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Particle Physics Physics 3: Particle Physics Lecture 9: Electroweak Model and the Higgs boson March 10th 2008 Electroweak Theory Interactions of W and Z bosons at high energy The Higgs boson 1 Electroweak Theory We’ve seen already that wherever a ! boson can be exchanged a Z can also be exchanged: • The weak and electromagnetic force are linked. • At short distances (or high energies) the strength of the electromagnetic force and the weak force are comparable. Can be related by a parameter, sin !W e = gW sin θW The weak and electromagnetic interactions are manifestations of a underlying force: the electroweak force. • Couplings of the !, W (and Z) bosons are related: e = gW sin θW 2 2 2 • Mass of the W and Z bosons are related: mZ = mW /cos θW Just three fundamental parameters required to describe: • couplings of W, Z and ! to quarks and leptons • masses of the W, Z, ! bosons • interactions of the W, Z, ! bosons with each other Normally use three most accurately measured parameters e.g. e, GF, mZ 2 6 Summary of Standard Model Vertices ! At this point have discussed all fundamental fermions and their interactions with the force carrying bosons. ! Interactions characterized by SM vertices ELECTROMAGNETIC (QED) - e q Couples to CHARGE - e Q e e q Does NOT change FLAVOUR e2 α = γ γ 4π STRONG (QCD) q Couples to COLOUR g q s Does NOT change FLAVOUR g 2 16 α = s g 2004 s 4π W and Z boson at WEAKlowChar energiesged Current Lent : , νe q $d’µ Changesq FLAVOUR comes the √α At low energies, q m , m : ). Z W " g V q - g w ckm the w µ a ! gW is Q Q The W and Z bosons are virtual: e u For$ e! QUARKS: coupling r • o - BETWEEN generations f or 2 g 2 + state 2 2 2 colour W w W 1 q q = EZ p!Z p!Z = mZ αw = γ W Z 4π gW ( − · " of 2 2 2 erence q = E p!W p!W = m " final , W W WEAK Neutral Current e represent section les W − · " - " " diff µ # e $e! $µ e , ν √α Y q the e tic where ( - + - Annihilation 2 2 .g. e e oss e , ν . virtual W-bosons are responsible for the decayse of q = m of • W e xistence W Does NOT change par cr " " q ! ONL e the leptons, and the lightest hadrons e.g. µ # e $e! $µ + - FLAVOUR case 0 µ µ 0 pair Z the the the Z state the r √α masses r o " " Z Drf M.A. Thomson Lent 2004 • interactions of virtual Experimental-boson are not clearly Tests - Le EP e o f then 2 final ) the II evident, as they look similar to ! interactions 1 q ermion γ Annihilation. Z (! interactions are much strongerin than Z-boson the !"#$% !&'()$"*)+,'-.$#-/0,'-.$1-**02)' uons calculating interactions) vidence of y !"#$%&'(%)%* +,e --./%#0( 12(34 +.#+546%#%7+% or e √α $e b $e neglect + - g t 8%7'#%*,6*4"&&(%7%#$9((!