Deflected Mirage Mediation

Transcription

1 Deflected Mirage Mediation A Framework for Generalized SUSY Breaking Based on PRL101:101803(2008) (arxiv: ), JHEP 0808:102(2008) (arxiv: ) in collaboration with L.Everett, P.Ouyang and K. Zurek Ian-Woo Kim University of Wisconsin-Madison Johns Hopkins University, Nov 18, 2008

2 Outline Introduction Moduli stabilization and Mixed mediation Soft terms in Deflected Mirage Mediation Superparticle spectrum and phenomenology Conclusion

3 Introduction At LHC, first collision will be within a year finally! We may discover SUSY particles and measure their masses.

4 Paradigm of SUSY Observable sector Hidden Sector SUSY Messengers of SUSY may have information on high-scale dynamics.

5 Different mediation mechanisms lead to different soft mass pattern: Gravity Mediation Gauge Mediation Anomaly Mediation m soft ¼ g2 F m soft ¼ m 3=2 ¼ F M 16¼ 2 P M mess m soft ¼ g2 À m 3=2 ¼ F 16¼ 2 m 3=2 M P m 3=2 m soft m 3=2 m soft m soft m 3=2 Tree level One loop level One loop level

6 Take recent lesson from top-down approach! Different kinds of SUSY can be comparable with each other when considering stabilization of moduli in hidden sector! AMSB GrMSB moduli Mixed Modulus-Anomaly Mediation (Mirage Mediation)

7 Consider stabilization of gauge mediation moduli X: Comparable Anomaly/Gauge/Gravity Mediation Deflected Mirage Mediation Gravity Mediation Moduli Gauge Mediation Moduli

8 Mirage Mirage Mediation Mediation GrMSB AMSB Deflected Mirage Mediation Deflected Deflected Anomaly Anomaly Mediation Mediation GMSB Relative ratios of each contribution in soft masses shows the information of stabilization.

9 Moduli stabilization and Mixed mediation KKLT Setup : Kachru, Kallosh, Linde, Trivedi (2003) Superpotential : Flux + Nonperturbative W = w 0 Ae at Stabilize moduli T to SUSY AdS vacuum

10 T SUSY AdS vacuum m 3=2 = w 0 (2T ) 3=2

11 W = w 0 Ae at EW scale SUSY requires w 0» at» log(m P =m 3=2 ) T SUSY AdS vacuum m 3=2 = w 0 (2T ) 3=2

12 W = w 0 Ae at EW scale SUSY requires w 0» at» log(m P =m 3=2 ) (m T ) W T SUSY AdS vacuum m 3=2 = w 0 (2T ) 2» (at )2 m 2 3=2

13 Anti-D brane : source for SUSY Uplifting scalar potential V» D (T + ¹T ) 2+n Cancel cosmological constant

14 Shift in T T inversely proportional to m T F T T + ¹T» m 3=2 at» 1 log(m P =m 3=2 ) F C C Uplifting potential (m T ) W T SUSY AdS vacuum m 3=2 = w 0 (2T ) 2» (at )2 m 2 3=2

15 Anomaly mediation and moduli mediation are comparable. F T T + ¹T» m 3=2 at» 1 log(m P =m 3=2 ) F C C Mirage Mediation K.Choi, Nilles, Olechowski, Porkorski (2004,2005) K.Choi, K.S.Jeong, Okumura (2005) Endo, Yamaguchi, Yoshioka (2005)

16 stabilized T W ht i Moduli T Sequestered SUSY naturally m 3=2» e aht i cosmological constant =0 m T» log(m P =m 3=2 )m 3=2 F T M P» m2 3=2 m T» m 3=2 log(m P =m 3=2 )

17 Matter Moduli Stabilization and Gauge Mediation In most of string compactification, L.Everett, IWK, P. Ouyang and K. Zurek (2008) 1. Vector-like pairs charged under SM gauge symmetry. (ª; ª) 2. mass for such vector-like pairs obtained by matter moduli X. W = Xªª 3. X is stabilized due to SUSY. Anomaly Mediation distributes SUSY to Gauge Mediation.

