Bounds on Scalar Lepto quark Masses

from S T U in the Minimal Mo del

With the FourColor Symmetry

AD Smirnov

Department of Theoretical Physics Yaroslavl State University

Sovietskaya Yaroslavl Russia

Abstract

The contributions into radiative correction S T U parameters

from the scalar lepto quarks are considered in frame of the minimal

mo del with the fourcolor gauge symmetry Taking the current exp er

imental data on S T U into account the b ounds on the scalar lep

to quark masses are obtained and discussed In particular it is shown

T U allow the existence of that the current exp erimental data on S

relatively light scalar lepto quark with electric charge

The search for a new physics beyond the Standard Mo del SM is now

one of the aims of the high energy physics It is interesting to know what

kind of the new physics can manifest itself as the energy of the colliding

particles increase What are the p ossible manifestations of such new physics

at attainable energies One of the p ossible variants of the new physics b eyond

the SM can turn out to be the variant induced by the p ossible fourcolor

symmetry b etween quarks and leptons

The main feature of the fourcolor gauge symmetry is the prediction of

the vector lepto quarks with the masses of ab out the mass scale M of the

c

fourcolor symmetry breaking In the mo dels induced by the grand uni

cation ideas the fourcolor symmetry can manifest itself as an intermediate

Email asmirnovunivuniyaracru

symmetry with mass scale M exp ected to b e usually very high For instance

c



in SO mo del it is of ab out M GeV but it can be essentially

c

 

lowered up to M GeV by appropriate scheme of the symmetry

c

breaking In the mo dels regarding the fourcolor symmetry as a primary

symmetry the lower limit on the mass scale M is determined

c

mainly by the low energy exp erimental data and it can be essentially lower

for example of ab out TeV or ab out TeV or slightly less

or even of ab out TeV

The fourcolor symmetry can manifest itself not only by the vector lep

to quark physics but also due to the scalar lepto quarks Some of the scalar

lepto quarks should have SU doublet structure and hence can mani

fest themselves in the oblique radiative corrections in particular aecting

the S T U parameters of Peskin and Takeuchi Taking into account the

rather stringent current exp erimental limits on S T U it is in teresting to

know what b ounds on the scalar lepto quark masses can be extracted from

the current exp erimental data on S T U For this purp ose it is interesting

to know the eect of the scalar lepto quarks on S T U in some simple gauge

mo del predicting these particles

In this talk I would like to consider the contributions into S T U pa

rameters from the scalar lepto quarks in frame of a minimal mo del with the

fourcolor symmetry in comparison with the current exp erimental data on

S T U and to discuss the b ounds on scalar lepto quark masses which can b e

extracted in this mo del from these data

The minimal quarklepton symmetry mo del MQLSmo del to b e

used here as a minimal extension of the SM containing the fourcolor gauge

symmetry is based on the gage group SU SU U The fermion

V L R

sector of the mo del contains only the known fermions quarks and leptons

whereas the gauge sector predicts the new gauge particles vector lepto quarks



V with electric charge and an extra neutral Z boson

The scalar sector of the mo del contains in general the four multiplets

   

a transforming according to the

a a

representations of the SU SU U group and

V L R

having the VEVs resp ectively the content of the multiplets

  

and notations can be found in more detail in Refs

As regards the S T U parameters the most intersting of these multiplets



is the muliplet which has b een intro duced to split the masses of quarks

and leptonsThis multiplet contains fteen doublets which can be arranged

  

into two scalar lepto quark doublets S and S with the SM hy

a a

SM 

percharge Y and resp ectively eight scalar gluon doublets F

ja



SM  

j with Y and the doublet which in admixture with

a

a

p

p



SM 

 



G gives the SM doublet with SM VEV

  F



GeV and an additional scalar doublet

 

In addition to the scalar lepto quark doublets S of the multiplet

a

  

the multiplets and contain the singlet scalar leoto quarks S and

  



S with electric charge which give in admixture with S S the

 

Goldstone mo de S and three mass eigenstate lepto qurk elds S S S As

 

a result in the unitary gauge we obtain in general ve scalar lepto quarks

  

