TeV scale Mirage Mediation in Next-to-MSSM Takashi Shimomura (Niigata Univ., Japan/MPIK, Heidelberg, Germany) based on T. Kobayashi, T. S., T. Takahashi, arXiv:1203.4328 T. Kobayashi, H. Makino, K-I. Okumura, T. S., T. Takahashi, arXiv:1204.3561 12年7月4日水曜日 Table of Talk 1. Introduction i. Fine-tuning and Supersymmetry ii. Little Fine-tuning and Mediations iii. Naturalness and Next-to-Minimal SSM iv. False vacua in SUSY models 2. TeV Scale Mirage Mediation 3. (Old) Numerical Results 4. Summary & Future Works 12年7月4日水曜日 Introduction The Standard Model (SM) has been successful to explain almost all of experimental results so far. In particular, the gauge interactions of the electroweak sector agree with precise measurements very well. The only mysterious part of the SM is the physics of ElectroWeak Symmetry Breaking (EWSB) How is the EW symmetry broken? Probably the (fundamental) Higgs mechanism Why is the EWSB scale O(100) GeV? New Physics... 12年7月4日水曜日 Fine-tuning in the Standard Model In the SM, the EW symmetry is broken by spontaneous symmetry breaking, i.e. the Higgs mechanism. The mass of the Higgs receives large quadratic radiative corrections from UV physics (e.g. Planck/GUT) t 2 0 0 3Y h h µ2 = µ2 + t Λ2 eff 8π2 Λ : cutoff scale t¯ A very strong fine-tuning is required to stabilize the EW scale. (100)2(GeV2) (1016)2 (1016)2 (GeV2) hierarchy problem ∼ − Such fine-tuning is “unnatural” and new physics is required to stabilize the scale 12年7月4日水曜日 Supersymmetry Supersymmetry (SUSY) is a very attractive candidate of new physics for the hierarchy problem. Each of the SM particles has a SUSY partner which has the same quantum charge but a different spin. e.g.) MSSM SM particles SUSY particles quarks Q, q Q,˜ q˜ squarks leptons L, e L,˜ e˜ sleptons Higgses H1,H2 H˜ 1, H˜ 2 Higgsinos gauge bosons B, W, G B,˜ W,˜ G˜ gauginos Higgses 0 + charged Higgs H1 H2 H1 = H2 = H− H0 1 2 neutral Higgs 12年7月4日水曜日 Supersymmetry The quadratic divergences cancel due to SUSY partner contributions, and only log divergence remains. t ˜ 0 0 t 2 2 h h 3 Yt Λ + 0 0 | | m2 log h h 2 t˜ 2 Yt Yt ∼ 16π m˜ Y 2 t t¯ t Λ:cutoff scale The hierarchy problem can be solved if SUSY scale is around TeV. SUSY also provides Dark Matter candidate (if R-parity is conserved) Grand Unification of the gauge interactions Quantum Gravity (?) (superstring) 12年7月4日水曜日 Single sector SUSY breaking Suppose SUSY breaking is transferred directly like = F ΦΦ F ΦΦ= mΦΦ L → F : SUSY breaking field Φ : SM particles or their partners The supertrace formula predicts the very light SUSY particles. Str( 1)F m2 = (boson mass)2 - (fermion mass)2 = 0 − SUSY particles the SM particles SM fermion mass = SUSY particle mass Such light SUSY particles already excluded SUSY breaking must be mediated indirectly 12年7月4日水曜日 Two Sector Paradigm SUSY world requires two sector and (some) mediation mechanism. “visible sector” “hidden sector” indirect SM particles SUSY breaking and fields SUSY particles SUSY breaking some (non-perturbative) F n mediation dynamics at high energy = ΦΦ L M Mediation mechanism Supertrace does not • hold anymore. supergravity (Planck scale) • gauge interaction (intermediate scale) soft SUSY br. terms • superconformal anomaly (Planck scale) are generated 12年7月4日水曜日 The little hierarchy problem Kim and Nilles, ’84 If SUSY scale is much above the TeV scale, another new fine- tuning is introduced. In the MSSM, the EWSB scale is determined by 1 2 2 2 m m + µ , (for large tan β ) −2 Z H2 m2 : H2 soft SUSY br. mass The little fine-tuning is needed if 2 2 2 m ,µ m the little hierarchy problem | H2 | Z SUSY suffers this problem because the LHC has been pushing up the bound on SUSY scale. This is a problem of mediation mechanisms, not SUSY! 12年7月4日水曜日 The little hierarchy problem (Martin, “susy primer”) 1500 ˜ u,˜ d g˜ µ =1.8TeV ex) mSUGRA mediation t˜ 1000 H • Universal soft masses at GUT scale d μ2 2 1/2 ( +m0) Hu M3 • RG running to the EWSB scale M 2 m1/2 Mass [GeV] Mass 500 M1 • Heavy SUSY particles at the EWSB squarks sleptons m0 0 scale 24681012141618 Log10(Q/1 GeV) large soft mass of the Higgs m2 m2 M 2 1.5TeV, Hu ∼− t˜ ∼− g˜ then, the little fine-tuning is needed 1 2 2 2 m m + µ , = (1 TeV)2 - (1 TeV)2 −2 Z H2 12年7月4日水曜日 Mediations We need another mediation mechanism in which •The soft masses are different in each particles. •The soft masses evolve over short scale. m2 g˜ m2 1.5 g˜ 0.5 u,˜ d˜ u,˜ d˜ t˜ t˜ Hu Hu log(Q) GUT log(Q) GUT One of such possibilities is Mirage Mediation. 