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What Makes the Proton Spin?

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What Makes the Proton Spin? What makes the proton spin? Carl Gagliardi Texas A&M University Outline • Atomic structure • Particle spin • Proton structure •Proton spin Looking inside the atom Typical atomic radius: Few x 10-10 m • J. J. Thompson discovered the electron in 1897 – Found electrons are components of all atoms – Found the electron mass is <0.1% of atomic masses • Formulated the “plum pudding” model of the atom in 1904 – Light negative electrons embedded in a distributed massive positive charge What makes the proton spin? – Carl Gagliardi 2 Geiger-Marsden experiment (1909) • Shoot energetic alpha particles at a very thin gold foil • Measure the deflection of the alpha particles as they pass through • Expected: – Alpha particles will be deflected by only a few degrees What makes the proton spin? – Carl Gagliardi 3 Geiger-Marsden experiment (1909) • Shoot energetic alpha particles at a very thin gold foil • Measure the deflection of the alpha particles as they pass through • Found: – Most alpha particles are deflected by only a few degrees – Some alpha particles are deflected through large angles – A few alpha particles bounce backwards toward the source What makes the proton spin? – Carl Gagliardi 4 Ernest Rutherford’s explanation (1911) “It was quite the most incredible event that has ever happened to me in my life. It was almost as incredible as if you fired a 15-inch shell at a piece of tissue paper and it came back and hit you.” • The atom consists of a very dense, positively charged nucleus (radius of a few x 10-15 m) with the light electrons orbiting at typical radii of a few x 10-10 m What makes the proton spin? – Carl Gagliardi 5 Stern-Gerlach experiment (1922) • Pass a beam of Ag atoms through a non-uniform magnetic field • Each Ag atom possesses a magnetic moment • Classical expectation: – Atoms will spread into a broad spot What makes the proton spin? – Carl Gagliardi 6 Stern-Gerlach experiment (1922) • Experimental observation: – Atomic beam split into two separate components • The magnetic moment of the Ag atom can only point in two possible directions • Discovery of spin What makes the proton spin? – Carl Gagliardi 7 Pauli exclusion principle (1924) • Chemists had concluded that rows of the periodic table involve filling certain electron shells • Various rows take different “magic numbers” of electrons (2, 8, 8, 18, …) • Pauli looked for a way to systematize these empirical observations • “No two electrons can have all the same quantum numbers” – For vintage-1925 quantum mechanics, this gave 1, 4, 4, 9, ... • Assumed the existence of a new quantum number for electrons that could only take on 2 values in order to double all of these – Electron spin provided a natural explanation What makes the proton spin? – Carl Gagliardi 8 What is spin? • Fundamental property of particles in quantum mechanics • For the electron, the spin takes on one of two possible values: –+1/2 ћ or +5.27 x 10-35 J s –-1/2 ћ or -5.27 x 10-35 J s • Often imagine a spinning top – Handy model to gain intuition – Not correct in detail – The electron spin has no true analog in the classical world of objects moving under the influence of Newton’s Laws What makes the proton spin? – Carl Gagliardi 9 Importance of structure • Rutherford’s insight into the structure of the atom, together with Pauli’s “exclusion principle” which works the way it does because of electron spin, have given us a detailed understanding of the chemical properties of the elements What makes the proton spin? – Carl Gagliardi 10 What about the proton? • Charge (1.60 x 10-19 C) is exactly opposite that of the electron • Mass (1.67 x 10-27 kg) is 1836 times that of the electron • Spin (+ or -1/2 ћ or 5.27 x 10-35 J s) has exactly the same magnitude as the electron • Proton magnetic moment is “too big” by a factor of 2.79 – Must be a composite object (unlike the electron) • Radius ~ 0.85 x 10-15 m • What is the internal structure of the proton? What makes the proton spin? – Carl Gagliardi 11 High energy proton-antiproton scattering • Scattering extends to very large angles, similar to that found by Geiger and Marsden for alpha particles on gold • Proton also composed of much smaller constituents – Quarks and gluons – How are they combined together? What makes the proton spin? – Carl Gagliardi 12 The proton in the quark model u u d • The proton is made of quarks •2 up quarks (charge = +2/3) and 1 down quark (charge = -1/3) provide the proton charge and spin • Quarks are bound together by gluons (charge = 0) What makes the proton spin? – Carl Gagliardi 13 Proton wavefunction in the static quark model 2 1 1 (u ↑)(u ↑)(d ↓) − (u ↑)(u ↓)(d ↑) − (u ↓)(u ↑)(d ↑) + 9 