SLAC-PUB-2924
May 1952
(TI
BREAKING
OF SUPERSYMMETRY
AT
INTERMEDIATE
J. Polchinski
Stanford
Linear
Accelerator
University,
Stanford,
Stanford
L.
Physics
Stanford
ENERGY*
Center
California
94305
Susskind
Department
Stanford,
California
University,
94305
ABSTRACT
We consider
midway
between
the
proposal
the
Planck
a phenomenological
emerge
below
scale
~250
scale
explicitly
scale
supersymmetry
that
I-I.
GeV gives
is
w u
M and
softly
The
breaking
supported
by
the
the
of
10'2
order
is
usual
broken
characteristic
broken
weak
at
a~zOl.
for
the
Identifying
p
We show
scale.
supersymmetric
scale
a scale
theory
Department
to
Physical
of
Energy,
Review
explicit
this
with
the
0
contract
how
can
GeV.
Submitted
* Work
supersymmetry
DE-AC03-76SF00515.
weak
1.
The
some
SUPERSYMMETRY
present
theory
of
13 independent
parameters.
energy
It
remnant
very
high
energy,
surprising
world
of
AND THE
elementary
field
is
believed
a more
symmetrical
possibly
the
of
characterized
such
by
and
that
Planck
about
some
20
this
free
theory
M.
the
very
17 orders
is
at
most
a low
manifest
at
the
most
Perhaps
of
contains
dimensionless
is
which
scale
is
PROBLEM
SU(31xSU(21XU(l),
theory
a theory
masses
GAUGE HIERARCHY
particles,
multiplets
widely
feature
2-
existence
of
magnitude
smaller
some
a low
energy
than
M.'
In
be
general
adjusted
such
to
general
radiative
leading
to
many
The
only
symmetry
obtain
ratios
these
order
by
will
order
known
which
remedy
can
for
prevent
occurring.
For
example
chiral
masses.
If
boson
dimensionless
leads
quantity
unbroken,
nonvanishing
symmetry.
in
classical
the
upset
occur
parameters,
to
this
not
the
stable.
of
Parameters
Lagrangian
delicate
may
but
in
adjustments,
.
fundamental
if
almost
would
is
parameters
Although
by
are
to
a symmetry
quantity
small
mechanism
exactly
dimensionless
not
vanish.
parameters
explain
the
the
from
prevent
by
fermion
very
small
small.
For
exist
a
term
remain
naturalness:
should
to
does
can
will
have
mass
violated
masses
of
to
spoiling
some
symmetries
symmetries
requirement
that
this
gauge
is
from
prevents
resulting
vanishes,
caused
corrections
and
the
require
situation
a symmetry
such
a fundamental
which
unnatural
radiative
can
idea
are
places.
This
gauge
scales
readjustment
hierarchy.
and
of
ratios
corrections
an
decimal
large
This
every
which,
if
The
which
smallness
break
of
the
such
-3quantities
it
against
does
provide
radiative
In the
"standard"
gauge
bosons
are
which
can
identified
Higgs
potential.
all
theory
could
quadratically
the
proportional
to
with
the
which
the
keep
divergent
a single
the
this
masses
smallness
scale
quarks,
is
stable
theory
terms
contains
This
no
fact
corrections
leptons
parameter
(mass)
zero.
radiative
of
mass
quadratic
Unfortunately
potentially
in
corrections.
current
be
a framework
*lo2
in
the
the
GeV
scalar
symmetry
manifests
to
and
which
itself
mass
of
in
the
Higgs
field.2
Two
the
ways
TeY
out
have
In one
region,
dynamically
been
bound
scheme
IS.S.1
in
Indeed,
S.S.6
is
only
zero
the
introduces
presence
partners
Typically
the
the
typical
shown
in
bosonic
cancel
the
partners.
Am2
is
of
by
H and
W circulate
in
which
the
order
can
fermions
parameter.4j5
keep
a scalar
in
are
the
graph
in
the
in
be
the
which
The
in
Higgs
will
example
loop.
equal
mass
supersymmetry
(massI
For
a second
mass
of
the
u. Am',
supersplitting.
mass.
+JU times
graph
the
cancellation
to
their
generally
*
in
by
mass
speaking
Higgs
physics
replaced
divergences
the
new
introduces.
Higgs
which
quadratic
cancelled
6rnHZ
where
are
Roughly
of
More
the
to
require
scheme
a supermultiplet.
within
limit
other
symmetry
corrections
be
which
scalars
control
known
which
1 will
partners
to
interactions.
radiative
Fig.
in
order
of
Higgs
The
of
splitting
fermionic
exact
the
both
the
composites.293
supersymmetry
in
proposed,
(1.11
is
-4Evidently
if
would
want
This
requires
the
SmH'
theory
to
be
is
no
to
be
bigger
in
free
of
unnatural
adjustments
order
of
magnitude
than
we
m$
itself.
1
Am’ S --_:xlOOGeV
+,
a few
TeV
(1.2)
.
Ja
The
obvious
the
same
conclusion
general
In this
paper
S.S.
can
be
S.S.
breaking
degrees
of
The
raised
argue
mechanism
is
in
breaking
S.S.
the
scale
sense
we shall
be
for
spontaneous
the
distant
among
the
large
the
weak
from
that
as
ought
to
be
M >> l.t limits
supersymmetry
and
Banks.e
Raby'O
Many
breaking
scale
the
if
of
the
ordinary
fundamental
as
+lfJ'*
.GeV without
superpartners
responsible
of
of
the
and
the
breaking
Recent
Earbieri,
features
models
of
models
at
an
by
Dine
intermediate
scale
and
FischlerP9
Ferrara
and
Nanopoulos'l
are
we discuss
are
also
in
Alvarez-Gaume,
evident
Claudson
and
was
also
the
Wise12
and
Fischler.'o
In Section
2 we describe
O'Raifeartaigh
breaking
mechanismlQ
however
it
of
scale.
than
show
can
breaking
weak
higher
some
scale
of
the
splitting
of
and
and
that
magnitude
Indeed
scale
as
of
Witten
type.
Instead
magnitude
orders
possibility
by
the
mHz small.
Dimopoulos
Dine
of
a corresponding
keeping
this
many
S.S.
inducing
that
we will
freedom.
spontaneous
for
order
is
is
is
coupled
not
a toy
at
an
directly
to
a world
model
in
which
intermediate
coupled
of
S.S.
mass
to
superheavy
the
is
scale
ordinary
supermultiplets
broken
p,.
light
by
The
the
S.S.
world.
of
mass
of
-5M >> p.
