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Vacuum$Polariza1on$In$QED$ Force$Between$Two$Electrons$ (In$Natural$Units)$ +! P E = 4⇡↵ -!

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Vacuum$Polariza1on$In$QED$ Force$Between$Two$Electrons$ (In$Natural$Units)$ +! P E = 4⇡↵ -! Vacuum$polariza1on$in$QED$ force$between$two$electrons$ (in$natural$units)$ +! p e = 4⇡↵ -! +! -! +! -! +! -! +! The$interac1on$strength$of$the$two$electrons$gets$stronger$as$the$distance$between$ them$becomes$smaller$ Electric charge 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 gluons 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;$quarks$are$not$observed$as$ isolated$par1cles$ g2 Strong coupling constant α = s 4π In quantum field theory, the coupling constant is an effec1ve constant, which depends on four-momentum Q2 transferred. For strong interac1ons, 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 quark 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 asympto1cally. In the limit of very large Q2, quarks can be considered to be “free” (asympto1c freedom). On the other hand, at large distances, the inter-quark coupling increases so it is impossible to detach individual quarks from hadrons (confinement). asympto1c 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 boson) Mesons quark wave function of the pion - 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 isospin coupling rules. Furthermore, the wave func1on must be an1symmetric among the quarks. This problem is similar to that of a two-nucleon wave func1on! 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- an1quark system or invoke s- and other more massive quarks The lightest strange mesons are kaons 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) strangeness is conserved! Pseudoscalar mesons ! J total angular momentum ! ! ! ! ! ! ! J = ℓ + S, S = s + s ℓ orbital angular momentum q q ! S total spin 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, pions are “scalar” particles. But what about their parity? 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 meson. 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 1me when the proposal of the Eighvold Way was leading to predic1ons and discoveries of new par1cles. € € € € € € Vector mesons Here S=1, hence J=1. They have negave parity. The vector mesons are more massive than their pseudoscalar counterparts, reflec1ng the differences in the interac1on between a quark and an an1quark 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 ) € € € € € € € Baryons (qqq) With three flavors, one can construct a total of 3×3×3=27 baryons baryon singlet t = 0 Completely asymmetric under flavor 1 Λ1 = { uds + dsu + sud − dus − usd − sdu } rotaons 6 The color and flavor wave-func1ons should be an1symmetric and thus zero orbital angular momentum and spin-1/2 are not possible if the wave-func1ons is to be overall 1 − an1symmetric as required by Fermi–Dirac stas1cs. 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 quark model 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 protons and neutrons as its members. The wave func1ons for each member in the group is symmetric under the combined exchange of flavor and intrinsic spin (the quarks are an1symmetric 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: proton 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 hEp://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. .
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