Constraints on singlet right-handed neutrinos coming from the Z0 width

(1)

PHYSICAL REVIEW D VOLUME 47, NUMBER 5 1MARCH 1993

Constraints

on singlet right-handed

neutrinos

coming

from

the

Zo

width

C.

O.

Escobar

Instituto de Fisica da Universidade de Sao Paulo, 01/98 970

-CP

20.516 Sa—oPaulo, Sao Paulo, Brazil O.

L.

G.

Peres and

V.

Pleitez

Instituto de Fisica Teorica, Universidade Fstadual Paulista, Rua Pamplona, 1/5, 01/05 900-Sao—Paulo, Sao PauLo, Brazil

R.

Zukanovich Funchal

Instituto de Fisica da Universidade de Sao Paulo, 01/98 970C-.

P.

20516 Sao P—auLo, Sao Paulo Brazil

(Received 1December 1992)

We study the constraints on masses and mixing angles imposed bythe measured Z invisible width, in a model in which asinglet right-handed neutrino mixes with all the standard model neutrinos. PACS number(s): 14.60.Gh, 12.15.Ff, 12.15.Ji, 13.38.

+c

If

neutrinos are massive an important question

to

be answered concerns the way the Z-pole observables con-strain their masses and mixing parameters. In particu-lar the measured

Z

invisible width

I"""

implies

that

the number

of

families iscompatible with three. Onthe other hand,

it

is well known

that

this number need not be an integer number ifright-handed neutrinos transforming as singlets under SU(2)1.

U(l)~

are added

to

the particle content

of

the theory.

Experimental searches for sequential neutral leptons beyond the three generations exclude stable Dirac neu-trinos below

41.

8 GeV and stable Majorana neutrinos below

34.

8 GeV. For the unstable case these values are

46.

4 and

45.

1GeV, respectively

[1].

However,

it

isworth stressing

that

these limits are valid for sequential leptons and do not apply

to

the case

of

singlets ofright-handed neutrinos.

Here we will consider the simplest extension of the standard electroweak model [2]with the addition ofone right-handed singlet neutral fermion [3],resulting in four physical neutrinos, two

of

them massless and two mas-sive ones _(vp,

vp).

It

has been argued

that

this simple extension allows the implementation of a seesaw mecha-nism [4]which would explain the smallness of the known neutrinos masses. Hence, from the theoretical point

of

view, usually this mechanism is assumed. In fact, within this view ithas been claimed

that

three generations and

a

single right-handed singlet are ruled out by experiments

(Z

invisible width and w decay) _[5]and for this reason a

fourth generation must be added

to

the standard model other than the singlet [6]. However, one should not be limited by the seesaw framework, as ultimately the ques-tion

of

neutrino masses will be settled by experiments.

In fact in this Rapid Communication three mass regions will be considered for the massive neutri-nos: (i) mp, mp

(

Mz/2,

(ii) mp

(

Mz/2,

and

Mz/2

& mp &Mz~ and (iii) mp

(

Mz/2,

mF

)

Mz.

We will take into account current experimental results for the

Z

invisible width in the particular model

of

Ref.

[3].

Let us first briefly review the model we work with.

The matter fields are those in the standard model plus

where the primed fields are not yet the physical ones. In this model, there are four physical neutrinos vq, v2,v~, and v~, the first two are massless and the last two are massive Majorana neutrinos with masses

mp

=

—

1

_(gM

+4az M),

mp

—

=

1

(y

M

+4—

a

+M)

2 2

(2) where Q

=

Qy

+

Qg

+

z3.

In terms of the physical fields the charged-current interactions are

(viiz

vpip)lp

4R

W+

₊

H.

c.

,

where

4 =

diag(1, 1,

i,

1)and

B

is the matrix cp

—

sps~

—

spc~ 0

0 c~

—

s~ 0

c~s_p c~cp sp c~ cycle

—

_8~

s~sp sc,cps~ s~cpc~ c~

)

In

Eq.

(4)

c

and s denote the cosine and the sine

of

the respective arguments. The angles o.,P, and p lie in the

first quadrant and are related

to

the mass parameter as follows:

s

=

gmp/(mp+

mp),

(5)

sp

=

ai/a,

cps~

=

aq/a, cpc~

=

as/a.

(6)

Notice

that

there are four parameters; we will choose two angles and the two Majorana masses.

The neutral-current interactions written in the physi-cal basis read

a

singlet right-handed neutrino. In this simple exten-sion of the standard model the most general form of the neutrino mass term is

3

1

l:M

=

—

)

_a~v'~v~

—

_MvRvrt

—

₊

_H.

_c.

_,

j=1

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R1748 ESCOBAR, PERES, PLEITEZ, AND ZUKANOVICH FUNCHAL 47

l.

=

(ViV2Vp

_VF)&P

&o

1 0 0 v2

0 c~ tc~so, vp 0

—

tC~So S~

) (

VF

)

Zp

+

H.

c.

The Majorana neutrinos have _{the property}

that

their di-agonal vector and nondiagonal axial-vector couplings

to

the Zo vanish.

For the masses in region

_(i),

both massive neutrinos contribute

to

the invisible width of the Zo which is given by [3]

I

(Z~vs)

=Ip(2+c

gpp+2c

s

_QPF+s

QF'F),

where we have defined

2

_{mF p}2

—

m2F

—

m2p. _{Thus, X,}₂

are bounded by unity whereby

I""

_(Z

_~

v's)

(

3I

o.