&(:(;<(= 1<<(>%? Handout " " e e Compare $e e # $e e ocess we QCD Thomson om At low energies we see the effect@A%#" 'of.,7 Z"- (boson6#,4(B;C; mainly',(1 <in<< har ermion-antif see f quarks/m c Direct fr ! If = 2 2 Star pr D,5#(%EA% #".4%7' &F"(G-%AH0(I%-AH.0(!J0(@KG! q = mZ M.A. scattering involving neutrinos e.g. $e e # $e e Z ! Dr e #e " ! Z 0 ! qq ! hadrons • as ! cannot couple to the neutral neutrinos 3 34$$5-/-./$&,$!"# L%&,7"7+%(A#,/5+'.,7("'(!&(:(MN W and Z bosonOP(4.--., 7(at%)(%* " highN< %Q%7'& R%energiesEA' 6! 5-/-./$&,$!"# Using a collider, we can create K#,/5+'.,7high enough"'( !&(# 1(MS( energies to make real W and Z OC<<<(bosons:%)(%* " S)(S* %Q%7'&R%EA' !"#$7)&/8')9).,/ q mZ , mW ∼ M"&& "7/(T./'H ,6(N< "7/(S! U,&,7& ! • e.g. LEP collider e+e"#Z, eN+e<""#7/W(S+W"U,&,7(+,5A-.7$& ',(V5"#3&("7/(-%A',7&(( S%"3(/%+"9& ,6(H%"Q9(4%&,7& • e.g. Tevatron and SppS! collider pp#! Z+X, pp#! W+X W8I(4%"&5#%4quarks%7'& within p K#%+.&.,7 '%&'&(,6(:,&.2&'2$7-2)*$-;$#&',0+*)$#<=/0+/ Can study the properties of the W and Z and p ! interact to W Z bosons in detail. Nuclear and Particle Physicsmake (orFran z M)uheim 5 • masses, lifetime/width, coupling strengths, decay modes, spin... Discovery of W and Z bosons at CERN in 1983 at the SppS! collider. Ep = Ep ! = 270 GeV # # pp"! W "e $e! event at UA1 experiment 4 Experimental Tests - LEP W and Z boson tests at LEP !"#$Experimental% !&'()$"*)+,'-.$ #-/0,'-.$Tests1-**02)' - LEP !"#$%&'(%)%* +,--./%#0( 12(34 LEP+.#+546%#%7+% - the Large Electron Positron Collider at CERN ! !"#$%8!%7&'()$'#%*,"*)+,'-.$6*4"&&(%7%#-/0,'-.$#$9(( &(:(The;1-**02)'<(= 1world’<<(>%s? highest energy e+e" collider: @A%#"'.,7"-(6#,4(B;C; ',(1<<< !"#$%&'(%)%* +,--./%#0( 12(34 +.#+546%#%7+% D,5#(%EA%#.4%7'&F(G-%AH0(I%-AH.•0(!27J0( @kmKG !circumference, ran from 1989 to 2000 8%7'#%*,6*4"&&(%7%#$9((!&(:(;<(= 1<<(>%? e #e " !EnergyZ 0 ! q qof! masshadrons energy, @A%#"'.,7"-(6#,4(B;C; ',(1<<< • √s = 89 to 206 GeV D,5#(%EA%#.4%7'&F(G-%AH0(I%-AH.0(!•J0Four(@KG !experiments: Aleph, Delphi, L3, Opal e #e " •! MeasurementsZ 0 ! qq ! hadrons corroborates unification of EM & Weak forces Z-boson production • ~4 million e+e"#Z0 events 34$$5-/-./$&,$!"# &s ~ 91 GeV L%&,7"7+%(A#,/5+'.,7("'(!&(:(M N s = (q + q )2 = q2 = m2 )( * < + Z 34$$5-/-./$OP(4.--&,$.,7(!"#% % " N %Q%7'&R%EA' e e− Z ! 6 L5-/-./$%&,7"7+%&,$(A#,!"#/5+'.,7("'(!&(:(MN OPK#,/5+'.,7(4.--.,7(%)(%"*'"(!&N(#< 1%(QM%S7'(&R%EWA'-boson production ! )( * " )( * + " + " 6 5-/-./$OC<<<(&,$% %!"# S S %Q%7'&R%EA•' ~8000 e e #Z#W W events &s ~ 160 GeV !"#$7)&/8')K#,/5+'.,7 "9'().,/!&(# 1(MS( M"&& ")(7/*(T./'H" )(,6(*N< "7/(S! U,&,7& OC<<<(% % S S %Q%7'&R%EA' 2 2 < ! s = (q + q ) = (2m ) N "7/(S U,&,7(+,5A-.7$& ',(V5"#3&("7/(-%A',7&(( + W !"#$7)&/8')9).,/ e e− MS%"3"&& "7(//%+"9&(T./'H,,66((H%"Q9(N< "7/4%&,(S! 7&U,&,7& N<W"87I/(4S%!"&U5,#&%,47(%+7,'5&A-.7$& ',(V5"#3&("7/(-%A',7&(( 5 S%"3K#%+.