Subatomic Physics: Particle Physics Handout 8. The Weak Force

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1 Sbaomic Physics: Paricl Physics Hando 8 Th ak Forc ak inracions and inracions a low nrgy Frmi hory Elcrowak hory and bosons a high nrgy QCD Smmary QCD: Qanm Chromodymanics is h anm dscripion of h srong forc. Only arks fl h srong forc. Glons ar h propagaor of h srong forc Qarks and glons carry color charg. Glons slfinrac: Elcromagnic copling consan! dcrass as a chargd paricls g frhr apar. Srong copling consan!s incrass as frhr apar arks bcom. Hadrons can b dscribd as consising of parons: arks and glons, which inrac indpndnly Color Confinmn nrgy rird o spara arks! " arks ar confind o hadrons Qarks and glons prodcd in collisions hadronis: hadrons ar prodcd. Th dcay prodcs of h hadrons appar in h dcor as js.

2 Inrodcion o h ak Forc Th wak forc is rsponsibl for som of h mos imporan phnomna: Dcays of h mon and a lpons Nrino inracions Dcays of h lighs msons and baryons Radioaciviy, nclar fission and fsion Characrisics of ak Procsss: Long lifims #3 3 s Small cross scions #3 mb ak Forc is propagad by massiv, # and bosons Th inracions of ± and ar diffrn (rlad by symmry of h wak inracion) Boson ± Mass GV/c charg, ± spin ± and can inrac wih ach ohr ± and " can inrac (as ± bosons ar chargd) 3 QED mdiad by h xchang of viral phoons acs on all chargd paricls ak Vrics boson mdiad by h xchang of boson acs on all ark and lpons copling srngh!!!! copling srngh! g! $! propagaor rm: /( #m" )= / propagaor rm: /( #m ) For many procsss: M / α = For many procsss: M g /( #m ) g w α w = g w Rcall: marix lmn, M, is h amplid of a procss. Scaring cross scion, $!M. Dcay widh,!! M ν 4

3 Inracions of h ± boson Known as chargd crrn inracions ± boson inracs wih all frmions (all arks and lpons) Chargd crrn changs h flavor of h frmion:.g. lcron miing an boson can rmain an lcron violas consrvaion of charg! an lcron rns ino a lcron nrino an p ark rns ino a down ark and vic vrsa! Copling srngh a vry vrx! g (mor abo arks lar) ( m ) Propagaor rm dscribing h boson! is h formomnm ransfrrd by h boson g w α w = g w g w V ckm ν d F B 5 Allowd Flavor Changs A a boson vrx: Lpon nmbrs: L, Lµ and L%, is consrvd: Allowd lpon flavor changs: " #& µ # #&µ % # #&% Toal Qark Nmbr, N, is consrvd Individal ark flavor nmbrs: N, Nd, Ns, Nc, Nb, N ar no consrvd Allowd ark flavor changs: (Q=+/3 ark) # (Q="/3 ark) ( d s b ) # ( c ) Each of h nin possibl ark flavor changs has a diffrn copling srngh:.g. gvd for o d arks (Vs ar rms in CKM marix mor lar) Main ark flavor changs ar wihin a gnraion: d # s # c b # g g w α w = g w α = g gvd w V ckm ν d F B 6

4 Inracions of h boson Known as nral crrn inracions Acs on all frmions (all arks and lpons) Nral crrn consrvs flavor of h frmion No allowd frmion flavor changs Propagaor rm!, ν ( m ), ν Copling srngh dpnds on frmion flavor w won considr his in his cors, ν, ν Anywhr a phoon cold b xchangd a boson can b xchangd. (Almos vicvrsa, xcp boson also has nrino inracions oo!) Elcromagnic and wak nral crrn inracions ar linkd! 7 and bosons a low nrgy If h momnm of h or boson, h bosons ar viral: = E p p = m m, m = E p p = m Viral bosons ar rsponsibl for h dcays of h lpons, and h lighs hadrons.g. µ # ' # &( &µ µ # µ # ' # &( &µ &µ &( = m # viral boson inracions can also b dscribd by Frmi Thory Many inracions of viral bosons ar no clarly vidn, as h sam inracion can ak plac d o " xchang. + # ' scaring can b d o or " Inracions involving % ms b d o (or ) A low nrgis w s h ffc of boson mainly in scaring involving nrinos.g. & # ' & # as " canno copl o h nral nrinos # # & & # ' & # & 8

5 Frmi Thory boson inracions a Low Momnm Transfr For mon dcay, and many ohr wak procsss: gw M ( m ) A low momnm ransfr m M g w m Inrodc Frmi copling consan: µ # M &µ g g m g &( # m 8 m Dimnsion [E] # From xprimnal masrmns: GF =.6637 & #5 GV # Masrmns of G F g w G F = g w G F & M g w =.66 α w = g w = 9 > α EM = 37 Rcall, from problm sh, Q7, rang of boson: x p = =. fm m c ak inracion no inrinsically wak appars wak d o larg boson masss. 9 inracions wih arks and lpons Lpon nivrsaliy: Copling of o boson o all lpons is al = g lcrons, mons and as all inrac idnically inrac wih h sam bosons wih sam copling srngh Qark inracions: In gnral, any vrx (Q=+/3 ark)(q=#/3 ark) is valid. boson copling o arks spprssd by a flavordpndn facor V c d d d gvd gvcd c s s s gvs gvcs c b b b gvb gvcb Known as h CKM marix. (vals from xprimnal masrmns) Vd=.974 Vs=.7 Vb=.4 Vcd=.3 Vcs=.97 Vcb=.4 Vd=.8 Vs=.4 Vb=.999 gvd gvs gvb Largs coplings ar wihin a gnraion: d ' s ' c b '

