Particle Physics Handout 8 the Weak Force

Subatomic Physics: Particle Physics Handout 8 The Weak Force

Weak interactions W and Z interactions at low energy Fermi theory Electroweak theory W and Z bosons at high energy

6 6 SELF-INTERASELF-INTERACTIONSCTIONS hhhljkhsdlkh 1 At this point, QCDhhhljkhsdlkhlooks like a stronger version of QED. At this point, QCD looks like a stronger version of QED. This is true up to a point. However, in practice QCD This is true up to a point. However, in practice QCD behaves very differently to QED. The similarities arise from behaves very differently to QED. The similarities arise from QCD Summarythe fact that both involve the exchange of MASSLESS the fact that both involve the exchange of MASSLESS spin-1 bosons. The big difference is that GLUONS carry spin-1 bosons. The big difference is that GLUONS carry colour “cQuarksharge”. and gluons carry QCD: Quantum Gluonscolour are“c theharg e”. colour charge. GLUONS CAN INTERACT WITH OTHER GLUONS: Chromodymanics is the propagatorGLUONS of theCAN INTERACT WITH OTHER GLUONS: quantum description of strong force Gluons self-interact:g g the strong force. g gg g g Only quarks feel the g g g strong force. g gg g 3 GLUON VERTEX 4 GLUON VERTEX 3 GLUON VERTEX 4 GLUON VERTEX Hadrons can be Electromagnetic coupling constant ! decreasesEXAMPLE: Gluon-Gluon Scattering • EXAMPLE: Gluon-GluondescribedScattering as consisting as a charged particles get further apart. of partons: quarks and •Strong coupling constant !S increases as gluons, which interact + + further apart quarks become. + independently+ Quarks and gluons produced in Colour Confinement collisions hadronise: hadrons are energy required to separate produced. quarks ! " The decay products of the hadrons quarks are confined to hadrons appear e.g.in ther g detector+e.g.gb→r gr as+r+g jetsrbb→.r r+r b 2

Dr M.A. Thomson Lent 2004 Dr M.A. Thomson Lent 2004 3 ! Two types of WEAK interaction Introduction to the CHARGEDWeak CURRENTForce(CC) - Bosons NEUTRAL CURRENT (NC) - Boson The weak force is responsible for some of the most important phenomena: • Decays of the muon and tau leptons ! WEAK force mediated by MASSIVE VECTOR • Neutrino interactions BOSONS:Boson W± Z0 Decays of the lightest mesons and baryons • Mass Radioactivity, nuclear fission and fusion 80.4 91.2 • GeV/c2 Characteristics of Weak Processes: ! e.g. the WEAK interactions of electrons and • Long lifetimes 10#13 - 103 s charge, e ±1 0 electron neutrinos: #13 • Small cross sections 10 mb - spin 1 1 - e νeℏ ℏ e νe W- Z0 Z0 W+ Weak Force is propagated by massive W+, W# and Z0 bosons + + ± 0 ν ν e e • The interactions of W and Z are different e e (related by symmetry of the weak interaction)BOSON SELF-INTERACTIONS

W- W- W± and Z0 can interact with each other 0 • Z γ ± ± • W and " can interact (as W bosons are charged) + + W W 6 W- WSummar- Z0 yWo-f Standarγ Wd- Modelγ VWer- tices 3 ! At this point have discussed all fundamental fermions W+ andW+theirZ0interactionsW+ withZ0 the fWor+ce carrγ ying bosons.W+ Weak Vertices! Interactions characterized by SM vertices ! also interactions with PHOTONS (W-bosons ELECTROMAGNETIC (QED) QED are charged)W-boson- e q Couples to CHARGE mediated by the exchange of mediated -by thee exchangeQ of e W e Does NOT change virtual photons boson q Dr M.A. Thomson FLAVOUR Lent 2004 e2 α = γ γ acts on all charged particles acts on all 4quarkπ and leptons 6 STRONG (QCD) coupling strength e !! coupling strength gW $!W Summary!of !Standard Model Vertices ! ! q Couples to COLOUR g ! At this point 2have discussed2 2 all fundamental fermions 2 s2 Does NOT change propagator term: 1/(q #m" )= 1/q propagator term: 1/(qq#mW ) and their interactions with the force carrying bosons. FLAVOUR g 2 α = s g For! manyInteractions processes:characteriz ed by SM verticesFor smany4π processes: 2 2 2 2 2 ELECTRM ∝ OMAe /q GNETIC (QED) WEAKM ∝ gCharW /(qg#emd WCurrent) - e q Couples to CHARGE νe d’ Changes FLAVOUR g V - e Q e - gw w ckm e q Does NOTe change u For QUARKS: coupling 2 FLAVOUR - BETWEEN generations e g 2 W + α = γ γ α = w W 4π w 4π STRONG (QCD) Recall: matrix element, M, is the amplitudeWEAK ofNeutral a process.Current q - Scattering cross section, $ !M2.Couples Decay to width,COLOUR !e !, ν M2 q - e gs e , Does NOT changeνe 4 q Does NOT change FLAVOUR q g 2 FLAVOUR α = s g 0 s 4π Z Z0 WEAK Charged Current Dr M.A. Thomson Lent 2004 νe d’ Changes FLAVOUR g V - gw w ckm e u For QUARKS: coupling - BETWEEN generations g 2 W + α = w W w 4π WEAK Neutral Current - e , ν q - e e , νe q Does NOT change 0 FLAVOUR Z Z0

