QCD --- Quantum Chromodynamics

Outlin QCD --- Quantum Chromodynamics QCD Principls Quantum fild thory, analogy with QED Vrtx, coupling constant Colour rd, grn or blu Gluons Quark and Gluon Intractions Confinmnt Asymptotic Frdom QCD potntial QCD Exprimnts Exprimntal vidnc for uarks, colour and gluons - annihilations Charmonium Scattring, DIS Qustions Why is strong intraction short rang? Why ar fr uarks not obsrvd? How do uarks and gluons fragmnt into hadronic jts? Nuclar and Particl Physics Franz Muhim 1

QCD vs QED QED Quantum thory of lctromagntic intractions mdiatd by xchang of photons Photon coupls to lctric charg Coupling strngth α QCD Quantum thory of strong intractions mdiatd by xchang of gluons btwn uarks Gluon coupls to colour charg of uark Coupling strngth α S Fundamntal vrtics QED QCD α = /4π 1/17 α S = g S /4π ~ 1 Coupling constant Strong intraction probability α S > α Coupling strngth of QCD much largr than QED Nuclar and Particl Physics Franz Muhim

What is Colour? Quarks Charg of QCD Colour Consrvd uantum numbr Rd, grn or blu Com in thr colours Anti-uarks hav anti-colours r g b Lptons, othr Gaug Bosons - γ, W ±, Z 0 Cavat r g b Don t carry colour, zro colour charg Don t participat in strong intraction colour is not to b takn litrally. Intraction QED QCD Consrvd charg Coupling constant lctric charg colour chargs r, g,b α = /4π α S = g S /4π Gaug boson Photon 8 gluons Charg carrirs frmions ( 0) uarks gluons Nuclar and Particl Physics Franz Muhim

Gluons Gluon Proprtis Gluons ar masslss spin-1 bosons QCD propagator 1/ Emission or absorption of gluons by uarks changs colour of uarks - Colour is consrvd Gluons carry colour charg thmslvs.g. rg gluon changs rd uark into grn QCD vry diffrnt from QED, (photon) = 0 Numbr of gluons Naivly xpct 9 gluons rb, rg, gb, gr, br, bg, rr, gg, bb Symmtry -> 8 octt and 1 singlt stats 8 gluons ralisd by Natur (colour octt) Nuclar and Particl Physics Franz Muhim 4

Quark & Gluon Intractions Quark-Antiuark Scattring dscribs a mson.g. π = (u-dbar) Singl gluon xchang at short distanc 0.1 fm QCD Potntial 4 α at short distanc ~ 0.1 fm S VQCD( r) = r attractiv -ngativ sign QED-lik apart from colour factor 4/ Mor than on gluon -> colour factor Gluon Slf-Intractions QED vrsus QCD - So far prtty similar Photons and gluons masslss spin-1 bosons Big diffrnc - gluons carry colour charg Gluons intract with ach othr -gluon vrtx 4-gluon vrtx Origin of hug diffrncs btwn QCD and QED Nuclar and Particl Physics Franz Muhim 5

Confinmnt Exprimntal Evidnc Do not obsrv fr uarks Quarks confind within hadrons Strong Intraction Dynamics Gluons attract ach othr - slf-intractions Colour forc lins pulld togthr in QCD Colour Forc btwn uarks at long distancs O(1 fm) String with tnsion k -> Potntial V(r) = kr Stord nrgy/unit lngth is constant Sparation of uarks ruirs infinit amount of nrgy Confinmnt Dirct consunc of gluon slf-intractions Particls with colour - uarks and gluons - confind insid QCD potntial, must combin into hadrons with zro nt colour charg Nuclar and Particl Physics Franz Muhim 6

Msons QCD Potntial uark-antiuark pair with zro nt colour charg colour wav fct. Singl gluon xchang -> colour of individual or anti- can chang QCD potntial QED-lik at short distanc r 0.1 fm Quarks ar tightly bound α S 0... 0. String tnsion -> Potntial incrass linarly at larg distanc 4 αs V QCD( r) = kr r rr rr r 1 fm rr bb α S = 0. k = 1 GV/fm Potntial similar for uarks in baryons Forc Btwn two uarks at larg distanc F = dv/dr = k = 1.6 10-10 J/ 10-15 m = 16000 N Euivalnt to wight of larg car Nuclar and Particl Physics Franz Muhim 7

