Anomaly-mediated supersymmetry breaking demystified based on - - PowerPoint PPT Presentation

Anomaly-mediated supersymmetry breaking “demystified”

based
on
JHEP03(2009)123
(arXiv:0902.0464) Jae
Yong
Lee
(KIAS)

in
collaboration
with
Dong-Won
Jung
(NCU)

PHENO
2009
SYMPOSIUM

1

OUTLINE

Introduction Conformal
symmetry,
gravity
and
anomaly Superconformal
symmetry
and
anomaly
 Chiral
anomaly
supermultiplet
(CASM)
and
chiral
 compensator Anomaly-mediated
SUSY
breaking
in
MSSM Conclusion

2

Hidden Sector Visible Sector SUSY
breaking
by
(superconformal)
anomaly-mediation

SUSY

Randall,
Sundrum
(’98);
Giudice,
Luty,
Murayama,
Rattazzi
(’98)

Introduction


Chiral
compensator
χ in
Einstein
supergravity χ3 = 1 + θθm3/2 m3/2 : gravitino mass 
gaugino
mass,
sfermion
mass,
A-term
∝
 m3/2

3

Conformal
symmetry,
gravity,
and
anomaly

xm → e̺xm pm → e−̺pm

renormalization
scale
transforms
as


µ → e−̺µ.

conformal
(or
scale)
transformations


µ

4

⊃ ln µ2 → ln µ2 − 2̺

The
ρ
is

• a
real
parameter
for
shifting
the
scale.
• the
Nambu-Goldstone
Boson
(NGB),
if
conformal


symmetry
is
“spontaneously”
broken.

• contained
in
Einstein
gravity
where
the
matter


Lagrangian
couples
to
the
integral
measure
√g
with
 ρ=ln√g.

• brought
in
at
loops
along
with
the
renormalization


scale
μ
in
quantum
theory.

5

⊃ ln µ2 → ln µ2 − 2̺

The
ρ
is

• a
real
parameter
for
shifting
the
scale.
• the
Nambu-Goldstone
Boson
(NGB),
if
conformal


symmetry
is
“spontaneously”
broken.

• contained
in
Einstein
gravity
where
the
matter


Lagrangian
couples
to
the
integral
measure
√g
with
 ρ=ln√g.

• brought
in
at
loops
along
with
the
renormalization


scale
μ
in
quantum
theory.

the
dilaton.

6

coupling
of
dilaton
to
conformal
anomaly

Seff =

• d4x̺ T m

m ,

T m

m

= βQCD(g) 2g F a

nlF anl

Example:
massless
QCD
theory Trace
(or
conformal)
anomaly Fugikawa’s
path-integral
method Feynman
diagrams
with
background
field
method Coupling See
Peskin’s
QFT
book

7

coupling
of
dilaton
to
conformal
anomaly

Seff =

• d4x̺ T m

m ,

T m

m

= βQCD(g) 2g F a

nlF anl

Example:
massless
QCD
theory Trace
(or
conformal)
anomaly Fugikawa’s
path-integral
method Feynman
diagrams
with
background
field
method Coupling See
Peskin’s
QFT
book

ZgZ1/2

A

= 1

8

coupling
of
dilaton
to
conformal
anomaly

Seff =

• d4x̺ T m

m ,

T m

m

= βQCD(g) 2g F a

nlF anl

Example:
massless
QCD
theory Trace
(or
conformal)
anomaly Fugikawa’s
path-integral
method Feynman
diagrams
with
background
field
method Coupling See
Peskin’s
QFT
book

ln µ2 → ln µ2 − 2̺

ZgZ1/2

A

= 1

9

Superconformal
symmetry
and
anomaly

Supersymmetry Conformal
symmetry

10

Hm(x, θ, ¯ θ) = θσa¯ θem

a (x) + i

2 ¯ θ¯ θθψm(x) − i 2θθ¯ θ ¯ ψm(x) + 1 4θθ¯ θ¯ θˆ νm(x) ˆ νm ψm

α

em

a

U(1)_R
gauge gravitino vierbein 3=4-1 8=16-4-4 5=16-6-4-1

jR

m

Sm

α

T m

n

∂mjR

m = 0

γmSm

α = 0

T m

m = 0

R-current SUSY
current Energy-momentum
 tensor

Conformal
supergravity (Matter)
Supercurrent

11

Hm(x, θ, ¯ θ) = θσa¯ θem

a (x) + i

2 ¯ θ¯ θθψm(x) − i 2θθ¯ θ ¯ ψm(x) + 1 4θθ¯ θ¯ θˆ νm(x) ˆ νm ψm

α

em

a

U(1)_R
gauge gravitino vierbein 3=4-1 8=16-4-4 5=16-6-4-1

jR

m

Sm

α

T m

n

∂mjR

m = 0

γmSm

α = 0

T m

m = 0

R-current SUSY
current Energy-momentum
 tensor

Conformal
supergravity (Matter)
Supercurrent

12

dilaton dilatino conformal
anomaly SUSY
anomaly more? more? chiral chiral vector current

MATTER GRAVITY

Gravity
and
Matter
Anomaly

13

˚ r ≡ ∂mjR

m

ξα ≡ γmSm

α

˚ t ≡ T m

m

1 4 1

a, b

2 Suppose
that
all
the
three
symmetries
are
“anomalous”.

X(x, θ) ≡ A(x) + √ 2θξ(x) + θθF(x), ¯ DX = 0 A = a + ib F = ˚ t + i˚ r

Chiral
anomaly
supermultiplet
(CASM)