The number

of

neutrinos

N„,

defined as

N„=

I"""/I'o,

as determined from recent

data

[7]from the CERN

e+e

collider

LEP,

is

N„=

3.

00

+

0.

05. (12)

~here

I'0 is the width for each massless neutrino pair in the standard model:

A(M2, m2, m2)

M2

'X

A isthe usual triangular function defined by A(a,b,c)

=

a

+

b

+

c

—

2(ah

+ ac+

bc),

Next, it is interesting

to

see how this value of

N„

constrains the allowed values for the neutrino masses mp) mph

Letus isolate the nonstandard contribution in

_{Eq. (8),}

and restrain it

to a

region compatible with

(12).

With the help

of

Eqs.

(5), (9),

and

(10)

we can write the relation

x2F(y)

+

y2F(x)

+

2xyG(x, y)

=

1.

00

+0.

05,

(x+

y)'

mp2

XPP

=~

4

₂₎

Z

m+2 XP'Q

=

1 4 ₂)

Z

Ampp mp

+

3mFmP

2M2_Z M2_Z

(1o)

(am2F

p)'

4M4

and A;~ include the mass dependence

of

the matrix

ele-ments. Explicitly, where we have defined

F(&)

=

(1

—

4')'

&(x

y)

= v'1+

(*'

—y')'

—

2(*'+

y')

x2

₊

y2 (x2 y2)2

(13)

0,5

0.35

0.3

0.25

0.2

FIG.

1.

Contour piot of function (13) where x

=

mF/Mz and y

=

mp/Mz. The 45' straight line limits the region where

fAF

)

~y.

0.15

0.1

0.05

0

(3)

DEDNEUTRINOS

.

T

RIGHT-HAND

CONSTRAINTS

0

R.1749

0.225xlg :-._:

0.175

g,l5

g.125 F)G 2' This bio p of Fig. ].shows the

d Zo ned by the measure regions constraine

nd two standard idth wi h

visible wi

'

tions (1

—

0.

05' 1 g.l

g.g75

g,g25

0 gg8 0.12 0.16 0.2 g24 g.28 0.32

a„d

_y

=

m~/Mz

P

z

1

t

f

the function

and we a

1 the contpur Pp

n from show in

F'g'

E

.

₍₁₃₎

As can be seen left hand side

«Eq

b heav. er

t

.

n the

ont

e e

-utrinos must

e e

'

'e

Eq. (2)

one

of

the neu

arameter be positi&e ~

chopse the

M

P _.

F

1

~

the region This limit aPP

a'

_'.

"

E

(]].

)

th«

45o _stra_ig

_t

iiie

tin will resu below the

d 1the neutrino coun ing

1D type pf

rilpde,

th case as }ieie ln

13)

;„s,

number

a;

ht hand side

«Eq

(

3].

As

a

result the rig fami»es

_%

_.

'

abpv, by

1. 0o.

Fg

d be

li~it~d

~o

_.

;

. 2 high»gh

'"g

A blpwup p g'

contours bel pne and t'wo

st

n

5 for the mixing ang dard deviatio n

cp"

_{. .}

1,

o,_,we 1

00. ~pm

Eq 5

1

h~

to

lie below

tral va ue '

s

_T}

_is _straight _me

—

_a

_tail

_o

.

der tp be consis en pbtam

_{J =}

oned

contou»

in or e

the mix-the before-ment pne _.

1,

a

constrajnt pn riments. This imp

_.

& 0 g3.

}n

terms with exPer _&'

OO55

i.e.

_,

»n~

a

&

ing angle

,

tan

of

the masses we have

mg»82~&

;„

the charged

JD

t

$$ XQ del the

m~»g

'"

I

036 04X10

cou lings we see 3

and(4).

~m

""

--~s'.

~t

lt we decay

a

o e

c

_.

h e~pace

facto»

[Sj accpunt the re P _..

11the masses in

t

e

ginemat-case pfregi (

h d egion (iii),we ical region

a

light«t

neu

.

,

f}ictwith the &r

foun

'

h

f

course &snot

ths,n

SGeV,

w mass limit

that

s glet rj,~ght-ha nded

neutri-cpnclilsion we se

f m

a

seesaw meehan'

which deserves

"

-

_{de Amparp}

Fundagap

.

P.

are very gra

-p

ulp

(FAPESP)

(O

~'

a dp Estado de

S~

d Conselho Nacio-pesqulsa

R

Z_{) for fu}}finan}

'

e Tecnologlco (C

cia&_suPP

an ~

ntp Cientifico e Desenvp vlmen

nal de

1financia support.

p

)f r psrtis, Ila

h

s.

Lett

8 g51,

321 n

B.

Adeva eta&,P y

1

' ' _{L3 Collaboration,}

A. (199

P s. .

19

1264 (1967);

in article Theory: Relatiuistic ro Salam, in

and Analyticity (Nobe y ' o. , ' N.

8vartholm (Almqvist and Wikse}, oc

ur of Torleif Ericson,

t

hrift in hono

H- 1990₍ bli }i

d;

CERN Report No.

TH-an y979, edited A.Sawada and A. S g

d G Senjanovic, P 7

.

(4)

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Rev. Lett. 44, 912 (1980).

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X.

Liand Z. Tao, Mod. Phys. Lett. A 5, 1933 (1990). [6

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Liand Z.Tao, Phys. Rev. D

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Foot and H. Lew, "Implications of a model with a longer tau lifetime,

"

Report No. FERMlLAB-PUB-92

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