These
indirect
coupling
The
softly
particle
points
S.S.
as
its
of
against
discuss
new
devoted
to
the
example
of
Witten's
general
framework.
the
of
which
the
Iliopoulos16
at
the
will
is
scalar
be
no
to
determine
influence
supersymmetry
mechanism
light
the
inverted
In
particular
a(p2/M).
from
mass
One
stability
of
fields
mass
explicitly
if
counterterms
of
the
such
Goldstone
a
by
central
a two
Section
6 we discuss
of
gravity
on
Appendix
the
one
loop
B we discuss
breaking
rather
class
at
than
scale
the
model
stage
our
how
it
theories.
gluino
mass
some
p is
O'Raifertaigh
5 analyzes
fits
.
into
conclusions
of
due
and
vanishes
features
to
and
4 is
Section
showing
this
the
Section
multiplet.
hierarchy,15
that
into
generation.
In
In
an
looks
a(~2/M).
gauge
a gaugino
of
A we show
theories.
like
p
corrections,
such
physics
than
than
the
an
states.
protected
bigger
produces
intermediate
a scale
is
This
world.
less
by
introduce
features
light
superheavy
energies
Higgs
3 we
Appendix
class
by
radiative
Section
In
the
paper
In
about
to
characterized
mass
this
hierarchy
couple
theory
such
then
turn
mediated
resulting
broken
S.S.
in
the
of
Fayet-
mechanism.
an
our
speculate
in
theories
a
in
-62.
Our
simplest
6 and
e,
example
are
heavy
involves
with
mass
b = B + i$B@
i
A superfieid
S.S.
is
The
ordinary
superfields.17
Two
them,
MM.
+ 6BFB
the
(2.1)
Goldstino
and
its
scalar
partner
+
getting
light
of
+
+. i-Ix9
Fx
a v.e.v.
world
is
= L + i+Le
superpotential
chiral
x eeFx
=
by
i
The
+ i$&
2 describes
broken
four
c eeFc
=
i
A TOY MODEL
of
replaced
order
by
(2.2)
p2,
a single
superfield
eeFL
+
t.
(2.31
is
iL2
fj2
wti,?,2,C,
=gj:
+rl'$i:
[ 1+tIci
9
+ g63
For
simplicity,
assume
The
the
g is
all
small
potential
equations
of
g$L + g&2 + gi3
+
dimensionless
enough
to
(2.4)
leads
motion
for
coupling
do
to
Fi
perturbation
spontaneous
arei
(2.4)
constants
theory
breaking
are
and
of
called
that
S.S.
g.
M )>
We
CL.
Recall
that
-
7EWi
Fi*
=
'
--
(2.5)
3=#
b3i
which
gives
Evidently
The
these
cannot
absolute
-
Fx”
=
gB2
-
Fc*
=
M'B
both
be
of
the
minimum
zero
X is
undetermined.
adjusting
M,
The
so
=
supersymmetry
is
broken.
CFi*Fi
S.S.
We assume
breaking
B=C
=L=O
We can
always
that
when
v.e.v.
is
<Fx>
Taking
original
w to
be
intent
quadratic
of
we would
consider
the
On dimensional
S.S.
breaking
can
potentially
as
S.S.,
assume
gBzp2
grounds
only
split
it
is
to
coupled
L masses
order
by
of
0.
according
X to
by
._
to
seem
keep
be
the
(2.6)
order
Fig.
2,
the
to
is
100
g3p2/4n2.
where
intermediate
GeV or
For
the
cross
from
Note
the
corrections
order
Lagrangian
g3y2/4T2.
undetermine
radiative
of
of
L through
*pt.
zero
(2.9)
in
in
to
v.e.v.
M-f
potential
graph
of
done
GeV might
would
appears
the
w2
ef,fective
Feynman
which
is
=
10 l2
these
set
which
namely
scalar
ordinary
is
large
the
light
Normally
insertion
as
(2.8)
,
this
Fx
the
(2.7)
at
while
the
(2.6)
potential
V
occurs
~2
-
the
that
to
less.
example
indicates
term
even
superheavies
Fx*Fx.
though
it
-8However
finds
the
the
graph
exactly
by
combining
order
shown
cancels
expressed
as
Consider
which
arises
series
in
S.S.
combinations
p2
contributions
cancel
in
Fig.
Fig.
2.
part
This
of
quadratic
when
powers
=
theorem
is
S.S.
of
this
LZv2
is
co(g)
represented
by
Figs.
2 and
v.e.v.
Calculating
the
broken
to
at
scale
I-L2
>- +
+ c,(g
as
general
the
effective
u.
It
Fig.
2.
and
can
C<?>
It
be
can
be
V(L)
written
as
MQ
effective
= <Fx>f30
a
(2.10)
I
in
a supersymmetric
a "spurion"
w2.
(2.11)
= 0
For
formalism
line
example
in
in
a supergraph.
Fig.
4 shows
which
The
the
S.S.
breaking
spurion
supergraph
is
Fx
containing
3.
this
graph
is
equ
valent
to
computing
the
correction
term
the
example
potential
1-b’ + ...
cz(9
tl2
i i)F
ti
in
supergraph
very
For
g.
one
that
we work
has
same
in
graphs
pz/Mz:
asserts
which
Feynman
orders
is
contribution
Co(g)
To see
the
all
cancellation
I
The
to
ordinary
a theorem:
the
Vz(L)
3 is
of
action.
= w208)
When
Eq.
(2.12)
i
is
given
becomes
(2.12)
its
pzLL.
v.e.v.
to
-9Although
dimensional
devergent
tii2>r
Rocek-Siegel
loop
of
analysis
counterterm
(GRSI
and
it
symmetry
vanishes
theorem
which
remains
that
says
that
a "D
term"
The
possibility
the
L supermultiplet.
Giving
For
example
"F
orders
by
terms"
2 its
v.e.v.
produces
f
the
We shall
discuss
contain
anything
Another
yielding
the
are
the
a log-
Grisaru-
not
induced
by
to
operator
term
(2.141
i)F
For
the
a splitting
scalar
now
we note
components
that
of
it
does
not
L.
is
ti i 2”)o
(2.15)
!-.12(i
(2.16)
operator
operator
it
the
rise
(2.13)
effective
interest
give
?)I,
later.
in
of
effective
this
masses
operator
quadrative
operator
Curiously
boson
this
might
consider
v2(i"
does
so
i>,
is
supersymmetric
and
in
a supersymmetric
although
it
can
We shall
manner.
produce
return
to
later.