18 What happens if condition 3 is not satisfied? X is stabilized by supersymmetric mechanism at high scale. F-term stabilization : W = 1 2 m X(X X 0 ) 2 B-term like soft term due to Anomaly Mediation V» m 3=2 m X (X X 0 ) 2 If, no additional SUSY m X À m 3=2

19 D-term stabilization: Fayet-Illiopoulos term ( gauged U(1) R symmetry or anomalous U(1) ) U(1) A scale: O µ Mst 16¼ 2 À m 3=2 Moduli dependent FI term. Shift in T induces SUSY to F X However, F X X = O µ F T No dominant SUSY contribution. by Green-Schwarz mechanism T + ¹ T K.Choi, K.S.Jeong (2006)

20 X stabilization by SUSY breaking F X is given (roughly) by F X = e K=2 K X ¹X D ¹ X ¹W = e K=2 K X ¹ X ¹W {z } (A) e K=2 K X ¹X K ¹ X ¹W {z } (B) (A) is from global SUSY. (B) is SUGRA correction. Because anomaly mediation dominates, (B) becomes important.

21 Radiative Stabilization X is stabilized purely by SUSY terms. m 2 Coleman-Weinberg mechanism X W K ¹ X W Since (B) = e K=2 K X ¹X K ¹ X ¹W ¼ m 3=2 X F X X = m 3=2 + O µ m3=2 8¼ 2 ; F T T + ¹T

22 Higher-order stabilization X is stabilized due to superpotential term W = Xn n 3 and SUSY masses, X W» K X W (A) ~ (B). F X X» m 3=2 M 1=2» 4¼ m 2 0» µ 4¼ F X X F X 2 X

23 More precisely, we need to consider the effect of modulus T. Z Z L = d 4 µg + d 2 µw + h:c: G = 3C ¹ Ce K=3 = pc ¹ C(T + ¹ T ) + (T + ¹ T ) 1 n X C ¹ CX ¹ X W = C 3 W 0 (T ) + C 3 Xn n 3 Consider mixing terms between C, T and X F X = G X ¹ C W G X ¹ T W G X ¹ X W Keeping only the leading order terms V» O(X 2n 2 ) + O(m 3=2 X n ) + O(m 2 3=2 X2 )

24 We obtain F X X = 2 n 1 F C C independent of T! n 3 (higher order term) n < 0 (nonperturbative) m 3=2 F X X 2m 3=2 Ratios among anomaly mediation, moduli mediation and gauge mediation contributions are determined by discrete parameters.

25 Soft terms in Deflected Mirage Mediation We parameterize SUSY by (m 0 ; m ; g ) F T T + ¹T = m 0 F C C = m 3=2 = m log(m P =m 3=2 )m 0 F X X = g F C C L.Everett, IWK, P.Ouyang, K. Zurek (2008) We also have tan and M mess hxi Discrete parameters: Modular weights of (Q,U,D,L,E,Hu,Hd) Number of messenger pairs: N

26 This scenario has two threshold scales : M G and M mess MSSM MSSM+ (ª; ª) scale M EW M mess = hxi M G Soft terms (detailed derivation in arxiv: ) Gaugino mass: M a (M G ) = F T T + T + G 4¼ b0 a M a (M mess ) = N a(m mess ) 4¼ F C C µ F C C + F X X

27 A term: A ijk = A i + A j + A k A i (M G ) = (p n i ) F T T + T A i (M mess ) = 0 i F C 16¼ 2 C Soft scalar mass-squared: m 2 i (M G ) = (p=3 n i ) F T 2 T + ¹T Ã! µ0 i F T C F ¹ 32¼ 2 T + ¹T ¹C + h:c: m 2 i (M mess ) = X a 2c a N 2 a(m mess ) 16¼ 2 _ 0 i (16¼ 2 ) 2 F X X + F C C 2 F C C 2