Coupling Constant α S Proprtis α S --- coupling strngth of strong intraction Rcall QED - coupling constant varis with distanc - running α In QED bar lctron charg is scrnd by cloud of virtual - pairs In QCD similar ffcts QCD Quantum Fluctuations Cloud of virtual -anti- pairs around a uark Scrning of colour charg Colour charg dcrass with distanc Cloud of virtual gluons --- no uivalnt in QED du to gluon slf-intractions Colour charg of gluons contributs to ffctiv colour charg of uark Anti-scrning of colour charg Colour charg incrass with distanc Nuclar and Particl Physics Franz Muhim 8

Running of α S Scrning and Anti-scrning Anti-scrning dominats Effctiv colour charg incrass with distanc At larg distancs / low nrgis α S ~ 1 - larg Highr ordr diagrams -> α S incrasingly largr Summation of diagrams divrgs Prturbation thory fails Asymptotic Frdom Coupling constant α S = 0.1 at = (100 GV) small at high nrgis Running of α S dpnds on and # of colours and flavours Enrgtic uarks ar (almost) fr particls Summation of all diagrams convrgs QCD Prturbation thory works αs( µ ) αs( ) = 1 β αs( µ )ln µ 11n f β = 1π n = colours f = 6 flavours Nobl priz 004 Gross, Politzr, Wilczk Nuclar and Particl Physics Franz Muhim 9

Hadronisation & Jts What happns whn uarks sparat? Exampl: annihilation Quarks sparat E string incrass - whn E string > m String braks up into pairs - fragmntation Hadronisation As nrgy dcrass Formation of hadrons (msons and baryons) Hadrons follow dirction of original LEP s = 91 GV Jts hadronisation hadrons Obsrv collimatd jts back-to-back in CoM fram Nuclar and Particl Physics Franz Muhim 10

- Annihilation Fynman Diagrams and µ µ Quark and muon masss ar nglctd Only diffrnc in coupling of virtual photon to final stat frmion pair is charg Q f muons Q µ = ±1 uarks Q = ±/ µ µ or ±1/ Cross sction For a singl uark flavour --- without colour xpct cross sction ratio ( ) ( µ µ ) σ Q R = = = Q σ Q With colour ach uarks has N C = final stats Rul is to sum ovr all availabl final stats ( ) ( µ µ ) Hadronisation Masur hadrons not -pairs fragmnt and form hadronic jts Jts from diffrnt -pairs ar similar at high nrgis compard to uark masss µ σ R = = N C Q = σ Nuclar and Particl Physics Franz Muhim 11 Q

Nuclar and Particl Physics Franz Muhim 1 - Annihilation Annihilation Ratio R Sum is ovr all uark flavours (u, d, s, c, b, t) kinmatically accssibl at CoM nrgy, s, of collidr, and colours (r,g,b) for ach flavour Masurmnts R incrass in stps with s R.85 11/ at s 10 GV Ovrwhlming vidnc for colour s < 10 GV -- rsonancs (c-cbar and b-bar) ( ) ( ) ( ) b c s d u m s R c s d u m s R s d u m s R b c s,,,, 11 1 1 1 ~ 10 GV,,, 10 1 1 GV ~,, 1 1 ~ 1GV = = > = = > = = > ( ) ( ) = = Q R hadrons µ µ σ σ u,d,s,c,b u,d,s,c u,d,s No colour s R

Charmonium Discovry of Charm Quark 1974 Brookhavn and SLAC Narrow rsonanc at.1 GV dcays into -, µµ-, hadrons did not fit in xisting schms J/ψ Mson Mass m J/ψ =.1 GV/c Narrow width, smallr than xprimntal rsolution Total width Γ = 0.087 MV Liftim τ = ħ/γ = 7.6 10-1 s = 1000 x xpctd for strong intraction procss Branching Fraction J/ψ dcays many final stats with partial dcay width Γ i Total dcay width Γ = Γ i i Branching fraction Γ B = i i Γ B( J / ψ ) = (87.7 ± 0.5)% B( J / ψ µ µ ) = (5.88 ± 0.10)%. B( J / ψ ) = (5.9 ± 0.10)% p B Nuclar and Particl Physics Franz Muhim 1 µ µ X

