60~ Nuclear Physics B (Proc. Suppl.) 13 (1990) 606-608 North-Holland

HOW IS ISOTOPIC SPIN SYMMETRY OF QUARK MASSES BROKEN ?

Stefan POKORSKI

Institute for Theoretical Physics, University of Warsaw, Ho~a 69, 00-681 Warsaw, Poland

I. INTRODUCTION

This talk is devoted to some aspects

of the fermion mass problem. The full

solution to this problem most likely re-

quires really new ideas and, I believe,

is closely related to our understanding

of the fermion generation puzzle. How-

ever, it is still conceivable that at

least part of the mass problem has more

conventional character. Here I mean the

question : how is the isotopic spin sym-

metry of the quark masses broken (why

mt>>m b etc.} ?

In fact, it is an old idea that the

up- and down- quark masses are driven by

two different Higgs doublets with VEVs

such that mt/m b ~ v2/v I whereas the

Yukawa couplings for the top and bottom

quarks are approximately equal, h t ~ h b.

For several reasons this mechanism of the

isotopic spin symmetry breaking looks ap-

pealing and it i3 a particularly attract-

ive possihi~ty in SUSY models which must

for consistency have at least two Higgs

doublets :

~uQLURH2+hDQLDRHI+hLLLERHI+... (I)

where hu' hD and hL are the Yukawa

coupling matrices for the up- and down-

quarks and leptons, respectively.

In this context we have recently ad-

dressed in some detail several questions.

2. WHAT ARE THE EXPERIMENTAL LIMITS ON

THE RATIO v2/v 1_ ?

0920-5632/90/$03.50 © Elsevier Science Publishers B.V. (North-Holland)

For light neutral scalar(s), mH<mT,

the ratio v2/v I is constrained by the

experimental upper limit for the decay

T ÷ >H to be smaller than 0(10) (for a

recent reanalysis see, for instance,

referencel). Otherwise, some bounds on

the ratio v2/v I can be obtained from

the limits on the charged scalar Yukawa

couplings. In the two Higgs doublet

model and in the mass eigenstate basis

the couplir~sr~ad :

L = 23/4GI/2~" " vl + F ~.mu~ --H PL +

v 2 v 2

KM D H+PR ) D-SMLPRL V2 + -- --H +hc (2)

v I v I

Bounds on the enhancement of the coup-

lings of the charged Higgs bosons have

been studied by a number of authors 2.

They have considered the effects of the o o additional bosons on the K s - K L mass

difference, the CP-violating part of the

neutral -K mass matrix and the B°-B °

mixing. Those one-loop contributions

are sensitive mainly to that part of the

coupling which is proportional to the up

quark masses = since the up quarks are

exchanged in the loops this contribution

is not subject to the full GIM cancel-

lation. Thus, a useful bound has been

obtained for the ratio Vl/V 2 :

Vl/V 2 0(2)~7~ , but not for the

v2/v I. Of course, the situation is re-

versed for the D°-D O mixing (it is sen-

sitive to the coupling proportional to

S. Pokorski /How is isotopic spin symmetry of quark masses broken? 607

M D) but the present experimental upper

limit for this mixing is too large to

provide a useful bound on v2/v I

At present, the best bound on v2/v I

has been obtained 3 from the tree level

processes : from the limits on the mag-

nitude of breaking of the e - ~ univer-

sality in T decays, as measured eg. by

the ratio ~(T÷~V~)-F(T÷ev~)]/F(T÷e~),

The obtained and from the BR(B~e~X).

bound 3 reads

v 2 < EMH+/IGeV] (3)

and it is certainly consistent with the

possibility of v2/vl-zmt/mb (even if MH+

is just above its present experimental

limit MH+>19GeV).

As a side remark, it is worth point-

ing out that the bound (3) is strong

enough to rule out the possibility of

the spontaneous CP violation a la

Weinberg, recently revived by Branco,

Buras and Gerard 4 .

3. CAN THE VACUUM WITH V2/V I >> 1 BE

GENERATED DYNAMICALLY (BY RADIATIVE

CORRECTIONS) IN SOFTLY BROKEN SUSY

MODELS ?

More specifically the question is

this : take the Yukawa couplings ht-=h b

at 0(MpL). Does there exist a space of

the boundary values at 0 (MpL) of the

free parameters of the lagrangian, such

that the RG evolution to low energies

generates the SU(2)×U(1) symmetry break-

ing with v2/v1>>1 and with = . and

mb(~)-z(4.0±0.5)GeV ? The problem has

been studied 5 in the minimal SUSY extent-

ion of the standard model and in a model

with an extra U(1) symmetry. In both

models, with ht=h b, a sizable space of

parameter values has been found for

which physically acceptable SU(2)×U(1)

symmetry breaking is generated. In fact,

the case ht~h b is in this respect as

natural as the previously (and extensiv-

ely) studied case of ht>>h b and v1~v 2.