Dr M.A. Thomson Lent 2004 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 6 Summary oELECTRf StandarOMAdGNETICModel(QED)Vertices - e q Couples to CHARGE ! At this point have discussed all fundamental fermions - e Q e and their interactionsewith the force carrq ying bosons. Does NOT change FLAVOUR ! Interactions characterize2ed by SM vertices α = γ γ ELECTROMAGNETIC4π(QED) - STRONG (QCD) e q Couples to CHARGEq Couples to COLOUR - e Q e e ± Doesg NOTs change Interactions of the W bosonq q Does NOT change 2 FLAVOUR FLAVOUR e γ g 2 α = α = s γ g • Known as “charged current interactions” 4π s 4π STRONG (QCD)WEAK Charged Current W± boson interacts with all fermions (all quarks and leptons) q 6 • νe Couples to COLOURd’ Changes FLAVOUR gg g V Summar- sw y of StandarDoesw NOTckm changed Model Vertices • Charged current changes the flavour of the fermion: qe u For QUARKS: coupling FLAVOUR BETWEEN generations e.g. electron emitting an W-boson can’t remain2 an electron! At this2point ha-ve discussed all fundamental fermions • gs g W + - violates conservation of charge! α = α = w g W s 4π and wtheir4πinteractions with the force carrying bosons. an electron turns into a electron neutrino 6 • WEAK Charged!CurrentInteractions characterized by SM vertices • an up quark turns into a down quark WEAK Neutral Current Summaryν oELECTRf StandarOMA-dd’GNETICModel(QED)Vertices and vice versa! e e , νe Changes FLAVOURq g g- V - ! At- thiswpoint have ediscussedw, νeckm alle fundamental fermionsq Couples to CHARGE e u For QUARKS: couplinDoesg NOT change • Coupling strength at every vertex ! gW (more about quarks later) - q and their interactions withethe force carrBETWEENyingQ ebosons. generations 1 2 - e 0 q FLAVOURDoes NOT change gw W Z + 0 • Propagator term describing the W-boson !! α(Interactionsqw2 = m2 ) characteriz2ed by WSM vertices Z FLAVOUR −4π W e γ q is the four-momentum transferred by the W-boson α = γ • ELECTROMADrGNETICM.A. Thomson4π(QED) Lent 2004 WEAK Neutral- Current -e STRONG (QCD)q Couples to CHARGE e , νe q - 5 q e-, ν e Q e Couples to COLOUR e e q Doesg NOT change q Does NOTs change Does NOT change 2 qFLAVOUR e γ0 FLAVOUR FLAVOUR Allowed Flavourα = ChangesZ g 2 γ0 4π α = s Z g s 4π At a W-boson vertex: STRONG (QCD) Dr M.A. Thomson WEAK Charged Current Lent 2004 • Lepton numbers: Le, Lµ and L%, is conserved: q Couples to COLOUR " # # νe d’ Changes FLAVOUR Allowed lepton flavour changes: e #&e µ #&µ % #&% gs g V q- ggWw Doesw NOTckm change e For QUARKS: coupling uFLAVOUR g 2 s 2 - BETWEEN generations αs = gg 2 Wg + • Total Quark Number, Nq, is conserved 4π α = wW W αW w= 4π • Individual quark flavour numbers: NuWEAK, Nd, Ns, NCharc, Nb,g Net d Current4π are not conserved WEAK Neutral Current νe -d’ Changes FLAVOUR Allowed quark flavour changes: e , ν q - g g-wWVVckmud e (Q=+2/3 e quark) # (Q="1/3 e quark) w e ue , νe For QUARKS: coupling Does NOT change ( d s b ) # ( u c t ) - BETWEENq generations g 2 W + FLAVOUR Each of the nine possible quark flavour αchanges = w has a W0 • w 4π Z 0 different coupling strength: e.g. gWVud for u to d quarks Z (Vs are terms in CKM matrix - more later) WEAK NeutralDr M.A.CurrentThomson Lent 2004 • Main quark flavour changes are within a generation: - e , νe q d # u s # c b # t - e , νe q 6 Does NOT change 0 FLAVOUR Z Z0

