Introductory Lecture on EIC Physics Experiment Ernst Sichtermann (LBNL) ? ~10-10 m ~keV -14 ~10 m -18 ~MeV < 10 m ? POETIC 8 - March 19-23 Regensburg, Germany ~10-15 m ~GeV 1 Many Thanks to the Organizers, in particular Prof. Andreas Schäfer ~10-10 m ~keV And many thanks to you -14 ~10 m -18 for taking~MeV part in this discussion< 10 m ~10-15 m ~GeV 2 Many Thanks to the Organizers, in particular Prof. Andreas Schäfer ~10-10 m ~keV And thank you for taking part -14 ~10 m -18 in~MeV this discussion < 10 m ~10-15 m ~GeV 2 What is a proton, neutron, nucleus? ? ~10-10 m ~keV -14 ~10 m -18 ~MeV < 10 m ? ~10-15 m ~GeV 3 What is a proton, neutron, nucleus? The proton is just 2 up quarks and 1 down quark, … Really? 4 What is a proton, neutron, nucleus? ? ~10-10 m ~keV -14 ~10 m -18 ~MeV < 10 m ? ~10-15 m Strongly bound objects with rich~GeV structure and dynamics; partially understood thanks to decades of interplay between theory and experiment 5 ~5 MeV Rutherford Scattering Ernest Rutherford, Nobel Prize 1908 Scattering off a hard sphere; r nucleus ~ (10-4 .r atom) ~ 10-14 m 6 ~200 MeV Elastic Electron Scattering Robert Hofstadter, Nobel Prize 1961 / steradian 2 Scattering off a spin-1/2 Dirac particle: 2 2 dσ ↵ E0 q 2 2 = cross section in cm Differential sin (✓/2) + cos (✓/2) d⌦ 4MEsin2(✓/2) E 2M ✓ ◆ The proton has an anomalous magnetic moment, g =2,g 5.6 p 6 p ' and, hence, internal (spin) structure. r nucleon ~ 0.7 fm 7 Elastic Electron Scattering l’ g4 dσ 2 = e Lµ⌫ K / |M| q4 lepton µ⌫ nucleon q D E l P The lepton tensor is calculable: µ⌫ µ ⌫ ⌫ µ µ⌫ 2 L =2 k k0 + k k0 + g (m k k0) lepton − · The nucleon tensor is not; it’s general (spin-averaged, parity conserved) form is: K K K K = K g + 2 p p + 4 q q + 5 (p q + p q ) µ⌫ nucleon − 1 µ⌫ M 2 µ ⌫ M 2 µ ⌫ M 2 µ ⌫ ⌫ µ Charge conservation at the proton vertex reduces the number of structure functions: q Kµ⌫ K = f(K ,K ),K= g(K ) µ nucleon ! 4 1 2 5 2 and one obtains the Rosenbluth form, with electric and magnetic form factors: 2 dσ ↵ E0 2 2 2 = 2K1 sin (✓/2) + K2 cos (✓/2) ,K1,2(q ) d⌦ 4MEsin2(✓/2) E 8 ✓ ◆ ⇥ ⇤ Inelastic Scattering l’ Considerably more complex, indeed! q l P Simplify - consider inclusive inelastic scattering, g4 dσ 2 = e Lµ⌫ W ,W (p, q) / |M| q4 lepton µ⌫ nucleon µ⌫ nucleon D E Again, two (parity-conserving, spin-averaged) structure functions: W1,W2 or, alternatively expressed,F1,F2 which may depend on two invariants, q2 Q2 = q2,x= , 0 <x<1 − −2q.p So much for the structure, the physics is in the structure functions. 9 Inelastic Scattering Not convinced of additional complexity? l’ q l P Simplify - consider inclusive inelastic scattering, Then forget this talk, and calculate this! g4 dσ 2 = e Lµ⌫ W ,W (p, q) / |M| q4 lepton µ⌫ nucleon µ⌫ nucleon D E Again, two (parity-conserving, spin-averaged) structure functions: W1,W2 or, alternatively expressed,F1,F2 which may depend on two invariants, q2 Q2 = q2,x= , 0 <x<1 − −2q.p So much for the structure, the physics is in the structure functions. 