IGGS&AT&LC Electroweak&symmetry&breaking&and&iggs& Lecture&9& Shahram&Rahatlou Fisica&delle&Par,celle&Elementari,&Anno&Accademico&2014815 htt://www.roma1.infn.it/eole/rahatlou/articelle/
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 2
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 2 2 2 [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? 3
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 4
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 5
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 6
arches: EXPERIMENTAL&CONSTRAINTS&ON&IGGS&MASS looked for in e + e Z C to W/Z masses: χ 2 Indirect search through recision measurement of W/Z SM sensitive to radiative corrections to iggs in loos 28 6 5 4 3 2 Direct&search&at&LEP&in&iggs8 strahlung&roduc,on&channel h 0 h 0 e + Z W ± W ± Z 0 MZ 0 > 114.4 GeV e Z @95%CL on measurements: 85 +39 ry uncertainty (5) had = 2761±0.00036 2747±0.00012 l. low Q 2 data GeV, or March 2008 Theory uncertainty α (5) α had = 0.02758±0.00035 0.02749±0.00012 incl. low Q 2 data m Limit = 160 GeV Direct searches at colliders: e + e CL s 1-1 -2-3 -4 Z Observed Exected for background LEP Z 1-5 114.4 115.3 Preliminary Excluded Preliminary 0 00 30 400 0 300 ev] m [GeV] -6 0 2 4 6 8 1 112 114 116 118 120 M (GeV) 7
IMPLICATIONS&OF&UNITARITY&ON&IGGS&MASS EW equivalence theorem: for boson m 2 W Recall: longitudinal W generated by absorbing a massless Goldstone boson W behaves like a Goldstone W + L W L W + L W L G + G G + G 2 Amlitude of such rocess can be comuted with the Jacob-Wick artial wave exansion final helicities M(λ 3 λ 4 ; λ 1 λ 2 )= initial helicities For longitudinal W λi,f= 0 so J0 = 0 with L L s Λ2 EW 8π s ( i f ) 1 /2 ei(λ i λ f )φ 1 2 3 4 (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 Partial wave unitarity imlies unitarity would be lost for M J=0 = ( G F s 16π 2. M J 2 Im M J 1 A(W + W W + W ) s M W 2 1 [ s + t v 2 (Re M J ) 2 Im M J 0 s2 s M 2 ] t2 t M 2 ( ) 1 Im M J 1 4 ( s c = 4π 2 =(1.2 TeV) 2 G F 8
UPPER&BOUND&ON&IGGS&MASS WW scattering sensitive to iggs mass W + W + W W For s m 2 h M J=0 = G F m 2 h 4π 2 Unitarity conservation rovides uer bound on iggs mass Re M J 1 2 m 2 h 4π 2 3G F (700 GeV) 2 9
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 articles Vector bosons always referred to fermions But must be kinematically allowed Fixing mass of iggs fixes decay rates for all final states
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, 1 3 3 ) t t for high M ;BR < 20%. -2-3 cc Z 0 200 300 500 00 M [GeV] LC IGGS XS WG 11
IGGS&WIDT [GeV] 3 2 1-1 -2-3 0 200 300 500 00 M [GeV] LC IGGS XS WG 12
PENOMENOLOGICAL&PROFILE&OF&IGGS&IN&1976 htt://cdsweb.cern.ch/record/874049 13
IGGS&PRODUCTION&AT&LEP dominant (BR 84%) and 14
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 15