Nucleon Spin Structure Longitudinal Spin of the Proton HUGS Summer School Jefferson National Laboratory June 1, 2011 Lecture 2 Abhay Deshpande Wednesday, June 1, 2011 Introduction & Overview (I) Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 2 Wednesday, June 1, 2011 Introduction & Overview (I) • Lecture 1: Introduction & importance to “spin” – What is the spin crisis? Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 2 Wednesday, June 1, 2011 Introduction & Overview (I) • Lecture 1: Introduction & importance to “spin” – What is the spin crisis? • Lecture 2 & Lecture 3 – Experimental method : Fixed Target Polarized Deep Inelastic Scattering (pDIS): early investigations – Spin Crisis, and the insights it enabled…. – Latest on pDIS experiments: result summaries – Principle limitations of fixed target experiments Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 2 Wednesday, June 1, 2011 Introduction & Overview (II) Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 3 Wednesday, June 1, 2011 Introduction & Overview (II) • Lecture 4 & Lecture 5 – Relativistic Heavy Ion Collider as a Polarized Collider – Comments experimental techniques – Review of results – Principle limitations Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 3 Wednesday, June 1, 2011 Introduction & Overview (II) • Lecture 4 & Lecture 5 – Relativistic Heavy Ion Collider as a Polarized Collider – Comments experimental techniques – Review of results – Principle limitations • Lecture 6: Future studies in nucleon spin – Review of all experimental limitations – Non-Longitudinal spin structure of the proton – Status and possibilities at an Electron Ion Collider (EIC) Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 3 Wednesday, June 1, 2011 Deep Inelastic Scattering: Kinematics Inclusive DIS: only measure the scattered electron Semi-Inclusive DIS: Inclusive + Current Jet remnants Exclusive DIS: Semi-Inclusive + Target Jet remnants Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 4 Wednesday, June 1, 2011 Perspective on x,Q2, Center of Mass Fixed target e-N experiments (center of mass < 30 GeV) Hadron-Hadron Collider: CM ~2 TeV Typically accessible By e-N collider experiments CM ~ 300 GeV Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 5 Wednesday, June 1, 2011 Deep Inelastic Scattering: Kinematics with spin k’ s k S K No transverse component/ “Deep Inelas+c” : Q2 >> 1 GeV2 projec+ons of spin on parton or “Scaling Limit” : Q2 à proton momentum Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 6 Wednesday, June 1, 2011 • Lepton Nucleon Cross Section Nucleon spin Lepton spin • Lepton tensor Lµν affects the kinematics (QED) • Ηadronic tenosr Wµν has information about the hadron structure Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 7 Wednesday, June 1, 2011 • Lepton Nucleon Cross Section Nucleon spin Lepton spin • Lepton tensor Lµν affects the kinematics (QED) • Ηadronic tenosr Wµν has information about the hadron structure Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 7 Wednesday, June 1, 2011 • Lepton Nucleon Cross Section Nucleon spin Lepton spin • Lepton tensor Lµν affects the kinematics (QED) • Ηadronic tenosr Wµν has information about the hadron structure Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 7 Wednesday, June 1, 2011 Structure Functions & PDFs • The F1 and F2 are unpolarized structure functions or momentum distributions • The g1 and g2 are polarized structure functions or spin distributions • In QPM – F2(x) = 2xF1 (Calan Gross relation) – g2 = 0 (Twist 3 quark gluon correlations) Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 8 Wednesday, June 1, 2011 Measurement of Glue at HERA 9 Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 Wednesday, June 1, 2011 Measurement of Glue at HERA 2 • Scaling violations of F2(x,Q ) 9 Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 Wednesday, June 1, 2011 Measurement of Glue at HERA 2 • Scaling violations of F2(x,Q ) 9 Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 Wednesday, June 1, 2011 Measurement of Glue at HERA 2 • Scaling violations of F2(x,Q ) 9 Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 Wednesday, June 1, 2011 Measurement of Glue at HERA 2 • Scaling violations of F2(x,Q ) • NLO pQCD analyses: fits with linear DGLAP* equations 9 Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 Wednesday, June 1, 2011 Measurement of Glue at HERA 2 • Scaling violations of F2(x,Q ) • NLO pQCD analyses: fits with linear DGLAP* equations 9 Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 Wednesday, June 1, 2011 Measurement of Glue at HERA 2 • Scaling violations of F2(x,Q ) • NLO pQCD analyses: fits with linear DGLAP* equations *Dokshitzer, Gribov, Lipatov, Altarelli, Parisi 9 Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 Wednesday, June 1, 2011 Measurement of Glue at