Dr M.A. Thomson Lent 2004 6 Summary of Standard Model Vertices

! At this point have discussed all fundamental fermions

and their interactions with the force carrying bosons. 6 ! Interactions characterizSummared byySMoverf Standartices d Model Vertices ELECTROMAGNETIC (QED) - ! At this point have discussed all fundamental fermions e q Couples to CHARGE and their interactions with the force carrying bosons. - e Q e 6 e ! Interactionsq characterizDoes NOTed bchangey SM vertices FLAVOUR e2 Summary of Standard Model Vertices α = γ ELECTROMAγGNETIC (QED) 4π - ! At this pointehave discussed allq fundamental fermions STRONG (QCD) Couples to CHARGE and-theireinteractions withQ thee force carrying bosons. e q Couples to COLOURDoes NOT change ! Interactions characterizq ed by SM vertices g FLAVOUR q e2 s Does NOT change ELECTRα = OMAγGNETIC (QED)γ 4π - FLAVOUR g 2 α = s eg q Couples to CHARGE s 4π STRONG (QCD) - e Q e q WEAK Charged Currente q DoesCouples NOT to changeCOLOUR ν 2 d’ gs FLAVOUR e e Changesq FLAVOURDoes NOT change αg = V γ γ - gw w4πckm FLAVOUR e u g 2 For QUARKS: coupling STRα =ONGs (QCD) g s 4 BETWEEN generations 2 - π gw W + q Couples to COLOUR αw = WEAK ChargWed Current 4π g 0 ν s d’ Does NOT change Interactions of theWEAK ZNeutral bosonCurrent e q Changes FLAVOUR - g g V FLAVOUR - 2w w ckm e , νe e gs q For QUARKS: coupling - αs = u g Known as “neutral current interactions” e , νe 4π BETWEEN generations • 2 - WEAKq gwChargWed CurrentDoes NOT change+ αw = W • Acts on all fermions - (all quarks and leptons) 0 4π FLAVOUR Z νe0 d’ Changes FLAVOUR • Neutral current conserves flavour of the fermion Z g V WEAK- gNeutralw Currentw ckm e - For QUARKS: coupling No allowed fermion flavour changes Dr M.A. Thomson e , ν u q Lent 2004 • - e - BETWEEN generations e , νge 2 W + α = w W Does NOT change 1 w 4π q 6 • Propagator term ! 2 2 Summary of Standard Model0 Vertices FLAVOUR (q mZ ) WEAK NeutralZ Current 0 − - Z ! At this point have discussed alle ,fundamental ν fermionsq • Coupling strength depends on fermion flavour - we - e and their interactionsDr M.A. Thomsonwith the force carrying bosons. Lent 2004 won’t consider this in this course e , νe Does NOT change ! Interactions characterized by SM verticesq 0 FLAVOUR ELECTROMAGNETIC (QED) Z 0 - Z Anywhere a photon could be exchanged a Z0 boson cane be exchanged.q Couples to CHARGE - e Dr M.A. ThomsonQ e Lent 2004 (Almost vice-versa, except Z0 boson also hase neutrino interactionsq too!)Does NOT change FLAVOUR e2 α = γ γ Electromagnetic and weak neutral current interactions4π are linked! STRONG (QCD) q Couples to COLOUR g 7 q s Does NOT change FLAVOUR g 2 α = s g s 4π W and Z bosons atWEAK lowChar geenergyd Current

νe &d’µ Changes FLAVOUR • If the momentum of the W or Z boson, q m Z , m W g V - gw µ# w ckm the bosons are virtual: 2 2 2e u For&( eQUARKS: coupling q = EZ pZ pZ = mZ Z 16 BETWEEN generations − · - 2004 g 2 + 2 2 α 2 = w W W q = EW pW pW = mwW W Lent W − · 4π

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• colour 1 q 0 γ FLAVOUR ( of Z Z0 erence • Many interactions of virtual Z-bosons are not clearly evident, as ﬁnal , represent section les diff the same interaction can take place due to " Drexchange.M.A. Thomson Lent 2004 √α Y the tic where ( + - Annihilation .g. e e oss .

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! 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 α = s g s 4π Fermi TheoryWEAK Charged Current &µ W-boson interactions at Low Momentum Transfer νe d’ Changes FLAVOUR g # g V - w µ w gckmW For muon decay, and many other weak processes: e u For&( eQUARKS: coupling 2 g - BETWEEN generations w g 2 W + 2 2 w W M ∝ (q m ) αw = W − W 4π gW 2 2 2 At low momentum transfer q mW g 2 WEAK Neutral CurrentW e# gw M- ∝ q2 m2 e , νe W q 2 - − M → ∝ mW e , νe Introduce Fermi coupling constant: q Does NOT change g2 √2 g2 0 FLAVOUR w w Z Z0 GF 2 GF = 2 ∝ mW 8 mW • Dimension [E]#2 Dr M.A. Thomson Lent 2004 #5 #2 • From experimental measurements: GF = 1.16637 & 10 GeV g2 1 1 Measurements of G & M g = 0.66 α = w = > α = F W ⇒ w ⇒ w 4π 29 EM 137

