HIGGS AT HADRON COLLIDER

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1 IGGS AT ADRON COLLIDER Electroweak symmetry breaking and iggs Lecture 8 24 October 2012 Shahram Rahatlou Fisica Nucleare e Subnucleare III, Anno Accademico htt://

2 WO NEEDS IGGS? Gauge invariance of Electroweak theory requires all fermions and W and Z to be massless Discovery of W and Z in 1983 roved them to be retty heavy Need a mechanism to dynamically generate mass for all articles and conserve the gauge invariance iggs mechanism and goldstone bosons address this roblem Exerimental evidence needed to validate theory Predict iggs roduction rocesses and decay rates Direct search roduce iggs and look for decay roducts: invariant mass and characteristic kinematics Indirect search Calculate contribution of iggs in corrections to well known SM rocesses Combined analysis of all recisely measured Z-ole observables and check validity with different iggs mass assumtions Shahram Rahatlou, Roma Saienza & INFN 2

3 GENERATING MASS FOR W AND Z Proagator for massless vector bosons at tree level Gauge invariance µ ν i Π µν () i( µ ν 2 g µν )Π( 2 ) µ Π µν () = ν Π µν () =0 Renormalized roagator at higher order = i(g µν µν 2 ) 2 [1+Π( 2 )] For a massless scalar article in the loo Π( 2 ) 2 0 g 2 v [1 + Π( 2 )] = 2 g 2 v 2, For =0 we have our vector boson with m = gv! Do we have already any such scalar? Shahram Rahatlou, Roma Saienza & INFN 3

4 GENERATING W AND Z MASS WIT π 0 W and Z coule to charge and neutral currents Charged and neutral ions have very small mass (comared to other hadrons) and are massless in the limit of massless quarks! Pions in the loo rovided needed mass term Prediction for W and Z mass L int = g Z j Z µ Zµ + g W (j W µ W +µ +h.c.) π 0 Z 0 Z 0 Π( 2 )= g 2 Z f 2 π /2, m W = g W f π. m Z = g Z f π. Pion decay constant measured from decay rate to be f π =93MeV W and Z mass related in SM through Good agreement with measurement We know g Z 0.37 which corresonds to mz = 35 MeV! Off by 3 orders of magnitude! Need a new scalar for dynamic mass generation m W m Z = g W g Z cos θ W 0.88 Shahram Rahatlou, Roma Saienza & INFN 4

5 SPONTANEOUS SYMMETRY BREAKING New comlex SU(2) doublet with four degrees of freedom (massless scalar articles) Self-interaction otential V (Φ) = λ 4 (Φ Φ 1 2 v2 ) 2 Non-zero vacuum exectation value (VEV) generates one massive scalar remaining 3 scalar absorbed by W, Z, and hoton Φ 0 = v/ 2, We want this scalar to coule to generate correct mass Therefore the VEV must be v =246GeV. m Z = g Z v 91 GeV. New massive scalar article commonly known as iggs Boson Interactions, decay rates known recisely But its mass not determined and must be measured m h = 1 2 λv2 Shahram Rahatlou, Roma Saienza & INFN 5

6 FERMION MASSED AND CP VIOLATION In addition to Z and W, also fermions acquire mass in SM thanks to Yukawa couling to iggs boson L Yukawa = h u (ū R u L Φ 0 ū R d L Φ + ) h d ( d R d L Φ 0 + d R u L Φ )+h.c. f f f f fermions SU(2) U(1) Y (ν,e ) L 2 1 e R 1 2 (u, d) L 2 1/3 u R 1 4/3 d R 1 2/3 v h 0 Couling roortional to fermion mass g hf f = m f /v Will determine iggs decay branching fractions Diagonalization of comlex mass matrix cornerstone of Kobayashi- Maskawa mechanism to introduce CP violation in Standard Model Discussed in detail in CP-violation lectures Shahram Rahatlou, Roma Saienza & INFN 6

7 earches: EXPERIMENTAL CONSTRAINTS ON IGGS MASS RC to W/Z masses: heory uncertainty #$ (5) had = 5 χ 2 Indirect search through recision measurement of W/Z SM sensitive to radiative corrections to iggs in loos March 2008 Direct search at LEP in iggs- strahlung roducjon channel h 0 h 0 e + Z W ± W ± Z 0 MZ 0 > e ision measurements: = ± ± incl. low Q 2 data GeV, or Theory uncertainty α (5) α had = ± ± incl. low Q 2 data m Limit = 160 GeV Direct searches at colliders: looked for in e + e Z e + e CL s Z Observed Exected for background LEP Z Preliminary Excluded Preliminary [GeV] m [GeV] Shahram Rahatlou, Roma Saienza & INFN M (GeV) 7

8 8 IMPLICATIONS OF UNITARITY ON IGGS MASS EW equivalence theorem: for W behaves like a Goldstone boson m 2 W s Λ2 EW Recall: longitudinal W generated by absorbing a massless Goldstone boson W + L W L W + L W L G + G G + G Amlitude of such 2 rocess can be comuted with the Jacob- Wick arjal wave exansion final helicities M(λ 3 λ 4 ; λ 1 λ 2 )= initial helicities For longitudinal W λ i,f = 0 so J 0 = 0 with L L 8π s ( i f ) 1 /2 ei(λ i λ f )φ (2J +1)M J λ (s)dj λ i λ (θ) f J=J { 0 J 0 max{λ i, λ f } λ i λ 1 λ 2 λ f λ 3 λ 4 ParJal wave unitarity imlies unitarity would be lost for M J=0 = ( G F s 16π 2. M J 2 Im M J 1 ( s c = 4π 2 =(1.2 TeV) 2 G F A(W + W W + W ) s M W 2 1 [ s + t v 2 (Re M J ) 2 Im M J 0 ] s2 t2 s M 2 t M 2 ( ) 1 Im M J 1 4

9 9 UPPER BOUND ON IGGS MASS WW scavering sensijve to iggs mass W + W W + W For s m 2 h M J=0 = G F m 2 h 4π 2 Unitarity conservajon rovides uer bound on iggs mass Re M J 1 2 m 2 h 4π 2 3G F (700 GeV) 2

10 IGGS COUPLINGS f f f f v h 0 g hf f = m f /v V V V V V V v v v h 0 h 0 h 0 g hv V =2m 2 V /v g hhv V =2m 2 V /v 2 iggs couling enhanced for heavier arjcles Vector bosons always referred to fermions But must be kinemajcally allowed Fixing mass of iggs fixes decay rates for all final states

11 11 IGGS BRANCING FRACTIONS Low Mass < 140 GeV b b dominant, BR = 60 90% τ + τ, c c, gg BR= a few % γγ, γz, BR = a few ermille Branching ratios 1-1 bb gg WW ZZ tt igh Mass > 140 GeV WW, ZZ u to > 2M W WW, ZZ above (BR 2, ) t t for high M ;BR < 20% cc Z M [GeV] LC IGGS XS WG

12 IGGS WIDT [GeV] M [GeV] LC IGGS XS WG 12

13 13 PENOMENOLOGICAL PROFILE OF IGGS IN 1976 htt://cdsweb.cern.ch/record/ Note mass scale all the way to 1 MeV! No track of b or t: not discovered yet!

14 14 IGGS PRODUCTION AT LEP dominant (BR 84%) and

15 15 IGGS PRODUCTION AT ADRON COLLIDERS X q g t V V X Gluon fusion Weak-Boson Fusion q q V t _ q _ t iggs Strahlung t t