Quantum Chromodynamics QCD

Transcription

1 Subamic Physics: Particl Physics Handout 7 Th Stron Forc: Quantum Chromodynamics Colour uantum numbr Th parn modl Colour coninmnt, hadronisation & jts Quantum Chromodynamics () QUANTUM ELECTRODYNAMICS: is th thory uantum o th dscription lctromantic is th uantum o intraction. th stron orc. thory o th lctromantic! mdiatd intraction. by masslss phons! mdiatd by masslss phons! QED! phon coupls lctric char, phon coupls! Strnth lctric o char, intraction :.! Strnth o intraction :. uantum thory o th lctromantic intractions mdiatd by th xchan o virtual phons acts on all chard particls coupls lctrical char couplin strnth!!!! uantum thory o th stron intractions QUANTUM CHROMODYNAMICS: is th uantum QUANTUM CHROMODYNAMICS: is th uantum thory o th stron intraction. thory o th stron intraction.! mdiatd by masslss luons, i..! mdiatd by masslss luons, i.. propaar propaar! luon coupls! luon stron coupls char stron char! Only uarks hav! Only nonzro uarks stron hav nonzro char, stron char, thror only uarks thror l stron only uarks intraction l stron intraction mdiatd by th xchan o luons acts on uarks only coupls colour char Basic intraction Basic looksintraction lik a stronr looks lik a stronr vrsion o QED, vrsion o QED, QED Q α QED α = /4π ~ /37 α = /4π ~ α S /37 = S /4π ~ QUANTUM ELECTRODYNAMICS: is th uantum Q α α S couplin strnth! S!!!S α S α S = S /4π ~ ( subscript m is somtims ( subscript usd misdistinuish somtimsth usd distinuish th o lctromantismorom lctromantism ). rom ).

2 !"#$%& '()*'&&")&& &,%./*0$&$%& 9&&$%*$(*'0&$(,5$%*$:*4"#$%&*0;*7#'(<&* =>'%4)&*=$"$#(*$:*7#'(<&. 5>)&)"?)& )A4A*(4 4"#$%*=>'%4)& 4())%** Nuclar and Particl Physics E*F.#/0*(&$&"#$%!"#$%&'($)*(,* E*F.#/0*(&$&"#$% G'?)"; )H,)=5*I*4"#$%&* (0B (4B 40B 4(B 0(B 04B ((B 44B 00 J;)5(;.K**L*$=5)5 &5'5)&*! 3&"#$% C=$"$#(*$=5)5D Franz Muhim Colour Colour char is th char associatd with intractions. Thr colours: rd, blu, rn. Lik lctric char, it is a consrvd uantum numbr. Quarks always hav a colour char: r, or b Antiuarks always hav an anticolour char: r, b or Lpns and bosons or othr orcs (", W, Z) don t carry colour char. Msons ar colour nutral; colour chars ar: (r r ), (b b ) or ( ) Baryons ar colour nutral; colour chars ar: ( r b ) Antibaryons hav: ( r b ) Formally dirnt colours o uarks ar dirnt undamntal particls. ar masslss, spin bosons. st nration is: # $ ur ub u dr db d Thy propaat th stron orc: xchan momntum btwn uarks. W draw luons as curlywurly lins:!"#$%& '()*'&&")&& &,%./*0$&$%&! 3*,($,'4'5$( /67 8 9&&$%*$(*'0&$(,5$%*$:*4"#$%&*0;*7#'(<&* =>'%4)&*=$"$#(*$:*7#'(<&. $"$#(*&*=$%&)(?)@ also carry colour char. Colour chard is always consrvd. Numbr o luons: thr ar iht dirnt luons. G'?)"; )H,)=5*I*4"#$%&* Symmtry o th stron intraction! tll!"#$%&*='((;*=$"$#(*=>'(4) us ths ar: 5>)&)"?)& rb r b br r b (rr )/! (rr bb )/!6 (0B (4B 40B 4(B 0(B 04B ((B 44B 00 )A4A*(4 4"#$%*=>'%4)& ()@*7#'(<*%5$ 4())%** J;)5(;.K**L*$=5)5 '%@*/*&%4 On bi dirnc btwn QED and! QED propaatd by phons: phons no lctric char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propaatd by luons: luons hav colour char (0B (4B 40B 4(B 0(B 04B! 3&"#$% ((B 44B 00()'"&)@*0;*G'5#() C= J;)5(;.K**L*$=5)5 '%@*/*&%4")5 &5'5)&*! 3&"#$% ()'"&)@*0;*G'5#() C=$"$#(*$=5)5D J;)5(;.K**L*$=5)5 '%@*/*&%4")5 &5'5)&* 3 4 Nuclar and Particl Physics Franz Muhim 4