• Recall, from problem sheet 2, Q7, range of W boson: ∆x = = 0.002 fm ≈ ∆p mW c Weak interaction not intrinsically weak - appears weak due to large boson masses. 6 6 6 9 Summary of StandarSummard Modely of StandarVeSummarrticesd Modely of StandarVerticesd Model Vertices

! At this point have discussed! At this allpointfundamentalhave discussed! Atfermionsthis allpointfundamentalhave discussedfermionsall fundamental fermions and their interactions withand theirthe fointeractionsrce carryingwithandbosons.theirthe fointeractionsrce carr6yingwithbosons.the force carr6ying bosons. 6 !SummarInteractionsycharacterizof StandarW!SummarInteractionsed binteractionsydSMModelverycharacterizoticesf Standar!VeSummarInteractionsredticesbydSMModelverycharacterizoticesf StandarVe rwithedticesbydSMModelvertices quarksVertices and leptons ELECTROMAGNETICELECTR(QED)OMAGNETICELECTR(QED)OMAGNETIC (QED) ! At this point have discussed!LeptonAt this allpoint universalityfundamentalha- ve discussed! Atfermionsthis:allpointfundamentalhave discussedfermionsall fundamental fermions e q eCouples to CHARGEq eCouples to CHARGEq Couples to CHARGE and their interactions withand theirthe fointeractionsrce carryingwithandbosons.theirthe fointeractionsrce carr6yingwithbosons.the force carr6ying bosons. 6 - e Q- e eCoupling ofQ - toe eW-boson toQ alle leptons is equal = gW !SummareInteractionsycharacterizof Standarq!SummareInteractionsed•bydSMModelverycDoesharacterizoticesf StandarNOTq!VeSummare InteractionschangeredticesbydSMModelverycDoesharacterizoticesf StandarNOTqVe changeredticesbydSMModelverDoestices NOTVe changertices FLAVOUR FLAVOUR FLAVOUR ELECTRe2 OMAγGNETICELECTR(QED)•e2 electrons,OMAγGNETICELECTR muons(QED)e2 OMA andγGNETIC taus(QED) all interact identically !αAt =this point have discussed!αAt =this allpointγ fundamentalha- ve discussed!αAtf =ermionsthis allpointγ fundamentalha- ve discussedfermionsallγ fundamental fermions 4π e 4π q e 4π q e q and their interactions withand theirthe fointeractionsrce carrCouplesyingwithandbosons. to CHARGEtheirthe fointeractionsrce carrCouplesyingwithbosons. to CHARGEthe force carrCouplesying bosons. to CHARGE STRONG (QCD) STRONG• interact(QCD) STRwithONG the(QCD) same bosons with same coupling strength - e Q- e e Q- e e Q e ! eInteractions characteriz! eInteractionsed by SM vercDoesharacteriztices NOT! e Interactionschangeed by SM vercDoesharacteriztices NOT changeed by SM verDoestices NOT change q Quark qinteractions:Couplesq to COLOURq Couplesq to COLOURq Couples to COLOUR 2 2 FLAVOUR 2 FLAVOUR FLAVOUR ELECTRe OMAγGNETICELECTRg(QED)s e OMAγGNETICELECTRg(QED)s e OMAγGNETICg(QED)s α = - q α = Does- NOTq α change = Does- NOTq change Does NOT change 4 e •4 Inγ general,e any4 vertexγ e W-(Q=+2/3 eγ quark)-(Q=#1/3 e quark) is valid. π π q FLAVOURCouples to CHARGEπ q FLAVOURCouples to CHARGEq FLAVOURCouples to CHARGE STRONGg 2 (QCD) STRONGg 2 (QCD) STRONGg 2 (QCD) α - = se Qα - =e sWe -bosong couplingQα - =e se tog quarks suppressedQ e g by a flavour-dependent factor V s s • Does NOT changes Does NOT change Does NOT change e 4π q e 4π q Couplesq toe COLOUR4π q Couplesq to COLOURq Couples to COLOUR WEAK 2Charged CurrentWEAK 2ChargeFLAVOURd CurrentWEAK 2ChargeFLAVOURd Current FLAVOUR e γ gs e γ gs e γ gs Known as the CKM matrix. α = q α = γ Does NOTq α change = γ Does NOTq change γ Does NOT change 4π νe 4π d’ νChangese FLAVOUR4π d’ νChangese FLAVOURd’ Changes FLAVOUR FLAVOUR FLAVOUR FLAVOUR (values from experimental STR- ONGgg2 (QCD) gSTRwVckm- ONGgg2 (QCD) gSTRwVckm- ONGgg2 (QCD) gwVckm = s w u = s wd u = s ws u b αes u αes g For QUARKS:u αes couplingg For QUARKS:u couplingg For QUARKS: coupling measurements) 4π 4π q Couples to COLOUR4π q Couples to COLOURq Couples to COLOUR - BETWEEN- generations BETWEEN- generations BETWEEN generations WEAKgChar2 gWed CurrentWEAKgChar2 g+gWWeVdudCurrentWEAKgChar2 g+gWWeVdusCurrent g+WVub α = w αgWs = w W αgWs = w W gWs W w 4 q w 4 Does NOTq changew 4 Does NOTq change Does NOT change π νe π d’ νChangese FLAVOURπ d’ νChangese FLAVOURd’ Changes FLAVOUR FLAVOUR FLAVOUR FLAVOUR gg2 g V gg2 g V gg2 g V Vud=0.974 Vus=0.227 Vub=0.004 WEAK- = sNeutralw CurrentWEAKcw ckm- = sNeutralwd CurrentWEAKcw ckm- = sNeutralws Currentcw ckm b αes - u αes g For- QUARKS:u αes couplingg For- QUARKS:u couplingg For QUARKS: coupling 4π e , ν 4π q e , ν 4π q e , ν q - -e - BETWEEN-e generation- s BETWEEN-e generations BETWEEN generationVcds =0.230 Vcs=0.972 Vcb=0.042 WEAKgChar2 ged CurrentWEAKgChar2 g+gWeVdcdCurrentWEAKgChar2 g+gWeVdcsCurrent g+WVcb αe , =νew W αeW, =νew W αeW, =νew W W w w W Does NOT changew W Does NOT change W Does NOT change 4π νe q 4π d’ νChangese q FLAVOUR4π d’ νChangese q FLAVOURd’ Changes FLAVOUR Vtd=0.008 Vts=0.041 Vtb=0.999 g 0 g V g FLAVOUR0 g V g FLAVOUR0 g V FLAVOUR WEAK- Neutralw Z CurrentWEAKtw ckm- Neutralwd0 Z CurrentWEAKtw ckm- Neutralws 0 Z Currenttw ckm b0 e - u e Z For- QUARKS:u e couplinZg For- QUARKS:u couplinZg For QUARKS: coupling e , νe q eBETWEEN, νe generationqseBETWEEN, νe generationqs BETWEEN generations - 2 - - 2 gWV-td - 2 gWV-ts gWVtb Dr M.A. Thomson g W Dr M.A. Thomson g + W Dr M.A. Thomson g Lent+ W2004 Lent+ 2004 Lent 2004 αe , =νew αeW, =νew W αeW, =νew W W W Largest couplings are within a generation: w 4π q w 4π Does NOTq changew 4π Does NOTq change Does NOT change 0 FLAVOUR0 FLAVOUR0 FLAVOUR d ' u s ' c b ' t WEAK NeutralZ CurrentWEAK Neutral0 Z CurrentWEAK Neutral0 Z Current 0 - Z - Z - Z e , ν q e , ν q e , ν q 10 - e - e - e Dr M.A. Thomsone , νe Dr M.A. Thomsone , νe Dr M.A. Thomsone , νe Lent 2004 Lent 2004 Lent 2004 q Does NOTq change Does NOTq change Does NOT change 0 FLAVOUR0 FLAVOUR0 FLAVOUR Z Z0 Z Z0 Z Z0

