Higgs Boson Physics, Part II

Higgs Boson Physics, Part II Laura Reina TASI 004, Boulder

Outline of Part II What do we know about the Standard Model Higgs boson? indirect bounds on M H from the theoretical consistency of the Standard Model. indirect bounds from precision fits of electroweak physics observables. direct bounds on M H from experimental searches at LEP II. The Higgs boson sector of the MSSM General structure. Higgs boson couplings to the SM gauge bosons. Higgs boson couplings to the SM fermions. Higgs boson decay branching ratios. direct bounds on M h -M A from experimental searches at LEP II.

Some References for Part II Theory and Phenomenology of the Higgs boson(s): The Higgs Hunter Guide, J. Gunion, H.E. Haber, G. Kane, and S. Dawson Introduction to the physics of Higgs bosons, S. Dawson, TASI Lectures 1994, hep-ph/941135 Introduction to electroweak symmetry breaking, S. Dawson, hep-ph/990180 Higgs Boson Theory and Phenomenology, M. Carena and H.E. Haber, hep-ph/00809 The Minimal Supersymmetric Standard Model: The Quantum Theory of Fields, V. III, S. Weinberg

Theoretical constraints on M H in the Standard Model SM as an effective theory valid up to a scale Λ. The Higgs sector of the SM actually contains two unknowns: M H and Λ. Bounds given by: unitarity triviality vacuum stability EW precision measurements fine tuning M H = λv M H determines the weak/strong coupling behavior of the theory, i.e. the limit of validity of the perturbative approach.

Unitarity: longitudinal gauge boson scattering cross section at high energy grows with M H. Electroweak Equivalence Theorem: in the high energy limit (s M V ) A(V 1 L...V n L V 1 L...V m L ) = (i) n ( i) m A(ω 1...ω n ω 1...ω m )+O ( M V s ) (V i L =longitudinal weak gauge boson; ωi =associated Goldstone boson). Example: W + L W L W + L W L A(W + L W L W + L W L ) 1 ( s t + + v s MH t MH ( ) A(ω + ω ω + ω ) = M H s t + v s MH t MH A(W + L W L W + L W L ) = A(ω + ω ω + ω ) + O ( M W s s t ) )

Using partial wave decomposition: A = 16π (l + 1)P l (cos θ)a l l=0 dσ dω = 1 64π s A σ = 16π s (l + 1) a l = 1 Im [A(θ = 0)] s l=0 a l = Im(a l ) Re(a l ) 1 Most constraining condition for W + L W L W + L W L from [ a 0 (ω + ω ω + ω ) = M H + M H 16πv s MH M H s log ( 1 + s M H Re(a 0 ) < 1 M H < 870 GeV Best constraint from coupled channels (W + L W L + Z LZ L ): )) s M H M H 8πv s M a H 0 5M H 3πv M H < 780 GeV

Observe that: if there is no Higgs boson, i.e. M H s: a 0 (ω + ω ω + ω ) M H s s 3πv Imposing the unitarity constraint s c < 1.8 TeV Most restrictive constraint s c < 1. TeV New physics expected at the TeV scale Exciting!! this is the range of energies of both Tevatron and LHC

Triviality: a λφ 4 theory cannot be perturbative at all scales unless λ=0. In the SM the scale evolution of λ is more complicated: 3π dλ dt = 4λ (3g + 9g 4y t )λ + 3 8 g 4 + 3 4 g g + 9 8 g4 4y 4 t + (t=ln(q /Q 0), y t = m t /v top quark Yukawa coupling). Still, for large λ ( large M H ) the first term dominates and (at 1-loop): λ(q) = λ(q 0 ) 1 3 4π λ(q 0 ) ln ( Q Q 0 ) when Q grows λ(q) hits a pole triviality Imposing that λ(q) is finite, gives a scale dependent bound on M H : 1 > 0 λ(λ) M H < 8π ( v 3 log where we have set Q Λ and Q 0 v. ) Λ v

Vacuum stability: λ(q) > 0 For small λ ( small M H ) the last term in dλ/dt =... dominates and: λ(λ) = λ(v) 3 4π y t log from where a first rough lower bound is derived: λ(λ) > 0 ( ) Λ v MH > 3v y π t log ( ) Λ v More accurate analyses use -loop renormalization group improved V eff.

