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Mirage Mediation of SUSY Breaking

Mirage Mediation of SUSY Breaking. K. S. Jeong KIAS 25 May, 2007 Based on hep-ph/0504037, hep-ph/0612258. 1.1 Supersymmetry. Fermion. Boson. Supersymmetry Low energy SUSY is a promising candidate for physics beyond the SM.

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Mirage Mediation of SUSY Breaking

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  1. Mirage Mediation of SUSY Breaking K. S. Jeong KIAS 25 May, 2007 Based onhep-ph/0504037, hep-ph/0612258

  2. 1.1 Supersymmetry Fermion Boson • 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)

  3. 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, fa : Holomorphic functions of chiral superfields • Chiral compensator C for the super-Weyl invariance • Auxiliary component of the SUGRA multiplet is encoded in FC.

  4. 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

  5. 1.3 Mediation of SUSY Breaking • Anomaly mediation (FC) • 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)

  6. 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 κij are flavor-blind Visible sector Hidden sector X

  7. 1.3 Mediation of SUSY Breaking • 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. Visible sector Secluded sector X

  8. 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 tothe 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

  9. 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

  10. 2.2 KKLT Scenario dS vacua in string theory : Kachru, Kallosh, Linde, Trivedi PRD 68,046005 • Moduli stabilizationby 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 condensationat a supersymmetric AdS minimum. • Nearly flat dS vacuum • Uplifting scalar potential provided by SUSY breaking branes → The negative vacuum energy density VF is compensated. • D-term contribution • Field configuration of DIW=0 with W ≠0 gives FI=0 and D=0 due to the gauge invariance. → VD cannot play a role of uplifting potential for the SUSY solution of VF.

  11. 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.

  12. 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/0703105 • Nearly vanishing vacuum energy density • Small warp factor

  13. 2.2 KKLT Scenario • Moduli Stabilization • Dilaton and complex structure moduli are fixed by fluxes through DS,UW=0. • Kaehler moduli are stabilized by fluxes and NP superpotential (DTW=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 Vlift.. • Small vacuum shift results in nonzero moduli F-terms. →Superheavy S, U are irrelevant for the low energy SUSY breaking.

  14. 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 w0 and A can be made to be real. → No CP violationg phases

  15. 2.3 KKLT Moduli Stabilization • Moduli stabilization • SUSY AdS minimum(Large supersymmetric mass) • Vanishing vacuum energy density : VF+Vlift≈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

  16. 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.

  17. 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 MGUT. • Minimal KKLT : α=1 • MSSM gaugino masses at TeV scale

  18. 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 MGUT • A-parameter and soft scalar mass also lead to the mirage messenger scale, either if (ai+ aj + ak )yijk=yijk and (ci+ cj + ck )yijk=yijk , or if the effects of Yukawa couplings can be ignored. • For the 1st and 2nd generations of squarks and sleptons, the involved Yukawa couplings are small. → Mirage mediation pattern(Mirage unification if ci are flavor universal.)

  19. 3.1 Mirage Mediation of SUSY Breaking • Generic mirage mediation is parameterized by . • In KKLT moduli stabilization • M0, ai, ci are determined by the moduli-dependence of Zi and fa at MGUT. • 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 ni={0(D7),1/2 (brane intersections), 1(D3)} and la={1(D7), 0(D3)} • Flavor universal modular weight • Matter fields with same gauge charges have a common geometric origin. → Flavor conservation

  20. 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 MZ against a variation of the input parameter .

  21. 3.2 EWSB in Mirage Mediation • Higgs mass parameters in Mirage mediation • In mirage mediation, B is generically of O(m3/2)∼4π2M0 • We consider the case that Higgs bilinear terms in the Kaehler and superpotential are forbidden by a symmetry G under which HuHd 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.

  22. 3.2 EWSB in Mirage Mediation • TeV scale Mirage mediation • By choosing the involved rational coefficients to give → The effective RG evolution of m2Hu 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 A2= O(10-2) : Small since the symmetry G is restored in the limit A2=0. • Successful EWSB can be achieved through

  23. 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 {M0, ai, ci, 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 • ai, ci, α have discrete values(up to small correction of O(1/8π2)).

  24. 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 Mmir • Flavor universal modular weight : → Flavor conservation → (approximately) Degenerate squark/slepton masses at Mmir. • 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 m2Hu. Thank you!!

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