Mirage Mediation of SUSY Breaking K. S. Jeong KIAS 25 May, 2007 Based on hep-ph/ , hep-ph/

1.1 Supersymmetry  Supersymmetry  Low energy SUSY is a promising candidate for physics beyond the SM. Solution to the hierachy problem : SUSY stabilizes the weak scale by cancelling large quantum corrections to the Higgs mass. Consistency with Grand Unification : The MSSM leads to gauge coupling unification. Radiative EWSB : Negative Higgs mass square is induced by the quantum correction from the top quark Yukawa coupling. Good dark matter candidate : Neutral LSP in models with R-parity  SUSY breaking Superpartners of ordinary particles have not been observed yet. Transmission of SUSY breaking to the visible superparticles → Soft terms : Insensitive to heavy thresholds (no quadratic divergences) FermionBoson

1.2 Supergravity  Supergravity (local supersymmetry) Effective low energy theory including gravity Gravity is so weak : For the study of SUSY breaking, we can replace the SUGRA multiplet by their VEVs (nearly flat dS vacuum ) except for its scalar auxiliary component. In the flat spacetime background, the effective action for supergraviy coupled to matter in which all SUGRA effects on SUSY breaking are contained. W, f a : Holomorphic functions of chiral superfields Chiral compensator C for the super-Weyl invariance Auxiliary component of the SUGRA multiplet is encoded in F C.

1.2 Supergravity In the Einstein frame (the gravity kinetic term is canonical)  Scalar potential Cosmological observations : small positive vacuum energy density SUSY breaking : Gravitino absorbs the (massless) Goldstino.  Auxiliary F-components  SUSY preserving extremum Supersymmetric field configuration is a solution of equations of motion. AdS vacuum

1.3 Mediation of SUSY Breaking  Anomaly mediation (F C ) Loop induced soft terms : SUSY breaking is transmitted through the super conformal anomaly. → Always present in supergravity In the matter wave functions and gauge couplings, the renormalization scale should appear in combination due to the super-Weyl invariance. UV-insensitive : soft masses are only functions of low energy gauge and Yukawa couplings. (insensitive to high energy flavor violating effects) → No dangerous flavor violating phases  Tachyons in pure anomaly mediation Negative slepton mass squares (SU(2) L, U(1) Y : IR free in the MSSM)

1.3 Mediation of SUSY Breaking  Gravity mediation Planck scale suppressed interactions between hidden and visible sectors → Induced by Planck scale physics (e.g. string mode exchanges) Soft scalar mass : Gaugino mass :  SUSY flavor problem Need to explain why κ ij are flavor-blind Visible sector Hidden sector X

 Gauge mediation Secluded sector (X : SUSY breaking) + Messenger sector (SM-gauge charged messengers) Non-supersymmetric threshold : Nontrivial X-dependence of the matter wave functions and gauge kinetic functions is determined by the matching conditions. → Soft terms are radiatively generated by the exchange of messengers. Flavor conservation : Soft masses depend only on the gauge quantum numbers.  The gravitino is generically the LSP. 1.3 Mediation of SUSY Breaking Visible sector Secluded sector X

1.3 Mediation of SUSY Breaking  Mirage Mediation Anomaly mediation gives comparable contribution to soft terms as other (gravity or gauge) mediation. Mirage messenger scale (not a physical threshold) : fine-cancellation between the RG evolution of soft parameters and anomaly mediated contribution. Gauge coupling unification leads to the phenomenon of mirage unification of gaugino masses at the mirage messenger scale. Phenomenological consequences are somewhat sensitive to the ratio of anomaly to other mediation.  Mirage mediation is naturally realized in the KKLT-type string compactification. Anomaly Mediation RG evolved part