EW precision fits: perturbatively calculate observables in terms of few parameters: M Z, G F, α(m Z ), M W, m f, (α s (M Z )) extracted from experiments with high accuracy. SM needs Higgs boson to cancel infinities, e.g. M W, M Z W,Z H W,Z Finite logarithmic contributions survive, e.g. radiative corrections to ρ=m W /(M Z cos θ W ): ρ = 1 11g ( MH 96π tan ln θ W M W Main effects in oblique radiative corrections (S,T-parameters) New physics at the scale Λ will appear as higher dimension effective operators. )

M H only unknown input... Precision measurements of the SM, which fully test the quantum structure of the theory by including higher order loop corrections, constrain the mass of the SM Higgs to be light: M H < 51 GeV (95%cl) m t [GeV] 00 180 160 High Q except m t 68% CL m t (TEVATRON) χ 6 5 4 3 Theory uncertainty α had = α (5) 0.0761±0.00036 0.0747±0.0001 incl. low Q data 1 140 Excluded Preliminary (a) 10 10 10 3 m H [GeV] 0 Excluded 0 100 400 m H [GeV] Preliminary

Consequences for Standard-Model Higgs Precision electroweak data: Constrain M H in the MSM χ 6 5 4 3 1 0 Region excluded by direct searches All data, with old world-average M top All data, with new world-average M top Theory uncertainty 0 100 400 Higgs Boson Mass [GeV/c ] Old: New: M top MH M H or M top MH M H or 174 1 96 178 117 3 98 0 0 60 5 1 38 GeV 0 07 0 0 (Procedure as in hep-ex/03103!) 67 4 0 1 95 45 GeV 95 19 GeV 51 GeV 1 GeV CL 3 GeV CL (from the EWWG home page: lepewwg.web.cern.ch/lepewwg/) MWG

Fine-tuning: M H is unstable to ultraviolet corrections M H = (M 0 H) + g 16π Λ constant + higher orders MH 0 fundamental parameter of the SM Λ UV-cutoff scale Unless Λ EW-scale, fine-tuning is required to get M H EW-scale. More generally, the all order calculation of V eff would give: µ = µ + Λ c n (λ i ) log n (Λ/Q) n=0 Veltmann condition: the absence of large quadratic corrections is guaranteed by: c n (λ i ) log n (Λ/M H ) = 0 n=0 or better n max n=0 c n (λ i ) log n (Λ/M H ) = 0

In summary: 600 Triviality 500 Higgs mass (GeV) 400 300 00 10% 1% Electroweak amount of fine tuning = Λ M H n max n=0 n max = 1 c n (λ i ) log n (Λ/M H ) 100 Vacuum Stability 1 10 10 Λ (TeV) (C. Kolda and H. Murayama, hep-ph/0003170)

Adding more Higgs fields... Main constraints from: ρ parameter: MW = ρm Z cos θ W, ρ 1. flavor changing neutral currents. Ex.: Two Higgs Doublet Models (HDM) L Y ukawa = Γ u ij,k Q i LΦ k,c u j R + Γd ij,k Q i LΦ k d j R + h.c. for k = 1, Φ k = vk Φ k = Φ k + v k L Y ukawa = ū i L Γ u v k ij,k k }{{} Mij u u j R d i L Γ d v k ij,k k }{{} Mij d Avoid FC couplings by imposing ad hoc discrete symmetry: { { Φ 1 Φ 1 and Φ Φ d i d i and u j ±u j d j R + h.c. + FC couplings Model I: u and d coupled to same doublet Model II: u and d coupled to different doublets

The Higgs bosons of the MSSM Two complex SU() L doublets, with hypercharge Y =±1: ( ) ( ) Φ u = φ + u φ 0 u and (super)potential (Higgs part only):, Φ d = V H = ( µ + m u) Φ u + ( µ + m d) Φ d µbɛ ij (Φ i uφ j d + h.c.) + g + g 8 ( Φu Φ d ) + g ( Φ u = 1 0 v u φ 0 d φ d Φ uφ d The EW symmetry is spontaneously broken by choosing: ) ) (, Φ d = 1 normalized to preserve the SM relation: M W = g (v u + v d )/4 = g v /4. v d 0

Five physical scalar/pseudoscalar degrees of freedom: h 0 = ( ReΦ 0 d v d ) sinα + ( ReΦ 0 u v u ) cos α H 0 = ( ReΦ 0 d v d ) cos α + ( ReΦ 0 u v u ) sinα A 0 = ( ImΦ 0 d sinβ + ImΦ 0 u cos β ) H ± = Φ ± d sinβ + Φ± u cos β where tanβ=v u /v d. All masses can be expressed (at tree level) in terms of tanβ and M A : M H ± = M A + M W (M A + M Z ± ((M A + M Z) 4M ZM A cos β) 1/) M H,h = 1 Notice: tree level upper bound on M h : M h M Z cos β M Z!

Higgs masses greatly modified by radiative corrections. In particular, the upper bound on M h becomes: Mh MZ + 3g m [ ( ) t M 8π MW log S m + X t t MS ( )] 1 X t 1MS where M S (M t 1 + M t )/ while X t is the top squark mixing parameter: ( M Q t + m t + Dt L m t X t m t X t M R t + m t + Dt R ) with X t A t µ cot β. D t L = (1/ /3 sin θ W )M Z cos β D t R = /3 sin θ W M Z cos β

In summary: M max h 135 GeV (if top-squark mixing is maximal) Moreover, interesting sum-rule : M H cos (β α) + M h sin (β α) = [M max h tan β] large tan β { M A > M max h M A < M max h M h M max h M H M max h, M H M A, M h M A

Higgs boson couplings to SM gauge bosons: Some phenomelogically important ones: g hv V = g V M V sin(β α)g µν, g HV V = g V M V cos(β α)g µν where g V =M V /v for V =W, Z, and g haz = g cos(β α) (p h p A ) µ g sin(β α), g HAZ = (p H p A ) µ cos θ W cos θ W Notice: g AZZ = g AWW = 0, g H± ZZ = g H± WW = 0 Decoupling limit: M A M Z { M h M max h M H M H ± M A cos (β α) M4 Z sin 4β M 4 A { cos(β α) 0 sin(β α) 1 The only low energy Higgs is h H SM.