The
next
class
of
operators
contain
ti*
which
of
i
X quadratically.
i*
Consider
(2.17)
i,D
gives
A contributing
is
all
allow
diagrams.'*
tf*
it
to
considerations
order:
coefficients
supergraph
(g"/4a2)(1/M2)
are
estimates).
pw*
i)A
= FL4 L*
L
is
shown
in
5.
(with
the
exception
the
induced
Thus
Fig.
(2.18)
By dimensional
of
scalar
Eq.
analysis
(5.13)
mass-squared
it
all
is
-
10
g’
-
w4
. --
The
operator
L*L
fermionic
partners
but
the
graph
Similarly
-*+.A
(LLXX*)D.
operator
to
induced
the
scalar
by
in
This
and
(2.151
sp lits
the
sea lar
leaves
6 gives
Fig.
(2.19)
rl2
4n2
operator
the
and
rise
gives
pseudoscalar
to
the
and
The
their
lar
pseudosca
equal
(mass12.
from
L-bosons
degenerate.
mass
term
opposite
magnitude
Lt
from
the
contributions
is
again
given
by
(2.191.
Fermion
masses
can
also
be
Consider
generated.
the
operator
ti
which
is
is
set
produced
equal
to
by
p2B8
Fig.
i
7 with
the
we obtain
the
g3
_I
is
Supersymmetry
powers
of
Soft
also
It
supersymmetric.
violating
p,2/M2.
supersymmetry
occur.
The
produces
fer'mion
(See
Fig.
81
yields
operator
ti
however
both
masses
Section
violating
are
3 for
interactions
(2.21)
i)F
fermion
and
suppressed
by
gaugino
cubic
boson
masses.
additional
masses.)
in
boson
fields
operator
ti*
(see
effective
.
When
(g3/4~21(1/tl).
tl
4n2
which
coefficient
I2
-
.
(2.20)
?*1l,
the
breaking
i
ic*il,
(2.22)
can
X
-
which
g3
-.-.
P2
4x2
M
g3
-.-.
lr2
4n2
M
11 -
(L* L)F
(2.23)
contains
Using
the
equation
supersymmetry
of
violating
motion
for
L*
FL
FL
this
becomes
g3
-.-
P2
4n2
M
the
sum
of
two'
terms
a L3 + b L2
g'
P2
4n2
M
a+-.-
Note
scale
that
effect
wave
so
far
proportional
stability
of
which
function
supersymmetric
b*
;
all
to
the
the
induced
p2/M.
This
hierarchy.
ruins
this
mixing
of
dimensional
circumstance,
However
the
stability.
the
present
Consider
Goldstino
multiplet
Fig.
2
1
(2.25)
constraints
have
if
insures
general,
model
9,
X with
does
this
have
graph
L through
operator
(2.26)
With
coefficient
g2/4n2.
It
gives
an
effective
operator
g2
-
4ll2
b2
FL
(2.271
a common
the
an
induces
the
-
This
is
a supersymmetric
~(g~2/4~2)1'2
giving
two
stage
get
masses
mix
with
it
hierarchy.
of
a mass
If
order
but
causes
a shift
~(g3p2/4n2)"2.
other
p from
it
light
(2.27)
It
fields
even
if
couple
they
are
of
L by
evidently
destroys
to
too
L they
forbidden
the
would
to
directly
X.
A similar,
which
operator
12 -
S.S.
violating,
effect
is
produced
by
the
graph
in
Fig.
10
gives
cl3
4lltrl
The
low
energy
This
effect
explicitly
will
(It
is
of
in
real
the
realistic
example
the
of
All
light
K4
4~r~
M
L
energy
S.S.
violating
by
an
throughout
this
is
the
amount
the
true
low
scale
..
(2.291
>>
(~2/M)3.
energy
of
This
sector.
supersymmetry
world.)
we can
fields
quarks,
g3
-.-
that
theories
light
(2.28)
St i*>rJ
is
low
S.S.
possible
chiral
bosons.
breaks
course
neutral
ex-tension
operator
introduce
violation
In
effective
ti
which
sector
chiral
couple
might
leptons,
easily
avoid
directly
consist
Higgs
multiplets
this
of
to
the
problem
by
light
sedtor.
the
minimal
bosons
and
are
non-neutral
not
having
For
supersymmetric
SU(3)xSU(2)WCl)
under
gauge
SU(~)XSU(~)XU(~)
in
the
and
graph
Thus
of
far
Consider
order
appropriate
out.
Thus
treat
Fig.
11
loop
logarithmically
shows
Fig.
11.
R2
that
the
the
Goldstino
this
When
the
is
as
graphs
Power
to
it
fie
Ids,
part
of
left
R2
loop
when
of
the
an
heavy
In
this
par ticipate
or
of
that
the
5 in
will
only
internal
of
which
Fig.
lines
order
is
M it
integrated
its
effects.
contributions
Fig.
Power
12.
order
come
counting
.
d4A
(2.30)
s-
for
all
R2
contributions
external
pieces
way
is
behave
to
separate
the
to subtract
out
This
shown
momentum.
now
Lb
<< M2.
A convenient
is
low
the
energy
value
of
schematically
and
the
high
right
in
Fig.
energy
loop
at
13.
The
zero
first
like
d4R
(2.311
s-
and
contributes
only
for
R y M.
52
This
can
be
is
diverge
significant
see
lines.
is
sector
example
i
the
line
c lines
case
For
<< M2.
i
to
involving
is
reveals
identical
N + EQ.
internal
occurs
momentum
integrations
+. t-l2 and
with
counting
graph
essentially
when
from
with
considered
M2.
to
Sometimes
both
not
contribution
R2 of
mix
10.
example
significant
carry
Fig.
we have
for
cannot
13 -
considered
as
part
of
the
integration
of
involves
the
only
large
light
mass
lines
14 -
degrees
and
is
of
The
freedom.
logarithmically
second
part
It
divergent.
is
just
il
the
contribution
S.S.
breaking
resulting
in
can
found
only
logarithmic
wave
function
all
on
The
the
The
models
can
to
breaking.
the
consider
i
lines
theorem
Graphs
consider
the
This
makes
This
graphs
coefficient
and
a mass
of
group
energy
theory
list
of
energy
soft
no
operators
we
The
breakings.lg
theory
are
of
method.
has
breaking
renormalization
considered
heavy
do
not
the
supersymmetric
effective
in
analyzed
order
are
are
14 involving
for
by
to
the
mass
the
above
the
small
same
method
the
Fig.
by
particles
($?Xii*c),.
12.
the
GRS
fields.