2.1 Low Energy Effective Theory form Strings  String theory compactification → Moduli Dilaton (S) : string coupling constant Kaehler (T) and complex structure moduli (U) : the size and shape of extra 6 dimenstions  String-inspired 4D N=1 Supergravity Supersymmetry is an essential ingredient in most string constructions.  Moduli Natural candidates for SUSY breaking messengers → Moduli mediation (Class of the gravity mediation) Flat directions : moduli describe the continuous degeneracy of string vacua at the leading order approximation. → Stabilization of moduli

2.2 KKLT Scenario dS vacua in string theory : Kachru, Kallosh, Linde, Trivedi PRD 68,  Moduli stabilization by Fluxes and NP effects Fluxes fix dilaton and complex structure moduli, which acquire a large supersymmetric mass. Kaehler moduli are stabilized by non-perturbative effects such as brane instantons or gaugino condensation at a supersymmetric AdS minimum.  Nearly flat dS vacuum Uplifting scalar potential provided by SUSY breaking branes → The negative vacuum energy density V F is compensated.  D-term contribution Field configuration of D I W=0 with W ≠0 gives F I =0 and D=0 due to the gauge invariance. → V D cannot play a role of uplifting potential for the SUSY solution of V F.

2.2 KKLT Scenario  Fluxes along the extra dimensions Fluxes are a source of warp factor → Warped geometry In a warped throat, SUSY breaking anti-brane is fixed at the end of the throat. Geometrical sequestering of the visible brane (located in a region where a warping in negligible) from the anti-brane Visible brane CY Warped throat Anti-brane  N=1 local SUSY is non-linearly realized on the anti-brane. Anti-brane action can be written by using Goldstino superfield confined on the SUSY breaking brane.

2.2 KKLT Scenario  Red-shifted anti-brane by a small warp factor Low energy consequence of the anti-brane is described by single D-type spurion operator. → only provides an additional energy to V. Geometrical separation of visible brane from the anti-brane → Contact terms between visible fields and Goldstino induced by bulk fields propagating through the (strongly) warped throat are negligible. For Klebanov-Strassler-type throat : Kachru, McAllister, Sundrum hep-th/  Nearly vanishing vacuum energy density Small warp factor

2.2 KKLT Scenario  Moduli Stabilization Dilaton and complex structure moduli are fixed by fluxes through D S,U W=0. Kaehler moduli are stabilized by fluxes and NP superpotential (D T W=0). V Dilaton (S) and Complex structure moduli (U) : Superheavy Kaehler moduli (T) : Heavy (NP effects) SUSY AdS minimum  dS Vacuum SUSY AdS minimum is uplifted to a dS vacuum by V lift.. Small vacuum shift results in nonzero moduli F-terms. → Superheavy S, U are irrelevant for the low energy SUSY breaking.

2.3 KKLT Moduli Stabilization  Effective action of Kaehler moduli Heavy moduli (S, U) can be integrated out in a supersymmetric manner. Perturbative axionic shift symmetry U(1) T → Broken by the NP superpotential → Holomorphic trilinear couplings are T-independent. (No quantum corrections due to the perturbative non-renormalization theorem) U(1) T and U(1) R : Both w 0 and A can be made to be real. → No CP violationg phases

2.3 KKLT Moduli Stabilization  Moduli stabilization SUSY AdS minimum (Large supersymmetric mass) Vanishing vacuum energy density : V F +V lift ≈0 → Small vacuum shift  Modulus F-term ( for the weak scale SUSY ) Moduli mediation is comparable to the loop-induced anomaly mediation. → Mixed modulus-anomaly mediation

3.1 Mirage Mediation of SUSY Breaking  Low energy soft parameters in KKLT moduli stabilization Low energy gaugino masses : Gauge couplings unification by a universal T- dependence of gauge kinetic functions RG evolution of soft parameters is cancelled by anomaly mediated contribution. → Mirage mediation Mirage messenger scale is determined by ratio between two mediations α.