S S with electric charge and resp ectively and S k

k

with electric charge

The resulting contributions into S T U from lepto quarks can be pre

sented in the form



X X X X

m n

c



 SM LQ

jC j Y ln B f m m S

kl  k l

k



m

k



k k l



X

f m m m

k V

V

 

f m m jC j

 V k k

 



m m

k V

k





X

m

m

V

ln ln

 

m m





X X

n

c



LQ 

T jC j f m m

k

k

  

s c m

W W Z



k

X X

B f m m

kl k l

k l

h

X X

 

f m m f m m jC j

V k V k



k

i



m f m m m

 k V

V

X X X X

n

c



 LQ

jC j f m m B f m m U

 k kl  k l

k



k k l

X X

 

f m m f m m jC j

 V  k V k



k

f m m f m m

V k v



m

V

   

 

m m m m

V V

k

where

  

m m m



 

ln m f m m m

 



 

m m m





   

m m m m

 

f m m

 

  

m m



      

m m m m m m m

  

ln



  

m m m





are well known functions and f m m m is dened by equation

  V

f m m m

  V

          

m m lnm m m m lnm m m lnm m

  V V   V

   

m m m m



V V

Here

q

      





p

C C kl B j C C C C j C

k k kl

k l k l k

       

g m

     V

SM

Y n m m m m m is the vector lepto



c k S V

k

S

quark mass g is the SU coupling constant C C are two unit

 V k k

mutually orthogonal complex vectors In general the vectors C C can b e

k k

parametrized by means of three mixing angles and three phases for example

as

i i

 

C fc c c s e s e g

k     

i  i 

 

C fc s e s s c e

k     

i  i

   

c c s s s e s c e g

      

where c cos s sin are the mixing angles and phases

ij ij ij ij ij ij

The contributions into S T U from the scalar lepto quarks have

some sp ecial features

Firstly the contributions from the scalar lepto quarks into T and

U are not p ositive denite due to the mixing b etween the scalar lepto quarks

with electric charge The mixing of the comp onents of two scalar doublets

as a p ossible mechanism for obtaining the negative T and U was p ointed out

in Ref But in our case the S S S mixing is caused by the

 

presence of Goldstone mo de in the scalar lepto quark sector and this mixing

is an intrinsic feature of the mo del

Secondly in the case of the degenerated scalar lepto quark masses m

k

LQ

m m m the expression gives the nonzero contributoin into S

 S

ie

LQ LQ LQ

S T U

whereas the contributions from the ordinary scalar doublets in the case of

all degenerated masses are known to be equal to zero see for example

Refs

Thirdly the p ossible large due to the large VEVs splitting of



the scalar lepto quark masses gives the p ossibility for S and T to take the

large values p ositive or negative in dep endence on the mass splitting and

the mixing parameters

Wehave carried out the numerical analysis of the contributions us

exp exp exp

ing the resp onsible for a new physics exp erimental values of S T U

new new new

exp exp exp

S T U

new new new



by minimizing dened as

exp  exp  exp 

S S T T U U

new new new



  

S T U

where S T U are the lepto quark contributions and S T U are

the exp erimental errows in

In following we assume for simplicity that In this case the

 

contributions dep end on the vector lepto quark mass m parameter

V

and on the four scalar lepto quark masses m m m m m

  



ofthe m m m and one mixing angle Here indexes

 





mass denote the electric charges of the corresp onding scalar lepto quarks

LQ LQ LQ

The dep endence of S T U on the large m of order of hun

V

dreds TeV is slight b ecause of the smallness of the parameter For denite



ness we assume further that m TeV and The numerical

V



analysis of the contributions by minimizing at these values of m

V

and shows that

LQ LQ LQ 

rstly S T U and dep end on the ratios of scalar lep

to quark masses for deniteness on the ratios m m

   

 

m and m m m

  

 

secondly the value of the mixing angle is favored





as a functions of each of the indep endent mass ratios are shown in

min

 