-For
mass
this
involving
mass
operator
as
To see
and
before.
intermediate
L from
"1-1 couple
lines
low
as
*v.
particular
analysis.
mass
of
mass
supersymmetry
supersymmetric
functions
Fx
In
of
not
the
graphs
external
Fig.
but
with
.
particles.
intermediate
wave
particles
particles
affect
internal
the
no
mass
sectors
These
to
have
scheme15
renormalization
be
The
generalized.
low
low
computed
renormalization
intermediate
with
couple
graph
is
far
particles
renormalize
can
the
hierarchy
graphs
which
a previously
supersymmetry
and
externally.
only
usual
Grisaru's
of
contain
light
These
be
effective
and
thus
inverted
directly
the
of
interactions.
we have
Mitten's
first
Girardello
violating
can
effective
renormalization
Generalizations
only
that
divergences
supersymmetry
-
in
by
shows
theory
procedure
treated
divergences.
have
light
This
be
counting
quadratic
effective
operator.
logs
Power
the
Its
example
I.
-
15 -
g6
(2.32)
(4Tr~I~rl~
Apart
from
diagrams
the
the
involving
inverted
only
heavy
lines.
order
term
tCi)
because
leads
loop
This
is
the
in
the
same
order
of
magnitude
The
logs
can
p that
might
be
present
is
mixing
models)
Figure
F.
it
to
of
hierarchy
pii.
(pZOl)
is
has
as
again
other
be
two
summed
loop
with
group.
mass
fields:
one
this
renormalization
Another
in
log
15 gives
is
an
a tree
mass
term
Fig.
6,
term
ugc
but
rise
F-term
level
the
but
the
to
the
supersymmetric
is
not
forbidden
graph.
Figure
g(~'+/M2)L2.
This
the
between
(and
coefficient
16
is
here
heavy
the
same
is
larger
and
mass
by
induces
generally
the
is
light
term
GRS theorem
g(y2/t12)(~~~)r
mass
.
term
unless
which
induced
the
at
mixing
small.
The
6 and
mass
i.
CO(p2/M2)1
Then
Fig.
Yukawa
could
have
16 appears
coupling
been
absorbed
explicitly
between
the
in
light
by
the
fields
a small
Lagrangian
and
redefinition
of
as
a smal
Goldstino
fie
Id.
EXAMPLES
3.
A simple
fields
6,
gauge
field
the
model
i
and
6 and
bosons
and
energy
theory
will
the
matter
is
particular
induced
c are
with
now
direct
Fig.
gauge
the
scalar
the
same
excluded
by
i?ii
scalar
17.
The
as
the
denoted
3,
i,
masses
would
resulting
LL*
momenta
integration.
diagram
WM.
the
the
Accordingly
it
be
of
the
in
of
goal
is
gauge
a low
there
the
LFS
dangerous
If
left-right
generated
magnitude
.
the
before
interaction
symmetry.
terms
there
are
linear
were
in
no
asymmetrical
by
of
their
two
loop
graphs
masses
is
e2g
-
such
(3.2)
4TI2
contribution
is
As
Much
The
case
still
significant
and
gauge
M
this
I?.
to
.
magnitude.
p2
-
In
and
supersymmetry.
LL,
order
in
Our
e.
2.
be
and'i
couplings
is
unbroken
may
the
fundamental
coupling
of
of
are
the
gauge
Section
fields
is
super-field-s
order
in
adjoint
light
usual
masses
fas
i
heavy
The
the
violations
same
utilizes
2.
multiplets
the
the
couplings
theories)
The
explicit
field
involves
containing
b_e soft
fields
superpotential
action
fermions.
discussion
as
some
GAUGE FIELDS
gauge
Goldstino
The
addition
WITH
light
a singlet
antifundamental.
In
In
involving
16 -
treated
occurs
as
part
of
when
the
high
all
lines
energy
have
A phenomenologically
this
in
necessarily
Fig.
important
breaks
18.
The
S.S.
the
D's
Giving
inside
X its
question
it
resulting
must
operator
e29
4n2M
where
17 -
(i? i
proceed
the
gaugino
via
heavy
intermediaries
denote
(3.3)
covariant
derivatives."
yields
4n"
X = gaugino
actual
coefficient
that
the
field.
a class
of
superheavy
masses
theories
of
-
is
to
this
see
careful
graph
contribution
vectors
of
this
This
Section
5.
In
Append
masses
is
Two
shows
the
A we have
proved
van ishes'identically
in
in
theories
with
diagrams
give
gaugino
not
loop
ix
that
so
order
(4liZ12
counter-term
zero.
type.
.
Iliopoul
inspection
gaugino
e2g3
Final
(3.4)
M
However,
of
one-loop
as
is
-et9 . P2
----xx
Here
Since
mass.
D B2 D $10
parentheses
v.e.v.
is
ly
if
the
OS D-term
in
low
Vn
the
energy
can
be
(3.5)
M
gauge
group
induced.
supersymmetric
(D"
P2
-
It
Lagrangian.
k,
?*
i,,‘
contains
is
not
U(1)
then
produced
However
the
directly
the
operator
(3.6)
Fayetas
a
is
not
with
excluded
by
coefficient
To
a variety
The
times
field).
we get
out
of
coefficient
coupling
general
theorem.
Giving
2 its
v.e.v.
pattern
here
as
k with
its
yields
*teg2/4nZ)(~'+/M21.
summarize,
Integrating
any
18 -
the
the
heavy
same
fields
supersymmetric
of
the
constants
and
effective
(except
general
and
replacing
nonsupersymmetric
interaction
for
the
effective
is
case
in
always
of
the
Section
v.e.v.
2.
leads
interactions.
y2/M
1 ight
to
singlet
a power,
matter
to
-
4.
The
operators
theory
also
consider
was
splitting
induce
determine
the
which
which
the
GOLOSTINO
supersymmetry
couplings
of
by
Fig.
5.
u g'p+/4n2M2.
The
The
the
term
-The
coupling
what
of
the
the
supersymmetry
violation
supersymmetry
breaking
It
diagrams
is
interesting
in
the
Goldstino.
As
low
an
energy
example
Fig.
*
-
identities
Goldstino
3x
Jlx 3L
v.e.v.
rise
to
Fx"fFx
Fxf3x
gave
a mass
is
(4.2)
L*
supersymmetry
proportional-to
the
proportional
require.
effective
to
the
= p.2.
also
to
broken
inversely
Fx
consider
of
is
Amz, and
19 give
to
IL2
Ward
to
proportional
proportional
4llzP-P
just
in
Am2
Jlx +'L L*
is
breaking
term
g4K2
This
SECTOR
operator
produced
6mt
THE
19 -
the
operators
containing
only
operators
(4.3a>
(4.3b)
9”
(2%ic*2 21,
(4.3cl
4rrtr12
(4.3d)
X.
