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Quantum Chromodynamics November 20Th 2009

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Quantum Chromodynamics November 20Th 2009 Subatomic Physics: Particle Physics Lecture 6 The Strong Force: Quantum Chromodynamics November 20th 2009 QCD Colour quantum number Gluons The parton model Colour confinement, hadronisation & jets The cross section ratio R 1 2 QCD 2 Quantum ChromodynamicsQCD (QCD) QUANTUM ELECTRODYNAMICS: is the quantum •QUQCDANTUM isELECTR thetheor quantumODyYNAMICS:of the descriptionelectris theomaquantumgnetic ofinteraction. the strong force. theory of the electr!omamediatedgnetic interaction.by massless photons ! mediatedQEDby massless! photonphotonscouples to electric charge,QCD ! photon couples! toStrengthelectricofcharinteractionge, : . quantum! Strength theoryof interaction of the : quantum. theory of the strong electromagnetic interactions interactions QUANTUM CHROMO-DYNAMICS: is the quantum QUANTUM CHROMO-DYNAMICS: is the quantum mediated by the exchangetheory of the ofstr ong interaction.mediated by the exchange of theory of the strong interaction. virtual photons! mediated by massless gluons, i.egluons. ! mediated by massless gluons, i.e. propagator propagator acts on all charged! particles acts on quarks only ! gluon couples togluon“strong”coupleschargtoe “strong” charge ! Only quarks ha!veOnlnon-zy quarksero “strhaong”ve non-zchargereo, “strong” charge, couplestheref to electricalore only quarkstheref chargeforeeel stronlongy quarksinteractioncouplesfeel strong tointeraction colour charge Basic QCD interactionBasic QCDlooksinteractionlike a stronglookser like a stronger coupling strength ! e ! !! coupling strength gS !!S version of QED, version of QED, ! ! QED QEDq QCD q QCDq q √α Q √α Qq√α √αS S q q q q q 2 α = e /4π ~ 1/137 2 α = g 2/4π ~ 1 2 α = e /4γ π ~ S1/137S γ αS = gS /4π ~ 1 g ( subscript em is sometimes( subscriptusedemtoisdistinguishsometimestheused to distinguish the 2 of electromagnetismoffrelectrom oma). gnetism from ). Dr M.A. Thomson Lent 2004 Dr M.A. Thomson Lent 2004 Colour • Colour charge is the charge associated with QCD interactions. • Three colours: red, blue, green. • Like electric charge, it is a conserved quantum number. • Quarks always have a colour charge: r , g or b • Anti-quarks always have an anti-colour charge: r ̅ , b ̅ or g̅ • Leptons and bosons for other forces (", W, Z) don’t carry colour charge. • Mesons are colour neutral; colour charges are: (r r)̅ , (b b)̅ or (g g)̅ • Baryons are colour neutral; colour charges are: ( r g b ) • Anti-baryons ( r ̅ g ̅ b ̅ ) Formally different colours of quarks are fundamental particles. Gluons # 1st generation is: e $e ur ub ug dr db dg !"#$%&'($)*(+,*- 4 4 3 F F !"#$%&* '()** +'&&")&& &,-%./*0$&$%& * * E E D D 8 Glu!o% 1n2s3*% ,($,'4'5$( /67 $=5)5D $=5)5D $ $ 5 5 4())%* 4())%* =$%&)(?)@ =$%&)(?)@ 7#'(<&* 7#'(<&* 9+-&&-$%*$(*&5'5)&* '0&$(,5-$%*&5'5)&* $:*4"#$%&*0;*7#'(<&* 5 5 -&* -&* 0;* 0;* ) ) " " 7C,>$ 7C,>$ Gluons -%5$ -%5$ C=$"$#(* C=$"$#(* =>'%4)&*=$"$#(*4 $:*4 7#'(<& . 2$"$#(*-&*=$%&)(?)@ !"#$%&'($)*(+,*- m m i i % % 5>)+&)"?)& 5>)+&)"?)& e e - - 0 0 h h & & u u 0 0 Gluons are massless, spin-1ℏ bosons. * * • M M 2$"$#(* 2$"$#(* 0$&$%& 0$&$%& / / B B !"