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Deep Inelastic Scattering Part 1 Dave Gaskell Jefferson Lab Deep Inelastic Scattering Part 1 Dave Gaskell Jefferson Lab CTEQ 2015 Summer School July 8-9, 2015 1 Outline Day 1: 1. Introduction to DIS and the Quark Parton Model 2. Formalism àUnpolarized DIS àPolarized DIS 3. Results and examples Day 2: 1. Nuclear Effects in DIS 2. Beyond inclusive scattering à Semi-inclusive reactions (SIDIS) 2 Disclaimer • I am an experimentalist, very interested in nuclear effects à Much of what I will say comes from this perspective • Most of my work has been at Jefferson Lab à You will be seeing a lot of examples from JLab 3 What is Deep Inelastic Scattering? Collective behaviorSome context: vs. two-body physics DIS: Using lepton (electron, muon, neutrino) scattering to explore the partonic structure of hadronic matter ? Advantages of leptonic (vs. hadronic) probes à It’s QED: at least one vertex is well understand à No complicated structure of the probe to deal with à Small value of αQED = 1/137 means higher order corrections are small*High -momentum region: short-range To access partonic structure (i.e.interactions, quarks and gluons) mainly we need 2-body “high” physics, energies and large inelasticities à want to avoid the complicationslargely from exciting A-independent resonances *Well, usually. Not always true. 4 Could these Short-Range Correlations be dense enough to modify the quark structure of protons and neutrons? Cioffi Degli Atti, et al, PRC53, 1689 (1996) 11 What is Deep Inelastic Scattering? Lepton scattering cross Nuclear elastic sections have rich, complex structure à Elastic scattering à Production of excited quark bound states – Resonance resonances! We are primarily Quasielastic interested in the regime in which quarks act like quasi-free, weakly interacting particles The boundary between these regimes not Figure from R.G. Roberts, The Structure of the Proton always so clear cut 5 DIS Experiments • Plethora of data available from a variety of fixed target experiments – SLAC à Electrons at 10’s of GeV – CERN (EMC/BCDMS/NMC/COMPASS) à Muons at 100’s of GeV – HERMES à 27 GeV positrons and electrons – E665 à Muons at 490 GeV – JLab à 6 GeV electrons à 12 GeV • Only one source of collider DIS data (so far) – HERA (Zeus and H1) : 27 GeV positrons (electrons) on 920 GeV protons • Neutrinos à CCFR, CHORUS, NuTeV, MINERνA • Important information can also be gleaned from hadron colliders (RHIC, LHC, etc.) 6 Deep Inelastic Scattering Kinematics: Beam: k= (E, 0,0,p) à Typically ignore electron mass so E=p Scattered electron: k’ = E’, θ Target: P = (Ep, 0,0,P) Useful quantities: Electron 2 2 2 Q = q = (k k) momentum transfer − − − Total energy in γ*p W 2 =(q + P )2 center of mass Q2 q P Bjorken scaling x = Inelasticity y = · k P variable 2p q · · 7 Kinematics: Lab frame Often DIS kinematics expressed in LAB frame (target at rest) à Experiments at HERA (or a future EIC) take place in collider I tend to think in a fixed-target framework – some useful expressions for working in the lab: Q2 Q2 x = 2p q → 2m ν ν = E E · p − W 2 =(q + P )2 Q2 + m2 +2m ν →− p p q P ν y = · Fraction of electron energy transferred to nucleon k P → E · 2 2 1 2 q θe − 1 y Ratio of long. to = 1+ tan = transverse photon | 2| − 1 2 Q 2 1 y + y flux − 2 8 DIS Cross Section Unpolarized cross section: dσ α 2 E = L W µν dΩdE / Q4 E / µν Parity and time invariance à only two structure functions required 2 / 2 dσ 4α (E ) ⎡ 2 2 θ 2 2 θ ⎤ / = 4 W2 (ν,Q )cos + 2W1(ν,Q )sin dΩdE Q ⎣⎢ 2 2⎦⎥ W1 and W2 parameterize the (unknown) structure of the proton 9 DIS Cross Section Unpolarized Cross section: dσ α 2 E = L W µν dΩdE / Q4 E / µν 2 / 2 dσ 4α (E ) ⎡ 2 2 θ 2 2 θ ⎤ / = 4 W2 (ν,Q )cos + 2W1(ν,Q )sin dΩdE Q ⎣⎢ 2 2⎦⎥ In the limit of large Q2, 2 2 MW1(ν,Q ) → F1(x) Q structure functions scale 2 x = νW2 (ν,Q ) → F2 (x) 2Mν 10 DIS Cross Section Virtual photon cross dσ section: = Γ(σT + σL) dΩdE 2 2 1 Longitudinal 2 q θe − Transverse photons = 1+ | | tan photons Q2 2 2 2 α E K 1 W m Γ = K = − p 2π2 E Q2 1 2m − p K K Q2 W = σ W = (σ + σ ) 1 4π2α T 2 4π2α Q2 + ν2 L T Pure transverse Transverse and longitudinal 11 DIS Cross Section 2 / 2 dσ 4α (E ) ⎡ 2 2 θ 2 2 θ ⎤ / = 4 W2 (ν,Q )cos + 2W1(ν,Q )sin dΩdE Q ⎣⎢ 2 2⎦⎥ 2 2 Replacing W1 and W2 MW1(ν,Q ) → F1(x,Q ) 2 2 νW2 (ν,Q ) → F2 (x,Q ) And defining: 4M 2x2 F (x, Q2)= 1+ F (x, Q2) 2xF (x, Q2) L Q2 2 − 1 dσ 4π2α = Γ 2xF (x, Q2)+F (x, Q2) dΩdE x(W 2 M 2) 1 L − 12 Deep Inelastic Scattering + At very high energies (HERA) – contributions from Z exchange can no longer be ignored dσe± 2πα2(1 + (1 y)2) 1 (1 y)2 y2 = − F˜ − − xF˜ F˜ dxdQ2 Q4x 2 ∓ 1 + (1 y)2 3 − 1 + (1 y)2 L − − F˜ = F κ v F γZ + κ2 (v2 + a2)F Z 2 2 − Z e 2 Z e e 2 F˜ = F κ v F γZ + κ2 (v2 + a2)F Z L L − Z e L Z e e L xF˜ = κ a xF γZ + κ2 2v a xF Z 3 − Z e 3 Z e e 3 Q2 1 Vector weak coupling Axial-vector weak κZ = =-1/2 Q2 + M 2 2 2 2 coupling 13 Z 4 sin θW cos θW =-1/2+2sin θW Quark Parton Model DIS can be described as inelastic scattering from non- interacting, point-like constituents in the nucleon Consequences: At fixed x, inelastic structure functions scale: MW (ν,Q2 ) → F (x) 1 1 Large Q2 2 νW2 (ν,Q ) → F2 (x) 2 Spin ½: F2(x)= ei xqi(x) F2(x)=2xF1(x) Callan-Gross i relation σ R = L =0 σ T 14 Quark Parton Model DIS can be described as inelastic scattering from non- interacting, point-like constituents in the nucleon 2 F2(x)= eqx(q(x)+¯q(x)) q q 1 2 gV = 2eq sin θW γZ q ±2 − F2 (x)= 2eqgV x(q(x)+¯q(x)) q u=+, d=- Z q 2 q 2 F2 (x)= [(gV ) +(gA) ]x(q(x)+¯q(x)) 1 q gq = A ±2 F γZ (x)= 2e gq (q(x) q¯(x)) 3 q A − q F Z (x)= [(gq )2 +(gq )2](q(x) q¯(x)) 3 V A − q 15 G. MILLER et al. 7.0— R=0.18 Scaling – SLAC-MIT6.0 —resultW 2.6 GeV from 1970 A series of experiments at SLAC (performed by SLAC-MIT collaboration) gave 2MpW1 first hints that the partonic hypothesis was valid5.0 à Cross sections at large angles (momentum transfers) larger than if proton was an amorphous blob-like object à Analogous to Rutherford’s alpha scattering experiments 0 VoLUME 2), NUMBER 16 PHYSICAL REVIEW0.6 LETTERS 20 GcTQBER 1969 FIG 6 2AfpSL and vW& R=0.18 are shown as functions of u for 8 =0.18, S'&2.6 GeV, 0/&2. 6 GeV range of q' and W. with a resolution of 0.3 mrad. The measured and q2& 1 (GeV/e)2. %e observe the excitation of several nucleon solid angle of the instrument was 6&&10 ' sr with resonances' ' whose cross sections fall rapidly an uncertainty of +2%. with increasing q'. The region beyond 8'= 2 GeV Extensive tests showed that there could be sig- exhibits a surprisingly weak q' dependence. This nificant reductions in target density due to beam Letter describes the experimental procedure and heating. In order to correct for changes in the reports cross sections for W» 2 GeV. Discus- density a second spectrometer" was simulta- sion of the results and a detailed description of neously used to measure protons from elastic the resonance region will follow. ' electron-proton scattering at low momentum The incident energies at 0 =10' were 17.7, 15.2, transfer. The angle and momentum settings of 0.1 Phys.Rev.Lett.13.5, 11, and 7 GeV, 23 (1969)and at 8=6930-934were 16, 13.5, this spectrometer remainedQfixed2=1-7for GeVeach 2spec- 10, and 7 GeV. For fixed E and 8, along a spec- trum. Usually the density reductions were less trum of decreasing E', W increases and q' de- than 4%, with the maximum value being 13%. creases. The maximum range of these variables An uncertainty of +1% was assigned to the mea- overBeama single energymeasured up tospectrum ~ 20 GeVoccurred at an sured cross sections for this correction. incident energy of 17.7 GeV and an anglePhys.Revof 10',diffractive. D5 (1972)Themodelsmainfor 528A,triggerbut we findfor thatan eventA is was providedin parton models.by " For this integral we find small for values of 2M~v/q' to about 8 and not where W varied from one proton mass to 5.2 a logical "or" betweenup x=0.25the total-absorptionis x=0.120d(dcount- 16 with kinematics. —vS' = 0.172 + 0.009 t strongly varying 2 GeV, and q' from 7.4 to 1.6 (GeV/c)'. For each er and a coincidence of two scintillation triggerJ Q)2 E' The new data permit further investigation of sum spectrum was changed in overlapping steps ofrules involvingcountersvtV2 reportedplaced beforewith the 6'andandafter10' the hodoscopes.which is about one half the value predicted on the 2% from elastic scattering, through the observeddata.
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