Overview of Elementary Particle Physics

Transcription

1 Overview of Elementary Particle Physics Michael Gold Physics 330 May 3, 2006

2 Overview of Elementary Particle Physics Rutherford e p elastic elastic scattering e p inelastic scattering zeus Parton model jets strong force flavors Weak Force the Higgs summary

3 Rutherford atomic size blob cross section would fall much faster.

4 e p elastic scattering, PRL 102, 851 (1956)

5 Simple exponential form for charge distribution, ρ(r) = ρ 0 e r/r 0 with Fourier transform G D (q 2 ) = 1 [1 + q 2 (r 0 / c) 2 ] 2 Agrees with data to < 10% for for q 2 < (5GeV ) 2 : G p E (q2 ) = G D (g 2 ) G p E (q2 ) = G p M (q2 )/g p, g p = 2.79 fit gives (r 0 / c) 2 = 1/0.71 GeV 2, r 0 = 0.24 fm and r rms = 0.81 fm.

6 e p resonance 1500 ~ > Q) CJ :c c: ~ 1000 i:u "b8 l l~ E=4.879GeV 8=10 ~* J~\ ~ I I~~\w!J~~ r ~I! III II /.~~ 11\~~~~ II I 411) Elasticscattering ~ (divided by 15) II I I! E' [GeV] W [GeV/c2] Fig Spectrum of scattered electrons from electron-proton scattering at an electronenergy of E = 4.9 GeV and a scattering angle of () = 10 (from [Ba68]).

7 Zeus experimental group

8 Schematic Zeus detector

9 inelastic scattering event e event

10 Note the different scales. The mean q 2 range increases with increasing energy. The resonances become less and less pronounced but the continuum decreases only slightly.

11 PRL 23, 935 (1969) The inelastic cross section closely follows the Mott elastic scattering cross section, indicating that the electron has struck something elementary inside the proton. Deep-inelastic cross section falls off very slowly with q 2 compared to elastic scattering (1 + q 2 ( c/r 0 ) 4 ; Evidence for point-like constituents of the proton.

12 parton model Inelastic scattering depends on two variables: CM scattering and final electron energy θ, E, or more convenient theoretically q 2, ν where ν = q 0 = E E. The cross section is: dσ dω e de = (α c)2 cos 2 ( θ 2 ) 4E 2 sin 4 ( θ 2 ) [W 2 + 2W 1 tan 2 ( θ 2 )] W 1, W 2 experimentally are (very nearly) dependent only on the dimensionless ratio x = q 2 /(2m p ν), 0 < x < 1.

13 Scaling of the proton structure function ZEUS em -log10 (x) F 2 5 x=6.32e-5 x= x= x= x= x= x= x= ZEUS NLO QCD fit tot. error ZEUS 96/97 x= BCDMS 4 x= x= E665 NMC x= x=0.008 x=0.013 x= x=0.032 x=0.05 x=0.08 x= x=0.18 x=0.25 x=0.4 x= Q 2 (GeV 2 )

14 This scaling of structure functions depends has the interpretation that x is the momentum fraction of the proton carried by the struck quark.. Then the cross section can be re-written in terms of the quark charges Q i e and the parton distribution functions f i (x) that are the probability density functions for the i th quark to have momentum fraction x. W 2 = 2Mc2 q 2 Q 2 i f i (x) W 1 = 1 2Mc 2 Q 2 i f i (x)

15 Universal parton distribution functions for the proton extracted from best fits to data. The functions give the probability to find a quark inside the proton with momentum fraction x.

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17 ..~, hadron jets W =34 GeV ~I] -i ~ 1.0, +-t1~ t t v+ 0.5 lcas HI Figure 8.14 Center.of.ma» angular distribution I>fthe twi>hallron jets(as in Fig. ~:!3) rd:uivc to the beam axis in If' If- annihilation at high energy. It is consistent with a (I -+-,,-us; 11) d~tributil>n. as exix--ctcll if the fundamental pnx.-.:» is If' If- - QQ. Expected angular distribution for point-like, spin-1/2 fermions of charge Qe in e + e f f in the CM (lab) frame is given by dσ dω = Q2 (α c) 2 4Ecm 2 [1 + cos 2 (θ)]. The distribution of the Jet axis shows the underlying quarks are spin-1/2

18 With e + e beams polarized transverse the circulating beams, the cross section shows a φ depedance predicted for spin-1/2 quarks (polarization P): dσ [1 + cos 2 (θ) + P 2 sin 2 (θ) cos(2φ)] dω = Q2 (α c) 2 4Ecm 2

19 Pion: Yukawa 1935 Yukawa, proton V (r) = g 2 r e r/r 0 neutron g g pion short-range nuclear force with strong coupling g and range r 0 fm predicted m π ( ) Mev. Scalar pion gives force that is always attractive. In cosmic rays, first discovered the muon (m µ c 2 = 106 MeV), a heavy electron making up the primary component of cosmic radiation at the earth s surface. Who ordered this? Later discovered pion.