The
- 20 Inserting
the
correction
to
v.e.v.
the
vacuum
applied
to
these
models.
This
Fx
ti*i??>~~
At
of
tree
level
itself
remains
(4.3d)
give
of
will
of
be
this
the
method
vacuum
published
in
g21~"/4-rr2.
It
is
this
is
easily
paper
(effective
represents
minimizes
must
a
potential)
in
a shift
the
of
effective
the
scalar
potential,
vanish.
superfield
(ignoring
used
energy
It
which
Goldstino
simply
separately.20
p4X.
operator
massless
becomes
The
becomes
the
rise
(4.3a)
energy,
In the state
X.
coefficient
At
Fx,
calculation
= ~2,
component
the
the
of
k is
gravity).
massless.
The
The
operators
Goldstino
(4.3~)
and
to
-
-
g4
P4
-
.
x*
(4.4)
x
rl2
4n2
and
-
g4
IL4
. - x2
which
are
masses
masses
in
In all
i.
the
low
so
that
the
energy
examples
In Appendix
D-term,
for
so
X scalars.
They
are
of
the
part
of
same
order
as
the
sector.
far,
B we briefly
the
(4.5)
M2
4ll2
Goldstino
the
Goldstino
consider
is
part
was
models
of
in
a gauge
which
a chiral
S.S.
multip1et.l"
superfield
is
broken
by
a
THE
5.
Witten's
interesting
induced
by
Ginsparg2'
(a
example,
in
and
coupled
2g
the
where
The
> X.
gauge
for
The
invariant
0 is
a matrix
full
scalar
in
<Y1,2>
Witten
we assume
an
the
particular
SU(2)
gauge
chiral
value
that
is
=
0
of
an &specially
M is
spontaneously
example
theory
is
with
Ya and
due
gauge
Bat
and
to
superfield
a singlet
is
of
the
appropriate
+-,,
=
with
chiral
fields
are
contained
energy,
=
=
scale
fields
fields
interactions
the
us
superheavy
chiral
potential
<Y3>
provides
The
kinetic
<B1,2>
expectation
the
adjoint
gauge
<B3>
The
of
to
HIERARCHY
modeli
which
consists
-
INVERTED
effects.
superpotential
with
in
hierarchy
radiative
= 1,2,3)
the
inverted
21
minimized
c
29
- x
representation.
at
J
x2
I 1
(5.3)
l/2
1 VP
<z>
2g2
0
Z is
quantum
undetermined
corrections
at
tree
produce
level.
a minimum
Following
at
a value
V.=J
2;
<I>
such
-'
that
An
w.
which
22
for
The
small
( <Z)/K
couplings
nonvanishing
1
*
makes
l/g2
<Z>
auxiliary
many
fields
orders
of
magnitude
larger
than
are
f.12x2
<Fz>
=
-
X2
[ 1
2!3
(5.4)
l/2
<Fy3>
=
-
TL~X
1 - -
2g2
The
supersymmetry
One
for
linear
both
is
broken
combination
scalar
and
at
of
auxiliary
fi
q
?3
order
.? and
W.
? a has
components
-
case
i
a vanis.hing
-
we call
expectation
.
it
fi:
(5.5)
sin6
where
case
The
other
linear
=
at492
-
x21-"*
(5.6)
c0se
(3.7)
combination
7
=
P3 sine
+ i
has
(5.8)
l/2
<FT>
E
f
value
-
The
expectation
large
scale
value
M.
of
To see
the
23
-
Y a breaks
the
spectrum
it
gauge
is
symmetry
convenient
to
to
U(1)
use
at
the
a unitary
,
gauge
A
Y’
and
to
shift
away
the
f2
=
=
scalar
0
field
(5.9)
expectation
values
(5.10)
The
superpotential
becomes
g
This
has
sections.
the
large
the
c0se
E-i
+ Xl.r.
c0se
same
general
The
fields
i2t3
if
-
g sine
form
important
Z and
-
piece
Yo.
+ gM
as
(5.11)
6i-t
the
from
In
s-i?
c0se
terms
superpotentials
the
of
kinetic
the
studied
in
Lagrangian
new
fields
is
it
is
that
previous
for
-
( I 2 c0se
f
=
+
Here
6 is
in
the
6 sine
-
tee9133
$*i
(
+ O*ij
only
A
or
v2,
Z.
supersymmetry
states
field
were
in
O'Raifertaigh
This
This
is
through
the
breaking
Fig.
not
)o
vertices
involving
Thus,
light
fields
This
the
undetermined
?.
This
is
about
From
2 also
include
to
always
comes
Fx.
is
bridge
.
the
intermediate
because
a fairly
$1,
between
requires
scalar
(5.111,
the
auxiliary
expectation
value
general
property
6 which
can
of
breaking.
contain
dangerous
value
superheavy.
fields.
and
(5.13)
Eabc
expectation
all
the
superfield
does
Zi?,
all
supersymmetry
model
+ tz2)
}s
a light
because
neutral
fi couples
field
to
the
other
light
mix
with
fields
?.
only
superheavies.
The
and
and
value
same
-
that
are
superheavy
the
(GT2
12
(5.121
=
fields
expectation
sin20
breaking
breaking
with
+ M sine
c0se
representation:
we see
These
12
interactions
adjoint
(5.131
case
-+ CJ
e
+ 2r12 e2
supersymmetry
(5.12)_and
-
+ M
1 2 sin
(bbc
The
24
20.
light
sector
unbroken
in
Abelian
masses
from
This
induces
this
model
consists
of
field
$3.
The
mediated
by
gauge
graphs
heavy
the
light
L scalars
vector
matter
get
fields
field
supersymmetry
such
as
i
-
25
-
(i-n
i
e4
4n2(eM
The
fields,
in
photinos
as
the
can
shown
get
in
mass
Figs.
supersymmetric
This
the
sort
mass
spontaneously
-
can
of
loops
and
22.
of
broken
heavy
22.
gauge
graphs
The
loop
I
found
obtained
R-symmetry.zo
from
and
have
photino
ezfZ
gauge
be
of
heavy
calculated
mass
is
I
=8ll2f-l
in
1t
Sn2M
loop
Appendix
a Tow energy
i
been
etf2
I-
+
cancellation
also
k,,
These
Ref.