6 v sn alrady ha whrvr a " boson can b xchangd a can also b xchangd: Th wak and lcromagnic forc ar linkd. A shor disancs (or high nrgis) h srngh of h lcromagnic forc and h wak forc ar comparabl. Can b rlad by a paramr, sin ( Elcrowak Thory = g sin θ Th wak and lcromagnic inracions ar manifsaions of a ndrlying forc: h lcrowak forc. Coplings of h ", (and ) bosons ar rlad: = g sin θ Mass of h and bosons ar rlad: m = m /cos θ Js hr fndamnal paramrs ar rird o dscrib: coplings of, and " o arks and lpons masss of h,, " bosons inracions of h,, " bosons wih ach ohr Normally formlad in rms of mos accraly masrd paramrs:, GF, m and boson a high nrgis Using a collidr, w can cra high nogh nrgis o mak ral and bosons: m, m.g. LEP collidr + # ', + # ' #.g. a h LHC: pp'+x, pp'+x Can sdy h propris of h and bosons in dail. masss, lifim/widh, copling srnghs, dcay mods, spin... arks wihin p (or (p) inrac o mak or ( ) "7/(%A',7&(( Discovry of and bosons a CERN in 983 a h Spp S collidr p )p collidr wih Ep = Ep! = 7 GV p )p! #! # )& vn a UA xprimn

7 6 Masring propris σ and R in + Collisions 4. Plos of cross scions and rlad aniis Smmary of Sandard Modl Vr ω Mos sdis of h boson wr mad a LEP. Annihilaion in Fynman Diagrams + Main procss was!hadrons: 5 ψ(s) Υ ρ!! Inracions characrizd by SM vrics 7 φ and hir inracions wih h forc carrying boso 6 ELECTROMAGNETIC (QED) 8 J/ψ Mixr of EM (") & ak () conribions ψ(s) 3 ρ! A ECM="s~m, mainly boson inracions:r ρ 4 A low ECM mainly # inracions. J/ψ Collisions! A his poin hav discssd all fndamnal f ω σ [mb] on σ and R in φ ρ 4 σ [mb] annihilaion phoon and + inrfrnc + " 3 3 Υ Υ J/ψ ψ(s) α= ρ φ ω mstrong ) A ( rsonanc: (QCD) σ(+ f f ) 5 xchang dominan for an massiv boson, shap of cross scion Asid: 6 also dpnds on oal dcay widh ) = /+: *(+#!hadrons) 6 4. Plos of cross scions and rlad aniis! Q s [GV] + σ(+ hadrons, s)/σ(+ Dos NOT ch FLAVOUR µ+ µ, s). )Michalmas = ±. GV 3 g 5 gw Changs FLA d ECM (GV) gwvckm 3 QUARKS: For BETEEN gn, ν f + Inracions of h boson EAK Nral Crrn J/ψ ψ(s).a M FLAVOUR,ν ρ! K boson dcay Dos NOT ch f disinc opology in h dcors,.g. Dr, ν φ ω No chang of ark or lpon flavor a boson vrx. om.t h boson inracs wih all arks and lpons. so n for yps of vn: nc mainly obsrv f g w V d g FL s A NO T UR ch VO 4 ck m Ch a F ng o rq s + B F E LA T UA V E RK O E UR N S: c g o n p ra lin io g ns 4 'b(b h a ng n '& &( L + #cross scion of + hadrons and h raio R(s) = σ(+ hadrons, s)/σ(+ µ+ µ, s). Figr 4.6: orld daa on h oal % % σ(+ hadrons, s) is h xprimnal cross scion corrcd for iniial sa radiaion and lcronposiron vrx loops, σ(+ (s)/3s. Daa rrors ar oal blow GV and saisical abov GV. Th crvs ar an dcaiv gid: h brokn on µ, s) = αfirs crossµ+scions con vns of ach yp (grn) is a naiv arkparon modl prdicion, and h solid on (rd) is 3loop pqcd prdicion (s Qanm Chromodynamics scion o know ingrad lminosiy of colliding bams Lpon Univrsaliy of his Rviw, E. (9.) or, for mor dails, K. G. Chyrkin al., Ncl. Phys. B586, 56 () (Erram ibid. B634, 43 ()). Briignr paramrizaions of J/ψ, ψ(s), and Υ (ns), n =,, 3, 4 ar also shown. Th fll lis of rfrncs o h original daa and h #) )('%+%daa #) fils ar availabl dails of h R raio xracion can b is fond in [arxiv:hpph/34]. M for,from µ, %hm dcay sam )('+#) Corrsponding )('µ+µcomprradabl a hp://pdg.lbl.gov/crrn/xsc/. (Corsy of h COMPAS (Provino) and HEPDATA (Drham) Grops, Ags 7. Corrcions 5 Michalmas 6 by P. Jano (CERN) and M. Schmi (Norhwsrn U.)) S fllcolor vrsion on color pags a nd of book. M for &, &µ, &% dcay is sam )('&&() = )('&µ&(µ) = )('&%&(%) '% % 'c) s c[gv]'s)s 'd)d '&µ&(µ 'µ+µ# ', Do FL s N A VO OT c '&&( UR '+# ra rr n ρ f, l C ν xcp op ark pair, as m < m N Dr M.A. Thomson can dcay ino any frmion!anifrmion pair, f f. ν Υα = gw w Cross Scion Masrmns EAK Chargd Crrn m = 9.88 ±. GV/c R Copls o C gs g αs = s Masrmns of!(+#!hadrons) a LEP drmind: FLAVOUR Figr 4.6: orld daa on h oal cross scion of hadrons and h raio R(s) = σ(+ hadrons, s) is h xprimnal cross scion corrcd for iniial sa radiaion and lcronposiron vrx loops, σ(+ µ+ µ, s) = α (s)/3s. Daa rrors ar oal blow GV and saisical abov GV. Th crvs ar an dcaiv gid: h brokn on (grn) is a naiv arkparon modl prdicion, and h solid on (rd) is 3loop pqcd prdicion (s Qanm Chromodynamics scion of his Rviw, E. (9.) or, for mor dails, K. G. Chyrkin al., Ncl. Phys. B586, 56 () (Erram ibid. B634, 43 ()). Briignr paramrizaions of J/ψ, ψ(s), and Υ (ns), n =,, 3, 4 ar also shown. Th fll lis of rfrncs o h original daa and h dails of h R raio xracion from hm can b fond in [arxiv:hpph/34]. Corrsponding comprradabl daa fils ar availabl a hp://pdg.lbl.gov/crrn/xsc/. (Corsy of h COMPAS (Provino) and HEPDATA (Drham) Grops, Ags 7. Corrcions by P. Jano (CERN) and M. Schmi (Norhwsrn U.)) S fllcolor vrsion on color pags a nd of book. 7 8 Dos NOT ch ρ Γ /4 σ(e = ) = σmax ( m ) + Γ /4 Copls o C

