Higgsportal The \Higgs" discovery Johan Rathsman - a portal to new physics Johan Rathsman Department of astronomy and theoretical physics, 2012-10-17 1 / 1 Higgsportal Johan Rathsman The \Higgs" discovery 2 / 1 Now also in the world of particle physics July 4th 2012 - a historic day in many ways ::: Higgsportal Johan Rathsman 3 / 1 Now also in the world of particle physics July 4th 2012 - a historic day in many ways ::: Higgsportal Johan Rathsman 4 / 1 Now also in the world of particle physics July 4th 2012 - a historic day in many ways ::: Higgsportal Johan Rathsman 5 / 1 July 4th 2012 - a historic day in many ways ::: Higgsportal Johan Rathsman Now also in the world of particle physics 6 / 1 July 4th 2012 - a historic day in many ways ::: Higgsportal Johan Rathsman Now also in the world of particle physics 7 / 1 and in Lund Higgsportal Johan Rathsman 8 / 1 Published Higgsportal Johan Rathsman 9 / 1 Published Higgsportal Johan Rathsman 10 / 1 Published Higgsportal Johan Rathsman 11 / 1 LHC data in H ! γγ channel proton proton collider with 7/8 TeV center of mass energy Higgsportal Two multipurpose experiments: ATLAS and CMS Johan Rathsman H ! γγ on-shell ) spin 0 or 2 12 / 1 ATLAS data { exclusion Standard Model Higgs particle excluded (95 % CL): 111 < mH < 122 GeV and 131 < mH < 559 GeV Higgsportal Johan Rathsman 13 / 1 ATLAS data { signal Compatibility with background only hypothesis: observed and expected in standard model Higgsportal Johan Rathsman ) mH = 126:0 ± 0:4(stat) ± 0:4(sys) GeV 14 / 1 CMS data { signal Compatibility with background only hypothesis: observed and expected in standard model Higgsportal Johan Rathsman ) mH = 125:3 ± 0:4(stat) ± 0:5(sys) GeV 15 / 1 preLHC experimental results in standard model Direct LEP-limit: mH > 114 GeV (95% CL) Indirect electroweak precision tests: mH < 158 GeV (95% CL) Higgsportal Johan Rathsman very good agreement with direct detection! 16 / 1 Higgsportal Johan Rathsman The standard model of particle physics 17 / 1 The particle content of the standard model Describes the electromagnetic, weak and strong forces Higgsportal Johan Rathsman All particles observed { that's it? 18 / 1 Gauge symmetries and Lagrangians dynamics of relativistic quantum field theory described by Lagrangian (density) L = K − V standard model with U(1)Y ⊗ SU(2)L ⊗ SU(3)C gauge iYf α(x)=2 3 Higgsportal symmetry (local transf. of type e , Yf = 2Qf − 2If ) Johan Rathsman uL LSM = (¯uL; d¯L)iD= +u ¯RiDu= R + d¯RiDd= R + ::: dL 1 1 1 − B Bµν − W i W µν − G a G µν 4 µν 4 µν i 4 µν a p 2 2 p 2 2 where (e = g1g2= g1 + g2 , sin θw = g1= g1 + g2 ): Y σ λ D = @ − ig f B − ig i W i − ig a G a µ µ 1 2 µ 2 2 µ s 2 µ Bµν = @µBν − @ν Bµ i i i ijk j k Wµν = @µWν − @ν Wµ + g2 WµWν a a a abc b c Gµν = @µGν − @ν Gµ + gs f GµGν explicit mass terms would break SU(2)L gauge symmetry 1 L = −m (¯u u +u ¯ u ) + M2 W 3W 3µ + ::: mass u R L L R 2 V µ 19 / 1 Englert{Brout{Higgs{Guralnik{Hagen{Kibble{ ::: mechanism Higgsportal Johan Rathsman Spontaneous breaking of SU(2)L gauge symmetry weak force carriers W and Z massive quarks and leptons can be given masses through Yukawa interaction with Higgs field one more massive particle { the Higgs boson 20 / 1 Spontaneous breaking of global symmetry µ Complex field φ with L = @µφ∂ φ − V (φ) and potential 1 1 V (φ) = − µ2jφj2 + λjφj4 Higgsportal 2 4 Johan Rathsman L unchanged under φ ! φeiα µ minimum: v = p λ expand around minimum φ = v + H + iG and identify term in 2 2 front of H and G p ) \Higgs" mass: mH = 2λv (radial excitations) Nambu-Goldstone mass: mG = 0 (angular excitations) Symmetry broken by ground state { spontaneous symmetry breaking (Nobel prize 2008) ) equations of motion unchanged If the symmetry is local (φ ! φeiα(x)) the Nambu-Goldstone boson is \eaten" by the gauge field making it massive 21 / 1 Electroweak symmetry breaking in Standard Model Higgs sector in Standard Model p Higgsportal 1 2G + Johan Rathsman Add complex doublet Φ = p 2 v + H + iG 0 2 with Lagrangian LHiggs = jDµΦj − V (Φ) where Y σ D Φ = @ − ig f B − ig i W i Φ µ µ 1 2 µ 2 2 µ and the potential contains all the self-interactions of Φ 2 y 1 y 2 V (Φ) = −µ Φ Φ + 2 λ Φ Φ Higgs mechanism in Standard Model µ2 > 0 ) vacuum expectation value v ≈ 246 GeV/c2 ) SU(2)L⊗U(1)Y \spontaneously" broken to U(1)e:m: three