3 In th limit stat bcoms: Quark & Gluon Intractions Quarkantiuark scattrin SELFINTERACTIONS dscribs a mson:.. % " = du hhhljkhsdlkh At this point, looks lik ahhhljkhsdlkh At this point, looks lik stronr a stronr vrsion vrsion o o QED. QED. stron orc This is rsponsibl or holdin mson thr. This is is tru tru up up a point. a point. Howvr, Howvr, in in practic practic bhavs bhavs vry vry dirntly dirntly QED. QED. Th Th similaritis similaritis aris aris rom rom carry th th colour act act that char. that both both involv involv th th xchan xchan o o MASSLESS MASSLESS spin bosons. Th bi dirnc is that GLUONS carry Thy also l spin th stron bosons. orc Th bi! dirnc luons can is that intract GLUONS with carry othr luons! colour colour char. char. GLUONS GLUONS 3luon CAN CAN vrtx INTERACT INTERACTWITH WITH 4luon OTHER OTHER vrtx GLUONS: GLUONS: 3 GLUON 3 GLUON VERTEX VERTEX 4 GLUON 4 GLUON VERTEX VERTEX EXAMPLE: EXAMPLE: GluonGluon GluonGluon Scattrin Scattrin Th Parn Modl.... r r b b r r rr br b V QED (r) = 4π 0 r = α r Short distanc potntial: V (r) = 4 3 M $ # # Dr M.A. Thomson Lnt 004 Dr M.A. Thomson Lnt α s r Runnin o! spciis th strnth o intraction! BUT just as in QED, isn runs 5! In QED th bar lctron ch by a cloud o virtual lctron! In a similar ct occu In uantum luctuations l Th parn modl proposs that, in hih nry intractions, hadrons intract as i thy wr mad o thir constitunt parts...: virtual pairs EXAMPLE: ( NONEXAMINABLE) th propaar or a DECAYING J/ψ In cntromass systm ( sction b o orm: c c 34 ElctronPron Scattrin (Handout 4, p) p&p scattrin.!"#$%&'()**,# Pron intracts as i it wr!" #$!!" # thr %&'()**,($.#/*0! indpndnt uarks. 0)!$!3(.'( &0/!) )*.#/!$*4$(!5/!6*(5$)#*() on o m such dia thos or At hihr nris, pron consist o mor $.//'/*0#%., than thr uarks: In th luon slintractio uarks ar constantly xchanin luons. 7&,8'8*/*3$4,&$)6'!&*(5$ can convrt cloud o virtual luons 4 in uark!antiuark pairs. d 3 6! $ M $ # " 4 4 d on o m Pron consists o thr valanc uarks 9".,.!(0.$&'()4!& plus luons and such dia sa uarks. % & # # p pi # p / pi p. pi %! & analoy i!! p # E, p Th sa uarks ar xactly balancd btwn # m uarks % E Ei and p pi cos0 &! hav sldon t carr pi # % Ei, pi & antiuarks., 0 ) # 4E sin * ' :;!($(!5/!6*(5$. Ei (! Nt uark contnt o pron is u, u, d. traction. #3*$4.$5'60"##*$%,7' First, not partial width or : ivin Partial width or : with (Problm sht, Q3) J/'&µ µ # dcay µ µ ) would xpct cross Elctron scattrs o on uark 4!" #3*$4.$5'60"##*$%,7 Dr M.A. Thomson </')*6$< 4 =$< * =$<>$$$$(!5/!6$#&,,($&!6,*/ d3 d Lab # 4E " 4, 0 ) sin * ' (, d3 " E ) *, 0 ), 0 ) # cos ' * ' sin * ' 6

