Introduction to Particle Physics strong interactions

Transcription

1 Introduction to Particle Physics strong interactions isto Orava Spring 6

2 the standard model strong interactions properties of the Strong Interaction colour the basic process comparison between QED and QCD uarks and hadrons the OZI rule, hadronization and jets

3 strong interaction QCD properties of the strong interaction exchange of gluons conserves all uantities flavour parity charge parity does not involve leptons (no colour) can only produce uarkantiuark pairs

4 the strong interaction examples K n π π p K Λ Λ π p p p p n π

5 colour each uark appears in three colours: red, green and blue. gluon has two colour indices; there are eight gluons ( ) a gluon couples to itself (three gluon vertex) each observed hadron is colourless; i.e. a colour singlet combination of uarkantiuark pairs (mesons) or three uarks (baryons) A colourless (white) combination can be formed by: () Eual mix of red, green and blue GB () Eual mix of antired, antigreen and antiblue GB () Eual mix of color and its complement, GG, BB 5

6 colour the charge of the strong interaction examples: proton antiproton πmeson GB GB GG BB Note: the wavefunctions of these baryons and a meson have to be properly symmetrized and normalized Combination GB is then asymmetric under interchange of a pair of colour labels as is reuired by the Fermi statistics of the uarks. 6

7 how to measure the electron charge? a long distance probe test charge electron is surrounded by the electronpositron pairs the electron charge is screened from the long distance probe Coulomb force 7

8 how to measure the electron charge? a short distance probe at a distance, the charge appears smaller it is shielded by the vacuum polarization Test charge the effect takes place in QED because the vacuum can be polarized some of the time, a photon is a virtual fermionantifermion pair as one gets closer to the charge, it gets larger since there is less screening. the closer the test charge is placed, the larger the measured charge by the Uncertainty Principle, to probe a small distance, one needs a high momentum (small wave length) probe 8

9 how to measure the uark charge? a long distance probe Test charge a red uark is surrounded by the antiuark pairs the uark colour is surrounded by the predominantly red colour as seen by a long distance probe. 9

10 how to measure the uark charge? a long distance probe Test charge a red uark is surrounded by the pairs the uark colour decreases when the probe is placed closer colour is antiscreened from the short distance probe. much larger screening by the fermion loops in QCD and with the opposite sign! due to the gluons that carry colour charges virtual emissions and absorbtions spreads the colour over a large volume and a highenergy probe sees a smaller charge. these effects are proportional to: n flavours n colours known as asymptotic freedom a side effect is known as infrared slavery (At low energies, the colour force is very strong and the perturbation series breaks down it is easy for many gluons to be exchanged. Empirically, the strong force tends to a constant as the distance becomes large.)

11 the strong interaction QCD... the basic process of the strong interactions, Quantum Chromo Dynamics (QCD): g the charge is now colour looks identical to the EM interactions, and indeed it almost is.. three important differences: a uark emits a gluon () three colour charges and eight gluons; since all the hadrons are colourless, this is not special by itself the colour uantum number is not an observable () the colour charge is larger than the electric charge: πα s and often the perturbation theory cannot be used the only other calculational techniue is iterative computer calculations using lattice of discrete spacetime points instead of continuous spacetime.

12 the strong interaction QCD... () unlike the photon, the gluon does carry a charge the colour charge and a basic interaction could look like: g blueantigreen blue profound conseuences: () gluons can interact with each other two additional fundamental vertices: and green in 97 it was realized that the effective coupling constant, or charge, varied with energy and became weak at high energy. i.e. perturbation theory could be used

13 comparison of QCD and QED Only Charge has values and photon γ does not carry electric charge QED Charges values red, green, blue also anticolours 8 gluons g QCD carry colour and anticolour charge rb, rg, bg, br, gb, gr, 6 ( rr gg) ( rr gg bb),

14 comparison of QCD and QED... QED QCD represented by the U() abelian symmetry group represented by the SU() nonabelian symmetry group Abelian Group: mathematical group of transformations in which the order of the transformations is unimportant