9 Inelastic Scattering l’ Considerably more complex, indeed! q l P Simplify - consider inclusive inelastic scattering, g4 dσ 2 = e Lµ⌫ W ,W (p, q) / |M| q4 lepton µ⌫ nucleon µ⌫ nucleon D E Again, two (parity-conserving, spin-averaged) structure functions: W1,W2 or, alternatively expressed,F1,F2 which may depend on two invariants, q2 Q2 = q2,x= , 0 <x<1 − −2q.p So much for the structure, the physics is in the structure functions. 9 Elastic scattering off Dirac Protons Compare: µ⌫ µ ⌫ ⌫ µ µ⌫ 2 L =2 k k0 + k k0 + g (m k k0) lepton − · with: qµq⌫ K 1 1 K = K g + + 2 pµ + qµ p⌫ + q⌫ µ⌫ nucleon 1 − µ⌫ q2 M 2 2 2 ✓ ◆ ✓ ◆✓ ◆ which uses the relations between K1,2 and K4,5 Then, e.g. by substitution of k’ = k-q in L: K = q2,K=4M 2 1 − 2 Note, furthermore, that inelastic cross section reduces to the elastic one for: 2 2 K1,2(q ) W1,2(q ,x)= 2 δ(x 1) − 2Mq − 10 Elastic scattering off Dirac Protons Imagine incoherent scattering off Dirac Partons (quarks) q : 2 2 2 e 2mqe q W q = q δ(x 1),Wq = q δ(x 1) and x = 1 2m q − 2 − q2 q − q −2q p q · q and, furthermore, suppose that the quarks carry a fraction, z, of the proton momentum x pq = zq p, so that xq = (also note mq = zqM !) zq which uses the relations between K1,2 and K4,5 Now, 1 e2 1 MW = M q δ(x z ) f (z ) dz = e2f (x) F (x) 1 2M − q q q q 2 q q ⌘ 1 q Z0 q q2 X1 X W = xe2δ(x z ) f (z ) dz = x e2f (x) F (x) −2Mx 2 q − q q q q q q ⌘ 2 q 0 q X Z X Two important observable consequences, 2 Bjorken scaling: F1,2(x), not F1,2(x, Q ) Callan-Gross relation: F2 =2xF1(x) 11 Elastic scattering off Dirac Protons Imagine incoherent scattering off Dirac Partons (quarks) q : 2 2 2 e 2mqe q W q = q δ(x 1),Wq = q δ(x 1) and x = 1 2m q − 2 − q2 q − q −2q p q · q and, furthermore, suppose that the quarks carry a fraction, z, of the proton momentum x pq = zq p, so that xq = (also note mq = zqM !) zq which uses the relations between K1,2 and K4,5 Now, 1 e2 1 MW = M q δ(x z ) f (z ) dz = e2f (x) F (x) 1 2M − q q q q 2 q q ⌘ 1 q Z0 q q2 X1 X W = xe2δ(x z ) f (z ) dz = x e2f (x) F (x) −2Mx 2 q − q q q q q q ⌘ 2 q 0 q X Z X Two important observable consequences, 2 Bjorken scaling: F1,2(x), not F1,2(x, Q ) Callan-Gross relation: F2 =2xF1(x) 11 Elastic scattering off Dirac Protons Imagine incoherent scattering off Dirac Partons (quarks) q : 2 2 2 e 2mqe q W q = q δ(x 1),Wq = q δ(x 1) and x = 1 2m q − 2 − q2 q − q −2q p q · q and, furthermore, suppose that the quarks carry a fraction, z, of the proton momentum x pq = zq p, so that xq = (also note mq = zqM !) zq which uses the relations between K1,2 and K4,5 Now, 1 e2 1 MW = M q δ(x z ) f (z ) dz = e2f (x) F (x) 1 2M − q q q q 2 q q ⌘ 1 q Z0 q q2 X1 X W = xe2δ(x z ) f (z ) dz = x e2f (x) F (x) −2Mx 