#$%& '()*+'&&")&& &,-%./*0$&$%& 193B* 193B* 4"#$%&* 4"#$%&* z z 7#'(<* 7#'(<* 4 4 . n n * * a a 4 4 r r @ @ s s 8 s s G'5#() G'5#() F F $:* $:* B B 8 8 They propagate the strong force: !exchange momentum ) ) • 123*,($,'4'5$( /67 '%@* '%@* ( ( 7 7 n n n n (( (( 6 6 :($+* :($+* &,-%./* &,-%./* between quarks. 0;* 0;* B B / / & & o o o o 9+-&&-$%*$(*'0&$(,5-$%*$:*4"#$%&*4 4 0;*7#'(<&* ) ) 7#'(<& 7#'(<& 0 0 4"#$%&* 4"#$%&* u u 4 4 u u $=5)5 $=5)5 B B l l l l % % I* I* $:* $:* ( ( ' ' =>'%4)&*=$"$#(*$:*7#'(<& . 2$"$#(*L* -&*L* =$%&)(?)@ 0 0 * * &&")&& &&")&& G G > > G G B B s s We draw gluons as curly-wurly lines: = = c c • '0&$(,5-$%* '0&$(,5-$%* * * i i ( ( ()'"-&)@* ()'"-&)@* .K* .K* s s +' +' % % 4 4 @-::)()%5* @-::)()%5* y y $,'4'5$( $,'4'5$( - - $ $ h h B B ( ( $(* $(* 2"#$%- 2"#$%- % % P P =$"$#(* =$"$#(* # # 0 0 , , )H,)=5* )H,)=5* " " ! $ $ !"#$%&*='((;*=$"$#(*=>'(4)e 5>)+&)"?)&e * * l l '()* '()* 4 4 4 4 # # c c i i " " 3 3 t t B B $1& $1& ?)(;* ?)(;* Gluons also carry colour charge. r r • 4 4 2 2 4 4 a a ( ( &2 &2 P P )A4A*(4 4"#( $%*=>'( %4)& ()@*7#'(<*-%5$ 4())%** '($)*(+,*- '($)*(+,*- 1 1 3 3 !"#$%&*='((;*=$"$#(*=>'(4) !"#$%&*='((;*=$"$#(*=>'(4) d d B B Colour charged is always conserved. n n 0 0 • a a ! ! J;++)5(; J;++)5(; ! ! ! )A4A* ! )A4A* !"#$%& 9+-&&-$%* !"#$%& =>'%4)&* 9+-&&-$%* =>'%4)&* G'-?)"; ( G'-?)"; ( 123* 123* 123*?)(;*@-::)()%5*:($+*193B*r 7C,>$r 5$%D E*F a a e e l l c c u u !"#$%& !"#$%& .#/0*(&.#/0*(& $1&2"#$%-.#/0*(& N N • Number of gluons: there are eight different gluons. G'-?)"; )H,)=5*I*4"#$%&* • Symmetry of the strong interaction! tell!"#$%&*='((;*=$"$#(*=>'(4) us these are: 5>)+&)"?)& (0B (4B 40B 4(B 0(B 04B ((B 44B 00 rb ̅ rg ̅ bg ̅ br ̅ gr ̅ gb ̅ (rr ̅ − gg)A4A*!)/"2 ((rr4 ̅4+" gg#$% ̅ −*= 2>bb'%)/̅ 4")6& ()@*7#'(<*-%5$ 4())%** J;++)5(; .K**L*$=5)5 '%@*/*&-%4")5 &5'5)&* 123*?)(;*@-::)()%5*:($+*193B*7C,>$5$%D E*F One big difference between QED and QCD .#/0*(&$1&2"#$%- ! QED propagated by photons: photons no electric charge ! QCD propagated by gluons: gluonsG'-?)"; have colour)H,)=5* chargeI*4"#$%&* (0B (4B 40B 4(B 0(B 0!4B 3((&2B "4#4$B%-00()'"-&)@*0;*G'5#() C=$"$#(*$=5)5D 4 J;++)5(; .K**L*$=5)5 '%@*/*&-%4")5 &5'5)&* Nuclear and Particle Physics Franz Muheim 4 ! 3&2"#$%- ()'"-&)@*0;*G'5#() C=$"$#(*$=5)5D Nuclear and Particle Physics Franz Muheim 4 Quark & Gluon Interactions Quark-anti-quark scattering q2 q1 α VQED(r) = = −4π0r − r 6 6 Short distance potential: SELF-INTERASELF-INTERACTIONSCTIONS 4 αs VQCD(r) = %# = duhhhljkhsdlkh̅ describes a meson: e.g. hhhljkhsdlkh −3 r AtAtthisthispoint,point,QCDQCDlookslookslikelikea stra strongongererverversionsionofofQEDQED. strong force is responsible for holding meson together. ThisThisis istruetrueupuptotoa point.a point.HoHoweweverver, in, ipracticen practiceQCDQCD behabehavesvesververy diffy differentlerently tyotQEDo QED. The. Thesimilaritiessimilaritiesarisearisefromfrom • Gluons carrythe thecolourfactfactthat charge.thatbothbothin vinolvevolvethetheexecxhangchange oefoMASSLESSf MASSLESS spin-1 bosons. The big difference is that GLUONS carry • They also feelspin-1 the strongbosons. forceThe big " diffgluonserence canis thatinteractGLUONS withcarr othery gluons! colourcolour“char“charge”.ge”. 