Hi Higgs Mass ss in in D- D-term Triggered Dy Dynamical SU - PowerPoint PPT Presentation

Hi Higgs Mass ss in in D- D-term Triggered Dy Dynamical SU SUSY Br SY Breakin ing No Nobuhito Maru (Osa saka Ci City Universi sity) with H. H. It Itoyama a wi (Osa saka Ci City Universi sity) 3/5/2015 SCG CGT15@Nagoya Universi sity �

Re Referenc nces � “126 GeV Higgs Boson Associated with D-Term Triggered Dynamical Supersymmetry Breaking” H. Itoyama and NM, Symmetry 2015 7 193 � “D-Term Triggered Dynamical Supersymmetry Breaking” H. Itoyama and NM, PRD88 (2013) 025012 � “D-Term Dynamical Supersymmetry Breaking Generating Split N=2 Gaugino Masses of Majorana-Dirac Type” H. Itoyama and NM, IJMPA27 (2012) 1250159 �

Pl Plan � � In Introduction n ! A New Mechanism sm of D-term Dy Dynamical SU SUSY Br SY Brea eakin king ! Higgs s Mass ss vi via D- D-term ef effects � Su Summa mary �

Introduction In n A Higgs boson was discovored, but… � -1 -1 CMS s = 7 TeV, L = 5.1 fb s = 8 TeV, L = 5.3 fb S/(S+B) Weighted Events / 1.5 GeV Events / 1.5 GeV Unweighted 1500 1500 γγ 1000 1000 120 130 m (GeV) γ γ Data 500 S+B Fit B Fit Component 1 ± σ 2 ± σ 0 110 120 130 140 150 m (GeV) γ γ

No No in indicatio ion of of SU SUSY ( SY ($ BSM BSM) �

Observed Higgs Mass 126 GeV � Severe constraints on MSSM parameter space (MSSM + light sparticles) � MSSM Extension + of heavy sparticles � MSSM �

Observed Higgs Mass 126 GeV � Severe constraints on MSSM parameter space (MSSM + light sparticles) � MSSM Dirac Gaugino + scenario heavy sparticles �

Dira Dirac Ga Gaug ugin ino Sc Scenario io � Fox, Nelson & Weiner (2012) � Gauge sector: N=2 extension � adj. chiral superfields added ( ) Φ a = SU 3 ( ) = ϕ a , ψ a , F ( ) , SU 2 ( ) , U 1 a Matter sector: N=1 � Dirac gaugino masses from � α Φ a = D 0 0 W d 2 θ 2 W ∫ L = λ a ψ a + … α a Λ Λ D 0 ≠ 0 ⊂ W 0 = θ α D 0 if in hidden U(1) � α

Once gaugino masses are generated at tree level, sfermion masses are generated by RGE effects � Sfermion masses @1-loop � ( ) α a ⎡ ⎤ 2 2 log m ϕ a 2 ≈ C a f ⎢ ⎥ (a = SU(3) C , M  M λ a π SU(2) L , U(1) Y ) � 2 f ⎢ ⎥ M λ a ⎣ ⎦ nd � No SUSY flavor & CP problems � Flavor b Fl r blind LHC bounds relaxed Dirac gauginos � � 4 π /g � (gluino/squark Sfermions � production suppressed) � Kribs & Martin (2012) �

A Ne New Mechanism sm of of D- D-term Dy Dynamical SU SUSY Br SY Breakin ing Itoyama & NM (2012,2013) �

SUSY U(N) gauge theory ������������������������� with adjoint chiral supermultiplets � ( ) ∫ L = d 4 θ K Φ a , Φ a , V Kahler potential � ( ) W a α W ( ) + h . c . b + + d 2 θ Im 1 ∫ ⎡ ∫ ⎤ 2 F ab Φ a d 2 θ W Φ a ⎣ ⎦ α Superpotential � Gauge kinetic function �

SUSY U(N) gauge theory ������������������������� with adjoint chiral supermultiplets � ( ) ∫ L = d 4 θ K Φ a , Φ a , V Kahler potential � ( ) W a α W ( ) + h . c . b + + d 2 θ Im 1 ∫ ⎡ ∫ ⎤ 2 F ab Φ a d 2 θ W Φ a ⎣ ⎦ α Superpotential � Gauge kinetic function � Fermion mass terms � ( ) ψ c λ a D 0 + F ab 0 Φ ( ) W a α W ( ) F 0 λ a λ b ∫ d 2 θ F ab Φ ⊃ F a 0 c Φ b α Dirac gaugino mass � ⊃ − 1 ( ) ( ) ψ a ψ b ∫ d 2 θ W Φ 2 ∂ a ∂ b W Φ