*
8-rr2 M
and
21
from
Ry gauge
[ I
2e2f
(5.14)
k*
sinBIt
A does
theorem
not
quite
for
occur.
6.
What
which
we have
shown
supersymmetry
superheavy
itself
the
light
the
breaking
practice,
this
The
Most
is
fields,
two
Explicit
Supersymmetry
violating
gaugino
3.
Supersymmetry
violating
scalar
only
supersymmetry
violating
interactian
are
the
calculate
requires
the
a detailed
gravity.
Planck
same
scale
place
of
significantly
actual
of
should
the
induce
or
made
M,,
connecting
very
small,
with
a strength
machinery
of
the
superheavy
explicitly
softly
than
the
double,ts,
of
the
order
scale.
In
broken
plus
pz/M
Higgs
the
quarks,
low
leptons,
their
would
be:
doublets.
.
mass.
masses.
the
the
is
a trilinear
constraints
S.S.
scalar
on
gravitinos
same
operators
Unless
gravity
the
gravity
violating
superheavy
and
scale.
than
manifests
S.S.
the
explicit
19.
of
of
the
superheavy
interactions
off
value
of
breaking
more
the
Ref.
gravitons
smaller
other
in
knowledge
Exchange
for
Curiously,
as
The
Higgs
2.
CCsil~.
terms
in
a
at
masses
exists
between
the
nothing
and
model
intermediate
of
hidden
contain
of
violations
mass
To
turned
explicit
Supersymmetric
breakings
all
p
1.
from
a class
~2/fl.
scale.
could
partners.
interactions
in
that
a phenomenological
gauge
supersymmetric
scale
mechanism
which
SU(31XSU(2)XU(l)
is
a scale
through
suggests
theory,
at
light
-
CONCLUSIONS
paper
a light
world
of
supersymmetry
this
broken
t-l and
characteristic
energy
is
mass
in
in
26
parameters
sector,
of
momentum
we have
the
cannot
be
ignored.
to
still
including
near
discussed
superheavy
Goldstino
would
perhaps
scale
In
normal
matter
connect
the
the
with
M,
is
fact,
if
were
.two.
Indeed,
the
one
definite
gravitino
The
into
fact
that
cosmological
Assuming
of
a spin
the
they
would
dominate
the
unless
they
had
scale
and
as
in
mass
the
GeV,
is
to
combine
of
mass
scalar
by
This
helium
gives
consistent
and
in
at
the
are
our
S.S.
and
Hung
massive
and
early
synthesis
a lower
with
Goldstino
1~.*/Plr.'~
partners
Weinbergzb
universe
the
14~r/3)"~
equilibrium
decayed.
~10"
its
noted
thermal
of
already
of
particle
Goldstino
are
-
gravity
312
implications,
that
breaking
effect
27
bound
breaking
has
Suzuki.25
universe,
they
temperatures
on
the
S.S.
scale.
ACKNOWLEDGEMENTS
We would
Raby,
-was
Steven
supported
like
to
Weinberg
by
the
thank
and
Tom
Banks,
Mark
Wise
Department
of
Mike
for
Energy,
Dine,
useful
Willy
Fischler,
discussions.
contract
Stuart
This
DE-AC‘03-76SF00515.
work
-
28
-
APPENDIX
A
THE ONE LOOP GAUGINO
Consider
a Lagrangian
?(ijEijgij
where
ii
and
convenience
G -
the
-
Ei
IJ.‘)
are
we take
argument
condition-for
is
mass
+ Pijtitj
a collection
of
fields
to
all
in
be
broken
the
(A.11
(i
representation
to
of
arbitrary
For
= l,...,n).
the
gauge
representations.
is
;
has
chiral
a real
extended
= 0
then
form
+ 2Nijiitj
trivially
S.S.
matrix
the
+ Mij$ihj
them
Pij
The
of
MASS
N-*13
(A.21
nonsingular
form
.
=
(A.31
PI
/
The
coupling
Let
X be
matrix
a matrix
of
which
the
Goldstino
diagonalizes
field
to
i
M and
define
and
t
is
group
The
- 29 -
In the
always
one
loop
CA.31
=
M'
x G 2“
=
C’
glu ino
diagonal.
mass
it
1
M'i
G' i j
follows
,
(A.51
diagonal
CA.G)
graph,
BY d imensional
c
i
From
X M %-'
Fig.
18,
analysis
=
Tr
=
TrCGffW1l
the
E G'
the
tota
gauge
vertices
are
is
1 contribution
1
tM')-l
(A.71
that
0
M-1
Y
I
.
(N+)-’
I
=
(A.81
1
I
N-1
-N-l
MCN+)-’
,
I
and from
(A.81
This
and
cancellation
momentum,
and
condition,
(A-21,
reason
the
eigenvalues
loops
two
of
The
to
that
the
N are
cancellation
effective
that
It
curious.
condition
that
it
supersymmetry
(though
for
we see
is
the
be accidental
~12.Ql.
CA.41
for
loop
a special
graph
small
to
opera,tors
vanishes.
takes
place
take
place
be
broken.
case,
~1,
appears
from
see
some
after
Ref.
adding
at
zero
precisely
In
mass
the heavy
only
is
In the
vanish.
(order
then
(A.71
general
20)
case
and
tha.t
eigenvalues
the
loops.
effect
gluino
the
it
appears
to
know of no
we
some
are
of
order
the
light
-
30 -
APPENDIX
SUPERSYMMETRY
In
the
this
S.S.
Appendix
breaking
A toy
model
gauge
symmetry,
at
has
are
L with
usual-kinetic
last
and
symmetry.
These
The
cannot
atB=C
symmetries
at
tree
effective
neutral
the
= 0,
are
and
= -~2
Fs*
= -
NC
Fc*
= -
MB
For
only
U(l)',
must
the
the
be
with
(ii,-11,
6,
e’(BSB
-
light
of
plus
D-term
3',
and
consists
+ p2(?')o
CL << M,
U(1)
gauge
the
breaking
assume
effective
with
Lagrangian
coupling,
e'
(8.1)
for
and
the
U(1)'
. gauge
C are
given
by
C+tC)
(8.2)
S.S.
(we
Because
operators
-
The
which
U(1)'
e and
6,
C,
in
additional
couplings
and
(F,O).
for
D’
unbroken
level).
under
fields
the
and
= (R,+l),
minimal
models
mechahism.16
an
superfields
Fayet-Iliopoulos
vanish.