20 QCD The parton model works so well to describe deep inelastic scattering because of the nature of the strong force. The theory is called Quantum chromo-dynamics or QCD. It is modeled after quantum electrodynamics (QED), mediated by a spin-1 bosons called the gluon that couples quarks that come in 3 types of charges called colors (red,blue,yellow, and anti-colors for the anti-quarks). The key difference is that the gluons also have color-charge, so that they couple to themselves. The force between quarks gets weaker at short distances ( asymptotic freedom ) and stronger at large distances quark confinement ). For this reason, the theory predicts that no free quarks or gluons can ever been observed (indeed, they have not). All strongly interacting particles (hadrons) must be color-neutral. For the nuclear force, the Yukawa pion-exchange model remains as a good approximation to the residual (Van der Wals type) force between color-neutral nucleons.

21 QED Pion: q _ q flux string tension ~ Mev/fm QCD q q q q Stretched string has enough energy to form has enough energy to form quark antiquark pair. String breaks leaving 2 pions.

22 The measured running of the strong coupling.

23 The gluon is observed as a third jet in e + e by the JADE detector.

24 Strangeness produced in strong processes, large σ 10 3 b: but long lifetimes s also, π p K 0 Λ 0 Λ 0 π p K 0 π + π π + p K + Σ + Σ + π + n K + π + π 0 assigned new quantum number called strangeness that was conserved by the strong force but decayed via the weak force. S(K + ) = 1, S(K 0 ) = 1, S(Σ + ) = 1, S(Λ 0 ) = 1, S(Ξ ) = 2 for example doubly strange cascade, K + p Ξ + K+

25 Lots of elementary particles Mesons: masses 135Mev to several Gev, spin=0, 1... π +, π, π 0, K +, K, K 0, ρ +, ρ, ρ 0... Baryons: masses 940 Mev to several Gev, spin = 1/2, 3/2... p, n, Λ 0, Σ, Σ 0, Σ +,, 0, +, ++, N,...

26 Baryons,Mesons construced from quarks (Gell-Mann) quarks have spin 1/2 and come in 6 flavors. Flavor quantum numbers are assigned according to the rule, Q = I 3 + Y where I is the iso-spin, and the hypercharge is Y = (B + F )/2, F being the flavor quantum number. flavor Q B I 3 F Mass u MeV d MeV 2 1 c GeV s Mev 2 1 t GeV b GeV Flavor symmetries arise due to approximately equal masses and the fact that all quarks have the same strong charge.

27 Spin 1 2 Baryons

28 Spin 3 2 Baryons

29 discovery of Ω

30 Baryon and Meson multiplets

31 3 8''''-''' Vi Vi' T1"T" 6 I- I I IIII 8 I 8 Q:; 18' I 11'1", " I I r- II, 41- I 81 I I I. Its u+d+s+c. I f' 2 " u+d+s No color I III Figure 8.3 R is plotted against electron energy (in GeV). (Source: F. Halzen and A. D. Martin, Quarks and Leptons (New York: Wiley, 1984, p Reprinted by permission of John Wiley & Sons, Inc.) 20 The total cross section for e + e hadrons measured relative to point (µ + µ ) pair production, R = σ had σ µ = 3 iflavors Q2 i. The factor 3 is for 3 colors of quarks. Note the steps for production of additional quark flavors.

