Supersymmetric Fine-tuning Problem and Little Hierarcy in Mixed Modulus-Anomaly Mediation Ken-ichi Okumura Department of Physics, Kyushu University Discoveries of Higgs and Supersymmetry to Pioneer the particle physics in 21st Century Kiwoon Choi, Kwang-Sik Jeong and K.O. JHEP 59:39, Kiwoon Choi, Kwang-Sik Jeong, Tatsuo Kobayashi and K.O. hep-ph/5829 Typeset by FoilTEX
I. Introduction Supersymmetry (SUSY) is considered to be the first candidate of physics beyond the SM not only as a solution of hierarchy problem but also for many attractive features like gauge coupling unification and natural candidate for cold dark matter. However lower bound for m h measured in LEPII suggests a direction to heavy t and some degree of fine-tuning in parameters of the MSSM (SUSY fine-tuning problem). We propose a new scenario which solves the SUSY fine-tuning problem without any modification of the MSSM based on SUSY braking model inspired from KKLT flux string compactification. Typeset by FoilTEX 1
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I. Introduction Supersymmetry (SUSY) is considered to be the first candidate of physics beyond the SM not only as a solution of hierarchy problem but also for many attractive features like gauge coupling unification and natural candidate for cold dark matter. However lower bound for m h measured in LEPII suggests a direction to heavy t and some degree of fine-tuning in parameters of the MSSM (SUSY fine-tuning problem). We propose a new scenario which solves the SUSY fine-tuning problem without any modification of the MSSM based on SUSY braking model inspired from KKLT flux string compactification. Typeset by FoilTEX 3
II. Supersymmetric Fine-tuning Problem Radiative electroweak symmetry breaking 3 5 4 2 3 2 1 1-1 5 1 15-2 5 1 15 K.Inoue, A.Kakuto, H.Komatsu and S.Takeshita, L.E.Ibanez and G.G.Ross, J.R.Ellis, D.V.Nanopoulos and K.Tamvakis, L.Alvarez- Gaume, J.Polchinski and M.B.Wise Typeset by FoilTEX 4
Tuning in the radiative electroweak symmetry breaking Radiative correction to m 2 H 2 is order of m 2 t Δm 2 H 2 3 ( ) Λ 4π 2y2 t m 2 t ln 2m 2 t m t m 2 Z /2 is given by the difference between m2 H 2 and μ 2. m 2 Z 2 = m2 H 1 m 2 H 2 tan 2 β tan 2 β 1 μ 2 m 2 H 2 μ 2 m t m H 2 μ>5gev means < 2% fine-tuning in the measure, Δ 1 μ 2 m2 H 2 μ 2 μ 2 m2 Z 2 μ 2 Typeset by FoilTEX 5
Radiative correction in the lightest Higgs boson mass Theoretical upper bound for m h is given by m Z at tree-level. However, radiative correction from y t can raise the bound, H.E.Haber and R.Hempfling, Y.Okada, M.Yamaguchi and T.Yanagida, J.R.Ellis, G.Ridolfi and F.Zwirner m 2 h <m 2 Z + 3g2 m 4 t 8π 2 m 2 W where X t = A t μ cot β. [ ln ( m 2 t m 2 t ) + X2 t m 2 t For instance, the current SM bound is translated into, ( 1 X2 t 12m 2 t m h > 114.4 GeV m t > 5 GeV (X 2 t << m 2 t ) Here we call this tention between the tuning in determination of m Z and m h lower bound as supersymmetric fine-tuning problem. )] Typeset by FoilTEX 6
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III. Mixed Modulus-Anomaly Mediation in KKLT model Compactified string theory predicts moduli fields (S, T, Z α )in4d. KKLT stabilized all of them with tunable positive cosmological constant. S, Z α : flux, K = 3ln(T + T ), W = w A exp( at ) Type IIB orientifold S.Kachru, R.Kallosh, A.Linde and S.P.Trivedi (23) Typeset by FoilTEX 8