Dr M.A. Thomson Dr M.A. Thomson Dr M.A. Thomson Lent 2004 Lent 2004 Lent 2004 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 Experimentale = gW sin θW Tests - LEP The weak and electromagnetic interactions are manifestations of a underlying force: the electroweak force.!"#$ % !&'()$"*)+,'-.$#-/0,'-.$1-**02)' • Couplings of the ", W (and! "Z#)$ %bosons&'(%)%* are+,- -.related:/%#0( 12e(3=4 +.#+546%#%7+%gW sin θW 8%7'#%*,6*4"&&(%7%#$9((!2&(:(;<(= 21<<(>%?2 • Mass of the W and Z bosons are related: mZ = mW /cos θW @A%#"'.,7"-(6#,4(B;C; ',(1<<< D,5#(%EA%#.4%7'&F(G-%AH0(I%-AH.0(!J0(@KG! Just three fundamental parameters are required to describe:e #e " ! Z 0 ! qq ! hadrons • 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 formulated in terms of most accurately measured parameters: e, GF, mZ

11 34$$5-/-./$&,$!"#

L%&,7"7+%(A#,/5+'.,7("'(!&(:(MN W and Z bosonOP(4.--., 7(at%)(%* " highN< %Q%7'& Renergies%EA' 6! 5-/-./$&,$!"#