2 q − q q q q q q ⌘ 2 q 0 q X Z X Two important observable consequences, 2 Bjorken scaling: F1,2(x), not F1,2(x, Q ) Callan-Gross relation: F2 =2xF1(x) 11 ~10 GeV Deep-Inelastic Electron Scattering Scattered electron is deflected by a known B-field and a fixed vertical angle: determine E’ Spectrometer can rotate in the horizontal plane, vary ✓ ~10 GeV Deep-Inelastic Electron Scattering Scattered electron is deflected by a known B-field and a fixed vertical angle: determine E’ Spectrometer can rotate in the horizontal plane, vary ✓ e.g. J.T.Friedman and H.W. Kendall, Ann.Rev.Nucl.Sci. 22 (1972) 203 Deep-Inelastic Electron Scattering Bjorken scaling: J.T. Friedman R. Taylor H.W. Kendall Nobel Prize 1990 F2 Callan-Gross relation: Q2 (GeV2) Point particles cannot be further resolved; their measurement does not depend on wavelength, hence Q2, Spin-1/2 quarks cannot absorb longitudinally polarized vector bosons and, conversely, spin-0 (scalar) quarks cannot absorb transversely polarized photons. 13 Deep-Inelastic Neutrino Scattering Recognize this from CERN? Gargamelle bubble chamber, observation of weak neutral current (1973). Charged-current DIS! Nucl.Phys. B73 (1974) 1 Nucl.Phys. B85 (1975) 269 Nucl.Phys. B118 (1977) 218 Phys.Lett. B74 (1978) 134 14 Deep-Inelastic Scattering - Fractional Electric Charges Neutral-current (photon) DIS: 2 F2 = x eq(q +¯q),p: uud, n : ddu Xe2 + e2 F N = x u d (u +¯u + d + d¯) 2 2 Charged-current DIS: ⌫p ⌫n ¯ F2 =2x(d +¯u),F2 =2x(u + d) ⌫N ¯ F2 = x(u +¯u + d + d) 15 Deep-Inelastic Scattering - Fractional Electric Charges Neutral-current (photon) DIS: 2 F2 = x eq(q +¯q),p: uud, n : ddu Xe2 + e2 F N = x u d (u +¯u + d + d¯) 2 2 Charged-current DIS: ⌫p ⌫n ¯ F2 =2x(d +¯u),F2 =2x(u + d) ⌫N ¯ F2 = x(u +¯u + d + d) Ratio: N F2 1 2 2 5 ⌫N = (eu + ed)= 0.28 F2 2 18 ' 15 Deep-Inelastic Scattering - Valence and Sea Quarks Charged-current DIS: ⌫ F2 =2x (q +¯q) X xF ⌫N =2x (q q¯) 3 − X 1 dx 1 xF ⌫N = (u + d )dx 3 x v v Z0 Z0 d2σ⌫¯N u¯ + d¯+(u + d)(1 y)2 Gross Llewellyn-Smith: 3 dxdy / − ⇥ ⇤ Gargamelle: 3.2 +/- 0.6 d2σ⌫N u + d +(¯u + d¯)(1 y)2 dxdy / − 16 ⇥ ⇤ Deep-Inelastic Scattering - Valence and Sea Quarks Charged-current DIS: ⌫ F2 =2x (q +¯q) X xF ⌫N =2x (q q¯) 3 − X 1 dx 1 xF ⌫N = (u + d )dx 3 x v v Z0 Z0 d2σ⌫¯N u¯ + d¯+(u + d)(1 y)2 Gross Llewellyn-Smith: 3 dxdy / − ⇥ ⇤ Gargamelle: 3.2 +/- 0.6 d2σ⌫N u + d +(¯u + d¯)(1 y)2 dxdy / − 17 ⇥ ⇤ Deep-Inelastic Scattering - Momentum Conservation Neutral-current (photon) DIS: e2 + e2 F N = x u d (u +¯u + d + d¯) 2 2 Charged-current DIS: ⌫N ¯ F2 = x(u +¯u + d + d) Momentum fraction: 1 e2 + e2 1 F N dx = u d x(u +¯u + d + d¯) 2 2 Z0 Z0 Gargamelle: 0.49 +/- 0.07 Quarks carry half of the nucleon momentum! SLAC: 0.14 +/- 0.05 18 3-jet events at PETRA Recall the intro on colour: Observation of its higher order process, marks the discovery of the gluon.