Supersymmetric Higgs bosons and beyond José Francisco Zurita (ITP, Univ. Zürich) Phys.Rev.D81:015001, 2010 (and work in progress)* * in collaboration with: Marcela Carena, Kyoungchul Kong, Eduardo Pontón Thursday, March 4, 2010
Outline • Motivation • Higgs Physics in the SM and in the MSSM • BMSSM Higgs sectors • Collider phenomenology • Conclusions Thursday, March 4, 2010
Motivation • MSSM Higgs sector is strongly constrained • LEP search: m h > 90 GeV • MSSM 2 loops: m h < 130 GeV • Tension can be relaxed with new d.o.f (i.e: NMSSM) • Effective Field Theory (EFT) analysis by: • Brignole, Casas, Espinosa, Navarro (2003). • Dine, Seiberg, Thomas (2007). • This talk: collider phenomenology Thursday, March 4, 2010
SM Higgs L = ( D µ φ ) † D µ φ − 1 4 F µ ν F µ ν − V V = µ 2 φ ∗ φ + λ ( φ ∗ φ ) 2 = µ 2 2 ) + λ 2 ( φ 2 1 + φ 2 4 ( φ 2 1 + φ 2 2 ) 2 V has minima at � | φ | = − µ 2 / λ 1 Expand φ = 2[ v + h ( x )] √ One gets m 2 h = λ v 2 h 3 , h 4 , hA 2 , h 2 A 2 m 2 A = g 2 v 2 ⊕ ⊕ A single unknown parameter: m h � ¯ fermion masses Yukawa couplings g � ψ L φ ψ R g hV V = 2 m 2 V /v 2 g hf ¯ f = m f /v Thursday, March 4, 2010
Searching for the Higgs ! (pp " H+X) ! pb " 10 2 # s = 14 TeV M t = 175 GeV gg " H 10 CTEQ4M 1 qq " Hqq _ ’ " HW -1 qq 10 -2 10 _ " Htt _ gg,qq -3 10 _ " Hbb _ _ " HZ gg,qq qq -4 10 0 200 400 600 800 1000 M H ! GeV " M. Spira, Fortsch.Phys. 46 (1998) g W, Z H H 114 . 4 GeV < m h < 1 TeV W, Z g ( a ) ( b ) Exclusion (Tevatron, Jan. 2010) W, Z Q W, Z H 162 GeV < m h < 166 GeV ¯ Q H ( c ) ( d ) Thursday, March 4, 2010
Why Supersymmetry? • Solves the hierarchy problem. • Relates bosons and fermions: multiplets. • Gauge coupling unification. • Gaugino mass unification. • Includes gravity. • Provides a DM candidate. • Within a given supermultiplet: same quantum numbers, and same mass. • usw Thursday, March 4, 2010
MSSM • Supersymmetrized version of the SM. • Fermion Sfermion • Gauge boson Gaugino Since no scalar particle SUSY is broken with the electron mass and charge has been detected... Thursday, March 4, 2010
MSSM Lagrangian breaks SUSY explicitly. L = L SUSY + L soft � � − 1 g + M 2 � W � W + M 1 � B � L MSSM = M 3 � g � B + c.c soft 2 � � u a u � QH u − � d a d � e a e � � QH d − � LH d + c.c − − � Q Q − � L � u † − � Q † m 2 L † m 2 u m 2 d m 2 d d † − � e m 2 e † L − � u � e � e e − m 2 u H u − m 2 H u H ∗ H d H ∗ d H d − ( bH u H d + c.c) . Soft terms come in two kinds: • Sparticle masses (gauginos, sfermions) • Yukawa couplings (Higgs-sfermion-sfermion) Thursday, March 4, 2010
Superfield Formalism The 4D spacetime is extended to the superspace x µ , θ , ¯ x µ θ Fields become superfields: θ − 1 i √ Φ ( x µ , θ , ¯ 2 θψ + θ 2 F + i ∂ µ φθσ µ ¯ 2 θ 2 ∂ µ ψσ µ ¯ 4 ∂ µ ∂ µ φθ 2 ¯ θ 2 θ ) = φ + θ − √ : scalar : fermion : auxiliary φ ψ F � �� The Lagragian is d 2 θ d 2 ¯ d 2 θ W + c.c � L = θ K + K : Kähler potential (kin. terms and gauge int.) W : Super potencial (Yukawa-like interactions) Thursday, March 4, 2010