4 Parn Distributions in th Pron Positronpron scattrin masurmnts (at HERA acclrar) hav masurd th valanc and sa uarks and luon in th pron. Ky paramtr is Fynman x : x = p parn p pron Graph shows masurd raction,, o ach parn (u, d, s, cuarks & luons) as a unction o x. also dpnds on momntum, Q = () transrrd by th boson (").! Th hihr th Q, th mor nrtic th parns. CONFINEMENT! At LHC nris, pron contain lots o luons! NEVER OBSERVE: sinl FREE uarks/luons LHC collisions will b a mixtur o: uarkuark,! uarks uarkluon, ar always luonluon, conind within hadrons antiuark!uark,! This is a consunc antiuark!luon o th tc. stron On challn: slintractions or ach individual o luons. collision w do Qualitativly, not know th pictur lavour th or colour momntum ild btwn two o th intractin parns! uarks. Th luons mdiatin th orc act as 7 additional sourcs o th colour ild thy attract ach othr. Th luonluon intraction pulls th lins o colour orc in a narrow tub or STRING. In this modl th strin has a tnsion Colour Coninmnt and as th uarks sparat th strin srs Exprimntally w do not s r uarks: potntial uarks nry. ar conind within hadrons attract ach othr: thy sl intract Gluonluon intraction pulls th colour ild lins in a narrow tub. Considr th pair producd in : Potntial incrass linarly with distanc: V(r) = kr Ininit nry is ruird sparat two uarks. Colour Elctric COLOUR CONFINEMENT Enry srd ild pr unit lins lnth ild lins constant. Colour coninmnt is a dirct consunc o luon slintractions! Ruirs ininit nry sparat two Total potntial: uarks. Quarks always V = 4α com s in combinations As th α uarks sparat, th 3r kr s with zro nt colour 0 char: CONFINEMENT. V (r) = 4 3 Forc ruird sparat uarks: F = dv r kr nry srd in th colour Dr M.A. Thomson JETS V (GV) ild ( strin ) starts incras linarly with sparation. Whn nw pairs can b dr = 4 α s 3 r k cratd. 3 At lar distancs F ( k # 00 GV/m = 60,000 N!!! V = 4α s 3r α s =0. k= GV/m r(m) 9 8 Lnt

5 Hadronisation V = 4α s As th uarks sparat, th V = What happns whn w try pull apart two JETS 4α 3r kr s As th uarks sparat, th uarks? nry srd in th colour 3r kr nry srd in th colour 0 V = At LHC production ild ( strin ) o nrtic starts incras linarly with spara uarks is common.. 4α s $$. V = 4α 3r s ild ( strin ) starts incras linarly with spara 3r producd at sam point in spac. tion. Whn α and hav vry lar momntum! thy ly apart. s =0. tion. Whn nw pairs can b α k= s =0. GV/m V = 4α s 3r cras linarly with spara rom th potntial nry o th colour ild. This α s =0. as nry dcrass... hadrons rz out nw pairs can b k= GV/m cratd. 3 As th kintic nry dcrass nry tion. dcrass... Whn th hadrons rz rz out out V V (GV) This procss is known as hadronisation. Considr th pair producd in : nw pairs can b cratd. 3 cratd r(m) 0.8 r(m) Th nry btwn th incrass as thy mov apart E(V(r)(kr Whn E > mc V = 4α s... As th uarks sparat, th 3r kr nry srd in th colour 0 As uarks sparat, mor ild ( strin ) starts in V (GV) π (ud) tc... Jts as nry dcrass... hadrons rz out π A collision producs nrtic uarks, which hadronis. π 0 π K π Th producd hadrons dcay... (in mor hadrons and π 0 mayb π 0 π lpns) TIME p π 0 In th dtcr this appars as a collimatd jt o particls. k= GV/m pairs ar producd procss is calld HADRONIZATION. Start out with uarks and nd up with narrowly collimatdr(m) JETS o HADRONS Fynman Diaram SPACE 9 CoM Fram 9 0 Typical Evnt rom LEP collidr ECM = 9 GV # $" jts in dtcr Evnt Th hadrons in a uark(antiuark) jt ollow th dirction o 0 th oriinal uark(antiuark). Consuntly