Chiral
anomaly
supermultiplet
and
chiral
compensator

14

˚ r ≡ ∂mjR

m

ξα ≡ γmSm

α

˚ t ≡ T m

m

1 4 1

a, b

2 Suppose
that
all
the
three
symmetries
are
“anomalous”.

ˆ νm ψm

α

em

a

U(1)_R
gauge gravitino vierbein 3=4-1 8=16-4-4 5=16-6-4-1

X(x, θ) ≡ A(x) + √ 2θξ(x) + θθF(x), ¯ DX = 0 A = a + ib F = ˚ t + i˚ r χ3(x, θ) ≡ e2̺(x)+2iδ(x)[1 + √ 2θ ¯ Ψ(x) + θθM ∗(x)] M ∗

2

¯ Ψα ∼ σα ˙

α m ¯

ψm

˙ α (Nambu-Goldstino = dilatino)

Chiral
anomaly
supermultiplet
(CASM)

C h i r a l 
 c

• m

p e n s a t

• r

Chiral
anomaly
supermultiplet
and
chiral
compensator

15

˚ r ≡ ∂mjR

m

ξα ≡ γmSm

α

˚ t ≡ T m

m

1 4 1

a, b

2 Suppose
that
all
the
three
symmetries
are
“anomalous”.

ˆ νm ψm

α

em

a

U(1)_R
gauge gravitino vierbein 3=4-1 8=16-4-4 5=16-6-4-1

X(x, θ) ≡ A(x) + √ 2θξ(x) + θθF(x), ¯ DX = 0 A = a + ib F = ˚ t + i˚ r χ3(x, θ) ≡ e2̺(x)+2iδ(x)[1 + √ 2θ ¯ Ψ(x) + θθM ∗(x)] M ∗

2

¯ Ψα ∼ σα ˙

α m ¯

ψm

˙ α (Nambu-Goldstino = dilatino)

Chiral
anomaly
supermultiplet
(CASM)

C h i r a l 
 c

• m

p e n s a t

• r

Chiral
anomaly
supermultiplet
and
chiral
compensator

16

Coupling
of
the
CASM
to
the
chiral
compensator SX =

• d4x d2θ χ3(x, θ)X(x, θ) + h.c.

SX =

• d4x [e2̺+2iδ(M ∗A + ¯

Ψξ + F) + h.c.]

in
components, conformal
anomaly gaugino
mass
term

M ∗ = m3/2, A = the lowest comp. of CASM M ∗A ⇒ m3/2λaλa

soft
susy
breaking
terms

X = W a

αW aα ⇒ A| = λaλa

for
example,

17

S =

• d4x d2θd2¯

θ φi

+e2gV φi

+ d4x d2θ 1 4 W aαW a

α + 1

3! yijk φiφjφk

• + h.c.
• X

1 4W aαW a

α

β(g) 2g W aαW a

α

Mλ = β(g) g m3/2 1 3! yijk φiφjφk − 1 3! (γi + γj + γk) yijkφiφjφk Aijk = −(γi + γj + γk)yijkm3/2

interaction soft
term CASM (Simplified
MSSM
action)

Anomaly-mediated
SUSY
breaking
in
MSSM

18

X 1 4W aαW a

α

β(g) 2g W aαW a

α

Mλ = β(g) g m3/2 1 3! yijk φiφjφk − 1 3! (γi + γj + γk) yijkφiφjφk Aijk = −(γi + γj + γk)yijkm3/2

interaction soft
term

S =

• d4x d2θd2¯

θ φi

+e2gV φi

+ d4x d2θ 1 4 W aαW a

α + 1

3! yijk φiφjφk

• + h.c.
• CASM

(Simplified
MSSM
action)

β-function γ-function

β(g) = − g3 16π2 [3CA(adj.) −

• i

TA(φi)]

Anomaly-mediated
SUSY
breaking
in
MSSM

γj

i = −

1 32π2 [y∗

iklyjkl − 4g2δj i CA(φi)]

19

Supergraphs
:
(a)
vector,
(b)
ghost,
(c)
chiral
one-loop
contribution to
the
vector
superpropagator.

ln µ2 → ln µ2 − 2̺

20

Supergraphs
:
(a)
vector,
(b)
ghost,
(c)
chiral
one-loop
contribution to
the
vector
superpropagator.

ln µ2 → ln µ2 − 2̺

β-function

β(g) = − g3 16π2 [3CA(adj.) −

• i

TA(φi)]

Mλ = β(g) g m3/2

ZgZ1/2

V

= 1

21

Supergraphs
:
one-loop
contribution
to
the
Yukawa
term.

ln µ2 → ln µ2 − 2̺

22

Supergraphs
:
one-loop
contribution
to
the
Yukawa
term.

ln µ2 → ln µ2 − 2̺

ϒ-function

γj

i = −

1 32π2 [y∗

iklyjkl − 4g2δj i CA(φi)]

Aijk = −(γi + γj + γk)yijkm3/2

23

Supergraphs
:
these
one-loops
do
NOT
contribute
to
the
Yukawa
term.

Due
to
the
non-renormalization
theorems

24

We
have
reviewed
SUSY
breaking
of
anomaly
mediation
from
a
field- theoretical
perspective,
using
superspace
perturbation
theory
and
 supergraphs. This
approach
is
physically
more
understandable
in
comparison
with
 the
conventional
spurion
technique. We
can
even
adopt
this
scheme
to
study
the
connection
between
the
 hidden
sector
and
Einstein
supergravity. We
can/may
systematically
study
various
SUSY
breaking
mediation
 scenarios
at
once
using
this
scheme.
(i.e.
GMSB+AMSB)

Conclusion

25

• The
End
-

Thanks
for
listening!

26