HOMESITE HELPABOUTSEARCH NOBELPHYSICSCHEMISTRYMEDICINELITERATUREPEACEECONOMICS The Nobel Prize in The Nobel Prize in Physics 2004 Physics 2004 Prize Announcement Press Release "for the discovery of asymptotic freedom in the Advanced theory of the strong interaction" Information Information for the Public David J. Gross Nobel Lecture Interview Other Resources H. David Politzer Nobel Lecture David J. Gross H. David Frank Wilczek Other Resources Politzer 1/3 of the 1/3 of the 1/3 of the Frank Wilczek prize prize prize Nobel Lecture USA USA USA Interview Other Resources Kavli Institute California Massachusetts for Theoretical Institute of Institute of Physics, Technology Technology 2003 University of Pasadena, CA, (MIT) The 2004 Prize in: California USA Cambridge, Physics Santa Barbara, MA, USA Chemistry CA, USA Physiology or b. 1941 b. 1949 b. 1951 Medicine Literature Peace Find a Laureate: Name Bryan Webber, Asymptotic Freedom, CPS, 3 Nov 2004 1 Asymptotic Freedom: History and Implications Bryan Webber University of Cambridge Cavendish Laboratory ² Quantum Chromodynamics { Quarks { Colour ² Asymptotic Freedom { E®ective charge { Non-Abelian ¯elds { History ² Implications { Con¯nement { Grand uni¯cation? ² Conclusions RP Crease and CC Mann, The Second Creation, Macmillan 1986 L Hoddeson et al., The Making of the Standard Model, CUP 1997 Bryan Webber, Asymptotic Freedom, CPS, 3 Nov 2004 2 Quark Model of Hadrons ² In the early 1960's, many new strongly-interacting particles (hadrons) were discovered, all apparently as `fundamental' as the familiar proton, neutron and ¼-meson. ² In 1964, Gell-Mann and Zweig (independently) noticed that the quantum numbers of all the known hadrons corresponded to those of collections of 2 or 3 spin one- half, fractionally-charged constituents, called quarks by Gell-Mann (Nobel Prize 1969). ddd udd uud uuu ∆ K 0 K + n p ds us udd uud dds uds uus Σ * du uu,dd ud dds uds uus + π − π 0,η π + Σ Σ 0, Λ Σ dss uss Ξ* su sd dss uss K − K 0 sss Ω Ξ Ξ0 { Zweig (unpublished CERN preprint) called them `aces'. { Quarks were regarded as `mathematical' entities because they were not seen individually. { Also they seemed to violate the spin-statistics theorem: some hadrons corresponded to totally symmetric combinations of 3 identical quarks. Bryan Webber, Asymptotic Freedom, CPS, 3 Nov 2004 3 Colour ² Han and Nambu (1965, also Greenberg) solved the spin-statistics problem by proposing that quarks have a new \colour" degree of freedom which can take 3 values (red, green, blue), with respect to which the `symmetrical' quark states are antisymmetric. Associated symmetry group SU(3). { Originally thought of as a global symmetry, 0 qa ! qa = Uab qb where a = 1; 2; 3 and the symmetry transformations are represented by constant (i.e. space-time independent) 3£3 unitary matrices U, which mix the colours while preserving the normalization. { Observed states qq¹, qqq are colour singlets. { It was necessary to postulate that non-singlet states (q, qq, (qq¹)8, . ) are forbidden. ² The notion of quarks as `real' rather than `mathematical' constituents of hadrons was considered quite implausible . until amazing experimental data started arriving from the new Stanford Linear Accelerator Centre (SLAC). Bryan Webber, Asymptotic Freedom, CPS, 3 Nov 2004 4 Deep inelastic electron scattering ² The SLAC experiments (1967) probed the structure of the proton by scattering high-energy electrons ² Useful dimensionless variables are: ¡q2 Q2 q ¢ p E0 x = = ; y = = 1 ¡ 2p ¢ q 2M(E ¡ E0) k ¢ p E where Q2 = ¡q2 > 0, M = proton mass, and energies refer to target rest frame. ² Elastic scattering has x = 1. Deep inelastic scattering (DIS) means Q2 À M 2 and x < 1. Bryan Webber, Asymptotic Freedom, CPS, 3 Nov 2004 5 2 ² Structure functions Fi(x; Q ) parametrise target structure as `seen' by virtual photon: d2σ 8¼®2ME 1 + (1 ¡ y)2 = 2xF1 + (1 ¡ y)(F2 ¡ 2xF1) ¡ (M=2E)xyF2 dxdy Q4 2 ·µ ¶ ¸ ² Bjorken limit is Q2 ! 1 and p ¢ q ! 