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Subatomic : Handout 8 Introduction to the Weak

Weak interactions Charged and Feynman Rules for weak force

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3 ! Two types of Introduction to the CHARGEDWeak CURRENTForce(CC) - NEUTRAL CURRENT (NC) - 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 • interactions BOSONS:Boson W± Z0 Decays of the lightest mesons and baryons • Radioactivity, nuclear fission and fusion 80.4 91.2 • GeV/c2 Characteristics of Weak Processes: ! e.g. the WEAK interactions of and • Long lifetimes 10!13 - 103 s charge, e ±1 0 : !13 • Small cross sections 10 mb - 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 W- W- Z0 W- γ W- γ W- 2

W+ W+ Z0 W+ Z0 W+ γ W+

! also interactions with (W-bosons are charged)

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

! At this point have discussed all fundamental and their interactions with the force carrying bosons. Weak Vertices! Interactions characterized by SM vertices ELECTROMAGNETIC (QED) QED 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 FLAVOUR e2 α = γ γ acts on all charged particles acts on all 4quarkπ and leptons 6 STRONG (QCD) 6 couplingSummar strengthy !o ef !Standar !" d ModelcouplingVe rstrengthtices ! gW ! ""W SummaryqofCouplesStandar to COLOURd Model Vertices 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/(q q#mW ) and their interactions with the force carrying bosons. ! At this point haveFLAVOURdiscussed all fundamental fermions g 2 α = s g For! manyInteractions processes:characteriz ed by SM verticesFor smany4π processes:and their interactions with the force carrying bosons. 2 2 2 2 2 ∝ e /q ∝ gW /(q #mW ) ELECTRM OMAGNETIC (QED) WEAKM 6 - ! Interactions characterized by SM vertices e q Couples to CHARGE νe d’ Changes FLAVOUR g V - e Q e Summar- gyw oELECTRf Standarw OMAckm dGNETICModel(QED)Vertices e Does NOTe change - For : coupling q u e q 2 FLAVOUR - BETWEEN generations Couples to CHARGE e ! At this pointg 2have discussed all +fundamental fermions γ = w W α = γ αw - e W Q e 4π and their interactions4π ewith the force carrying bosons. Does NOT change STRONG (QCD) q Recall: matrix element, M, is the amplitudeWEAK ofNeutral a process.Current q - 2 FLAVOUR Scattering cross section, $ !!M2.Interactions Couples Decay to width,COLOURc haracteriz#e !, ν M2 e ed by SMγq vertices - αe = γ gs e , Does NOT changeνe 4π 3 q ELECTROMAGNETIC (QED) Does NOT change FLAVOUR - STRONGq (QCD) g 2 FLAVOUR α = s g e 0 q Couples to CHARGE s 4π Z Z0 q Couples to COLOUR WEAK Charged Current - e Q e g e Dr M.A. Thomson ± q Does NOTs changeLent 2004Does NOT change Interactionsνe ofd’ theChanges WFLAVOUR boson q g g V 2 FLAVOUR FLAVOUR - w w ckm e γ 2 e u Forα = QUARKS: coupling gs αs = γ g • Known as “charged current- interactions” BETWEEN4π generations 4π g 2 W + α = w W w 4π STRONG (QCD)WEAK Charged Current W± boson interacts with all fermions (all quarks and leptons) q Couples to COLOUR • WEAK Neutral Current νe d’ Changes FLAVOUR - e , νe q gg g V - - sw Doesw NOTckm change Charged currente , νchangese the flavour of the : eq u For QUARKS: coupling • Does NOT change q FLAVOUR BETWEEN generations • e.g. electron emitting an W-boson can’t FLAVOURremaing 2 an 2 - 0 s gw W + electron - violates conservationZ of charge!0 αs = α = g W Z 4π w 4π • an electron turns into a electron neutrino Dr M.A. Thomson WEAK ChargedLentCurrent2004 • an up turns into a down quark WEAK Neutral Current ν -d’ and vice versa! e e , ν Changes FLAVOURq g g- V e - w e ,w νeckm e u For QUARKS: couplinDoesg NOT change • Coupling strength at every vertex ! gW q BETWEEN generations 1 2 - 0 FLAVOUR gw W Z + 0 • Propagator term describing the W-boson ! α(qw2 = m2 ) W Z −4π W • q is the four-momentum transferred by the W-boson WEAK NeutralDr M.A.CurrentThomson Lent 2004 - e , νe q - 4 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. 6 ! Interactions characterized by SM vertices Summary oELECTRf StandarOMAdGNETICModel(QED)Vertices - ! At this point have discussed alle fundamental fermionsq Couples to CHARGE and their interactions -withethe force carryingQ ebosons. e q Does NOT change ! Interactions characterized by SM vertices FLAVOUR e2 α = γ γ ELECTROMAGNETIC4π(QED) - e STRONG (QCD)q Couples to CHARGE q - e Q e Couples to COLOUR e q Doesg NOT change s Does NOT change 2 qFLAVOUR e γ FLAVOUR Allowed Flavourα = Changesg 2 γ 4π α = s g s 4π 6 At a W-boson vertex: STRONG (QCD) Summary oWEAKf StandarChard Modelged CurrentVertices • Lepton numbers: Le, Lµ and L%, is conserved: q Couples to COLOUR ! !# At this#point have discussed all fundamentalνe fermions d’ Changes FLAVOUR Allowed lepton flavour changes: e $&e µ $&µ % $&% g and their interactions withgtheWs force carryingDoesgbosons.V NOT change q- gw w ckm 6 e For QUARKS: coupling ! Interactions characterized by SM verticesuFLAVOUR 2 Summary of Standard Model Vertices gs - BETWEEN generations αELECTR = OMAGNETIC (QED)22 g Total Quark Number, Nq, is conserved s ggw W + • 4π - ! Atαthis = pointW have discussed all fundamentalW fermions e αW w= 4π q Couples to CHARGE • Individual quark flavour numbers: NuWEAK, Nd, Ns, NCharc, Nb,g Net dandCurrenttheir interactions4π with the force carrying bosons. - e Q e 6 are not conserved e q Does NOT change ν !WEAKInteractionsNeutralcharacterizd’Currented by SM vertices 2 e Summary o- f FLAVOURStandarChangesd Model FLAVOURVertices Allowed quark flavour changes: e e , ν α =g γ ELECTRgWVVOMAud GNETICe (QED) q - w4 -w ckm γ (Q=+2/3 e quark) $ (Q=!1/3 e quark)e π ! Ate this, ν point -have discussedFor QUARKS:all fundamental couplinfgermions STRONG (QCD) u e e q Couples to CHARGE ( d s b ) $ ( u c t ) and their interactions withBETWEENqthe force carr generationying bosons.Doess NOT change 2 - - e q CouplesQ e to COLOUR gw W!eInteractions characteriz0q+ ed by SM verDoestices NOTFLAVOUR change • Each of the nine possible quark flavour αchangesw = has a g W 0 4π 2 s ZDoes NOT change FLAVOUR different coupling strength: e.g. gWVud for u to d quarks q e Z ELECTR = OMAγGNETIC (QED) α - FLAVOUR γ (Vs are terms in CKM matrix VCKM - more nextg lecture)2 4π e WEAKα =Neutrals Dr M.A.CurrentThomson g q Couples to CHARGE Lent 2004 s 4π - STRONG (QCD) • Main quark flavour changes are within a generation:e , ν - e Q e WEAK Chargede Currente qq q CouplesDoes NOT to COLOURchange d $ u s $ c b $ t - e , νe ν 2 d’ g FLAVOUR e e γ Changesq s FLAVOURDoes NOT change g αg = V 5 Does NOTγ change - w qw 4πckm FLAVOUR e u g 2 For QUARKS:FLAVOUR coupling 0STRα =ONGs (QCD) g Z - s 4π BETWEEN0 generations g 2 W + q α = w W Z Couples to COLOUR w 4π WEAK Charged Current gs Dr M.A. Thomson 0 ν d’ Does NOT changeLent 2004 Interactions of theWEAK ZNeutral bosonCurrent e q Changes FLAVOUR - g g V FLAVOUR e , ν - g 2w q w ckm - e αe = s u g For QUARKS: coupling e , s 4π • Known as “neutral current interactions” νe BETWEEN generations 2 - Does NOT change WEAKq gwChargWed Current + 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 Dr M.A. Thomson u Lent 2004 • No allowed fermion flavour changes e , νe q - - BETWEEN generations e , νeg 2 W + α = w W 1 w 4π q Does NOT change • Propagator term ! (q2 m2 ) 0 FLAVOUR Z WEAK NeutralZ Current 0 − - Z Coupling strength depends on fermion flavour - we e , νe q • Dr M.A. Thomson- Lent 2004 won’t consider this in this course e , νe q Does NOT change 0 FLAVOUR Z Z0 Anywhere a could be exchanged a Z0 boson can be exchanged. Dr M.A. Thomson Lent 2004 (Almost vice-versa, except Z0 boson also has neutrino interactions too!)