Using a collider, we can create K#,/5+'.,7high enough"'( !&(# 1(MS( energies to make real W and ZOC<<<( bosons:%)(%* " S)(S* %Q%7'&R%EA' !"#$7)&/8')9).,/ q mZ , mW ∼ M"&& "7/(T./'H ,6(N< "7/(S! U,&,7& • e.g. LEP collider e+e#'Z,N e<+e"#7'/(SW+!WU,#&,7(+,5A-.7$& ',(V5"#3&("7/(-%A',7&(( • e.g. at the LHC: pp'Z+X,S%"3 pp'(W+X/%+"9& ,6(H%"Q9(4%&,7& W8I(4%"&5#%4%quarks7'& within p K#%+.&.,7 '%&'&(,(or6(:,& (p) interact.2&'2$7-2)*$ to -;$#&',0+*)$#<=/0+/ Can study the properties of the W and Z make W or Z bosons in detail. Nuclear and Particle Physics Franz Muheim 5 • masses, lifetime/width, coupling ( ) strengths, decay modes, spin...

Discovery of W and Z bosons at CERN in 1983 at the SppS̅ collider

p )p collider with Ep = Ep! = 270 GeV

# # p )p !W !e )&e event at UA1 experiment

12 6 40. Plots of cross sections and related quantities

0 + 6 40. Plots of cross sections and related quantities σ and R in e e− Collisions Measuring Z properties 6 -2 10 ω φ J/ψ Most studies of the Z boson were made at LEP. -3 Summary of Standard Model Vertices + - 10 ψ(2S) e e Annihilation in Feynman Diagrams Υ ρ + " -4 ρ ! Main process was e e !hadrons: + Z • σ and R in e e− C10oll!isioAtnsthis point have discussed all fundamental fermions

+ - ] -5 In general e e annihilation b 10 m involves both photon and [ and their interactions with the force carrying bosons. σ -6 -2 10 Z exchange : + interference ! Interactions characterized by SM vertices 10 -7 10 ω φ -8 ELECTROMAGNETIC (QED) J/ψ 10 -3 - 2 Mixture of EM (") & Weak (Z) contributions1 e 10 10 10 ψ(2S) q Couples to CHARGE

3 Υ Υ - J/ψ ρ! 10 e ψ(2S) Q e e Z Does NOT change • -4At low ECM mainlyρ # interactions. q 2 Z 10 10 2 FLAVOUR At ECM="s~mZ, mainly Z-boson interactions: φ hadrons) • R ω e γ 1 α = ! γ 10 # ] -5 + 4π σ(e e− Z ff) ρ! e b 2 2 2 + 10 → → A∝t Z (reqsonanmce: Z) e (

Well below Z: photon m STRONG (QCD) 1 Z [ exchange dominant exchange− dominant * Aside: for an massive boson, shape of cross section ρ q Couples to COLOUR σ • -1 -6 10 also depends on total decay width )Z = /+Z: 2 10 ℏ 1 10 g 10 2 √s [GeV] s Does NOT change 2 ΓZ /4 q + + + + 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). σ(E = q ) = σmax + → → → + σ(e e− hadr2 ons, s) is the experimental cross section corrected for initial state radiation and electron-positron vertex loops, σ(e e− FLAVOUR -7 2 2 + → 2 → (q mZ ) +µ µ−, sΓ) = 4πα /(s)/43s. Data errors are total b2elow 2 GeV and statistical above 2 GeV. The curves are an educative guide: the broken one (green) is a Znaive quark-parton model predgictison, and the solid one (red) is 3-loop pQCD prediction (see “Quantum Chromodynamics” section 10 − of this Review, Eq. (9.12) oαr, for m=ore details, K. G. Chetyrkin et al., Nucl. Phys. B586, 56 (2000) (Erratum ibid. B6g34, 413 (2002)). Breit-Wigner parameterizations osf 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 + # details of the R ratio extraction from them4caπn be found in [arXiv:hep-ph/0312114]. Corresponding computer-readable data ﬁles are available Measurements of !(e e !hadrons) at LEP determined:at http://pdg.lbl.gov/current/xsect/. (Courtesy of the COMPAS (Protvino) and HEPDATA (Durham) Groups, August 2007. Corrections • by P. Janot (CERN) and M. Schmitt (Northwestern U.)) See full-color version on color pages at end of book. WEAK Charged Current -8 2 10 • mZ = 91.188 ± 0.002 GeV/c νe 100d’2 Changes FLAVOUR )ZM =ich 2.4953aelmas 2 ±00 0.0026 GeV 500 Dr M.A. Thomson • 1 10 g V 10ECM (GeV) - gw w ckm e u For13 QUARKS: coupling - BETWEEN generations Υ g 2 W + 3 α = w W