Fig at Here denotes the minimal value of obtained at



min



xed value of one of the mass ratios by minimizing over two other mass



ratios The doublets and F j are supp osed to b e degenerated

j

It is seen from Fig that exp erimental values favor one scalar lepto

quark S with electric charge to be the lightest one the solid line the



with electric charge to be slightly heavyer the scalar lepto quark S

 

bold line whereas the other scalar lepto quarks S and S with electric



charges the dotted line and resp ectively to be the heavyest ones

The Fig shows the regions in the plane of the lightest masses and



compatible with the data at CL and CL the inner regions



b ounded by the solid and b old lines resp ectively

Some remarks resulting from the analysis of numerical calculations should

be made

The scalar lepto quarks improve the agreement of the exp erimental

 

values with the theory so that can b e reduced from the value



ie CL of the SM to the value ie CL in the

mo del under consideration For example at the mass ratios near the values



the formulas give the values

 



LQ LQ LQ

S T U



which agree with with ie at CL

The attainment of the values demands however a ne mutual

tting of the mass ratios near the values mentioned ab ove as if there were

some relation between the masses of the scalar lepto quarks Possibly such

mass relation can arise as a result of the broken fourcolor symmetry implied

here



The account of the mass splitting of the doublets and F mo dies

j

the result not essentially by ab out preferring slightly the down neutral

comp onents of these doublets to b e lighter than the up charged ones

The existence of the salar lepto quark doublets allows the mass split

tings of other doublets to be rather large The arising in this case large

positive contribution into T from these doublets can be absorb ed by the

large negative contribution from the scalar lepto quark which results in the

values compatible with the exp erimental ones

Recently a new analysis of the current electroweak data has b een carried

out in Ref Using the results of Ref one can obtain

exp exp exp

S T U

new new new



at m GeV m GeV

t

H

The contributions have a large mass region compatible with these

data even at more high CL As an example the dotted curve in Fig shows

the region in plane of compatible with the data at CL

 

that b oth data and do not imp ose any It should be p ointed out

lower limit on the mass m of the scalar lepto quark S with electric charge



as seen the solid line in Fig go es down monotonically as decrease



and the allowed regions in Fig are op en from the side of the small values of

This gives the p ossibility for the mass m in contrast for example

 

to m to be light p erhaps to lie even not far from the SM mass scale



If this is the case the scalar lepto quark S could manifest itself in exp eri

ments at mo derate energies in particular through the e d S coupling in

e p collisions and for this reason the exp erimental search for this scalar

lepto quark seems to b e reasonable

In conclusion I resume the results of the work

The contributions into radiative correction parameters S T U from the

scalar lepto quarks are considered in the minimal gauge mo del with the four

color quarklepton symmetry in comparison with the current exp erimental

data on S T U

It is shown that the contributions into T and U from the scalar lepto

quark doublets are not p ositive denite due to the mixing b etween the scalar

lepto quark elds with electric charge which is caused by the existence

of the Goldstone mo de among these elds

Using the current exp erimental limits on S T U the numerical analysis

of these contributions is carried out and the b ounds on the scalar lepto quark

masses are obtainedIn particular it is shown that the current exp erimental

data on S T U allow the existence of the relatively light scalar lepto quark

with electric charge The search for this scalar lepto quark seems to be

reasonable

Acknowledgments

The author is grateful to Organizing Commitee of the International Sem

inar Quarks for p ossibility to participate in this Seminar

The work was partialy supp orted by the Programme Universities of Rus

sia Basic Researc h under grant No

References

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AD Smirnov Pro c of the th International Seminar Ouarks

Yaroslavl Ed by VA Matveev et al INR Moscow V

AD Smirnov Phys Lett B to b e published

L Lavoura and LF Li Phys Rev D

Particle Data Group RM Barnet et al Phys Rev D

part

K Hagivara D Haidt S Matsumoto DESY preprint DESY

KEK preprint KEKTH hepph







min







     

  

 





as a function of the scalar lepto quark mass Figure

min

ratios m m the solid line m m

     

 

the b old line and m m the dotted line



 

















         



Figure The regions in plane of mass ratios



m m m m compatible with the data

    

at CL the solid line at CL the bold line and

with the data at CL the dotted line