Peccei-Quinn extended MSSM in anomaly mediation
Seodong Shin
Seoul National University, Korea
IDM 2012, Chicago, USA, July 25th, 2012
Work in progress with K.S. Jeong Outline
Introduction Higgs μ and Bμ terms Stabilization of the PQ scale Higgs mass around 125 GeV Dark matter Conclusions Introduction
Supersymmetic axion model in anomaly mediaton Naturalness problems in the SM
Gauge hierarchy problem Strong CP problem
Promising solutions Supersymmetry : stabilizes the EW scale Peccei-Quinn symmetry : axion coupling to gluon anomaly ⇨ strong CP phase θ dynamical Supersymmetric axion model
Axion chiral multiplet : axion, axino, saxion H.P. Nilles, S. Raby, NP B198, 102 (1982), ......
Solution to the gauge hierarchy problem Solution to the strong CP problem R-parity : LSP is a good DM candidate Gauge coupling unification Radiative EW symmetry breaking Minimal model in anomaly mediation
Why anomaly mediation?
Higgs mass around 125 GeV at the LHC : Minimal model in gauge mediation mt˜ 10TeV P. Draper, P. Meade, M. Reece, D. Shih, PR D85, 095007 (2012)
No SUSY flavor problem : 1, 2 gen. almost flavor blind At tree level, no SUSY felt by the matter fields Negative slepton mass² ? MSSM : at least 1% fine tuning for 125 GeV Higgs L.J. Hall, D. Pinner, J.T. Ruderman, JHEP 1204, 131 (2012) MSSM : at least 1% fine tuning for 125 GeV Higgs L.J. Hall, D. Pinner, J.T. Ruderman, JHEP 1204, 131 (2012)
If allowing as least as possible fine tuning of O(1%)
125 GeV Higgs Minimal description
PQMSSM in anomaly mediation without new mass parameters
μ and Bμ term 2 m˜ > 0 PQ scale Dark matter Higgs μ and Bμ terms Higgs μ and Bμ terms
MSSM : The origin of μ term?
W = y uQH¯ y dQH¯ y eLH¯ + µH H MSSM u u − d d − e d u d from supersymmetric term
EW symmetry breaking µ 2 + m = Bµcot β +(M 2 /2) cos 2β | | Hu Z µ 2 + m = Bµtan β (M 2 /2) cos 2β | | Hd − Z Higgs μ and Bμ terms
Once μ is somehow generated, soft Bμ ?
Bµ F √F : SUSY scale B = µ ∼ M M : messenger mass
Some mechanism F m B msoft If soft M Higgs μ and Bμ terms
Once μ is somehow generated, soft Bμ ?
Bµ F √F : SUSY scale B = µ ∼ M M : messenger mass
Some mechanism F m B msoft If soft M
Unnatural fine-tuning to achieve EW g2 F gauge mediation m SM ,B = (100m ) soft 16π2 M soft anomaly mediation ∼ O Solution in supersymmetric axion model?
Origin from the superpotential S2 = d2θλ H H + h.c. LKN M u d Pl S2 F S J.E. Kim, H.P. Nilles, PL B138, 150 (1984) µ = λ ,B= 2 MPl − S
Origin from the Kähler potential S = d4θκ ∗ H H + h.c. LGM S u d F S∗ F S µ = κ ,B= G.F. Giudice, A. Masiero, PL B206, 480 (1988) S S Minimal models in gauge mediation
PQ scale : fixed through SUSY breaking
Radiative stabilization : additional Yukawa mediation
K.S. Jeong, M. Yamaguchi, JHEP 1107, 124 (2011)
Stabilization with additional SM singlets : KN mechanism
K. Choi, E.J. Chun, H.D. Kim, W.I. Park, C.S. Shin, PR D83, 123503 (2011) KN mechanism : NOT in anomaly mediation F C m3/2 B has additional contribution by C ∼
GM mechanism : KN mechanism : NOT in anomaly mediation F C m3/2 B has additional contribution by C ∼
OK connection with v GM mechanism : PQ scale stabilization scheme Radiative stabilization A. Pomarol, R. Rattazzi, JHEP 9905, 013 (1999) R. Rattazzi, A. Strumia, J.D. Wells, NP B576, 3 (2000) S. Nakamura, K.-I. Okumura, M. Yamaguchi, PR D77, 115027 (2008)
Higher dimensional terms in Kähler potential or superpotential N. Abe, T. Moroi, M. Yamaguchi, JHEP 0201, 010 (2002) Giudice-Masiero mechanism in our model