15 comparison of QCD and QED... QED QCD Interaction between fermion (anti)fermion pairs Interaction between uarks (antiuarks) only 5

16 comparison of QCD and QED... f C γ g C C α α S f C, C r,g,b C α EM /7 α g s.. S π! cε 6

17 comparison of QCD and QED... QED QCD forbidden allowed 7

18 comparison of QCD and QED... QED f QCD f QCD vacuum states produce uarkantiuark pairs and gluon loops where EM only produces fermionantifermion pairs. 8

19 comparison of QCD and QED... Q QED Q QCD r coupling only increases for very small separations < 6. r coupling increases at large separations and decreases at small r. asymptotic freedom: as the distance becomes asymptotically small, the interactions between uarks becomes asymptotically free Nobel prize! 9

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22 uarks and hadrons consider a uark antiuark pair moving apart with a large energy due to an interaction with a photon: g proton gp nπ π π π π

23 uarks and hadrons... photon proton u u d u d d u d neutron the confinement: no free uarks or gluons.

24 uarks and hadrons... γ π o γγ γ this is not a Feynman diagram since it is not possible to calculate the decay width of π from it the two uarks making up the π ο are in a bound state continuously exchanging gluons for calculating the decay width, we need to know the π ο wave function, specifically Ψ() nevertheless, these "uark diagrams" are used all the time for describing the basic uark level processes in particle physics.

25 the OZI rule the Ψ decay width is about times narrower than other strong decays, why?? the effect is known as the OZI rule (after Okubo, Zweig and Iizuka) ϕ π π π o much slower (has a larger width) than expected: ϕ ϕ s s s s s s u u K K π π π m ϕ 9 MeV/c m K± 9 MeV/c Q m ϕ m K± MeV B(ϕ K K ) 8.5% m π± MeV/c m πo 5 MeV/c Q m ϕ m π± m πo 6 MeV B(ϕ π) 5.% 5

26 the OZI rule... the difference between the two decays is that in ϕ K K, the gluons can be soft (of low energy), but in the decay ϕ π, they must carry all of the mass of the ϕ, because if we cut the diagram at the right point in time, there are only gluons present. Because of asymptotic freedom, the couplings of those gluons will be weaker. Ψ ( cc) Υ( bb ) The same thing happens for the and the, except in these cases, the decays, to the analogue of, K K, DD and are kinematically forbidden since m D > m Ψ and m B > m Υ. BB 6

27 hadronization consider e e hadrons at high energy have two high energy uarks moving apart hadrons will be produced between the uarks until the final state is colourless t x 7

28 jets jets are formed as asymptotic states of the scattered partons η φ.7 QCD reuires that only colourless objects are observable (hadrons) e.g..: π, K, η, etc. a jet is defined to consist of the particles within the cone, or in a cluster defined by an algorithm 8

29 jets... 9

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31 electronpositron annihilation

32 Heavy Ion Collision ProtonProton Collision ElectronProton Collision Introduction to High Energy Physics Hard Scattering. Orava Spring

33 QCD vs. QED QCD looks much like QED, the basic diagram is g g three main differences (mathematically QED and QCD differ because in QED the gauge transformation is a simple phase rotation, while in QCD it involves x matrices): () the charge g s (πα s ) is about 5 times larger than g e (πα) ; α s will vary with because of asymptotic freedom è the perturbation series will not converge & there is uncertainty because calculations only at the parton level the measurements involve hadrons, their composite ( asymptotic ) states. a typical QCD calculation might be pp t t anything, i.e. to calculate: p X p p G ( x) G ( x) ( x) ( x) p p For reference see Halzen&Martin Chapter t t X p p p X t t X

34 QCD () the uarks have colour and the gluons have colour and anticolour and there are three types of uarks and eight types of gluons. uark colour is given by a vector c: c for red for blue for green. the colours form a representation of SU(); a colouranticolour combination will form 8 the gluons form a colour octet (an 8) use the following combinations: ( rb br) ( rr bb ) 5 i ( rg gr) 7 i ( bg gb ) ( rb br) ( rg gr) 6 ( bg gb ) 8 ( rr bb gg) 6

