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

Introduction SUSY Hidden Sector Visible Sector SUSY 
 breaking 
 by 
 (superconformal) 
 anomaly-mediation Randall, 
 Sundrum 
 ( ’ 98); 
 Giudice, 
 Luty, 
 Murayama, 
 Rattazzi 
 ( ’ 98) 
 Chiral 
 compensator 
 χ in 
 Einstein 
 supergravity � χ 3 � = 1 + θθ m 3 / 2 m 3 / 2 : gravitino mass 
 gaugino 
 mass, 
 sfermion 
 mass, 
 A-term 
 ∝ 
 m 3 / 2 3

Conformal 
 symmetry, 
 gravity, 
 and 
 anomaly renormalization 
 scale 
 transforms 
 as 
 conformal 
 (or 
 scale) 
 transformations 
 x m e ̺ x m µ → e − ̺ µ. → p m e − ̺ p m → µ 4

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. ⊃ ln µ 2 → ln µ 2 − 2 ̺ 5

The 
ρ
 is the 
 dilaton. • 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. ⊃ ln µ 2 → ln µ 2 − 2 ̺ 6

coupling 
 of 
 dilaton 
 to 
 conformal 
 anomaly Example: 
 massless 
 QCD 
 theory � d 4 x ̺ T m = S e ff m , Coupling β QCD ( g ) T m F a nl F anl = Trace 
 (or 
 conformal) 
 anomaly m 2 g Fugikawa ’ s 
 path-integral 
 method Feynman 
 diagrams 
 with 
 background 
 field 
 method See 
 Peskin ’ s 
 QFT 
 book 7

coupling 
 of 
 dilaton 
 to 
 conformal 
 anomaly Example: 
 massless 
 QCD 
 theory � d 4 x ̺ T m = S e ff m , Coupling β QCD ( g ) T m F a nl F anl = Trace 
 (or 
 conformal) 
 anomaly m 2 g Fugikawa ’ s 
 path-integral 
 method Z g Z 1 / 2 = 1 Feynman 
 diagrams 
 with 
 background 
 field 
 method A See 
 Peskin ’ s 
 QFT 
 book 8

coupling 
 of 
 dilaton 
 to 
 conformal 
 anomaly Example: 
 massless 
 QCD 
 theory � d 4 x ̺ T m = S e ff m , Coupling β QCD ( g ) T m F a nl F anl = Trace 
 (or 
 conformal) 
 anomaly m 2 g Fugikawa ’ s 
 path-integral 
 method Z g Z 1 / 2 = 1 Feynman 
 diagrams 
 with 
 background 
 field 
 method A See 
 Peskin ’ s 
 QFT 
 book ln µ 2 → ln µ 2 − 2 ̺ 9

Superconformal 
 symmetry 
 and 
 anomaly Supersymmetry Conformal 
 symmetry 10

Conformal 
 supergravity ψ m ( x ) + 1 a ( x ) + i θθψ m ( x ) − i H m ( x, θ , ¯ θ ) = θσ a ¯ θ ¯ ¯ 2 θθ ¯ θ ¯ 4 θθ ¯ θ ¯ θ ˆ ν m ( x ) θ e m 2 U(1)_R 
 gauge gravitino vierbein ψ m e m ν m ˆ α a 3=4-1 8=16-4-4 5=16-6-4-1 (Matter) 
 Supercurrent Energy-momentum 
 R-current SUSY 
 current tensor j R S m T m m α n ∂ m j R γ m S m T m α = 0 m = 0 m = 0 11

Conformal 
 supergravity ψ m ( x ) + 1 a ( x ) + i θθψ m ( x ) − i H m ( x, θ , ¯ θ ) = θσ a ¯ θ ¯ ¯ 2 θθ ¯ θ ¯ 4 θθ ¯ θ ¯ θ ˆ ν m ( x ) θ e m 2 U(1)_R 
 gauge gravitino vierbein ψ m e m ν m ˆ α a 3=4-1 8=16-4-4 5=16-6-4-1 (Matter) 
 Supercurrent Energy-momentum 
 R-current SUSY 
 current tensor j R S m T m m α n ∂ m j R γ m S m T m α = 0 m = 0 m = 0 12

Gravity 
 and 
 Matter 
 Anomaly GRAVITY MATTER dilaton conformal 
 anomaly SUSY 
 anomaly dilatino more? more? chiral chiral vector current 13

Chiral 
 anomaly 
 supermultiplet 
 and 
 chiral 
 compensator Suppose 
 that 
 all 
 the 
 three 
 symmetries 
 are 
“ anomalous ” . r ≡ ∂ m j R ˚ a, b ξ α ≡ γ m S m t ≡ T m ˚ m α m 2 1 4 1 √ ¯ X ( x, θ ) A ( x ) + 2 θξ ( x ) + θθ F ( x ) , Chiral 
 anomaly 
 supermultiplet 
 (CASM) D X = 0 ≡ = a + ib A ˚ = t + i ˚ F r 14

Chiral 
 anomaly 
 supermultiplet 
 and 
 chiral 
 compensator Suppose 
 that 
 all 
 the 
 three 
 symmetries 
 are 
“ anomalous ” . r ≡ ∂ m j R ˚ a, b ξ α ≡ γ m S m t ≡ T m ˚ m α m 2 1 4 1 √ ¯ X ( x, θ ) A ( x ) + 2 θξ ( x ) + θθ F ( x ) , Chiral 
 anomaly 
 supermultiplet 
 (CASM) D X = 0 ≡ = a + ib A ˚ = t + i ˚ F r U(1)_R 
 gauge gravitino vierbein ψ m e m M ∗ ν m ˆ α a 2 3=4-1 8=16-4-4 5=16-6-4-1 √ r o 2 θ ¯ t χ 3 ( x, θ ) ≡ e 2 ̺ ( x )+2 i δ ( x ) [1 + a s Ψ ( x ) + θθ M ∗ ( x )] n e p m o c 
 l a r i h C Ψ α ∼ σ α ˙ m ¯ α (Nambu-Goldstino = dilatino) ¯ α ψ m ˙ 15

