down-type quarks are generated by different Higgs
doublets, as it takes place in the MSSM. In this case one can expect the following
relation:
v m
u t
tan = ,
v m
d b

where vu and vd are vacuum expectation values of the corresponding Higgs fields.
Unfortunately, the MSSM contains huge number of free parameters, namely more than
160 for three MSSM families, and for this reason it seems more natural that SUSY should
be realized at more fundamental, preonic or even pre-preonic level (for details see [18]
and references therein).
Turning back to the SM with extended Higgs sector, let me finish this subsection with
two remarks:
a) going further in this direction, one can assume that the masses of the charged leptons
and neutrinos are generated by their own Higgs doublets,
b) introducing the isotriplet and vector isotriplet Higgs fields in addition to Higgs
isodublet, one can change the tree level prediction =1 and, therefore, relatively large
mass splittings of the fourth family fermions may be allowed.


5.2. Exotic New Fermions
Another way to explain the relation mb,<<mt is the introduction of exotic fermions.
Let me consider as an example the extension of the SM fermion sector which is inspired
by E6 GUT model initially suggested by F. Gursey and collaborators [19]. It is known
that this model is strongly favored in the framework of SUGRA (see [20] and references
therein). For illustration let me restrict myself by quark sector:


  






 0

 0
 0
 u
 c
 t
L
 , 0
u , 0
d ; L
 , 0
c , 0
d ; L
 , 0
t , 0
b
0 R R 0 R R 0 R R
d s b
L L Ll

0
D , 0
D ; 0
D , 0
D ; 0
D , 0
D .
1L 1R 2L 2R 3L 3R





6


According to Flavor Democracy the down quarks' mass matrix has the form:

 





a a a a a a












a a a a a a








a a a a a a
M0 = ,






M M M M M M







M M M M M M






 
M M M M M M


where M is the scale of "new" physics which determines the masses of the isosinglet
quarks. As the result we obtain 5 massless quarks and the sixth guark has the mass
3M+mt .

6. Conclusion


There are two different approaches concerning the fourth SM family. The first one is
following [9]: "Allowing arbitrary S, an extra generation of ordinary fermions is now
excluded at the 99.2% CL. This is in agreement with a fit to the number of light
neutrinos, N=2.9930.011".
However, I prefer the moderate one [21]: "Today we have not any experimental
indication of the new families. Precision electroweak data allow the one additional family
at 2 level. On the other hand, there are some arguments, including Flavor Democracy,
favoring the fourth SM family. Therefore, let us wait the results from the LHC and at the
same time carefully analyze the data on the Higgs boson search at the Tevatron".


Acknowledgements
I am grateful to A. Celikel, A.K. Ciftci and I.F. Ginzburg for useful discussions and
valuable remarks. I would like also to express my gratitude to DESY Directorate for
invitation and hospitality.



References


1. H. Harari, H. Haut and J. Weyers, Phys. Lett. B 78 (1978) 459;
H. Fritzch, Nucl. Phys. B 155 (1979) 189; B 184 (1987) 391;
P. Kaus and S. Meshkov, Mod. Phys. Lett. A 3 (1988) 1251;
H. Fritzch and J. Plankl, Phys. Lett. B 237 (1990) 451.
2. A. Datta, Pramana 40 (1993) L503.
3. A. Celikel, A.K. Ciftci and S. Sultansoy, Phys. Lett. B 342 (1995) 257.
4. C.T. Hill and E.A. Paschos, Phys. Lett. B 241 (1990) 96.
5. H. Fritzsch, preprint MPI-Ph/92-42 (1992), unpublished.
6. ATLAS Detector and Physics Performance Technical Design Report,
CERN/LHCC/99-15 (1999), p. 663.
7. I.F. Ginzburg, I.P. Ivanov and A. Sciller, Phys. Rev. D 60 (1999) 095001.
8. E. Arik et al., ATLAS Internal Note ATL-PHYS-98-125 (1999).


7


9. J. Erler and P. Langacker, in Review of Particle Physics, Eur. Phys. J. 3 (1998) 90.
10. M.S. Chanowitz, M.A. Furlan and I. Hinchliffe, Nucl. Phys. B 153 (1979) 402.
11. A. Datta and S. Rayachaudhiri, Phys. Rev. D 49 (1994) 4762.
12. S. Atag et al., Phys. Rev. D 54 (1996) 5745.
13. M. Maltoni et al., Phys. Lett. B 476 (2000) 107.
14. E. Arik et al., Phys. Rev. D 58 (1998) 117701.
15. E. Arik et al., ATLAS Internal Note ATL-PHYS-99-061 (1999).
16. V.D. Barger and R.J.N. Philips, Collider Physics, Addison-Wisley, 1997.
17. T. Han and R.-J. Zhang, Phys. Rev. Lett. 82 (1999) 25.
18. S. Sultansoy, Ankara University preprint AU-HEP-00-01; .
19. F. Gursey, P. Ramond and P. Sikivie, Phys. Lett. B 60- (1976) 177;
F. Gursey and M. Serdaroglu, Lett. Nuovo Cim. 21 (1978) 28.
20. J.L. Hewett and T.G. Rizzo, Phys. Reports 193 (1989) 193.
21. This paper.





8