35 5 these assignements are not uniue any linear combination of these would work as well. the 9 th orthogonal combination: is the singlet, and not a gluon state. to specify the Feynman rules, have to give the SU() matrices (analogues of the Pauli spin matrices for SU()) the structure functions f abg are defined by the commutators of the matrices: QCD ) ( gg bb r r i i i i i i [ ] 8, γ γ αβγ β α f i

36 QCD of the 8 5 structure functions, only 5 are nonzero: f f 7 f 6 f 57 f 5 f 56 f 67 ½ f 58 f 678 / even permutations of these have the same value, odd permutations have negative value and all others are zero 6

37 QCD the Feynman rules are: QED QCD external lines internal lines Vertex in out in out in out γ or γ u u v v or or γ or iq a g g g ε ε µ µ * i(/ m) m ig πα γ µν µ ε ε g e g s i ig uc uc vc vc µ µ µν a a δ α πα α* / m m αβ s γ µ α (c is a component vector) (a is a 8component vector) a b 7

38 QCD α,µ γ, g s f αβγ [ g ( k k ) g ( k k ) g ( k k ) ] µν ν µ µ ν k k k ig f s [ αγη f f αβη δβη f ( g γδη µρ ( g g ν µν g νρ g µν g g µρ ρ g )] ν ) f αδν f βγη ( g µν g ρ g µ g νρ ) β,ν β,ν γ, note: except for the multigluon diagrams, the Lorentz structure is the same, and for a simple diagram, such as the dependence on momenta and angles will be the same as in QED. the only change will be due to the colour factor. α,µ δ,ρ 8

39 9 look at the colour factor for a and attracting or repelling each other by gluon exchange: a Coulomb s law for the strong force, it will be the uarkantiuark pair can be either in an octet or singlet state. to calculate the octet potential, we take the uark to be red and the antiuark antiblue since this state is orthogonal to the singlet, it must be octet colour factor f a b QCD [ ] [ ] [ ] [ ] [ ] ) ( () () () () µ µ δ γ δ γ β αβ α ν β αβ µν µ α e e im g g C C C C C v g i C v g i C u g i C u im e s s s r c f r V s! α ) (

40 since colour is conserved: the only matrices with nonzero diagonal elements are and 8, i.e. QCD and C C C C ( ) ( ) α α α α α α α,,,, C C C C f [ ] r c f α s! 6 V 6,8 8 8 repulsive

41 for a colour singlet state of: QCD ) (, g g bb rr { } r c V f s! α α α α α (,,) (,,) (,,) (,,), attractive

42 QCD in the uarkuark case 6 the antitriplet turns out to be attractive, f /, and the sextet repulsive, f / forming a baryon: [ 6 ] 8 8 all pairs attractive all pairs repulsive some pairs attractive some repulsive

43 summary: QED vs. QCD QED is an abelian gauge theory with U() symmetry: i QCD is a nonabelian gauge theory with SU() symmetry: Both are relativistic uantum field theories that can be described by Lagrangians: QCD: QED: m electron mass Ψ electron spinor L u u L ψ ( iγ u m) ψ eψγ Auψ F electrong interaction u u a jk ( iγ u m) jk g( jkγ a jk ) Gu muark mass jcolor (,,) kuark type (6) uark spinor uarkgluon interaction ψʹ( x, t) e uv Fuv A υ photon field () F υϖ υ A ϖ ϖ A υ ief ( x, t) ig ψʹ ( x, t) e G 8 iωi ( a uv G ψ( x, t) x, t) uv a ψ( x, t) gluongluon interaction (g and g) G a u gluon field (a8) G a uv u Ga v v Ga u gf abc Gb u Gc v [l a, l b ]if abc l c l a s (a8) are the generators of SU(). l a s are x traceless hermitian matrices. f abc are real constants (56) f abc structure constants of the group