+ e. 1.1 Two-jet events and production of colored q q. indicates fractional charges and N C

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1 V. eimental studies of CD. Test of CD in e + e - annihilation. Stuctue of the oton 3. Stuctue functions and uak densities 4. Scaling violation in DIS. Test of CD in e + e - annihilation. Two-jet events and oduction of coloed a clea two-jet event stuctue in e + e hadons σ ee hadons b R had indicates factional chages and N C 3 σ ee µµ Additional indications fo N C 3: ++ statistic oblem: Sin J ++ 3/ L0, uak content uuu> + + u u u fobidden by Femi statistic Solution is additional uantum numbe fo uaks colo + ε u u u i, j, 6 k ijk i j k + colo inde

2 Additional indications fo N C 3: Tiangle anomalie γ f W Divegent femion loos Divegences cancel if N C 3: f W f N 3 f C 3 geneations of u/d-tye uak. Discovey of the gluon Discovey of 3-jet events by the TASSO collaboation PTRA in 977: 3-jet events ae inteeted as uak ais with an additional had gluon. #3 jet events 0.5 ~ α s # jet events α s is lage at s0 GeV

3 Sin of the gluon llis-kalinge angle Odeing of 3 jets: > > 3 easue diection of jet- in the est fame of jet- and jet-3: K Gluon sin J.3 ulti-jet events and gluon self couling Non Abelian gauge theoy CD Casimi colo factos: 4-jet events 4-jet coss section: F A,B,C,D, ae kinematic functions 3

4 loiting the angula distibution of 4-jets: Bengston-Zewas angle cos χbz 3 4 Nachtmann-Reite angle cosnr 3 4 Allows to measue the atios T F /C F and N C /C F SU3 edicts: T F /C F and N C /C F.5 N C /C F 0 contibution fom gluon self-couling in the 4-jet events Confims CD ediction SU3 and gluon self-couling.4 easuement of stong couling α s a α s fom total hadonic coss section σ R had α s measuements ae done at fied scale : α s D α s s αs s s σ had s π π σ ee hadons α s α s σ ee µµ π π had Not vey ecise. α s s b α s fom hadonic event shae vaiables 3-jet ate: σ 3 jet R3 deends on α s σ had 3-jet ate is measued as function of a jet esolution aamete y cut 4

5 Jet Algoithm Hadonic aticles ae i and j goued to a seudo aticle k as long as the invaiant mass is smalle than the jet esolution aamete: m ij < ycut s m ij is the invaiant mass of i and j. Remaining seudo aticles ae jets. n-jet ate as function of y cut CD calculations ovide a theoetical ediction fo R 3 theo α s, y cut fit R 3 theo α s, y cut to the data to detemine α s α s s Similaly othe event shae vaiables sheicity, thust, can be used to obtain a ediction fo α s c α s fom hadonic τ decays R τ had Γ τ τ + Hadons ~ f αs Γ τ + eυ τ e α s m τ d α s fom DIS dee inelastic scatteing 5

6 e Running of α s Simila to D thee ae oagato coections to be taken into account sceening anti-sceening ffective stong couling α s αs µ αs αs µ + 33 nf log π µ n f active uak flavos µ the enomalization scale Conventionally enomalization scale is µ Z Fo α s 0: At lage uaks ae asymtotically fee Running of α s and asymtotic feedom αs µ αs αs µ + 33 nf log π µ 6

7 The Nobel Pize in Physics 004 David J. Goss H. David Politze Fank Wilczek "fo the discovey of asymtotic feedom in the theoy of the stong inteaction".5 Descition of hadon oduction in e + e - annihilation Descibed by onte Calo ogams: HRWIG: Paton showe atons ae associated to cololess clustes. Clustes with masses lage than Cl ae slit. JTST: Sting fagmentation. Colo sting between coloed uaks. Gluons lead to kinks. Stings ae fagmented 7

8 . Stuctue of the oton. lastic electon-oton scatteing 4 sin 4 Geneal fom of diff. coss section Pointlike taget w/o sin ott scatteing d σ α dω 4 4 sin { KK} non ointlike Ruthefod scatteing atnes w/ sin ecoil elastic { } KK ott cos e k, e k, k k Pointlike taget w/ sin elastic { KK} e µ eµ cos sin tended oton w/ sin G + τ G + τ 4 elastic { KK} e e cos τ G sin mit τ Size of the oton Rosenbluth Plot: dσ dω dσ dω ott A + B tan τ τ τ G G mit A B - τ G 4 Allows the detemination of electic and magnetic fom factos Sachs fom factos 8

9 lectic and magnetic fom factos can be descibed by diole ansatz: G 0.7GeV Diole fom facto is the Fouie tansfom of an eonential distibution adius of the chage magnetic moment distibution: dg 6 d 0 G G n G el mag m lectic and magnetic size of oton and neuton ae the same.. Inelastic e scatteing k, e k, vent ate Invaiant mass W had Inelastic scatteing: W indeendent vaiables: - had W Altenative: Bjoken-Vaiables and y Inelasti -city Poton beaks u Obsevation: Lage coss section at lage Fom elastic fom facto one eects lage suession at lage lastic scatteing: W only one fee vaiable W 9

10 a Diffeential coss section and stuctue functions lastic eµ eµ dσ α cos sin dω 4 4 sin Inelastic e ex dσ α W, cos + W, sin d dω 4 4 sin dσ d d πα W, cos 4 + W, sin 4 With stuctue functions W, and W,. Scatteing at oint-like objects: int W o int δ + W o δ + W and W functions of only one vaiable b Fist measuement of W SLAC & IT eiment e - beam, u to 0 GeV [ 0.%; 0.5% ] Diole and uaduole magnets Sectomete at fied ~ 0.% ~ 0.7mad Cheenkov counte fo e/π seaation 0

11 Stuctue function W does not deend elicitly on but deends only on the dimensionless vaiable : Scale invaiance: scaling Indicates elastic scatteing at oint-like constituents of the oton: atons Real sensation in 970

12 The Nobel Pize in Physics 990 Richad. Taylo Heny W. Kendall Jeome I. Fiedman "fo thei ioneeing investigations concening dee inelastic scatteing of electons on otons and bound neutons, which have been of essential imotance fo the develoment of the uak model in aticle hysics" c Stuctue functions F and F Instead of W and W the stuctue functions F and F ae used today:,, W F W W F W + sin, cos, 4 4 πα σ W W d d d + sin cos 4 4 πα σ F F F d d d + sin cos 4 4 πα σ F F d d d dimensionless

13 .3 Paton odel fo electon-nucleon scatteing: e ex e e i σ incoheent sum of all ossible aton uak contibutions. Nucleon consists of uasi-fee oint-like constituents atons. Leton scattes elastically on fee sin ½ atons 3. Scatteed aton inteacts stongly with the othe constituents sectatos to fom obsevable hadons Infinite momentum fame Bjoken Infinite momentum fame: P Poton caies infinite momentum tansvese mom. + mass of uaks can be neglected 4-mom faction of aton: P Infinite momentum fame: + P + + P + Poton est fame: P, 0, P Conseuence of elast. scatteing: m if fomally m P Bjoken vaiable momentum faction of aton 3