THDM v 2 = v 2 u + v 2 H u , H d → h, H, A, H ± d scalars pseudoscalar Tree level: , , mixing between h y H tan β = v u /v d m A α Φ ¯ Φ ¯ uu dd Φ V V Φ h 0 cos α / sen β − sen α / cos β sen( β − α ) H 0 sen α / sen β cos α / cos β cos( β − α ) A 0 1 / tan β tan β 0 22 H † m 2 11 H † u H u + m 2 = d H d − [ bH u H d + c . c] V 1 d H d ) 2 + 1 u H u ) 2 + λ 3 ( H † 2 λ 1 ( H † u H u )( H † u H † 2 λ 2 ( H † d H d ) + λ 4 ( H u H d )( H † + d ) � 1 � 2 λ 5 ( H u H d ) 2 + � � λ 6 ( H † d H d ) + λ 7 ( H † + u H u ) ( H u H d ) + c . c . Thursday, March 4, 2010
Higgs in the MSSM MSSM: λ 1 = λ 2 = ( g 2 1 + g 2 λ 3 = ( g 2 2 − g 2 λ 4 = − g 2 2 ) / 4 , 1 ) / 4 , 2 / 4 , λ 5 = λ 6 = λ 7 = 0 m (0) m (0) Tree level: tan β ≈ 1 ≤ m Z | cos(2 β ) | 0 , ≈ h h m (0) tan β > 10 2-loops: m Z , ≈ m h < 130 GeV h m S , A t , A b LEP 88-209 GeV Preliminary LEP 88-209 GeV Preliminary tan ! tan ! m h ° -max m h ° -max M SUSY =1 TeV M 2 =200 GeV 10 10 10 10 µ =-200 GeV m gluino =800 GeV Stop mix: X t =2M SUSY Excluded by LEP Excluded 1 1 1 1 by LEP Theoretically Inaccessible 0 20 40 60 80 100 120 140 0 100 200 300 400 500 m h ° (GeV/c 2 ) m A ° (GeV/c 2 ) Thursday, March 4, 2010
Higgs BMSSM Thursday, March 4, 2010
BMSSM BMSSM can MSSM M. Dine, N. Seiberg, manifest in the S. Thomas (2007) 114 . 4 GeV < m h < 135 GeV Higgs sector Starting point: Effective theory (valid below scale M) W = µH u H d + ω 1 2 M (1 + α 1 X )( H u H d ) 2 Spurion: Only 2 parameters: ω 1 , α 1 ∼ O (1) X = m S θ 2 m S µ O (1 /M ) ≡ Dim5 ∆ λ 5 = α 1 ω 1 ∆ λ 6 = ∆ λ 7 = ω 1 M M Thursday, March 4, 2010
Related work in HDO • MSSM: Antoniadis, Dudas, Ghilencea, Tziveloglou (‘08, ’09), Strumia (’99) • Stability: Blum, Delaunay, Hochberg (’09) • Fine tuning: Casas, Espinosa, Hidalgo (’04), Cassel, Ghilencea, Ross (’10) • DM: Cheung, Choi, Song (’09), Berg, Edsjo, Gndolo, Lundstrom, Sjors (’09) • Cosmology: Bernal, Blum, Losada, Nir (’09) • EW baryogenesis: Grojean, Servant, Wells (’05), Bodeker, Fromme, Huber, Seniuch (’05), Delaunay, Grojean, Wells (’08), Noble, Perelstein (’08), Grinstein, Trott (’08) • S(upersymmetric)EWSB vacua: Batra, Pontón (’09) EWSB takes place in the supersymmetric limit (different from the MSSM!). Thursday, March 4, 2010
Dimension 6 Lagrangian d e V H d + H † u e V H u H † = K c 1 d e V H d ) 2 M 2 (1 + γ 1 ( X + X † ) + β 1 XX † )( H † + c 2 u e V H u ) 2 M 2 (1 + γ 2 ( X + X † ) + β 2 XX † )( H † + c 3 u e V H u )( H † d e V H d ) M 2 (1 + γ 3 ( X + X † ) + β 3 XX † )( H † + c 4 M 2 (1 + γ 4 ( X + X † ) + β 4 XX † )( H u H d )( H u H d ) † + { [ c 6 M 2 (1 + β 6 XX † + γ 6 X + δ 6 X † ) H † d e V H d + c 7 M 2 (1 + β 7 XX † + γ 7 X + δ 7 X † ) H † u e V H u ]( H u H d ) + h.c } , + : 20 extra free parameters. O (1 /M 2 ) Thursday, March 4, 2010