12 GLUONSGLUONS3-gluonCANCAN vertexINTERAINTERACTCTWITHWITH4-gluonOTHEROTHER vertexGLUONS:GLUONS: g g Running of g g g g ! g g specifies the strength of the strong interaction g g g g g g 3 GLUON VERTEX 4 GLUON VERTEX ! BUT just as in QED, isn’t a constant, it 3 GLUON VERTEX34 4 GLUON VERTEX “runs” 5 EXAMPLE: Gluon-Gluon Scattering EXAMPLE: Gluon-Gluon Scattering ! In QED the bare electron charge is screened by a cloud of virtual electron-positron pairs. In the limit the propagator for a DECAYING+ + state becomes: The Parton+ Model+ ! In QCD a similar effect occurs. • The parton model proposes that, in high energy interactions,In QCD hadronsquantum interactfluctuations lead to a ‘cloud’ of EXAMPLE: ( NON-EXAMINABLE)as if they were made of their constituentEle parts.ctro ne.g.-Proton: vir tualScatteringpairs q • (Problem sheet 3, Q2) J/'&µ+µ# decay • (Lecture 3, p11) ep&ep scattering. - - !"#$%&'()*+*Proton interacts,# as if it were !" #$! !" # e one of many (an infinite set) J/ψ e.g. rµ g+gb→r r%&'()*+*,($+r b -.#/*+01! q q γ c γ e.g. r g+gb→threer r+ independentr b quarks. q 0)!$2!3(.'( &0/!) such diagrams analogous to + + Electron scatters off one quark e c µ )*.#/!$*4$(!5/!6+*(5$)#*() q those for QED. q In centre-of-mass system ( ) would expect cross 1 e 2 4!" M $ e e # # q Dr M.A. Thomson 2 2 2 Lent 2004 section to be of form: Dr M.A. Thomson q q q Lent 2004 • At higher energies, proton consist of more-$.//' than/*0#%., three quarks:In QCD the gluon self-interactions ALSO lead to a quarks are- constantly+ exchanging gluons. Gluons7&,8'8 */can*+3$4 ,convert&$)6'++!&* (5$ 4 2 2‘cloud’ of virtual gluons d3 2 e 16! " First, note partialintowidth quarkfor !anti-quark :pairs. $ M $ # d2 q4 q4 g one of many (an infinite set) • Proton consists of three “valance quarks9”" .plus,.!( gluons+0.$+&'( )and4!& such diagrams. Here there is no 2 g “sea quarks”. q2 # q 1 q # p1 - p1 # p2 / p2 - 2 p . p g 1 % f i & f i f i 1 q ! analogy in QED, photons don’t giving p f # %E f , p f & - + 2 ! ! The sea quarks are exactly balanced between# 2me quarks- 2%E f Ei - andp f pi cos0 & 1 • p # %E , p! & have self-interactions since they anti-quarks. g i i i Partial width for : 2 , 0 ) q don’t carry the charge of the in- # -4E f Ei sin * ' :;!($(!5/!6+*(5$. + 2 ( q ! • Net quark content of proton is u, u, d. teraction. 12#3*$4.$5'60"##*$%,712#3*$4.$5'12#3*$4.$5'60"##*$%,7'60"##*$%,7'Dr M.A. Thomson Lent 2004 with </')+*6$<4 =$<* =$<>$$$$(!5/!6+$#&,+,($&!6,*/ d3 " 2 Dr M.A. Thomson Lent 2004 # d2 2 4 , 0 ) Lab 4E sin * ' 6 + 2 ( 2 2 d3 " E f , , 0 ) q , 0 )) # *cos2 * ' - sin2 * '' * 2 ' d2 Lab 2 4 , 0 ) E + 2 ( 2M + 2 ( 4E sin * ' i + p ( + 2 ( Nuclear and Particle Physics Franz Muheim 8 Parton Distributions in the Proton • Positron-proton scattering measurements (at HERA accelerator) have measured the valance and sea quarks and gluon in the proton. pparton • Key parameter is “Feynman x”: x = | | p | proton| • Graph shows measured fraction, f, of each parton (u-, d-, s-, c-quarks & gluons) as a function of x. • f also depends on momentum, Q 2 = ( q ) 2 transferred by the boson ("). − ! The higher the Q2, the more energetic 7 the partons. ! At LHC energies,CONFINEMENT proton contain lots of gluons! NEVER OBSERVE: single FREE quarks/gluons • LHC collisions will be a mixture of: quark-quark,! quarks quark-gluon,are always gluon-gluon,confined within hadrons anti-quark! This!quark,is a consequence anti-quark!gluonof the etc.strong • One challenge:self-interactions for each individualof gluons.
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