10 J/ψ ψ(2S) w 4π

Interactions of the Z bosonZ M.A. WEAK Neutral Current Thomson Cross Section Measurements - At Z resonance mainly observe2 four types of event: e , νe qf Z10 boson interacts with all quarks and leptons. - φ e , νe

No change of quarkω or lepton flavour at Z boson vertex. q Does NOT change

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Each has a distinct topology in the detectors, e.g. 0 e

10 Z ZZ

Z boson decay ρ! 0 α

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Dr M.A. Thomson w Lent 2004 e

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Z can decay into any fermion!anti-fermion pair, f f .̅ q

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Figure 40.6: World data on the to+tal#cross section of e+e hadrons and the ratio R(s) = σ(e+e hadrons, s)/σ(e+e + µ+µ , s). − 2004 − − −

Z'% % Z'&%&(% Z'b(b =

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To work out cross sections− first count events of each type q 2

Then need to know(green“)integratedis a naive qua rluminosityk-parton model”pofred icollidingction, and th ebeamssolid one (red) is 3-loop pQCD prediction (see “Quantum Chromodynamics” section -

Lepton Universality ELECTR

of this Review, Eq. (9.12) or, for more de⇒tails, K. G. Chetyrkin et al., Nucl. Phys. B586, 56 (2000) (Erratum ibid. B634, 413FLAVOUR (2002))Changes .

g e

s γ 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 g

details of the R•ratiMo ex trforactio e,n f rµ,om %th edecaym can be isfo usamend in [a r X i ⇒v:h e)p-(pZh'/03e12+1e1#4)] .-C )orr(eZsp'ondingµ+µco#)mputer - )(-Zrea'%dable+%d#a)ta ﬁles are available ! Interactions

at http://pdg.lbl.gov/current/xsect/. (Courtesy of the COMPAS (Protvino) and HEPDATA (Durham) Groups, August 2007. Corrections and

Dr M.A. Thomson Michaelmas 2006 501 !

by P. Janot (CERN) and M. Schmitt (Northwestern U.)) See full-color version on color pages at end of book. OMA FLAVOUR

their

for &e, &µ, &% decay is same )(Z'&e&(e) = )(Z'&µ&(µ) = )(Z'&%&(%) e

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tices 6 Number of Neutrinos

Total width of the Z-boson ()Z) is sum of all partial widths: + + + Γ = Γ(Z qq¯) + Γ(Z e e−) + Γ(Z µ µ−) + Γ(Z τ τ −) + N Γ(Z νν¯) Z → → → → ν → LEP directly measured: • partial widths: )(Z'e+e#), )(Z'µ+µ#) , )(Z'%+%#), )(Z'hadrons) = )(Z'q(q ) • total width, )Z " 2" ̅ nb Cannot measure )(Z '& &) directly as !

3" neutrinos leave no signal in the detector. had 30 ALEPH ! DELPHI Can predict )(Z '& &)̅ using (Z '& &)̅ • M L3 4" • Use prediction & measurements to find OPAL 20 number of neutrinos contributing to )Z average measurements, N%=2.999±0.011 error bars increased • by factor 10 10 Consistent with exactly three neutrinos! ⇒ Gives us confidence that there are exactly 0 24 three generations of quarks and leptons 86 88 90 92 94 at LEP Ecm !GeV" 15 ! collisions Ws produced in pairs. ! In Standard Model 3 possible diagrams for

+ + Measuringe+ WW+ -bosone W+ e propertiesW+ + - γ Z0 W W Pair Producνe tion At LEP: W-bosons produced- in pairs - - e W- e 24W- e At Whadron- colliders: W-

!"#$%#&%'()%*+',-#.&#/0Three possible modes:] 25 bosons produced from at LEP 0

pb σ(Without Z ) [

quarks and anti-quarks 20 0 Cross section sensitive to pres- σ(With Z ) ! collisions Ws prWW oduced in pairs. ence of the Triple Gauge Boson σ 15 ! In Standard Model 3 possible diagrams for vertex 10 1996-2000, LEP operated above + + + + + + the threshold for pro- e W e 5 W e W ! 0 duction 1 2)0)$',*3#40 γ Z + #0 !!"#$ν%e&'()*+%,- ./$("(e+'0e,/150'$) WW)160*$1170"2'*3" measured180 19045*(3"200 210'%6'$),*,') at LEP Predicted- - - √s [GeV] e - e - e 0 + # - + # + + W + confirms+ W +Z -W+ -W1 W vert! ex "#W ( e % e $) "#W ( ' % ' $ ) "#W ( & % & $) 3 "#W ( l% $ $(e e 'WW) LEP Preliminary ] 25 + + + + + "#W ( d'0u$) "#W ( s'c $ 20) N c"#W ( e % e $ "#W ( b't $) 0 pb σ(Without Z ) RacoonWW / YFSWW 1.14 ( ) [ 20 0 ! Cross section! sensitive to pres- σ(With* " #ZW) ( q'q $ ) 2"#W ( l% $ ] WW