Chiral 
 anomaly 
 supermultiplet 
 and 
 chiral 
 compensator Suppose 
 that 
 all 
 the 
 three 
 symmetries 
 are 
“ anomalous ” . r ≡ ∂ m j R ˚ a, b ξ α ≡ γ m S m t ≡ T m ˚ m α m 2 1 4 1 √ ¯ X ( x, θ ) A ( x ) + 2 θξ ( x ) + θθ F ( x ) , Chiral 
 anomaly 
 supermultiplet 
 (CASM) D X = 0 ≡ = a + ib A ˚ = t + i ˚ F r U(1)_R 
 gauge gravitino vierbein ψ m e m M ∗ ν m ˆ α a 2 3=4-1 8=16-4-4 5=16-6-4-1 √ r o 2 θ ¯ t χ 3 ( x, θ ) ≡ e 2 ̺ ( x )+2 i δ ( x ) [1 + a s Ψ ( x ) + θθ M ∗ ( x )] n e p m o c 
 l a r i h C Ψ α ∼ σ α ˙ m ¯ α (Nambu-Goldstino = dilatino) ¯ α ψ m ˙ 16

Coupling 
 of 
 the 
 CASM 
 to 
 the 
 chiral 
 compensator � d 4 x d 2 θ χ 3 ( x, θ ) X ( x, θ ) + h.c. S X = � d 4 x [ e 2 ̺ +2 i δ ( M ∗ A + ¯ in 
 components, S X = Ψ ξ + F ) + h.c. ] soft 
 susy 
 breaking 
 terms conformal 
 anomaly � M ∗ � = m 3 / 2 , A = the lowest comp. of CASM α W a α ⇒ A| = λ a λ a X = W a for 
 example, gaugino 
 mass 
 term M ∗ A ⇒ m 3 / 2 λ a λ a 17

Anomaly-mediated 
 SUSY 
 breaking 
 in 
 MSSM � + e 2 gV φ i d 4 x d 2 θ d 2 ¯ = S θ φ i � � � (Simplified 
 MSSM 
 action) � 1 � α + 1 3! y ijk φ i φ j φ k d 4 x d 2 θ 4 W a α W a + + h.c. interaction CASM soft 
 term X β ( g ) M λ = β ( g ) 1 2 g W a α W a m 3 / 2 4 W a α W a α g α A ijk = − 1 1 3! y ijk φ i φ j φ k 3! ( γ i + γ j + γ k ) y ijk φ i φ j φ k − ( γ i + γ j + γ k ) y ijk m 3 / 2 18

Anomaly-mediated 
 SUSY 
 breaking 
 in 
 MSSM � + e 2 gV φ i d 4 x d 2 θ d 2 ¯ = S θ φ i � � � (Simplified 
 MSSM 
 action) � 1 � α + 1 3! y ijk φ i φ j φ k d 4 x d 2 θ 4 W a α W a + + h.c. β - function CASM interaction soft 
 term X β ( g ) M λ = β ( g ) 1 2 g W a α W a m 3 / 2 4 W a α W a γ - function α g α A ijk = − 1 1 3! y ijk φ i φ j φ k 3! ( γ i + γ j + γ k ) y ijk φ i φ j φ k − ( γ i + γ j + γ k ) y ijk m 3 / 2 β ( g ) = − g 3 � 16 π 2 [3 C A (adj . ) − T A ( φ i )] i 1 γ j ikl y jkl − 4 g 2 δ j i = − 32 π 2 [ y ∗ i C A ( φ i )] 19

ln µ 2 → ln µ 2 − 2 ̺ Supergraphs 
 : 
 (a) 
 vector, 
 (b) 
 ghost, 
 (c) 
 chiral 
 one-loop 
 contribution to 
 the 
 vector 
 superpropagator. 20

ln µ 2 → ln µ 2 − 2 ̺ β - function Supergraphs 
 : 
 (a) 
 vector, 
 (b) 
 ghost, 
 (c) 
 chiral 
 one-loop 
 contribution to 
 the 
 vector 
 superpropagator. Z g Z 1 / 2 = 1 V β ( g ) = − g 3 � 16 π 2 [3 C A (adj . ) − T A ( φ i )] i M λ = β ( g ) m 3 / 2 g 21

ln µ 2 → ln µ 2 − 2 ̺ Supergraphs 
 : 
 one-loop 
 contribution 
 to 
 the 
 Yukawa 
 term. 22

ln µ 2 → ln µ 2 − 2 ̺ ϒ - function Supergraphs 
 : 
 one-loop 
 contribution 
 to 
 the 
 Yukawa 
 term. 1 γ j ikl y jkl − 4 g 2 δ j i = − 32 π 2 [ y ∗ i C A ( φ i )] A ijk = − ( γ i + γ j + γ k ) y ijk m 3 / 2 23

Supergraphs 
 : 
 these 
 one-loops 
 do 
 NOT 
 contribute 
 to 
 the 
 Yukawa 
 term. Due 
 to 
 the 
 non-renormalization 
 theorems 24