For htsh b at 0(MpL) the mechanism of

the SU(2)xU(1) breaking by radiative

corrections in SUSY models has several

interesting features. Firstly, the 2 2

SU(2)×U(1) breaking (i.e. mH1>mH2 after

the RG evolution) is driven by the

right-handed squark masses and indirect-

ly by gaugino mass (M1):su R and sd R mas-

ses evolve differently simply because

of different U(1) charge assignment.

Secondly, the SU(2)×U(1) breaking oc-

curs only for such values of ht~h b at

that the two constraints Mw=~ Xp 0(Mp)

and mb(M W)=(4.0±0.5)GeV imply

v2/v 1% 10-20 and in consequence

mt(Mw)~(60-100)GeV (there is weak renor-

malization of the Yukawa couplings such

that ht(Mw)>hb(~}}. The minimal value

of the top quark mass is obtained when

the SUSY breaking is driven only by the

gaugino masses.

4. WHAT IS THE PHENOMENOLOGY OF THE

HIGGS SECTOR WITH V2/V1>>1 ?

This point has been discussed at

this meeting by Grz~dkowski and

Kalinowski 6 . In particular several

experimental signatures typical only

for v2/v1>>1 have been emphasized.

5. CAN WE EXTEND OUR CONSIDERATIONS TO

THE LIGHTER GENERATIONS ?

Given v2/v1~mt/m b can we also account

for mc/m s and mu/m d ? At least two sce-

nario can be considered. In the first

one, at the Planck scale only ht~h b

whereas the remaining up and down quark

Yukawa couplings are adjusted to ac-

608 S. Pokorski / How is isotopic spin symmetry of quark masses broken ?

count for the difference

m t m m -- = ~ = ~ (4) m b m s m d

This is perfectly consistent with the

mechanism of Section 3 for which to a

good approximation only the large coup-

lings h t and h b are relevant, and oc-

curs in some interesting string inspir-

ed models 7. Another possibility, in

fact more appealing, is that the approx-

imate equality ht~h b extends in the fol-

lowing sense to the whole Yukawa coup-

ling matrices:

i , hD [ (5)

Here we mean t h a t t h e c o u p l i n g s

hlili=1,2,3)<<h2i(i=2,3)<<h33 in the up

quark matrix (those which do not vanish

by some symmetry) are of a similar mag-

nitude as the couplings from the respec-

tive set in the down quark matrix. (Of

course, because of the quark mixing, the

two matrices cannot be exactly propor-

tional to each other.) It has been

shown 5 that the masses and mixing for

the second and the third generation of

quarks are easily consistent with (5).

In particular, with renormalization ef-

fects of the Yukawa couplings included

it is easy to get at the M W scale:

m t v 2 m c -- > -- > -- (6) m b v I m s

The main problem is the ratio mu/m d

for which no simple explanation exists

within this scenario. A radical pos-

sibility is to have the bare m = 0. u There is a recent claim 8 that the entire

low energy current mass of the u quark

can be generated by the nonperturbative

mass renormalization by instantons.

Advertised 8 as the solution to the

strong CP problem, this possibility may

also have interesting implications for

the structure of the mass matrices.

For instance, imagine that due to some 9

symmetries the mass matrices are :

MU= 0 , = ' 0 8' 171

* B* B' ~'

This ansatz is entirely consistent 9 with

all the available data (including B°-B O

mixing, ~, ~'/E) when

IYI , (8)

i 'i i 'l LY'i

in accord with (51.

To conclude, we have discussed vari-

ous aspects of the v2/v1>>1 to be the

dominant mechanism for the breaking of

the isotopic spin symmetry of the quark

masses.

REFERENCES

I. P.Q. Hung and S. Pokorski, Fermilab preprint PUB-87/211-T.

2. L.F. Abbott, P. Sikivie and M.B. Wise, Phys.Rev. D21(1980), 1393. G.G. Athanasiu and F.J. Gilman, Phys. Lett. 153B(1985), 27~. G.G. Athanasiu, P.J. Franzini and F.J. Gilman, Phys.Rev. D32(1985), 3010.

3. P. Krawczyk and S. Pokorski, Phys. Rev.Lett. 60(1988), 182.

4. G.C. Branco, A.J. Buras and J.M. Gerard, Nucl.Phys. B259(1985), 306.

5. M. Olechowski and S. Pokorski, Phys. Lett. B214(1988), 393.

6. B. Grz~dkowski, Higgs Bosons at 90GeV, this volume J. Kalinowski, SJSYHiggsSector,thisvoltm~.

7. G.G. Ross, New Directions in Theory, this volume.

8. K. Choi, C.W. Kim and W.K. Sze, Phys. Rev.Lett. 61(1988), 794

9. H.P. Nilles, M. Olechowski and S. Pokorski, in preparation.