W = yX X1X2S + yH SHuHd K/3 2 2 2 Ω 3e− = X + X + S +(κX∗X + h.c.) ≡− | 1| | 2| | | 1 2 PQ(X )=PQ(X )= 1, PQ(S)=2, PQ(H )=PQ(H )= 1 1 2 − u d −
X =0 Once 1 at high scale X2,S heavy : integrate out
ˆ yH 4 X1∗ ˆ κ d θ H H X1 CX1 u d ≡ basis − yX Xˆ 1 Stabilization of PQ scale
Radiatve stabilizaton : witout new mass parametrs in te model Stabilization of PQ scale
W = yX X1X2S + yH SHuHd +(y1X1 + y2X2)ΨΨ¯ K/3 2 2 2 Ω 3e− = X + X + S +(κX∗X + h.c.) ≡− | 1| | 2| | | 1 2 PQ(X )=PQ(X )= 1, PQ(S)=2, PQ(H )=PQ(H )= 1 1 2 − u d −
Ψ+Ψ¯ :5+5¯ of SU(5) Stabilization of PQ scale
W = yX X1X2S + yH SHuHd +(y1X1 + y2X2)ΨΨ¯ K/3 2 2 2 Ω 3e− = X + X + S +(κX∗X + h.c.) ≡− | 1| | 2| | | 1 2 PQ(X )=PQ(X )= 1, PQ(S)=2, PQ(H )=PQ(H )= 1 1 2 − u d −
Ψ+Ψ¯ :5+5¯ of SU(5)
V = V + m2(Q = X ) X 2 0 1 | 1| | 1| Stabilization of PQ scale
W = yX X1X2S + yH SHuHd +(y1X1 + y2X2)ΨΨ¯ K/3 2 2 2 Ω 3e− = X + X + S +(κX∗X + h.c.) ≡− | 1| | 2| | | 1 2 PQ(X )=PQ(X )= 1, PQ(S)=2, PQ(H )=PQ(H )= 1 1 2 − u d −
Ψ+Ψ¯ :5+5¯ of SU(5)
V = V + m2(Q = X ) X 2 0 1 | 1| | 1| radiative stabilization Running soft mass² of X1 : cross zero at some scale 2 2 2 m (y g ) yX =0! 1 ∝ − roughly Stabilization of PQ scale
Example in this model
Difference : Not affected by SUSY breaking (pure anomaly mediation effect) Spectrum after the PQ scale fixing
5N y2 m2 Ψ 1 m2 σ aa Mass of saxion σ ∼ 8π2 soft →
m m /8π2 Mass of axino a˜ ∼ soft DM
F-term of X1 at the minimum F X1 = (m3/2) X1 O deflected positive slepton mass² Higgs mass around 125 GeV
LHC result on July 4t, 2012 Higgs mass around 125 GeV
5σ after combining the 2011 & 2012 1/2 LHC result from the diphoton & 4l
Constrain MSSM parameters 2 2 2 Tree level m h 4 2 2 2 2 2 2 3 mt mt˜ Xt Xt mh MZ cos 2β + 2 2 log 2 + 2 1 2 ≈ (4π) v mt mt˜ − 12mt˜ X = A µ cot β Stop mixing parameter t t − X /m˜ = √6 Maximal mixing at | t| t To obtain the Higgs around 125 GeV in the minimal model, we need large Xt around the maximal value to allow the fine tuning as least as possible. Parameter scan with the conditions Perturbativity of the gauge interaction up to MGUT The absence of tachyonic sfermion masses X /m˜ 1.5 Obtain moderate | t| t m˜ 2TeV t ∼ M 2 3TeV (bino can be lightest) a ∼ − NLSP : stau or Higgsino 600 GeV LSP : Axino Hall et al. 2012 Parameter scan with the conditions Perturbativity of the gauge interaction up to MGUT The absence of tachyonic sfermion masses X /m˜ 1.5 Obtain moderate | t| t m˜ 2TeV t ∼ M 2 3TeV (bino can be lightest) a ∼ − NLSP : stau or Higgsino 600 GeV LSP : Axino Hall et al. 2012 Dark matter Axino Light axino is a generic feature of radiatve stabilizaton wit 1 axion superfield X Axino mass is obtained from ! 1" the effective Kähler potential ¯ Ψ A Ψ 2-loop order a˜ Ψ˜ Ψ¯˜ a˜ X G˜ NLSP a˜ ! 1" →···→ → Gravitino problem resolved if m3/2 = O(10) TeV m = (100) MeV a˜ O (gravitino decay after or during BBN, over production of neutralino) S. Nakamura, K.-I. Okumura, M. Yamaguchi, PR D77, 115027 (2008) Conclusions Supersymmetric axion models : hierarchy + strong CP PQ extended MSSM in anomaly mediation without new mass parameter : motivated from Higgs 125 GeV Radiatively stabilizing the PQ scale : Higgs μ and Bμ Sparticle : deflected by the PQ field stabilization to resolve the negative slepton mass² problem. Moderate stop mass mixing parameter for the 125 GeV Higgs (but) with stop mass around 2 TeV. Dark matter : axino, the gravitino problem solved m3/2 = O(10) TeV & axino O(0.1)GeV Tank you!!