HERA 2 • Scaling violations of F2(x,Q ) • NLO pQCD analyses: fits with linear DGLAP* equations Gluon dominates *Dokshitzer, Gribov, Lipatov, Altarelli, Parisi 9 Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 Wednesday, June 1, 2011 Nucleon spin & Quark Probabilities • Define – With q+ and q- probabilities of quark & anti-quark with spin parallel and anti-parallel to the nucleon spin • Total quark contribution then can be written as: • The nucleon spin composition Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 10 Wednesday, June 1, 2011 Nucleon’s Spin: Naïve Quark Parton Model • Protons and Neutrons are spin 1/2 particles • Quarks that constitute them are also spin 1/2 particles – And there are three of them in the nucleons: Proton: u u d Neutron: u d d S proton = Sum of all quark spins! ? 1/2 = 1/2 + 1/2 + 1/2 1/2 = 1/2 - 1/2 + 1/2 Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 11 Wednesday, June 1, 2011 How was the Quark Spin measured? • Deep Inelastic polarized electron or muon scattering µ Spin 1/2 quarks Spin 1 γ∗ µ Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 12 Wednesday, June 1, 2011 Lepton-nucleon Cross Section Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 13 Wednesday, June 1, 2011 Polarized lepton-nucleon cross section… For high energy γ is small Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 14 Wednesday, June 1, 2011 Cross section asymmetries…. • Δσ|| = anti-parallel – parallel spin cross sections • Δσperp= lepton-nucleon spins orthogonal • Instead of measuring cross sections, it is prudent to measure the differences: Asymmetries in which many measurement imperfections might cancel: which are related to virtual photon-proton asymmetries A1,A2: Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 15 Wednesday, June 1, 2011 d, η, ξ are kinematic factors D = Depolarization factor: how much polarization of the incoming electron is taken by the virtual photon, calculable in QED Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 16 Wednesday, June 1, 2011 • A|| could be written down in terms of spin structure function g1, and A2 along with kinematic factors: Where A1 is bounded by 1, and A2 by sqrt(R=σΤ/σL), when terms related A2 can be neglected, and γ is small, • Where: and Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 17 Wednesday, June 1, 2011 Relation to spin structure function g1 Quark and anR-quark with spin orientaon along and against the proton spin. Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 18 Wednesday, June 1, 2011 Relation to spin structure function g1 Quark and anR-quark with spin orientaon along and against the proton spin. • In QCD quarks interact with each other through gluons, which gives rise to a weak Q2 dependence of structure functions Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 18 Wednesday, June 1, 2011 Relation to spin structure function g1 Quark and anR-quark with spin orientaon along and against the proton spin. • In QCD quarks interact with each other through gluons, which gives rise to a weak Q2 dependence of structure functions Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 18 Wednesday, June 1, 2011 Relation to spin structure function g1 Quark and anR-quark with spin orientaon along and against the proton spin. • In QCD quarks interact with each other through gluons, which gives rise to a weak Q2 dependence of structure functions • At any given Q2 the spin structure function is related to polarized quark & gluon distributions by coefficients Cq and Cg Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 18 Wednesday, June 1, 2011 Composition & Q2 or t dependence of Structure Functions In this equaon: t = ln(Q2/Λ2) αS = strong interac+on constant S & NS stand for flavor singlet & flavor non-singlet Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 19 Wednesday, June 1, 2011 Composition & Q2 or t dependence of Structure Functions In this equaon: t = ln(Q2/Λ2) αS = strong interac+on constant S & NS stand for flavor singlet & flavor non-singlet Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 19 Wednesday, June 1, 2011 Composition & Q2 or t dependence of Structure Functions In this equaon: t = ln(Q2/Λ2) αS = strong interac+on constant S & NS stand for flavor singlet & flavor non-singlet Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 19 Wednesday, June 1, 2011 Composition & Q2 or t dependence of Structure Functions Singlet quark distribuRon And its t dependence (Singlet) Gluon distribuRon And its t dependence Non-Singlet quark distribuRon And its t dependence Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 20 Wednesday, June 1, 2011 At leading order g1 decouples with ΔG Beyond the leading order coefficient & splitting functions are not uniquely defined: There are some favorite schemes of theorists, each with distinct calculation advantage.