&.,7(/%+"9&'%&,'6&((H%"Q9(,6(:,&4%&,.2&'2$7& 7-2)*$-;$#&',0+*)$#<=/0+/ NucleWar8 aInd(4 Pa%r"tic&le5 #Ph%y4sic%s7'& Franz Muheim 5 K#%+.&.,7 '%&'&(,6(:,&.2&'2$7-2)*$-;$#&',0+*)$#<=/0+/ Nuclear and Particle Physics Franz Muheim 5 0 6 40. Plots of cross sections and related quantities 6 40. Plots of cross sections and related quantities + Z resonance σ and R in e e− Collisions -2 + - 10 ω φ J/ψ e e Annihilation in Feynman+ Diagrams" -3 • Both ! and Z contribute to e e "hadrons 10 ψ(2S) ρ Υ -4 ρ ! + 10 Z In general e+e- annihilation σ and R in e e− Collisions ] -5 b 10 m involves both photon and [ σ -6 Z exchange : + interference 10 -2 -7 10 10 -8 10 2 • At low ECM mainlyω ! interactionsφ 1 10 10 -3 J/ψ 3 Υ • At $s~mZ, mainly Z-boson: 10 J/ψ ψ(2S) 10 ψ(2S) Z " 1 2 0 + 10 ! nb Υ φ ! ons) σ(e e− Z ff) ρ ω -4 → →ρ ∝ (q2 ! m2 )2 40 R Z had ALEPH 10 ρ! 10 − ! DELPHI Z L3 hadr 30 OPAL 1 ρ " " ] -5 At Z resonance: Z -1 Well below Z: photon 10 e b 2 exchange dominant " 1 + 10 10 exchange dominant 10For a massive boson, also depends Z e M ( m • 20 √s [GeV] [ & + + + + Figure 40.6: World data on the total cross section of e e− hadrons and the ratio R(s) = σ(e e− hadrons, s)/σ(e e− µ µ−, s). on total width %Z = /'Z. Shape of %: + → → → + σ(e e− hadrons, s) is the experimental cross section corrected for initial state radiation and electron-positron vertex loops, σ(e e− ℏ measurements (error+ bars→ 2 → µ µ−, s) = 4πα (s)/3s. Data errors are total below 2 GeV and statistical above 2 GeV. The curves are an educative guide: the broken one σ increased by factor 10) -6 (green) is a naive quark-parton model prediction, and the solid one (red) is 3-loop pQCD prediction (see “Quantum Chromodynamics” section of this Review, Eq. (9.12) or, for more details, K. G. Chetyrkin et al., Nucl. Phys. B586, 56 (2000) (Erratum ibid. B634, 413 (2002)). 2 10 ! from fit Breit-Wigner parameterizations of J/ψ, ψ(2S), and Υ (nS), n = 1, 2, 3, 4 are also shown. The full list of references to the original data and the 10 Γ /4 QED correcteddetails of the R ratio extraction from them can be found in [arXiv:hep-ph/0312114]. Corresponding computer-readable data files are available 2 Z at http://pdg.lbl.gov/current/xsect/. (Courtesy of the COMPAS (Protvino) and HEPDATA (Durham) Groups, August 2007. Corrections σ(E = q ) = σmax 2 2 2 by P. Janot (CERN) and M. Schmitt (Northwestern U.)) See full-color version on color pages at end of book. (q m ) + Γ /4 M Z Z Z -7 − 86 88 90 92 94 10 E !GeV" • Measurements at LEP: cm 2 -8 • mZ = 91.188 ± 0.002 GeV/c Dr M.A. Thomson 10 Michaelmas 2006 500 • %Z = 2.4953 ± 0.002 GeV 1002 1 10 10ECM (GeV) 6 3 Υ 10 J/ψ ψ(2S) Cross Section Measurements Z At Z resonance mainly observe four types of event: 10 2 φ ω Each has a distinct topologyR in the detectors, e.g.
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