Fermion mass ss terms � Mixed Majorana-Dirac type masses � ( ) ψ c λ a D 0 + F ab 0 Φ ( ) W a α W ( ) F 0 λ a λ b ∫ d 2 θ F ab Φ ⊃ F a 0 c Φ b α Dirac mass � ⊃ − 1 ( ) ( ) ψ a ψ b ∫ d 2 θ W Φ 2 ∂ a ∂ b W Φ <F>=0 assumed � ⎛ ⎞ 2 − ⎜ ⎟ 4 F abc D b 0 ⎛ ⎞ λ c ( ) − 1 ⎜ ⎟ 2 λ a ψ a ⎟ + h . c . ⎜ ⎜ ⎟ ψ c ⎝ ⎠ 2 − ∂ a c ∂ c W ⎜ ⎟ 4 F abc D b ⎝ ⎠

D ≠ 0 & ∂ a ∂ a W ≠ 0 if � ⎡ ⎤ 2 ⎛ ⎞ 2 g aa ∂ a ∂ a W 2 D m ± = 1 ⎢ ⎥ 1 ± 1 + ⎜ ⎟ ⎢ ⎥ ∂ a ∂ a W ⎝ ⎠ ⎣ ⎦ 2 D ≡ − 4 F 0 aa D 0 ino (m � ) becomes Gaug Ga ugin s massi ssive by by nonzero <D> � SUSY is broken �

D-term equation of motion: � ( ) D 0 = − g 00 F 0 cd ψ d λ c + F 0 cd ψ d λ c 1 2 2 Dirac bilinears s condensa sation � The value of <D 0 > will be determined by th the gap equation �

Potential analysi sis � 3 constant ϕ ≡ ϕ 0 , D ≡ D 0 , F ≡ F 0 background fields: � Work in the region where <F 0 > << <D 0 > and perturbative � ( ) ∂ V D , ϕ , ϕ , F = F = 0 Stationary � gap equation � = 0 values � ∂ D ( ) D * , ϕ * , ϕ * ( ) ∂ V D , ϕ , ϕ , F = F = 0 = 0 ∂ ϕ ( ) ( ) , ϕ = ϕ * F , F ( ) , ϕ = ϕ * F , F ( ) , F , F ( ) ∂ V D = D * F , F = 0 F * , F ∂ F * D , ϕ , ϕ , F fixed

D- D-term effective potential@1-loop � 4 c 1 ϕ , ϕ ( ) Δ 0 V = N 2 m ϕ ⎡ 2 Tree � ⎣ ( ) ( ) 2 − λ ( ) 4 log λ ( ) 4 log λ ⎤ 4 − λ 1 ( ) 2 + + − − + 32 π 2 c 2 Δ 0 ⎥ ⎦ ( ) , Δ 0 ≈ ′′′ F ( ) = 1 ± C 2 : constants � λ 2 1 ± 1 + Δ 0 2 D 0 ′′ W 1-loop part = CW potential gauge + adjoint chiral superfield contributions �

Gap e Gap equa quatio ion � 0 = ∂ V Trivial solution Δ 0 =0 is NOT lifted � ∂ D ϕ , ϕ ⎡ ⎤ ⎧ ⎫ { } ⎪ ( ) − λ ( ) ⎪ 2 − ( ) 2 + 1 ( ) 2 + 1 1 1 ( ) 3 2log λ ( ) 3 2log λ ⎢ ⎥ + + − − = Δ 0 c 1 + 4 c 2 Δ 0 2 λ ⎨ ⎬ 64 π 2 ⎢ ⎥ 1 + Δ 0 ⎪ ⎪ ⎩ ⎭ ⎣ ⎦ Itoyama & NM (2012) � 1 ∂ V 1.0 ∆ 0 ∂ D 0.5 Δ 0 � 5 10 15 20 25 30 � 0.5 Nontrivial solution!! � � 1.0

( ) Δ 0* , ϕ * = ϕ * determined as the intersection point ( ) Δ 0* , ϕ = ϕ of two real curves in the plane � Δ 0 1.0 Solution of the gap eq. 0.8 ∂ V/ ∂ D=0 � 0.6 0.4 ∂ V/ ∂φ =0 � 0.2 ϕ Λ 0.0 0.0 0.2 0.4 0.6 0.8 1.0