Electromagnetic and weak neutral current interactions are linked!

6 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 Feynman Rules for Weak InteractionFLAVOUR g 2 How to calculate the matrix element, α, for= sa weak decay or scatteringg M s 4π WEAK Charged Current # # e.g. decay of a muon µ %e &µ &'e &µ (p3) νe d’ Changes FLAVOUR g # g V • Draw the for the process - w µ (p1w) ckmgW e u For&' QUARKS:(p2) coupling give a four momentum for each particle e • - BETWEEN generations g 2 W + α = w W W w 4π gW • Check quantum numbers conservation at every vertex WEAK Neutral Current # - e (p4) • For both W and Z: Le, Lµ and L%, Nq, Q e , ν q - e • For Z only: no change of quark or leptone flavour, νe q Does NOT change • Is and momentum conserved? For decay: minitial > mfinal 0 FLAVOUR Z 0 ￿ ￿Z Write down the coupling at each vertex: gW (for W) • Dr M.A. Thomson Lent 2004 Work out four-momentum transferred by boson: q = (p p ) = (p + p ) • 3 − 1 4 2 2 2 • Write down the propagator term for each boson: 1/(q mboson) 2 − • M is proportional to product of g w vertex and propagator terms: M ∝ (q2 m2 ) − W 7

Weak Force Summary

The weak force acts on all quarks and Weak interactions are leptons. characterised by:

Tw o massive bosons propagate the weak • Long lifetimes 10!13 - 103 s interaction: W± and Z0. • Small cross sections 10!13 mb

Z0-boson interactions conserve W±-boson interactions changes fermion the flavour of the fermion flavour 0 ! # # • Z -boson propagator term: e $&e µ $&µ % $&% (Q=+2/3 e quark) $ (Q=!1/3 e quark) 1 2 2 (q mZ ) ± − • quark coupling at W vertex: gW VCKM ± • lepton coupling at W vertex: gW Z0-boson interactions are ± 1 • W propagator term: strongly linked to the (q2 m2 ) − W electromagnetic interaction

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