pb ence of the Triple Gauge Boson σ [ 15 15 5' 6 5' 6 Cross section agrees ! WW vertex * * 1 1 #"'789 σ 10 78*90+'":;"'80'(%9'$,1996-2000, LEP operated above with Standard Model 10 From measurements at LEP & , + , + + the threshold for pro- prediction. Conﬁrma- 5 e e ( W W ( qqe % e 18 YFSWW 1.14 tion ofTevatron:the existence of duction RacoonWW 0 ), 17 the vertex 2 150<-160"G 170 180 190 200 210 5 • mW = 80.413 ± 0.048 GeV/c H √s [GeV] = 0*%( 16 • )W = 2.141 ± 0.041 GeV 0 LEP Preliminary 160 170 180 190 200 210

20 Ecm [GeV] RacoonWW / YFSWW 1.14

] Measurements ofDr M.A. WThomson and Z bosons validate the Electroweak ModelLent 2004 beautifully pb

[ 15 Cross section agrees WW

σ 16 <&)00'with !*3"-)$'Standard =0Model8$*&.4 10 prediction.I6('') 2%,J"Conﬁrma-K<"0('1%L,%/$ 18 YFSWW 1.14 tion of the existence of RacoonWW ! !/$.%(9)"'8%),'$L'"/. (#00'#$%'117 -%":');'1 2)0)$the vertex 5 =M"=N O@ &'(,'8 ! <= >"?@16ABCD" @A@;?""E'F Nuclear" and Particle Ph!ysics Franz Muheim 9 0 =">"CAGCB" A@A@BG"E'F 160 170 180 190 200 210

Ecm [GeV]

Dr M.A. Thomson Lent 2004 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) - 6 e q Couples to CHARGE Summar- e y of StandarQ e d Model Vertices e q Does NOT change ! At this point have discussed all fundamentalFLAVOURfermions e2 γ and αtheir = interactions with the force carrγ ying bosons. 4π !STRInteractionsONG (QCD)characterized by SM vertices 3 ! Two types of WEAK interaction ELECTROMAGNETIC (QED) q Couples to COLOUR - CHARGEDe CURRENTg q (CC) - Bosons q s CouplesDoes toNOT CHARGE change - eNEUTRAL CURRENTQ e (NC) -FLAVOURBoson e 2 Does NOT change gs q ! αWEAKs = force mediated by MASSIVEg FLAVOURVECTOR e24π α = γ γ WEAKBOSONS:4π Charged Current STRONG (QCD)νe d’ Changes FLAVOUR g V q - gw w ckm Couples to COLOUR e For QUARKS: coupling u gs q DoesBETWEEN NOT change generations ! e.g. the2 WEAK- interactions of electrons and gw W FLAVOUR+ αelectrw g=2 on neutrinos: W α = s 4π g Weak Force Summarys 4π - - e νe e νe WEAK- Neutral 0Current 0 + WEAKW Charge-dZCurrent Z W e , ν qf • The weak force acts on all quarks and - ν f’e e d’ Changes FLAVOUR e , νe g V + + leptons. - gw νe w ckmνe e e ef u fq For QUARKS:Does NOT couplin changeg • Tw o massive bosons propagate the BOSON SELF-INTERACTIONS FLAVOUR - 0 BETWEEN generations weak interaction: W± and Z0. g 2 WZ + 0 α = w - WZ - • Interactions characterised by: long w 4π W W Dr M.A. Thomson 0 Lent 2004 lifetimes 10#13 - 103 s and small cross WEAKAllowedNeutral ZCurrent γ #13 - sections 10 mb. vertices:e , ν + q + - e W W e , -ν - 0 - - - W e W Z W γ W γ W At low energies, virtual W and Z bosons •Lepton interactionsq are universalDoes NOT: change responsible for lepton and lightest same coupling0 to W, Z bosons FLAVOUR Quarks interactionsZ not universalZ0 : hadron decays and neutrino scatterings. • W+ W+ Z0 W+ Z0 W+ γ W+ ! W-(Q=+2/3 quark)-(Q=#1/3 quark) Fermi theory describes W-boson Dr M.A. Thomson Lent 2004 ! alsocouplinginteractions is gW Vwith, wherePHO VT ONSdepends(W-bosons interactions for low boson momentum. areonc flavoursharged) of quark involved. Described by Fermi constant: 2 2 ! V is largest within a generation: GF gw/mW Vud, Vcs, Vtb ∝ Dr M.A. Thomson Lent 2004 High energies colliders can produce real Electromagnetic & weak are W and Z bosons for study. These manifestations of a single unified validate electroweak model e.g. electroweak interaction, Z decays suggest exactly three described by just 3 parameters. generations of quarks and leptons.