E � 0 in SUSY � Trivial solution Δ 0 =0 is NOT lifted � Our SUSY breaking vac. is a local min. � V( φ ) � 15 10 ! 0 ≠ 0 5 φ � 1 2 3 4 5 Δ 0 =0 �

Metastability of our false se vacuum � <D> = 0 vacuum is not lifted ≠ � check if our vacuum <D> 0 is sufficiently long-lived � V( φ ) � Long-lived 15 for m φ << Δ � Λ � 10 5 our vac. � Δ V � (m φ Λ Δ 0 ) 2 � φ � 1 2 3 4 5 Δ φ � Δ 0 Λ ( Λ : cutoff scale) � Coleman & De Luccia(1980) � ( ) ⎡ ⎤ ⎡ ⎤ 2 ⎥ ≈ exp − Δ 0 Λ ∝ exp − Δ φ 4 Decay rate of ⎢ ⎥ ≪ 1 ⎢ Δ 0 Λ >> m φ � our vacuum � Δ V 2 m ϕ ⎢ ⎥ ⎣ ⎦ ⎣ ⎦

Numerical samples of solutions for the gap equation & the stationary condition for φ �

Hi Higgs Mass ss vi via D- D-term Ef Effects ts � Itoyama & NM (2013) �

Higgs Lagrangian � ∫ L Higgs = d 4 θ H u ⎡ † e − g Y V 1 − g 2 V 2 − 2 q u gV 0 H u + H d 1 − g 2 V 2 − 2 q d gV 0 H d ⎤ † e g Y V ⎣ ⎦ ( ) − B µ H u H d + h . c . ⎡ ⎤ ∫ + d 2 θ µ H u H d ⎣ ⎦ H u,d with U(1) charges q u,d assumed µ-term ��� q u + q d = 0 � <V 0 > = θ � <D 0 > �� additional Higgs mass@tree

Higgs potential � 2 ⎛ † σ a † σ a ⎞ 2 g 2 ∑ V H = 2 H u + H d ( ) H u 2 H d ⎜ ⎟ ⎝ ⎠ 2 1 + Im F 0 YY ϕ 0 a ( ) 2 − H d 2 g Y 2 2 + ( ) H u 8 1 + Im F 0 YY ϕ 0 ( ) 2 + q d g H d 2 − D 0 1 2 + ( ) q u g H u 2 1 + Im F 0 YY ϕ 0 ( ) + B µ H u H d + h . c . 2 + H d ( ) 2 H u 2 + µ 2 + g Y ( ) ( ) 0 2 − H d 0 2 + q d g H d 0 2 − D 0 2 ! g 2 2 + 1 2 0 2 H u 2 q u g H u 8 ( ) − B µ H u 0 2 + H d ( ) 0 + h . c . 2 H u 0 2 + µ 0 H d Im F 0 YY ϕ 0 ≈ ϕ 0 Λ ≪ 1

Higgs mass � 2 − 4 ! ⎡ ( ) ⎤ 2 + M A 2 − 2 + M A = 1 2 cos 2 2 β ! ! 2 2 2 M A m Higgs M Z M Z M Z ⎢ ⎥ ⎣ ⎦ 2 2 ≡ M Z 2 + q u 2 g 2 v 2 : q u = 0 ⇒ m Higgs ! = m MSSM Higgs 2 2 M Z Minimization conditions � ( ) 2 µ 2 + M Z q u g cos2 β − q u gv 2 cos2 β − 2 D 0 2 = 2 ≡ 2 B µ ( ) sin2 β = 2 µ 2 = − M Z 2 − q u g cos2 β − q u gv 2 cos2 β − 2 D 0 M A ⎡ ⎤ 2 ⎛ ⎞ cos2 β D 0 − = 1 2 − 2 q u g − 2 q u g 2 cos2 β + 4 ! 4 cos 2 2 β ⎢ ! ⎥ + 8 q u g D 0 2 cos2 β D 0 m Higgs M Z M Z ⎜ ⎟ ⎝ ⎠ ⎢ ⎥ ⎣ ⎦

A plot for 126 GeV Higgs �

Su Summa mary � ! Dirac gaugino scenario is s one of the interesting alternatives s ! A new dynamical mechanism sm of D- D-term DSB propose sed ! 126 GeV Higgs s mass ss possi ssible via D vi D-t -term tr m tree l ee level el e effects ts Work in progress (w/ Itoyama & Shindou) � Possi ssibility of 126 GeV Higgs s mass ss vi via t top-s -stop l loop e effects ts �