28 M a (M G ) = m g2 0 16¼ 2 b0 a m log M P m 3=2 M a = m 0 N g2 a(m mess ) 16¼ 2 m (1 + g ) log M P A i (M G ) = m 0 (1 n i ) i 16¼ 2 m log M P m 3=2 m 2 i (M G ) = m 2 0 m 2 i = m 2 0 " (1 n i ) µ0 i 16¼ 2 m log M P m 3=2 X 2c a N g4 a(m mess ) (16¼ 2 ) 2 a m 3=2 _ 0 i (16¼ 2 ) 2 m (1 + g ) log M P m 3=2 µ m log M P 2 m 3=2 2 # where µ i = 4 X a g 2 ac a ( i ) X lm jy ilm j 2 (p n i n l n m )

29 Superparticle spectrum and phenomenology Mirage Unification in Mirage Mediation K.Choi, K.S.Jeong, Okumura (2005) Mirage scale: M mirage = M G µ m3=2 M P m =2

30 Deflected Mirage Mediation changes the mirage pattern. L.Everett, IWK, P.Ouyang, K. Zurek (2008) M mirage = M GUT µ m3=2 M P m ½=2 ½ = 1 + 2Ng ¼ 2 1 m g Ng ¼ 2 log M GUT M mess log M P m 3=2

31 Mirage unification of gaugino masses leads to Light gluino (can be even the lightest.) Sizable mixing between bino and wino Well-tempered neutralino Relatively less severe fine-tuning due to light gluino, negative stop mass square and large A-term. But gauge mediation contribution does not help reducing fine-tuning.

32 RG evolution pattern Coleman-Weinberg stabilization (W=0)

33 Stabilization by nonrenormalizable op. W (X) = X4 M P

34 Stabilization by nonpertubative potential W (X) = 4 X» 10 7 GeV

35 Sparticle Spectrum and neutralino relic density work in progress, L.Everett, IWK, K.Zurek m 0 = 1 TeV; N = 1; g = 0:5

36 m 0 = 1 TeV; N = 3; g = 0:5

37 Conclusion In the top-down approach, considering moduli stabilization can lead to mixed SUSY breaking scenarios. Relative ratios of SUSY terms can encode information regarding high scale dynamics. Deflected Mirage Mediation: a generalized framework for mixed SUSY scenarios which includes the three standard mechanisms of anomaly mediation, gauge mediation, gravity/modulus mediation. Mirage unification of gaugino masses remains, but generically at a deflected scale. Patterns of soft terms at low energy distinctive, and should be testable at LHC

38 ¹=B¹ Problem and Axionic Mirage mediation ¹=B¹ Z d 4 µc ¹ C(H u ¹ Hu + H d ¹ Hd ) + Nakamura, Okumura, Yamaguchi (2008) For Problem, perhaps hint at the fact that we are exploring this idea in context of full deflected mirage mediation framework. ½Z ¾ d 2 µc 3 ¹H u H d + h:c: ¹=B¹ problem : When anomaly mediation dominates B» F C C» O m 3=2 Must forbid tree-level mass term PQ symmetry Use matter moduli X as a PQ symmetry breaking field.

39 Model H u H d X Y T PQ Charge W = y 1 T H u H d + y 2 XY T 3 exp( K=3) = jxj 2 + jy j 2 + jt j 2 + XY + h:c: Stabilize X by Coleman-Weinberg mechanism : hxi intermediate PQ scale Y and T get massive. Integrate out T Y ¼ y 1 H u H d y 2 X F X X ¼ F C C

40 Generate ¹ term and B term» µ F C C + F X X L = y1 y 2 Z d 4 µ CX CX (CH u)(ch d ) F C C + F X X ¼ O µ F T T + ¹T ¼ m 2 3=2