3.1 Mirage Mediation of SUSY Breaking  Phenomenon of mirage unification Universal T-dependence of gauge kinetic functions Gaugino masses are unified at the mirage messenger scale, while gauge couplings still unify at M GUT. Minimal KKLT : α=1  MSSM gaugino masses at TeV scale

3.1 Mirage Mediation of SUSY Breaking  Soft parameters associated with matter particles Tri-linear A-parameter and soft scalar masses depend on the associated Yukawa couplings. Pure moduli-mediated soft parameters at M GUT A-parameter and soft scalar mass also lead to the mirage messenger scale, either if (a i + a j + a k )y ijk =y ijk and (c i + c j + c k )y ijk =y ijk, or if the effects of Yukawa couplings can be ignored. For the 1 st and 2 nd generations of squarks and sleptons, the involved Yukawa couplings are small. → Mirage mediation pattern (Mirage unification if c i are flavor universal.)

3.1 Mirage Mediation of SUSY Breaking  Generic mirage mediation is parameterized by.  In KKLT moduli stabilization M 0, a i, c i are determined by the moduli-dependence of Z i and f a at M GUT. The ratio between anomaly and moduli mediations is determined by the mechanism of moduli stabilization and the subsequent uplifting. For generic KKLT set-up with where n i ={0(D7), 1/2 (brane intersections), 1(D3)} and l a ={1(D7), 0(D3)}  Flavor universal modular weight Matter fields with same gauge charges have a common geometric origin. → Flavor conservation

3.2 EWSB in Mirage Mediation  Higgs mass parameters  Little SUSY hierarchy problem (in the MSSM) RG evolution induced by the large top quark Yukawa coupling For the lightest Higgs boson mass to be larger than 114 GeV, a rather heavy stop mass > 600 GeV is needed. The EWSB conditions gives which requires fine tuning of parameters. → The sensitivity of M Z against a variation of the input parameter.

3.2 EWSB in Mirage Mediation  Higgs mass parameters in Mirage mediation In mirage mediation, B is generically of O(m 3/2 ) ∼ 4π 2 M 0 We consider the case that Higgs bilinear terms in the Kaehler and superpotential are forbidden by a symmetry G under which H u H d transforms. → Generated by non-perturbative effects breaking G NP Higgs bilinear term can be generated by a confining hidden SU(Nc) gauge interactions with hidden quarks and singlet.

3.2 EWSB in Mirage Mediation  TeV scale Mirage mediation By choosing the involved rational coefficients to give → The effective RG evolution of m 2 Hu is minimized. → Little hierarchy between the weak scale and the sparticle mass  EWSB in the TeV scale mirage mediation Proper size of B and μ can be obtained by choosing A 2 = O(10 -2 ) : Small since the symmetry G is restored in the limit A 2 =0. Successful EWSB can be achieved through

4. Summary  Mirage mediation of SUSY breaking Anomaly mediation ∼ Gravity (or gauge) Mediation → Particular correlation between RG evolution of soft parameters and anomaly mediated contribution. Soft paramters are generically parameterized by {M 0, a i, c i, α}. Mirage mediation is naturally realized in the KKLT moduli stabilization.  Mirage mediation in KKLT moduli stabilization Hierarchy among soft masses, the gravitino and moduli masses → Phenomenologically desirable because cosmological problems associated with late decays of gravitino and moduli can be avoid. Perturbative shift symmetry and U(1) R : CP conservation a i, c i, α have discrete values (up to small correction of O(1/8π 2 )).

4. Summary  Mirage mediation in KKLT moduli stabilization Gauge coupling unification with the universal moduli-dependence of gauge kinetic functions leads to the mirage unificaiton of gaugino masses at M mir Flavor universal modular weight : → Flavor conservation → (approximately) Degenerate squark/slepton masses at M mir.  TeV scale (α=2) mirage mediation Solution to the little SUSY hierarchy problem (in the MSSM) : The fine-tuning for EWSB can be significantly reduced by minimizing the effective RG evolution of m 2 Hu. Thank you!! Thank you!!