Standard Model - Electroweak Interactions. Standard Model. Outline. Weak Neutral Interactions. Electroweak Theory. Experimental Tests.

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1 Standard Modl - Elctrowak Intractions Outlin ak Nutral Intractions Nutral Currnts (NC) Elctrowak Thory ± and Z and γ Discovry of ± Exprimntal Tsts LEP Z Boson Mass and idth Numbr of Nutrinos ± Boson ± Pair Production Mass and idth Higgs Boson Mass, LHC Suprsymmtry SUSY Unification Standard Modl Summary and Z bosons Nuclar and Particl Physics Franz Muhim 1

2 ak Nutral Intractions ak Nutral Currnt (NC) Z boson coupls to all frmions: nutrinos, chargd lptons, quarks ak NC is flavour consrving.g τz vrtx dos not xist Coupling Strngth Proportional to wak nutral charg g For ach Z vrtx add factor g to matrix lmnt How ar g and wak charg g rlatd? Z Boson Propagator Nutral Currnt mdiatd by xchang of virtual Z boson Add propagator trm 1/(q 2 M Z2 ) to matrix lmnt/amplitud At small q 2 NC maskd by lctromagntic intractions Ar wak and lctromagntic forc rlatd? Discovry of Nutral Currnts 1973 Bubbl chambr Gargamll at CERN 3 vnts in lastic nutrino scattring Anti- bam Vry low background Nuclar and Particl Physics Franz Muhim 2

3 Standard Modl Elctrowak Intractions Elctrowak Unification Dvlopd in 196s by Glashow inbrg Salam Quantum Thory of wak chargd (CC) and nutral currnts (NC) and lctromagntic intractions (QED) Surpris - QED and wak intractions ar a unifid forc Elctrowak Gaug Bosons Initially four masslss bosons,, - and B Nutral bosons mix Physical bosons ± and Z and γ Z cosθ sinθ = γ sinθ cosθ B θ wak mixing (inbrg) angl ± and Z acquir mass via Higgs Mchanism Elctrowak Coupling Constants g and g ar rlatd to lctric charg = g sin θ = g cos θ Elctrowak Thory 3 fundamntal paramtrs,.g. Mass of ± and Z rlatd Prdicts coupling strngths of ± and Z to quarks and lptons, slf intraction couplings of ± and Z and γ Nuclar and Particl Physics Franz Muhim 3 α m 2 =, 4π M 2 Z G F 2 M 2 / cos 2 θ = g = 8M 2 2, sinθ

4 Nuclar and Particl Physics Franz Muhim 4 and Z Bosons and Z Bosons Virtual ± and Z Bosons Mdiat wak intraction in scattring and dcay of wakly intracting frmions.g. muon or mson dcay, v- scattring Ral ± and Z Bosons Producd in collisions if sufficint nrgy availabl Discovry of ± and Z Bosons at p-pbar collidr at CERN in 1983 Enrgy E(p) =E(pbar) = 27 GV K D,,, Z d d u u d u d u vnt UA1 xprimnt CERN -

5 Exprimntal Tsts - LEP LEP - Larg Elctron Positron Collidr Largst - collidr, 27 km circumfrnc Cntr-of-mass nrgy s = 9 2 GV Oprational from 1989 to 2 Four xprimnts: Alph, Dlphi, L3, OPAL Z qq hadrons Z Bosons at LEP Rsonanc production at s = M Z ~4 million - Z vnts/xpt ± Bosons at LEP Production at s 2 M ~8 - - vnts/xpt LEP Masurmnts Mass and width of Z and ± bosons Z and ± boson couplings to quarks and lptons ak dcays of havy msons QCD masurmnts Prcision tsts of Standard Modl of Particl Physics Nuclar and Particl Physics Franz Muhim 5

6 Z Rsonanc - Annihilations Hadrons at High Enrgis s < 5 GV xchang of γ dominats At largr nrgis s 5 GV Z and γ xchang diagram, also Z /γ intrfrnc Z Boson Production at nrgis s M Z production of ral Z boson diagram with Z boson dominats Z boson is Brit-ignr Rsonanc Z boson dcays vry fast, liftim τ ~ 1-25 s Masur nrgy width of Z rsonanc Z = ħ/τ Nuclar and Particl Physics Franz Muhim 6