Higgs boson couplings to quarks and leptons: Yukawa type couplings, Φ u to up-component and Φ d to down-component of SU() L fermion doublets. Ex. (3 rd generation quarks): L Y ukawa = h t [ tp L tφ 0 u tp L bφ + u ] + hb [ bpl bφ 0 d bp L tφ d ] + h.c. and similarly for leptons. The corresponding couplings can be expressed as (y t, y b SM): g ht t = cos α sin β y t = [sin(β α) + cot β cos(β α)] y t g hb b = sin α cos β y b = [sin(β α) tan β cos(β α)] y b g Ht t = sin α sin β y t = [cos(β α) cot β sin(β α)] y t g Hb b = cos α cos β y b = [cos(β α) + tan β sin(β α)] y b g At t = cot β, g Ab b = tan β g H ± t b = g [m t cot β(1 γ 5 ) + m b tan β(1 + γ 5 )] M W Notice: consistent decoupling limit behavior.

Higgs couplings modified by radiative corrections Most important effects: Corrections to cos(β α): crucial in decoupling behavior. )] where cos(β α) = K [ M Z sin4β M A + O ( M 4 Z M 4 A K 1 + δm 11 δm M Z cos β δm 1 M Z sinβ δm ij corrections to the CP-even scalar mass matrix. Corrections to 3 rd generation Higgs-fermion Yukawa couplings. L eff = ɛ ij [ (hb + δh b ) b R H i dq j L + (h t + δh t ) t R H j uq i L ] + ht t R Q k LH k d + h b br Q k LH k u +h.c. m b = h ( bv cos β 1 + δh b + h ) b tan β h b h b m t = h ( tv sin β 1 + δh t + h ) t tan β h t h t h bv cos β(1 + b ) h tv sin β(1 + t )

MSSM Higgs boson branching ratios, possible scenarios:

MSSM Higgs boson branching ratios, possible scenarios:

MSSM Higgs boson branching ratios, possible scenarios:

Experimental searches for a Higgs boson LEP looked for the SM and the MSSM Higgs bosons in three channels: e - e + Z Z H e - e + ν e,e - W,Z H W,Z ν e,e + e - e + h 0,H 0 Z e + e ZH e + e Hν e ν e, He + e e + e h 0 A 0, H 0 A 0 A 0 The absence of a convincing signal sets the lower bounds: smax = 189 09 GeV M H >114.4 Gev (95% c.l.) M h0 /H 0 >91.0 GeV, M A0 >91.9 GeV (95% c.l.)

LEP 88-09 GeV Preliminary LEP 88-09 GeV Preliminary tanβ 10 m h -max Excluded by LEP tanβ 10 m h -max M SUSY =1 TeV M =00 GeV µ=-00 GeV m gluino =800 GeV Stop mix: X t =M SUSY 1 1 Excluded by LEP Theoretically Inaccessible 0 0 40 60 80 100 10 140 m h (GeV/c ) 0 100 00 300 400 500 m A (GeV/c ) SM Higgs CERN-EP/003-011 MSSM HIggs LHWG Note 001-04 LHWG home page: http://lephiggs.web.cern.ch/lephiggs/www

Some puzzling events around M H =115 GeV... Events / 3 GeV/c 30 5 0 s = 00-10 GeV LEP loose background Events / 3 GeV/c 1 10 8 s = 00-10 GeV LEP medium background Events / 3 GeV/c 7 6 5 s = 00-10 GeV LEP tight background 15 10 5 hz Signal (m h =115 GeV) all > 109 GeV cnd= 119 17 bgd= 116.51 15.76 sgl= 10.0 7.1 6 4 hz Signal (m h =115 GeV) all > 109 GeV cnd= 34 5 bgd= 35.69 3.93 sgl= 5.3 3.88 4 3 1 hz Signal (m h =115 GeV) all > 109 GeV cnd= 18 4 bgd= 13.97 1.1 sgl=.9.1 0 0 0 40 60 80 100 10 Reconstructed Mass m H [GeV/c ] 0 0 0 40 60 80 100 10 Reconstructed Mass m H [GeV/c ] 0 0 0 40 60 80 100 10 Reconstructed Mass m H [GeV/c ] The resolution of this puzzle is now left to the Fermilab s Tevatron and the LHC. (L. Maiani, CERN Director)

Searching for (the) Higgs Boson...... a jazz fusion pianist in the UK...

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