G and
$t
6
+ MtB*i*>r*
auxiliary
all
and
of
Fayet-Iliopoulos
symmetry
K with
with
features
the
matter
(t-,0)
A..
ll(BC)r
is
to
$a
heavy
BY D-TERMS
general
due
gauge
charge)
terms
term
is
U(l)'
/
The
b
superfields
There
superfields
GREAKING
some
energy
with
representation,
the
scale
a lou
respectively.
IG
we consider
B
scalar
potential
v.e.v.
is
L = K = 0,
since
gauge
invariant.
operators
D'
invariance
Since
can
only
is
minimized
= -p2.
The
this
is
is
unbroken,
all
light
depend
gauge
undetermined
,
fields
on
the
are
field
-
31
-
strength
(8.3)
The
fields
light
gauge
6 and
?.
and matter
The
graph
fields
in
couple
Fig.
23
to
0'
only
through
the
heavy
induces
e2 e’2
(i;laa illa
4tl2
Inserting
(8.3)
this
renormaliiation,
(l.r/M14.
The
mass,
is
break
the
becomes
with
excluded
a supersymmetry
negligible
operator
Cfiaa
by
an
R invariance,
iida i?‘b),
k'o
fi'olr,
a two
loop
e2
gaugino
ef2
light
two
loops,
through
light
fields
to
5 is
unbroken
which,
additional
tnass
to
a gauge
fields
of
order
are
fermion
added
to
order
(8.5)
M"
produced.
The
matter
leads
function
of
p4
-
(4ll2)Z
at
wave
coefficient
which
If
R invariance.
_
be
violating
dimensionless
fiaa
g2
can
(8.4)
M'
matter
superfields
6 or
supersymmetry.
using
(5.31,
couple
gauge
bosons.
absent
Figure
becomes
to
in
this
24 gives
a light
scalar
the
supersymmetry
Direct
model,
rise
coupling
because
to
mass
breaking
the
of
of
it
operator
order
the
would
only
light
restore
e2
-
-
32 -
.
P4
-
e’2
The
masses
(8.5)
and
those
found
in
models
scale
b can
be
much
Other
the
but
this
are
operator,'which
of
is
if
(hat
gives
a Dirac
mixing
between
matter
and
spurion
analysis19
and
Grisaru,
whereas
Actually
dwarfs
all
if
other
scalar
shows
the
G has
two
a U(l)
effects.
a’
is
coefficient.
to
is
S.S.
M,
a large
than
breaking
fields
are
depend
on
(6.4)-(8.7).
a light
added
how
One
field
ca
in
to,break
this
is
interesting
the
adjoint
ia)F
the
light
gauge
and
gauge
auxiliary
that
it
pieces
is
soft
matter
the
DL are
there
is
graph
of
Fig.
et
er2
I-t2
fermions,
Power
fields.
in
XJ, and
factor,
and
one
25
sense
of
more
plus
counting
Girardello
separately
hard.
operator
which
gives
(B.9)
II
+
(5.8)
4Tr2
a Fayet-Iliopoulos
Such
if
coefficients
4Tf2
which
The
..
The
&IF
ing.
p and
=
mixing
mass,
given
models.
induced
there
tia"
break
those
comparable
(6’ Claa La)
It
in
The
for
smaller,
igh
be
model.
occur
G,
much
M than
can
generally
can
representation
to
breakings
of
they
are
O'Raifearta
closer
effective
R-symmetries
done,
(8.7)
with
(8.7)
t-l3
4Tr2
term
D term
for
for
the
low
ordinary
energy
U(l),
with
hypercharge
is
large
not
a
acceptab
e.
To make
semisimp
e group
a realistic
at
low
33 -
model
or
energy>
one
has
to
the
operator
exclude
imbed
hypercharge
(8.9)
in
by
a
a
symmetry.
The
small
size
invariance
forced
general
models
broken
at
symmetry
(B.4)-
the
be
large
broken
scale
mechanism
at
M.
M to
if
the
Is
it
break
a much
minimizes
the
about
operators
built
scale
at
vacuum
1 came
(8.7
effective
could
the
Iliopoulos
level
of
to
U(1)'
be
smaller
of
high
gauge
possible
the
UC1 1'
because
for
had
the
of
No,
D term
it
More
dimension.
invariance
supersymmetry
scale?
gauge
by
the
is
not.
been
a gauge
FayetThe
tree
energy
E
The
energy
extension
is
of
stationary
the
G9i
under
ga
Sa
Fi
in
all
variations,
including
the
complex
group,22
Tija
(without
9j
the
usual
i)
(5.111
which
E;a Db
where
(B.10)
CFi*Fi
under
gauge
=
=
(M2Jab
which
CM21
is
=
ga
=
_ (Mi!)ab + iga fabc
precisely
is
Tija
the
diagonal,
#+j
vector
GaE(fi,Db)
1
i,j
()a
boson
=
(8.12)
DC
mass
matrix.
Going
= 0 implies
Fi"
Tija
Fj
(8.13)
2ga
(Ma)2
to
a basis
-
Since
the
total
energy
density
is
34
-
O(ph),
F;
<<
!Az
(
~2,
and
for
heavy
gauge
fields
0”
w4
-
1
(6.14)
PlZ
and
the
S.S.
breaking
must
satisfies
our
intuition
including
the
auxiliary,
be
that
due
to
all
should
some
other
components
of
decouple
from
auxiliary
field.
a multiplet
of
the
physics
at
This
mass
M,
much
lower
scales.26
The
model
D term-of
pointed
with
The
exchange
F
,
l?=
in
this
11
broken
Ref.
11,
intermediate
models.
is
Ref.
a U(l)
out
an
of
most
of
not
at
high
a counterexample
energy
though,
v.e.v..
direct
a single
becomes
is
there
This
connection
heavy
a II term
for
gauge
the
is
has
to
a v.e.v.
is
also
an
interesting
between
boson.
heavy
of
order
an -auxiliary
RC and
Inserting
U(l),
There,
this.
1 TeV.
field,
variation
the
low
the
the
F
on
energy
v.e.v.
As
RC'
our
world
for
-
35
-
REFERENCES
ii
1.
H.
George,
H.
Quinn
and
S.
Weinberg,
Phys.
Rev.
Lett.
33,
II 19,
1277
451
(1974).
2.
L.
Susskind,
Phys.
Rev.
D 20,
2619
3.
S.
Weinberg,
Phys.
Rev.
D 13,
974
4.
E.
Witten,
5.
M.
Dine,
S.
Dimopoulos
Y.
A.
Gol'fand
Il.
V.
Volkov
J1
Wess
7.
E.
Witten,
8.
T.
Banks,
6.
Nucl.