Charmonium Quark Modl Explanation J/ψ is nw uark (c-cbar) bound stat Strong dcay for J/ψ (diagram b) is forbiddn by nrgy consrvation at s =m J/ψ < m D Allowd transition (diagram a) has thr gluons Dcay rat supprssd α 6 S J/ψ =ψ(1s) rsonanc stablishd uarks as ral particls Excitd Charmonium stats Found mor stats ψ(s), ψ(s).g. ψ (S) J / ψπ π J / ψ ψ stats - spin J = 1 (lik γ) Obsrv also η c (J = 0) and P stats χ c (L = 1) In agrmnt with QCD potntial calculations Similar to positronium (-) Nuclar and Particl Physics Franz Muhim 14

Evidnc for Gluons Quarks radiat Gluons nd ordr diagram g Exprimntal Signatur Gluons confind, fragmnts hadroniss into jt -jt vnts JADE s = 5 GV LEP s = 91 GV Masurmnt of α S Whn including gluon radiation additional factor α S in matrix lmnt adds trm with factor α S in cross sction ( hadrons) ( µ µ ) σ R = = σ α S Q 1 π.g R( = (5 GV) ).85 > 11/ α S = 0.15 Nuclar and Particl Physics Franz Muhim 15

Running of α S Masurmnts at many nrgis s = 1.5 GV to 00 GV - Annihilations Ratio R (1α S /π) Ratio of jt vrsus jt vnts α S Evnt shaps - angular distributions Hadronic collisions Dp Inlastic scattring Charmonium and Upsilon Tau dcays Lattic QCD calculations α S is running α S (M Z ) = 0.1187 ± 0.00 Many mthods - annihilation Nuclar and Particl Physics Franz Muhim 16

Evidnc for Colour Ratio R Discussd in prvious slids Baryon Strong intraction rsonanc - spin / Quark modl xplains as (uuu) Wav function for (u u u ) is symmtric undr intrchang of idntical uarks Appars to violat Pauli Principl Ld to introduction of colour 1964 Grnbrg Antisymmtric colour wav function for baryons Sam argumnts for - (ddd) and Ω -( sss) Dcay rat π 0 γγ Γ(π 0 γγ) N colour Masurmnt: N colour =.99 ± 0.1 Nuclar and Particl Physics Franz Muhim 17

-p Elastic -p Scattring -p Prob structur of proton with lctron bam Kinmatics Laboratory fram, proton at rst Enrgy and momntum transfr µ r ν = E E = ( ν, ) M ( p ) = p p = ( M,0) ( ν, ) p 1 4 = M r ν, r r = M ν < 0 = Mν and ν not indpndnt, E and scattring angl θ rlatd, only nd to masur E 1 and θ Cross Sction Form factor F( ) dscribs dviation from a point charg F( ) is Fourir transform of charg distribution insid proton, s Nuclar Physics dσ = dω F( ) dσ dω ( ) Nuclar and Particl Physics Franz Muhim 18 point F -

Dp Inlastic Scattring -p -X Scattring At high proton braks up into hadrons W = M x = Mν p M and ν indpndnt, hadronic mass W dfin dimnsionlss variabl x with 0 < x < 1 Form factor F( ) Structur function F (ν, ) Exprimntal Rsults Partons Inlastic cross sction indpndnt of dpndnt on x F (x) Evidnc for point-lik particls insid proton F Point-lik constitunts insid nuclons ν = 0 m m = x Fynman lctron scattrs off fr parton with mass m x is fraction of proton 4-momntum Nuclar and Particl Physics Franz Muhim 19 x = = Mν r E x p = x M m M -

Partons Parton Distribution Functions f i (x) Probability that parton i carris fraction x of particl momntum i = u,d,s (valnc uarks), sa uarks, gluons Ruir x fi ( x) dx = 1 Quarks carry only 54% of proton momntum Gluons carry rmaining 46% Partons ar i uarks and gluons Quark- Quark Scattring jt vnts at p-pbar collidr s = 15 GV 000 GV s QCD points αs αs M dσ αs dω sin 4 ( θ / ) QED points ar Gigr & Marsdn (1911) Ruthrford scattring Nuclar and Particl Physics Franz Muhim 0