8 Nmbr of Nrinos Toal widh of h boson ()) is sm of all parial widhs: Γ = Γ( ) + Γ( + ) + Γ( µ + µ ) + Γ( τ + τ ) + N ν Γ( ν ν) LEP dircly masrd: parial widhs: )(' + # ), )('µ + µ # ), )('% + % # ), )('hadrons) = )('( ) oal widh, ) Canno masr )( '& & ) dircly as nrinos lav no signal in h dcor. Can prdic )( '& & ) sing M( '& & ) Us prdicion & masrmns o find nmbr of nrinos conribing o ) N%=.999±. Consisn wih xacly hr nrinos! Givs s confidnc ha hr ar xacly hr gnraions of arks and lpons! had!nb" 3 ALEPH DELPHI L3 OPAL avrag masrmns, rror bars incrasd by facor " 3" 4" E cm!gv" 5 Masring boson propris A LEP: bosons prodcd in pairs!"#$%#&%'()%*+',#.&#/ Thr possibl mods: A hadron collidrs: bosons prodcd from arks and aniarks ))$',*3#4 Prdicd $( + # ') σ [pb] σ(iho ) σ(ih ) s [GV] $( + # ') masrd a LEP confirms # vrx σ [pb] 5 5 LEP Racoon / YFS YFS.4 Racoon Prliminary E cm [GV] ( ) From masrmns a LEP & Tvaron: m = 8.43 ±.48 GV/c ) =.4 ±.4 GV Masrmns of and bosons valida h Elcrowak Modl baiflly 6

9 Th wak forc acs on all arks and lpons. Two massiv bosons propaga h wak inracion: ± and. Inracions characrisd by: long lifims #3 3 s and small cross scions #3 mb. A low nrgis, viral and bosons rsponsibl for lpon and lighs hadron dcays and nrino scarings. Frmi hory dscribs boson inracions for low boson momnm. Dscribd by Frmi consan: ak Forc Smmary G F g w/m High nrgis collidrs can prodc ral and bosons for sdy. Ths valida lcrowak modl.g. dcays sggs xacly hr gnraions of arks and lpons. f g w α w = g w π Allowd vrics: ν f f f Lpon inracions ar nivrsal: sam copling o, bosons Qarks inracions no nivrsal:! (Q=+/3 ark)(q=#/3 ark) copling is g V, whr V dpnds on flavors of ark involvd.! V is largs wihin a gnraion: Vd, Vcs, Vb Elcromagnic & wak ar manifsaions of a singl nifid lcrowak inracion, dscribd by js 3 paramrs. 7