Mixed modulus-anomaly mediation SUSY breaking by uplifting potential is mediated to visible fields on D3/D7 branes via modulus F-term F T /(T + T ), which is hierarchically smaller than m 3/2 ( m 3/2 /4π 2 ) anomaly mediation is same order! K. Choi, A. Falkowski, H.P. Nilles, M. Olechowski and S. Pokorski (24) Relative siginificance α is calculable and contorolled by the power of modulus in the upligting potential [ D3 uplifting (KKLT) predicts α 1(n T =2)]. α m 3/2 ln ( M Pl /m 3/2 ) 1 M 2 n T, M F T T + T Visible fields on D3/D7 brane (W = λ ijk Q i Q j Q k ), L soft = 1 ( ) 1 2 M aλ a λ a m 2 i Q i 2 6 A ijky ijk Q i Q j Q k +h.c. Typeset by FoilTEX 9
Moduli mediation: Gauge k-fn. & Kähler on D3/D7: f a = T la, K eff = K + Z i Q i Q i, D3 l a =,n i =1 D7 (4 cycle) l a =1,n i = Z i =1/(T + T ) n i 2cycle n i =1/2 L.E. Ibanez, C. Munoz and R. Rigolin Nucl. Phys. B553, 43 (1999) L.E. Ibanez, hep-ph/4864; B.C. Allanach, A. Brignole and L.E. Ibanez, hep-ph/52151 M a = F T T ln(re(f a )) = l a M, M F T /(T + T ) ( ) A ijk = F T λ ijk T ln =(3 n e K i n j n k )M, Z i Z j Z k m 2 i = 2 ( ) 3 V F T F T T T ln e K /3 Z i =(1 n i ) M 2. * D3 visible gauge/matter fields no moduli-mediated contribution. Typeset by FoilTEX 1
Anomaly-Mediation: Randall and Sundrum (1998), G.F.Giudice, M.A.Luty, H. Murayama and R.Rattazzi (1998) M a = β a g a m 3/2 A ijk = 1 16π 2 (γ i + γ j + γ k ) m 3/2 where γ i 8π 2 = d ln Z i d ln μ. m 2 = 1 dγ i 32π 2 d ln μ m 3/2 { T + 1 8π 2 ( γi T M m 3/2 +H.c. )} β a, γ i /(8π 2 ) 1-loop suppressed, but always exists if m 3/2 Interference term in m 2 i via modulus dependence of γ i. K. Choi, A. Falkowski, H.P. Nilles, M. Olechowski and S. Pokorski (24) Typeset by FoilTEX 11
IV.MirageMessengerScaleandLittleSUSYHierarchyatTeV Correlation of R.G. running of modulus mediation with anomaly mediation. Modulus : M a (μ) = g2 a(μ) g 2 a(λ) M = M β a g a ln ( ) 2 Λ M μ Anomaly : M a (μ) = β a g a m 3/2 They cancel at μ =Λexp ( m 3/2 2M ) Λ ( m3/2 D3 uplifting (KKLT) predicts μ = Λm 3/2. Λ ) α/2. Typeset by FoilTEX 12
3 2.5 2 2 1.5 1.5 1 -.5 5 1 15-1 5 1 15 Anomaly mediation effectively shifts the messenger scale. (mirage messenger scale : M Mirage ) K. Choi, K-S. Jeong, K.O. (25) Typeset by FoilTEX 13
V. Solving SUSY Fine-tuning by Mirage TeV Hierarchy If we have uplifting of n T =1, M Mirage M (Mirage TeV Mediation) 3 1.5 2 1 -.5 5 1 15-1 5 1 15 We can realize the little hierarchy by setting m H1,H 2 =at M. Typeset by FoilTEX 14
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VI. Conclusion Raising lower bound for m h favors heavy t and m H2 in general which leads to fine-tuning in the electroweak symmetry breaking of the MSSM. We proposed a new scenario where the little hierarchy between Higgs and SUSY particles is realized by mirage messenger scale in mixed modulus-anomaly mediation without any modification of the MSSM. Tuning parameter Δ 1 μ 2 can be naturally above 1% and m h easily exceeds 12 GeV. The scenario favors light SUSY particles < 1 TeV and predics distinctive relation among the gaugino and sfermion masses. Heavy Higgs bosons and higgsinos are predicted around 1 2 GeV and LSP is pure higgsino. Typeset by FoilTEX 18