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33 1,000 I- 900 I-- CHARMONIUM Dissociation POSITRONIUM 33S1 t'" 7 energy j!j -0 c: 800 I-- ::J 0 23S, 23P2 -'? ".. '" 2 'P, \ >" 700 ::J Q) a 5 23p / X 2 'So > '" 600 Q) > lp 23p'/ <:'... Q) 0 Q) - c: 2 'so (T/) 2 3S, (",') > 4 Q) -0 Q) 500 c: <:' > 2 3P2 (X2) ::J Q) c: ';:; '" 2 'P, 0 Q) cc Q; ---- Q) 400 > a: 3 ";::; 2 3p, (X1) '" Q; a: 23po(Xo) I I 1 3S, ("') S, I-- 1 ' So (T/c) hi - 1'S x 's States 3S States I 1P States 3P States 1S States 3S States ' P States 3P States... m C,.) Figure 5.7 Spectrum of energy levels in positronium and charmonium. Note that the scale is greater by a factor of 100 million for charmonium. In positronium the various combinations of angular momentum cause only minuscule shifts in energy (shown by expanding the vertical scale), but in charmonium the shifts are much larger. All energies are given with reference to the 138, state. At 6.8 electron volts positronium dissociates. At633MeVabovethe energyofthe '" charmoniumbecomesquasi-bound,becauseitcandecayintojyiand 15 mesons.(from "Quarkonium," by E. Bloom and G. Feldman. May 1982 by Scientific American, Inc. All rights reserved.)

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37 Weak Force The leptons also come in 3 families of spin 1/2 fermions, corresponding to the three families of quarks. Leptons do not have strong interactions, only weak and electromagnetic. They have 0 baryon number. The most striking fact is the violation of Parity (space inversion). Only the Left-handed fermions (quarks and leptons) couple to the mediators of the weak force (W,Z)! The weak force is weak because the W, Z bosons that mediate the force are so heavy: m W = 80 GeV, m Z = 91 GeV. G F = 4 2πα( c) 3 (m W c 2 ) GeV fm 3

38 Parity violation Parity (P) is spatial inversion. Weak decays couple only to Left-handed particles (Right-handed anti-particles), violating P maximally. neutron Left handed electron proton Right handed anti neutrino

39 Leptons The leptons have weak-isospin and weak-hypercharge quantum numbers (couplings) satisfying Q = I 3 + Y /2. lepton I 3 Q Y Mass ν e < 3 ev e L MeV e R lepton I 3 Q Y Mass ν µ <.2 MeV µ L MeV µ R lepton I 3 Q Y Mass ν τ < 18 MeV τ L MeV τ R 0 1 2

40 charged current event

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43 Plots of cross sections and related quantities σ and R in e + e Collisions σ(e + e _ qq hadrons) [pb] ρ ω φ J/ψ ψ(2s) Z s (GeV) 10 3 J/ψ ψ(2s) Z 10 2 R 10 ρ ω φ s (GeV) Figure 39.6, Figure 39.7: World data on the total cross section of e + e hadrons and the ratio R = σ(e + e hadrons)/σ(e + e µ + µ, QED simple pole). The curves are an educative guide. The solid curves are the 3-loop pqcd predictions for σ(e + e hadrons) andthe Rratio, respectively [see our Review on Quantum chromodynamics, Eq. (9.12)] or, for more details, K.G. Chetyrkin et al., Nucl. Phys. B586, 56 (2000), Eqs. (1) (3)). Breit-Wigner parameterizations of J/ψ, ψ(2s), and Υ (ns),n = 1..4 are also shown. Note: The experimental shapes of these resonances are dominated by the machine energy spread and are not shown. The dashed curves are the naive quark parton model predictions for σ and R. The full list of references, as well as the details of R ratio extraction from the original data, can be found in O.V. Zenin et al., hep-ph/ (to be published in J. Phys. G). Corresponding computer-readable data files are available at zenin o/contents plots.html. (Courtesy of the COMPAS (Protvino) and HEPDATA (Durham) Groups, November 2001.)

44 Measurement of the width of the Z tells us that there are only 3 families of m ν < m Z /2 neutrinos.

45 CP Violation Weak interactions with three families of quarks and leptons violate CP symmetry (parity and particle-antiparticle exhange). This means that the laws of physics distinguish particle and anti-particle. K L ( π l + ν l ) K L ( π + l ν l ) K L ( π l + ν l ) + K L ( π + l = ± ν l ) where l = e or µ.

46 The problem of mass Less than 1% of the mass of the proton comes from the (valence uud) quarks. The rest is glue! This mass we understand. However, the masses of the elementary particles (leptons, quarks, W,Z bosons) are a problem handedness of the particle is only Lorentz invariant for massless particles. frame S frame S right handed left handed For the ν which has no conserved charge, it can have mass because it can be its own anti-particle ν L = ν R. For the other particles, they can only acquire a mass by interacting with a new (predicted) particle: the Higgs.

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