12年7月4日水曜日 Naturalness of the MSSM The MSSM Lagrangian is given by three potentials = K + W + V , L |D |F soft soft SUSY breaking terms 2 2 3 2 Vsoft = m φ + Aφ + MB˜ , scalar soft A-term gaugino soft m,A,M are EWSB or TeV scale supersymmetic interactions W = Y Φ1Φ2H + µH1H2, μ can be the Planck/GUT scale or keV scale, whatever... There are no reason why μ is around the EWSB scale, but it must be... 12年7月4日水曜日 Fayet, ’75, ’76, ’77; Nilles, Srednicki, Wyler, ’83 Next-to-Minimal SSM Frere, Jones, Saby, ’83; See review by Ellwaner’10 The NMSSM is an extension of the MSSM with a singlet and Z3 parity. κ 3 µHˆ 1 Hˆ 2 λSˆHˆ 1 Hˆ 2 + Sˆ , W⊃ · W⊃ · 3 No dimensionful parameter in the SUSY int. Only dimensionful parameters are soft breaking terms. 2 2 3 2 Vsoft = m φ + Aφ + MB˜ , • The EWSB occurs when the three Higgses develop vevs. • μ term is generated by the EWSB. µ = λ S eff • The vevs are determined by the soft breaking terms. SUSY breaking scale determines the EWSB scale! 12年7月4日水曜日 The Higgs mass In the SM, λ V = m2H2 + H4 m2 λv2 − 4 h ∼ In the MSSM, V = m2 H2 + m H2 + BµH H H1 1 H2 2 1 2 1 + (g2 + g2)(H2 H2)2 8 1 2 1 − 2 2 2 2 2 2 2 2 m (g + g2) v cos 2β = M cos 2β h1 ∼ 1 Z 125 GeV Higgs mass needs large radiative corrections 4 2 3m m˜ 1 ∆m2 = t log t + X 1 X2 2 2 h1 t t X = A /m 4π2v2 m2 − 6 t t t˜ t the heavy stops/large A-term increase the little hierarchy 12年7月4日水曜日 The Higgs mass in the NMSSM In the NMSSM, κ 3 λSˆHˆ 1 Hˆ 2 + Sˆ , W⊃ · 3 This superpotential gives a new quartic coupling V (kS2 λH H )2 + λ2S2(H2 + H2) ⊃ − 1 2 1 2 then the Higgs mass becomes m2 = M 2 cos2 2β + λ2v2 sin2 2β λ2/κ2v2 h1 Z − ··· + (radiative corrections) the Higgs mass can be heavier than in the MSSM the little hierarchy becomes milder in the NMSSM 12年7月4日水曜日 short summary Why is the EWSB scale O(100) GeV? This is one of the most important questions at this time. • tachyonic Higgs mass is very sensitive to UV physics the EWSB scale is unstable to radiative corrections SUSY can solve this problem • the LHC has been pushing the bound up and up The little hierarchy problem? This is a problem of mediations It can be solved by the Mirage Mediation • the naturalness problem? tension between the Higgs mass and the little hierarchy? Don’t worry. the NMSSM can solve it. 12年7月4日水曜日 2. Mirage Mediation 12年7月4日水曜日 Landall, Sundrum, ’99; Anomaly Mediation (AMSB) Giudice, Luty, Murayama, Rattazzi, ’98 the visible and the hidden sectors are physicaly separated. (3+1)d • only gravity propagates in the bulk. visible hidden gravity • Interactions are purely SUSY gravitational. • Scale invariant if no 5d SUSY mass terms The scale inv. is broken by super-Weyl anomaly 2 bag F F gaugino: M = a a 2 = m3/2 16π Mpl Mpl 1 F 2 2 scalar: mq = (βgγg + βyγy ) 2 −4 Mpl 12年7月4日水曜日 Modulus Mediation Kaplunovsky, Luis, ’93; Brignole, Ibanez, Munoz, ’94 Kobayashi, Suematsu, et al, ’95 • String theory is consistently defined in 10 dimensions. • Superfluous 6 dimensions should be compactified in small size. • moduli appear which parameterize shape and size of the extra-dimensions. • In KKLT setup, moduli can be stabilized, then SUSY is broken. Kachru, Kallosh, Linde, Trivedi, ’03 • F-term of modulus fields are suppressed and comparable to the AMSB contributions. the AMSB and the MMSB can contribute together 12年7月4日水曜日 Choi, Falkowski, Nilles, Olechowski, Pokorski ’04 Choi,Falkowski,Nilles,Olechowski, ’05 Mirage Mediation Endo, Yamaguchi, Yoshioka, ’05 The mirage mediation is a mixture of the modulus mediation and the anomaly mediation. gaugino soft mass ba 2 Ma(MGUT )=M0 + g (MGUT )m3/2 16π2 Mirage scale : special energy scale in the mirage med. MGUT M = mir α/2 (Mpl/m3/2) Mpl: Planck scale the ratio of the anomaly med. to the modulus med. m3/2 α ≡ M0 log(Mpl/m3/2) 12年7月4日水曜日 the gaugino masses are unified at the mirage scale Ma(Mmir)=M0 @ 1-loop This result is independent of α. 2 M, g g3 M1 M2 g2 g1 M3 Mirage log(Q) GUT This unification is just due to a cancellation between the anomaly med. and RGE’s contributions. 12年7月4日水曜日 A terms and scalar soft masses m3/2 Aijk(MGUT )=aijkM0 (γi + γj + γk) − 8π2 2 2 m3/2 2 m3/2 m (MGUT )=ciM γ˙i( ) M0θi, i 0 − 8π2 − 8π2 where aijk & ci : modular weight γi, θi : functions of gauge and Yukawa coupl.