7 Z Mass and idth Brit-ignr Rsonanc Cross sction for rlativistic initial and final stats 4π ff σ ( Z f f ) = g 2 s 2 ( s M ) / 4 Z Z Partial dcay widths = ( Z f f ) Spin: avrag initial stats & sum final stats Total Dcay idth Z Sum ovr all partial dcay widths ff Z = qq ττ ττ Cross sction at pak of rsonanc s = M Z Z Rsonanc Masur - Hadrons at nrgis clos to M Z QED corrctions Shift: - γ hadrons Mass and idth of Z M Z = (21) GV Z = (23) GV Pak cross sction σ qq = (37) nb ff g = π ( Z f f ) = σ = σ ff M Z Z 2J 1 Z ( 2s 1)( 2s 1) ff Nuclar and Particl Physics Franz Muhim 7

8 Z Partial Dcay idths Cross Sctions ( ) σ Z f f Masurmnts for all visibl frmions Obtain partial dcay widths using pak cross sction σ qq and M Z, Z Not --- all rsonanc curvs hav width Z Z qq ll = ± 2.3 MV = ± 2. MV Evidnc for N colour = 3 = = = = ±.86 MV Invisibl Z idth Dcays Comparison of total and partial dcay widths Z = qq = Numbr of Nutrino Flavours Prdiction = 167 MV Masurmnt Z,, = N = 499. ± 1.5 MV Numbr of light nutrinos N = ±.12 (with mass m < M Z /2) τ τ Consistncy also for,, τ Lpton univrsality holds ττ for Z,, ττ couplings = ττ ττ N N - numbr of nutrino flavours Nuclar and Particl Physics Franz Muhim 8

9 - Pair Production Standard Modl Diagrams ± Boson Dcays CC Univrsality for lptons and wak quark ignstats 1 ± ( ) = ( ) = ( τ τ ) = ( ) 3 l ( d' u) = ( s' c ) = N c( ) ( b' t ) ± ± ( q' q ) = 2( l ) - - at LEP Exampl L3 xprimnt My 1 st ± pair qq = Mass and idth of ± Boson M = ±.38 GV = ±..41 GV Cross Sction vs Enrgy Agrs with SM prdiction Confirms xistnc of - Z vrtx Nuclar and Particl Physics Franz Muhim 9

10 Higgs and Unification Elctrowak Thory Prcis masurmnts of α m, G F, M Z, M and sin 2 θ Only 3 indpndnt paramtrs Powrful constraints, corrctions: highr ordr diagrams Higgs Mchanism Only missing particl in Standard Modl Scalar, i. Spin, Non-zro vacuum -> All particls acquir mass by Higgs intraction Ptr Higgs Higgs coupling mass g Hff = ( 2 G F ) m f Prof mritus Dirct Mass Limit M H > 114 GV Univ of Edinburgh Rquir Larg Hadron Collidr (LHC) starts in 27 Suprsymmtry - SUSY SUSY Partnrs: Frmion Boson frmion sfrmion Unification of lctrowak boson ino and strong intraction α 1 = α m α 2 = α α 3 = α S Nuclar and Particl Physics Franz Muhim 1

11 Standard Modl of Particl Physics On-pag Summary Frmions Quarks and Lptons 3 Gnrations of Lptons & Quarks Charg [] τ - - τ- u c Elctromagntic (QED) t -1 2/3 d s b -1/3 γ coupls to charg consrvs q, l flavour Intraction Gaug Bosons Mdiat intractions Gaug Goson Charg [] Strong (QCD) g coupl to colour Coupling Constant Strong g α S.2 Elctro magntic ak Z γ α m.8 ± ±1 α.3 quark flavour consrvd ak Chargd Currnt (CC) ± coupls to wak charg g Flavour changing for quarks Nutral Currnt (NC) Z coupls to g consrvs q, l flavour Nuclar and Particl Physics Franz Muhim 11

12 Fynman Diagrams On-Pag Tutorial On-pag Tutorial Scattring, annihilation or dcays Only Standard Modl vrtics Initial and final stats rit down quark/lpton/boson contnt for all initial and final stat particls Intractions Try to find out which xchang bosons ar rsponsibl for raction by chcking consrvation laws Consrvation Laws For all intractions at ach vrtx Enrgy-momntum Elctric charg, Baryon numbr For strong and lctromagntic intractions Quark and Lpton flavour, Parity, Isospin, Strangnss For wak chargd intractions (CC) Quark flavour is not consrvd, Lpton univrsality For wak nutral intraction (NC) Quark and lpton flavour ar consrvd Usful Hints Photon only intracts lctromagntically Nutrinos and Z only intract wakly Only Quarks and Gluons intract strongly If mor than 1 possibility, fastr raction wins Kp it as simpl as possibl Nuclar and Particl Physics Franz Muhim 12