Dimension 6 Lagrangean • At this order, two new contributions: • Genuine (honest) dimension 6 operators: 1 M 2 | H u H d | 2 ( λ 8 H † 8 H † d H d + λ ′ u H u ) V non − ren . ⊃ • Kinetic Mixing (after EWSB) L kin mix ⊃ − 2 c 3 O ( v 2 /M 2 ) M 2 { ( D µ H d ) † H d ( D µ H u ) † H u � � } λ (0) ∆ λ (5) 1 , 4 ∼ g 2 1 , 4 = 0 Dimension 6 analysis is needed ! λ (0) ∆ λ (5) 5 , 7 � = 0 5 , 7 = 0 Thursday, March 4, 2010
Masses at O(1/M) h ) MSSM + ( ∆ m 2 h ) 5 d + . . . m 2 h = ( m 2 2 v 2 (4 µ − α 1 m s ω 1 tan β ≈ 1 ) M h ) 5 d ( ∆ m 2 tan β > 10 0 300 300 Μ � m s � 200 GeV max m h for � pars � � 1 Μ � m s � 200 GeV M � 1 TeV M � 1 TeV 250 250 tan Β � 2 tan Β � 20 200 200 m h � GeV � m h � GeV � max m h for � pars � � 1 150 150 MSSM 100 100 50 50 MSSM 0 0 0 100 200 300 400 0 100 200 300 400 m A � GeV � m A � GeV � sEWSB vacua MSSM vacua M. Carena, K. Kong, E. Pontón, J. Z (2009) Thursday, March 4, 2010
Couplings at O(1/M) (I) x = m 2 Z /m 2 A , y = µ/M, m s /M hV V = 1 + O ( x 2 , y 2 ) A 1 , A 2 ∼ O (1) HV V = A 1 x + A 2 y 1.0 1.0 h 0 h 0 and g HVV � g hVV and g HVV � g hVV SM SM MSSM 0.5 0.5 H 0 H 0 MSSM 0.0 0.0 g hVV � g hVV g hVV � g hVV SM SM Μ � m s � 200 GeV � 0.5 � 0.5 Μ � m s � 200 GeV M � 1 TeV M � 1 TeV MSSM tan Β � 2 MSSM tan Β � 20 � 1.0 � 1.0 0 100 200 300 400 0 100 200 300 400 m A � GeV � m A � GeV � M. Carena, K. Kong, E. Pontón, J. Z (2009) Thursday, March 4, 2010
Couplings at O(1/M) (II) hb ¯ b = 1 + ( A 1 x + A 2 y ) / tan β + O ( x 2 , y 2 ) Hb ¯ b = − tan β (1 + ( A 1 x + A 2 y ) / tan β ) + O ( x 2 , y 2 ) 20 H 0 2 H 0 SM and g Hbb � g hbb SM SM and g Hbb � g hbb SM 15 MSSM 1 10 MSSM h 0 h 0 5 0 0 g hbb � g hbb g hbb � g hbb � 1 Μ � m s � 200 GeV � 5 Μ � m s � 200 GeV M � 1 TeV M � 1 TeV � 10 tan Β � 2 tan Β � 20 � 2 0 100 200 300 400 0 100 200 300 400 m A � GeV � m A � GeV � M. Carena, K. Kong, E. Pontón, J. Z (2009) M. Carena, K. Kong, Thursday, March 4, 2010
Combining with loops λ i = λ (0) + ∆ λ (5) + ∆ λ (6) + ∆ λ (1 − loop ) i i i i • Obtain masses and couplings of the Higgs sector • BRs: Modifying HDECAY v 3.4 A. Djouadi, J. Kalinowski, M. Spira (1996) • Experimental Bounds: HiggsBounds v1.2.0 * P. Bechtle, O. Brein, S. Heinemeyer, G. Weiglein, K. E. Williams (2008-2009) * includes LEP bound h to jets + LEP charged Higgs + latest Tevatron data Thursday, March 4, 2010
Collider phenomenology Thursday, March 4, 2010
Lightest Higgs mass Excluded by LEP Tevatron upgrade Excluded by Tevatron Allowed Thursday, March 4, 2010
Heavy CP-even Mass Excluded by LEP Tevatron upgrade Excluded by Tevatron Allowed Thursday, March 4, 2010
Charged Higgs mass Excluded by LEP Tevatron upgrade Excluded by Tevatron Allowed Thursday, March 4, 2010
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