Supersymmetric Higgs bosons and beyond Jos Francisco Zurita (ITP, - PowerPoint PPT Presentation

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