18 18 2 1 1 (d ↓)(u ↑)(u ↑) − (d ↑)(u ↑)(u ↓) − (d ↑)(u ↓)(u ↑) + 9 18 18 2 1 1 (u ↑)(d ↓)(u ↑) − (u ↓)(d ↑)(u ↑) − (u ↑)(d ↑)(u ↓) 9 18 18 x (totally anti-symmetric color wavefunction) • If mu = md = mp/3. Then: • Proton magnetic moment: – Calculate +3 μN; find +2.793 μN • Neutron magnetic moment: – Calculate -2 μ ; find -1.913 μ If assume quarks are slightly N N heavier to allow for some binding • Ratio matches prediction to ~3% energy, can match the observed magnetic moments very well What makes the proton spin? – Carl Gagliardi 14 Too good to be true • The proton radius is ~0.85 fm • Heisenberg Uncertainty Principle implies quark motion must be relativistic • Relativistic quark model – Quarks are no longer restricted to s-wave states – Quark spin accounts for ~60% of the proton spin – Rest of proton spin comes from quark orbital angular momentum • No binding force in these calculations • Strong force (Quantum Chromodynamics) provides the quark binding – Gluons must also be present – Can also have additional quark-antiquark pairs What makes the proton spin? – Carl Gagliardi 15 Looking inside the proton e or μ γ* q or q p • “Deep-inelastic scattering” (DIS) of electrons and muons off protons has taught us a great deal about the internal structure of the proton • Interaction is electromagnetic Æ only quarks and anti-quarks participate directly • Obtain information about gluons indirectly What makes the proton spin? – Carl Gagliardi 16 Parton distribution functions • Probability of finding a quark or gluon inside the proton carrying a fraction x of the total momentum of the proton • Find more gluons than anything else • Gluons carry half the momentum of the proton What makes the proton spin? – Carl Gagliardi 17 Microscopic origin of the proton spin e or μ γ* q or q ⇒ ⇒ ⇒ p e or μ p sz = +1 Helicity + or - ? γ* q or q • Measure deep-inelastic scattering with polarized electrons or muons off polarized protons • Difference in cross section for like vs. unlike helicity beams provides information about spin orientations of the quarks inside the polarized proton What makes the proton spin? – Carl Gagliardi 18 Proton “spin crisis” EMC, PLB 206, 364 • First measurement over a broad kinematic region was performed by the European Muon Collaboration in the mid-’80s • Found that quarks contribute only (14 ± 9 ± 21)% of the proton spin What makes the proton spin? – Carl Gagliardi 19 Since EMC DSSV, PRD 80, 034030 • Many subsequent measurements • Results are well described by “global analyses” that find best-fit polarized parton distribution functions • Polarization of u+u and d+d quarks well determined – Individual u, u, d, d polarizations have much larger uncertainty •Only~30% of the proton spin arises from quarks and antiquarks What makes the proton spin? – Carl Gagliardi 20 What about gluon polarization? Three fits of equal quality: – ΔG = 0.13 ± 0.16 – ΔG ~ 0.006 Kinematic region of – ΔG = -0.20 ± 0.41 2 2 polarized measurements all at Q = 1 GeV Leader et al, PRD 75, 074027 What makes the proton spin? – Carl Gagliardi 21 What contributes to the proton spin? Consider a proton moving toward the right Proton spin ⇒ Helicity ⇒ ⇐ Δq(x) Δg(x) Polarized DIS: ~ 0.3 Poorly constrainedAnselmino et al, arXiv:0812.4366 1 1 Spin sum rule: 〈 S p 〉 = = ΔΣ + ΔG + 〈 L〉 z 2 2 Proton spin ⇑ Transversity RHIC spin program: δq(x) ⇑ ⇓ Exploring poorly determined components of the proton Very little data What makes the proton spin? – Carl Gagliardi 22 p + p collisions in perturbative QCD p Jet a, xa P fa a c d b Jet b, x P fb b pQCD hard scatter p σ = f (x ,Q 2 ) f (x ,Q 2 )σˆ ∑ a a b b a+b→c+d a and b can be quarks, gluons, Parton distribution functions or a combination What makes the proton spin? – Carl Gagliardi 23 Exploring gluon polarization at RHIC ++ +− σ − σ Δf a Δfb ALL = ++ +− ∝ aˆ LL σ + σ f a fb Δf: polarized parton distribution functions Partonic fractions in jet production at 200 GeV cosθ ∗ For most RHIC kinematics, gg and qg dominate, making ALL sensitive to gluon polarization. 0 10 20 30 pT(GeV) What makes the proton spin? – Carl Gagliardi 24 Separating quark and anti-quark polarizations u + d → W + → e+ + ν u + d → W − → e− + ν • Weak interaction process – Only left-handed quarks – Only right-handed anti-quarks • Perfect spin separation Measure parity violating single helicity asymmetry AL (Helicity flip in one beam while averaging over the other) + W − W AL ∝−Δd(x1)u (x2) + Δu (x1)d(x2) AL ∝−Δu(x1)d (x2) +Δd (x1)u(x2) What makes the proton spin? – Carl Gagliardi 25 RHIC: the world’s first (and only!) polarized hadron collider Absolute Polarimeter (H↑ jet) RHIC pC Polarimeters PHOBOS BRAHMS Siberian Snakes Siberian Snakes PHENIX STAR Spin Rotators Spin flipper (longitudinal polarization) - Spin Rotators Pol.
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