would be Nambu-Goldstone bosons G 0 and G ± (longitudinal components of Z and W ) 2 2 one massive Higgs field H, mH = λv 22 / 1 Vector boson masses and interactions with Higgs field 1 0 In unitary gauge Φ = p 2 v + H Higgsportal 1 1 W ± = p (W 1 ∓ iW 2) and Z = (g W 3 − g B ) Johan Rathsman µ µ µ µ p 2 2 2 µ 1 µ 2 g1 + g2 couple to the Higgs field through 1 1 jD Φj2 = g 2W +W −µ(v + H)2 + (g 2 + g 2)Z Z µ(v + H)2 + ::: µ 4 2 µ 8 1 2 µ giving masses 1 1q m = g v ; m = g 2 + g 2v W 2 2 Z 2 1 2 and interactions 2 2 2mW + −µ 2mZ µ L 2 = W W H + Z Z H + ::: jDµΦj ;int v µ v µ 23 / 1 Fermion masses and interactions with Higgs field Add Yukawa type interaction (example d-quark) Higgsportal LY = −yd (¯u; d¯)LΦdR + h:c: Johan Rathsman In unitary gauge v H H LY = −yd p (d¯LdR + d¯RdL) 1 + = −md dd¯ 1 + 2 v v giving mass v md = yd p 2 and coupling to Higgs m L = − d ddH¯ Y;int v 24 / 1 Why is the Higgs boson so \light"? Standard Model is an effective theory ) expect it to break Higgsportal down at some high scale Λ (e.g. Planck mass ∼ 1019 GeV ) Johan Rathsman Calculating the one-loop corrections to the Higgs boson mass one finds 3Λ2 m2 = m2 + 4m2 − 2m2 − 4m2 − m2 H H;0 8π2v 2 t W Z H ) \natural scale" for Higgs boson mass given by Λ and not v 2 2 (tree-level mH = λv ) Solutions: 2 fine-tuning { mH;0 cancels one-loop correction \exactly" Higgs boson is not a fundamental scalar (e.g. Technicolor) There is a symmetry that protects the Higgs boson from acquiring a large mass 25 / 1 Higgsportal Johan Rathsman Theory beyond the standard model 26 / 1 Supersymmetry - one possible solution Why is this not a problem for fermions? Protected by Chiral symmetry: Higgsportal the Lagrangian gets an additional symmetry if mf ! 0 ) higher order corrections have to be proportional to m Johan Rathsman f ) only log(Λ) dependence ) no fine-tuning SUSY solution introduce Higgsino { SUSY fermion partner to Higgs boson Higgsino mass mH~ is protected by the Chiral symmetry Imposing (exact) SUSY mH = mH~ is also stabilized SUSY complications Anomaly cancelation and analytic structure of SUSY Lagrangian ) the SM cannot be supersymmetrized as is { have to add an additional Higgs doublet No supersymmetric partners observed ) Supersymmetry has to be softly broken ) plethora of parameters 27 / 1 Particle content minimal supersymmetric model Higgsportal Johan Rathsman 28 / 1 Higgs sector of minimal supersymmetric model Two complex Higgs doublets: Hu and Hd ) 5 scalar degrees of freedom after electroweak symmetry breaking Higgsportal ± CP conserved: h, H (CP-even, mh ≤ mH ), A (CP-odd), H Johan Rathsman supersymmetry ) Higgs potential very constrained { only two parameters at tree-level: 0 vu hHu i mH± ; tan β = = 0 vd hHd i Other masses determined at tree-level 2 2 2 mA = mH± − mW 1 q m2 = m2 + m2 ∓ (m2 + m2 )2 − 4m2 m2 cos2 2β h;H 2 A Z A Z A Z 2 2 2 ) mh ≤ mZ cos 2β (equality in decoupling limit, mH± ! 1) approximate custodial symmetry mA ≈ mH ≈ mH± 29 / 1 Couplings and mixings mixing of CP-even Higgs bosons 0 H cos α sin α Hd Higgsportal = 0 h − sin α cos α Hu Johan Rathsman 2 2 mH + mh at tree-level sin 2α = − 2 2 sin 2β mH − mh Couplings relative to standard model ZZh, WWh: sin(β − α) ZZH, WWH: cos(β − α) uuh : cos(α)= sin(β) = sin(β − α) + cot β cos(β − α) uuH : sin(α)= sin(β) = cos(β − α) − cot β sin(β − α) ddh : − sin(α)= cos(β) = sin(β − α) − tan β cos(β − α) ddH : cos(α)= cos(β) = cos(β − α) + tan β sin(β − α) standard model limit: sin(β − α) ! 1, mH± ! 1 30 / 1 Higher order corrections to Higgs sector All particles enter through loops Higgsportal Sensitivity to supersymmetry breaking parameters Johan Rathsman 4 2 2 2 2 2 3mt mS Xt Xt mh = mh;tree + 2 2 log 2 + 2 1 − 2 + ::: 2π vu mt mS 12mS where m~ + m~ - m = t1 t2 with ~t the two stop mass eigenstates S 2 1;2 - Xt = At − µ cot β, At is a supersymmetry breaking contribution to the Higgs-stop-stop coupling, µ is the Higgsino mass parameter 2 2 Maximal mixing: Xt = 6mS ) mh . 135 GeV 2 No mixing: Xt = 0 ) mh . 120 GeV Supersymmetry predicts at least one light Higgs boson 31 / 1 Higgsportal Johan Rathsman Interpretation of data beyond the standard model 32 / 1 ���������������������������������������������� ����������������������������������������������������������������������� 2 2 2 M M M ± , β ΔM MSUSY,X ,..