1 with x ¯xed. In this limit structure functions were found to obey approximate Bjorken scaling (1969), i.e. they depend only on dimensionless variable x: 2 Fi(x; Q ) ¡! Fi(x) ² Although Q2 varies by two orders of magnitude, in ¯rst approximation data lie on universal curve. Bryan Webber, Asymptotic Freedom, CPS, 3 Nov 2004 6 Implications of Bjorken scaling ² Bjorken scaling implies that virtual photon is scattered by pointlike constituents { partons (Feynman, 1969) | otherwise structure functions would depend on ratio Q=Q0, with 1=Q0 a length scale characterizing size of constituents. ² Quantitative study over the next few years established that these pointlike partons had spin one-half and fractional charges, consistent with those expected for the quarks of Gell-Mann and Zweig. { However, the quark were found to carry only about one-half of the momentum of the target proton { The other half must be carried by strongly-interacting, neutral, bosonic constituents. ² Modern data show weak (logarithmic) scaling violation, understood as a calculable higher-order e®ect. Bryan Webber, Asymptotic Freedom, CPS, 3 Nov 2004 7 x=6.32E-5 (x) x=0.000102 ZEUS NLO QCD fit 10 x=0.000161 x=0.000253 tot. error -log x=0.0004 em 2 x=0.0005 5 H1 94-00 F x=0.000632 x=0.0008 H1 96/97 x=0.0013 ZEUS 96/97 BCDMS x=0.0021 4 E665 x=0.0032 NMC x=0.005 x=0.008 3 x=0.013 x=0.021 x=0.032 2 x=0.05 x=0.08 x=0.13 1 x=0.18 x=0.25 x=0.4 x=0.65 0 2 3 4 5 1 10 10 10 10 10 Q2(GeV2) Bryan Webber, Asymptotic Freedom, CPS, 3 Nov 2004 8 Yang-Mills theory ² Back in 1954, Yang & Mills had shown that one could extend the notion of local gauge invariance from the Abelian U(1) symmetry group of QED: 0 Ãe(x) ! Ãe(x) = U(x) Ãe(x) where U(x) = eiÁ(x), to a non-Abelian symmetry group: 0 Ãa(x) ! Ãa(x) = Uab(x) Ãb(x) where a = 1; : : :N and U(x) 2 SU(N) is a space-time dependent N£N unitary matrix, which mixes the N states Ãa while preserving the normalization. { As in QED, gauge invariance then requires the existence of a vector gauge ¯eld { Quanta of the gauge ¯eld would be massless spin-1 particles, analogous to the photon, communicating long-range forces ² In 1954, this did not ¯t with the properties of either strong or weak nuclear interactions. So Yang-Mills theory was ignored. ² Even QED was regarded as a sick theory (see later), and quantum ¯eld theory went out of fashion for about 15 years. Bryan Webber, Asymptotic Freedom, CPS, 3 Nov 2004 9 AND THEN . ² The SLAC results prompted renewed interest in a ¯eld theory of the strong interactions of pointlike quarks. ² Fritzsch & Gell-Mann (1971, also Weinberg) proposed that the strong interaction is an SU(3) Yang-Mills gauge theory: Quantum ChromoDynamics. { Quanta of the colour ¯eld (gluons) would communicate the strong force between quarks { Gluon exchange forces would be attractive in colour singlet states { Gluons could also carry the `missing momentum' of the proton ² But why should quarks behave like almost-free particles in DIS? ² And why should colour non-singlet states be forbidden? Bryan Webber, Asymptotic Freedom, CPS, 3 Nov 2004 10 Quantum Chromodynamics ² QCD is an SU(3) gauge ¯eld theory: quarks come in 3 \colours" (a = 1; 2; 3) and the gauge transformations are represented by 3£3 unitary matrices U, which mix the colours while preserving the normalization: 0 qa(x) ! qa(x) = Uab(x) qb(x) it¢θ(x) Uab(x) = e 8 t ¢ θ ´ tAθA XA=1 where θA are 8 real parameters and tA, the generators of SU(3), are the 8 linearly independent 3 £ 3 traceless hermitian matrices. A B 1 { Conventional normalization is Tr (t t ) = 2±AB { The theory is non-Abelian, i.e., successive gauge transformations do not commute: [tA; tB] = if ABCtC where the structure constants of the gauge group, f ABC, are totally antisymmetric. 4 { t ¢ t = CF I where CF = 3 is the \quark colour charge squared" ABC ABD { A;B f f = CA ±CD where CA = 3 is the \gluon colour charge squared" P Bryan Webber, Asymptotic Freedom, CPS, 3 Nov 2004 11 ² The QCD Lagrangian density is 1 A A¹º f ¹ f LQCD = ¡4F¹ºF + q¹a [iγ (D¹)ab ¡ mf ±ab] qb flavoursX f A A A ABC B C { Gluon ¯eld strength tensor F¹º = @¹Aº ¡ @ºA¹ ¡ gSf A¹ Aº { Covariant derivative (D¹)ab = @¹ ±ab + igS (t ¢ A¹)ab A { A¹ are the gluon ¯elds (A = 1; : : : ; 8) 2 { gS is the QCD coupling; by analogy with QED we de¯ne ®S ´ gS=4¼ ² The third term in the gluon ¯eld strength tensor is essential for gauge invariance of LQCD. Notice that it would vanish for an Abelian (commuting) gauge group (f ABC = 0). ² As a consequence of this term, there are 3-gluon and 4-gluon self-interactions: A,µ B,ν B,ν A,µ q p r C,λ C,λ D,ρ Bryan Webber, Asymptotic Freedom, CPS, 3 Nov 2004 12 E®ective Charge ² In QED the observed electron charge is distance-dependent () momentum transfer dependent) due to vacuum polarization: α eff - - + - - + + - + + 1 - + + - 1 128 - + + 137 + + - - + - - 2 2 mZ q ² The one-loop vacuum polarization diagram is log-divergent and can be regularized by introducing a cut-o® ¤. Bryan Webber, Asymptotic Freedom, CPS, 3 Nov 2004 13 ² Then the observed coupling at momentum transfer q¹ is q q 2 2 ® q ®(q ) = ®bare 1 + ln + ¢ ¢ ¢ à 3¼ ¤2 ! Thus 2 2 d® ® q = + ¢ ¢ ¢ ´ ¯QED(®) dq2 3¼ where the QED ¯-function ¯QED(®) > 0.