6 Runnin o! spciis.*##/ th strnth o th intraction Rviw: btwn an lctron QED and phon. Couplin Constant! spciis th strnth o th intraction btwn an lctron and phon.! BUT isn t a constant 6)"($7"89(.#):%5(*#$$($$,"#)%(! BUT isn t a constant Strnth o intraction btwn,#$."/)%(.%5(.%%/'/."/)% Considr a r lctron: Quantumlctron luctuationsand ladphon a α = Howvr, cloud! s o virtual not rally lctron/positron a )*(;/#":.($$,"#)%<7)4/"#)%(7./#4 constant... pairs 4π 0 37 An lctron is nvr 0*'&'( alon: it mits virtual phons, =.#$(,'.#&$ this is ths can.%5(.44 just on o convrt )*($$,"#)%()%8(;/4/>$( this is just on o lctron positron many (anpairs... ininit."(;$#8(4')#"(5/4".%,$4 many (an ininit st) st) such diarams. such diarams. Any tst! /%,#$.4$4(?/"'(?/"'.#&$#()$%":("#.%4*$# char will l th # pairs: tru char o th lctron! Th vacuum is scrnd. acts lik a dilctric mdium $ # $ # At hihr! nry Th virtual (shortr pairs distancs) ar polarizd th tst! varis as % a & unction & o! At lar distancs th bar lctron char is scrnd. char can s th bar char o th lctron. nry and distanc Considr a r lctron: Quantum luctuations lad a cloud o virtual lctron/positron pairs! Th vacuum acts lik a dilctric mdium! Th virtual pairs ar polarizd! At lar distancs th bar lctron char is scrnd. At lar R tst char ss scrnd char Tst Char Tst Char intraction!"#$%&'()*"',',)!!"#$%&"'()*($$,"#).&%$"/,(/%"$#.,"/)% 4 Runnin o! 0($ 3" /4(%)"(.(,)%4".%"(."(.(5/4".%,$4 At lar R tst char ss scrnd char At small R tst char ss bar At small R tst char char ss bar char runs Tst Tst Char! A In QED th bar lctron char is scrnd 0(B((((((((((((((!! 0(CCDE Runnin o F"(4')#"(5/4".%,$4 by a cloud o virtual lctronpositron pairs. A! 0(GHB(I$JK In a similar!! 0(CCL ct occurs.! spciis th strnth o th stron In uantum luctuations lad a cloud o intraction virtual pairs! BUT just as in QED, isn t a constant, it Nuclar and Particl Physics Franz Muhim Couplin Constant runs on o many (an ininit st) In! In QED th intraction th bar lctron strnth char is!s is also scrnd not rally a constant. such diarams analoous Quark by mit a cloud luons: o virtual which lctronpositron can orm virtual uark pairs. thos antiuark or QED. pairs.! In a similar ct occurs. Howvr th luons thmslvs also carry colour char, which cts th In scrnin. uantum luctuations In lad th luon a cloud slintractions o ALSO lad a virtual pairs cloud o virtual luons such diarams. Hr thr is no on o many (an ininit st) analoy in QED, phons don t such diarams analoous hav slintractions sinc thy thos or QED. don t carry th char o th intraction. In th luon slintractions ALSO lad a cloud!s dcrass o virtual at hih luons nris!!s incrass at lar distancs! At low nris th couplin constant bcoms lar,!s ~. W cannot us such diarams. Hr thr is no prturbation thory calculat cross sctions! analoy in QED, phons don t Th undrstandin o this phnomna won th Nobl priz in 004. on o many (an ininit st) hav slintractions sinc thy don t carry th char o th intraction. 4 Runnin o! spciis th strnth o th stron! BUT just as in QED, isn t a constant, it on o many (an ininit st)

7 Dr M.A. Thomson sction. Evidnc or Particl Physics!S is lar at hih nry (hih ) nvr uarks sar rvry luons likly du coninmnt. mit a luon. Hih nry Dr luons M.A. also Thomson hadronis, and also orm jts. Fynman Diaram α α S Q α ivin an xtra acr o lmnt, i.. an xtra acr o in th matrix in cross In QED w can dtct th phons. In w Exprimntally dtct luons as an additional jt: 3Jt Evnts.! Anular distribution o luon jt dpnds on luon spin 3 jts vnt: # & CoM Fram Evnt rom PETRA collidr at DESY ECM =35 GV SELFINTERACTIONS SELFINTERACTIONS 3 hhhljkhsdlkh Part II, Lnt Trm 004 hhhljkhsdlkh HANDOUT III Evnt rom LEP collidr at CERN ECM = 9 GV Summary spin bosons. ThQuarks bi dirnc and luons is that GLUONS carry carry colour char. : Quantum colour ar char. th colour char. Chromodymanics is th propaar o GLUONS th CAN INTERACT WITH OTHER GLUO GLUONS CAN INTERACT WITH OTHER GLUONS: uantum dscription o stron orc slintract: th stron orc. Only uarks l th stron orc. 3 GLUON VERTEX 4 GLUON VERTEX 3 GLUON VERTEX 4 GLUON VERTEX Hadrons can b Elctromantic couplin constant! dcrass EXAMPLE: dscribd GluonGluon as consistin Scattrin EXAMPLE: GluonGluon Scattrin as a chard particls t urthr apart. o parns: uarks and Stron couplin constant!s incrass as luons, which intract urthr apart uarks bcom. indpndntly At this point, looks lik a stronr vrsion o QED At this point, looks lik a stronr vrsion o QED. This is tru up a point. Howvr, in practic This is tru up a point. Howvr, in practic bhavs vry dirntly QED. Th similaritis aris bhavs vry dirntly QED. Th similaritis aris rom th act that both involv th xchan o MASSLESS th act that both involv th xchan o MASSLESS spin bosons. Th bi dirnc is that GLUONS carr 6 Colour Coninmnt nry ruird sparat uarks $ % uarks ar conind hadrons Quarks and luons producd in collisions hadronis: hadrons ar producd. Th dcay products o th hadrons appar.. in th r dtcr.. b r r as r b jts. r b r r r b 4

8 Nots 5 Nots 6