W.
Tel-Aviv
Phys.
Fischler
and
and
S.
and
and
and
8.
E.
V.
Zumino,
private
Dine
and
10.
S.
Dimopouios
11.
R.
Barbieri,
12.
L.
Alvarez-Gaume,
(19761,
Srednicki,
Nucl.
Phys.
Likhtam,
JETP
Akulov,
Phys.
Nucl.
Nucl.
Phys.
m,
353
(19811.
Lett.
13,
323
Lett.
Phys.
preprint
(1978).
(1981).
870,
468,
39
8189,
109
Fischler,
and
S.
(1971).
(1973).
.
T,
Banks
and
V.
Kaplunovski
S.
Princeton
Raby,
Ferrara
M.
Los
and
Alamos
D.
Claudson
preprint
V.
and
(1982).
preprint
(1982).
Nanopoulos,
CERN preprint
N.
Harvard
B.
Wise,
(1981).
M.
Dine
and
14.
L.
O'Raifeartaigh,
15.
E.
Witten,
16.
P.
Fayet
W.
Fischler,
Nucl.
Phys.
and
(1981).
(1982).
W.
13.
575
(1974).
(19821.
communication.
preprint
M.
P.
P.
513
M.
Raby,
Princeton
9.
8185,
(1979).
J.
Lett.
Iliopoulos,
Princeton
Phys.
1058,
preprint
896,
271
Phys.
331
(1981).
(1975).
(1981).
Lett.
518,
461
(1974).
preprint
(1982).
17.
An excellent
theory
review
is
J.
Wess
Grisaru,
M.
of
36 -
super-fields
and
J.
and
Bagger,
superfield
Princeton
perturbation
University
preprint
(19811.
18.
M.
T.
19.
L.
Girardello
20.
J.
Polchinski
21.
P.
Ginsparg,
22.
B.
A.
23.
S.
Deser
24.
S.
Weinberg,
25.
P.
4.
26.
S,
Dimopoulos
Rocek
and
and
M.
Grisaru,
(in
preparation).
Harvard
Ovrut
and
and
Hung
B.
J.
preprint
Wess,
Zumino,
Phys.
and
T.
M.
and
W.
Rev.
Nucl.
Rev.
Phys.
Rev.
Lett.
48,
Georgi,
Nucl.
Phys.
m,
Phys.
8194,
65
429
(1982).
(1981).
Phys.
Suzuki,
H.
Siegel,
Berkeley
Nucl.
D 25,
Lett.
1303
409
38,
1433
(19771.
(1982)
preprint
Phys.
(1982).
(1982).
8193,
150
(19811.
(1979).
-
37 -
FIGURE
Fig.
1.
Renormalization
Fig.
2.
Graph
of
the
contributing
represents
Higgs
to
the
CAPTIONS
the
order
boson
mass
v2
splitting
Fig.
3.
Another
Fig.
4.
Supergraph
containing
Fig.
5.
Supergraph
inducing
Cc++ i
Fig.
6.
Supergraph
inducing
ti
i
i+
Fig.
7.
Supergraph
inducing
ti
i
2s)~.
Fig.
8.
Supergraph
inducing
ti*
i
Fig.
9.
-
Supergraph
inducing
ti
i*)o.
Fig.
10.
Supergraph
inducing
ti
2% i>o.
Fig.
11.
Supergraph
with
a light
internal
Fig.
12.
Two
Fig.
13.
Decomposition
graph
loop
a low
the
contribution
supergraph
energy
right,
Figs.
graph
2 and
heavy,
loop
the
mass
The
X
B multiplet.
of
the
L scalar.
3.
210.
21~.
._
line.
light
The
L scalar.
~X)D.
of
piece.
the
?*
the
of
to
with
of
of
mass.
internal
Fig.
12
heavy
at
circle
zero
Fig.
14.
Super-graph
with
intermediate
Fig.
15.
Supergraph
inducing
tC
i)~.
i
into
lines.
a high
represents
external
mass
The
energy
and
value
of
momentum.
lines
small
the
piece
which
are
circle
is
designated
the
mass
I.
term
pili.
Fig.
16.
Supergraph
inducing
ti
Fig.
17.
Supergraph
inducing
ti*
c 2% i()o
via
gauge
Fig.
18.
Supergraph
inducing
tka
CJa 21,.
This
is
Appendix
A.
2)~.
lines.
shown
to
vanish
in
Fig.
19.
Supergraphs
inducing
38 -
operators
(a)
The
operator
ti*
?)a.
(b)
The
operator
t?*
2 ?)a.
Cc)
The
operator
ti+
?*
Cd)
The
operator
C?*
2 f? 21,.
Fig.
20.
Supergraph
inducing
Cc*
Fig.
21.
Supergraph
inducing
Fig.
22.
Supergraph
Fig.
23.
Fig.
Fig.
involving
? only:
2 21,.
i
g*
210
via
heavy
gauge
bosons.
(hoa
Gsa
2)~
via
heavy
gauge
loop.
inducing
(i?oa
Ijoa
i)r
via
heavy
matter
Supergraph
inducing
(Gas
k’a
d&”
fir/3)a.
24.
Supergraph
inducing
CC*
i
25.
Supergraph
inducing
tka
i’a).
GJa
CJ’c
fi’,
61i)a.
loop.
H
5-
H
82
H
4317Al
Fig. 1
.
L
L
4317A2
5-w
Fig. 2
5-82
B
Fig. 3
4317A3
5-82
Fig. 4
h
h
5-82
4317AS
Fig. 5
L
5-82
4317A6
Fig. 6
.
4317A7
5-82
Fig. 7
4317A8
Fig. 8
5-82
3
Fig. 9
._
431749
I
.
,
t
5-82
4317AlO
Fig. 10
t
5-82
4317All
Fig. 11
t
t
4317A12
5-82
Fig. 12
L
L
B
B
L
B
-
B
L
L
B
B
I4
L
L
.
+
5-82
4317A13
Fig. 13
5-82
4317A14
Fig. 14
I
.-,
/
t
\
\
/
$
5-82
a
/
-
\
2
4317A15
Fig. 15
..
5-82
4317A16
Fig. 16
5-82
4317A17
Fig. 17
5-82
4317A18
Fig. 18
(a)
(b)
(cl
(d)
5-82
4317A19
Fig. 19
.
5-82
4317420
Fig. 20
5-82
4317A21
Fig. 21
4317A22
5-82
Fig. 22
5-82
4317A23
fig. 23
5-82
4317A24
Fig. 24
4317A25
5 -82
Fig. 25