Vacuum$polariza1on$in$QED$ force$between$two$$ (in$natural$units)$ +! p e = 4⇡↵ -!

+! -! +! -! +!

-! +!

The$interac1on$strength$of$the$two$electrons$gets$stronger$as$the$distance$between$ them$becomes$smaller$ Electric is screened; interaction becomes weak at large distances Vacuum$polariza1on$in$QCD$

The left diagram is shared by QED and QCD which renders the interaction stronger at shorter distance (screening). The second diagram arising from the nonlinear interaction between in QCD has the antiscreening effect, which makes the coupling weaker at short distance.

• Color$is$an1Mscreened$ • Color$builds$up$away$from$a$source$ • Interac1on$becomes$strong$at$large$distances$(low$ momenta)$ • Confinement$of$;$quarks$are$not$observed$as$ isolated$par1cles$ g2 Strong coupling constant α = s 4π In quantum field theory, the coupling constant is an effecve constant, which depends on four-momentum Q2 transferred. For strong interacons, the Q2 dependence is very strong (gluons - as the field quanta - carry color and they can couple to other gluons). A first- order perturbave QCD calculaon (valid at very large Q2) gives:

2 12π running coupling α Q = s ( ) 2 2 constant! (22 − 2n f )⋅ ln(Q / ΛQCD )

nf =6 − number of flavors ΛQCD − a parameter in QCD (~0.22 GeV), an infrared cutoff

The spaal separaon between quarks goes as " ! = Q2

Therefore, for very small distances and high values of Q2, the inter-quark coupling decreases, vanishing asymptocally. In the limit of very large Q2, quarks can be considered to be “free” (asymptoc freedom). On the other hand, at large distances, the inter-quark coupling increases so it is impossible to detach individual quarks from (confinement).

Asymptoc freedom was described in 1973 by Gross, Wilczek, and Politzer (Nobel Prize 2004). It is customary to quote αs at the 91 GeV energy scale (the mass of the Z ) quark wave function of the

- Consider π (t=1 and t0=1). The only possible combinaon is π − = ud In general, it is possible to find several linearly independent components corresponding to the same t and t0. The appropriate combinaon is given by coupling rules. Furthermore, the wave funcon must be ansymmetric among the quarks. This problem is similar to that of a two- wave funcon! 1 1 0 − uu dd π = τ − π = ( − ) T=1 triplet: 2 2 π + = − ud

What about the symmetric combinaon? 1 T=0 singlet: η0 = uu + dd 2 ( )

To produce heavier mesons we have to introduce excitaons in the quark- anquark system or invoke s- and other more massive quarks The lightest strange mesons are or K-mesons. Since s-quark has zero isospin, kaons come in two doublets with t=1/2: {K + (us ), K 0 (ds )}, {K − (us), K 0 (ds)}

Y = A + S +C +B +T hypercharge 1 Q = −t0 + Y 2 the SU(3) symmetry limit is met for massless u,d,s quarks π − (ud)+ p(uud) → K 0 (ds )+ Λ(uds) is conserved! Pseudoscalar mesons ! J total angular momentum ! ! ! ! ! ! ! J = ℓ + S, S = s + s ℓ orbital angular momentum q q ! S total

S can be either 0 or 1. The mesons with the relative zero orbital angular momentum are lower in energy. For the pion, S=0, hence J=0. Consequently, are “scalar” . But what about their ? The parity of the pion is a product of intrinsic parities of the quark (+1), antiquark (-1) and the parity of the spatial wave function is 1. Hence, the pion has negative parity: it is a pseudoscalar . With (u,d,s) quarks, one can construct 9 pseudoscalar mesons (recall our earlier discussion about the number of gluons!): 9 (nonet)=8 (octet)+1 (singlet) Members of the octet transform into each other under rotaons in flavor space (SU(3) group!). The remaining meson, η0, forms a 1-dim irrep. (us ) 1 497.61 π 0 = uu − dd (ds ) 2 ( ) 1 493.68 η = uu + dd − 2 ss 8 6 ( ) 1 η = uu + dd + ss 547.86 134.98 (ud ) 0 3 ( ) (du )

139.57 957.78 In reality, since the SU3 (flavor) symmetry is not exact one, the observed mesons are:

(su ) (sd ) η = η8 cosϑ +η0 sinϑ η' = −η8 sinϑ +η0 cosϑ

ϑ - Cabibbo angle, ~11o for pseudoscalar mesons

masses are in MeV/c2 The eta was discovered in pion-nucleon collisions at the Bevatron (LBNL) in 1961 at a me when the proposal of the Eighold Way was leading to predicons and discoveries of new parcles.

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Here S=1, hence J=1. They have negave parity. The vector mesons are more massive than their pseudoscalar counterparts, reflecng the differences in the interacon between a quark and an anquark in the S=0 and S=1 states.

J π =1− 896 (us ) (ds ) 1 892 ρ 0 = uu − dd 2 ( ) 775 1 783 (ud ) ω = uu + dd (du ) 2 ( ) 775 ϕ = ss 1019

(su ) (sd )

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With three flavors, one can construct a total of 3×3×3=27 baryons

singlet t = 0

Completely asymmetric under flavor 1 Λ1 = { uds + dsu + sud − dus − usd − sdu } rotaons 6 The color and flavor wave-funcons should be ansymmetric and thus zero orbital angular momentum and spin-1/2 are not possible if the wave-funcons is to be overall 1 − ansymmetric as required by Fermi–Dirac stascs. Hence, L=1 J π = 2 Λ (1405) baryon decuplet

(ddd) (udd) (uud) (uuu)

3 + (dds) (uds) (uus) J π = 2

(dss) (uss)

(sss)

The discovery of the omega baryon was a great triumph for the of baryons since it was found only aer its existence, mass, and decay products had been predicted by Murray Gell-Mann in 1962. It was discovered at Brookhaven in 1964.

€ baryon octet The remaining 16 baryons constructed from u-, s-, and d-quarks have mixed symmetry in flavor. The lower energy octet contains and as its members. The wave funcons for each member in the group is symmetric under the combined exchange of flavor and intrinsic spin (the quarks are ansymmetric in color!)

939.6 938.3 (udd) (uud) (ddd) (uuu)

1115.7 (uds) 1 + 1197.4 J π = 2 (dds) 1192.5 (uus) 1189.4

1321.3 1314.9 (dss) (uss)

1 p = 2 u↑u↑d ↓ + u↑d ↓u↑ + d ↓u↑u↑ 18 { ( ) example: wave function −( u↑u↓d ↑ + u↑d ↑u↓ + d ↑u↑u↓ ) +( u↓u↑d ↑ + u↓d ↑u↑ + d ↑u↓u↑ )} New relatives of the proton

hp://www.fnal.gov/pub/ferminews/ferminews02-06-14/selex.html

Baryon Supermulplet using four-quark models and half spin

Two New Particles Enter the Fold http://physics.aps.org/synopsis-for/10.1103/PhysRevLett.114.062004 The Roper resonance [N(1440)P11] is the proton's first radial excitation. Its lower- than-expected mass owes to a dressed-quark core shielded by a dense cloud of pions and other mesons.