Naonal Nuclear Physics Summer School 2012 Spin Structure of the ? Zein-Eddine Meziani Temple University Philadelphia 2012 National Nuclear Physics Summer School St. John’s College, Santa Fe, NM July 9 – July 20, 2012

http://www.int.washington.edu/NNPSS/2012/!

Lecture topics:

• QCD and heavy ion physics • structure and spin physics • Nuclear structure and reactions • Nuclear astrophysics • Fundamental symmetries and

Seminar topics:

• Lattice QCD • Cold atoms • NIF physics • Medical applications of nuclear science • stars

Contact: [email protected] Application deadline: April 30, 2012

Lecturers:

• T. Hemmick (SUNY), B. Mueller (Duke) • Z.-E. Meziani (Temple U.), J. Jalilian-Marian (Baruch) • H. Schatz (MSU), R. Furnstahl (Ohio State) • C. Horowitz (Indiana U.), T. Strohmayer (NASA) • G. Fuller (UCSD), B. Holstein (UMass)

Seminar speakers:

• S. Beane (U. NH), P. Petreczky (BNL) • M. Zwierlein (MIT) • A. Hayes (LANL) • S. Lapi (Washington U.) • S. Reddy (INT)

Organizers: Joe Carlson, Vincenzo Cirigliano, Ivan Vitev (Chair)

Sponsors: National Science Foundation, Los Alamos National Laboratory US Department of Energy's Institute for Nuclear Theory

7/16/12 NNPSS 2012, Santa Fe, NM Coutesy of CERN Courier

! Outline  Lecture 1 ➥ Introducon to scaering and spin ➥ Spin of the from the basic constuents  Lecture 2: ➥ Spin at low energy scale, moments polarizabilies ➥ Spin at large x, moments, - correlaons  Lecture 3: ➥ Nucleon Tomography and Orbital Angular Momentum ➪ Generalized parton Distribuons ➪ Transverse momentum Distribuons

7/16/12 NNPSS 2012, Santa Fe, NM 7/16/12 NNPSS 2012, Santa Fe, NM Of fundamental importance in science: The structure of matter at all distances

Cell +DNA Our Galaxy

The focus of these lectures is the nucleon, a system made out of strongly interacng parcles, and , and its spin

7/16/12 NNPSS 2012, Santa Fe, NM Spin in everyday Life

Proton spins are used to image the structure and function of the human body using the technique of Magnetic Resonance Imaging (MRI)

Paul C. Sir Peter Lauterbur Mansfield Nobel Prize Medicine 2003:

“for their discoveries concerning Magnetic Resonance Imaging"

7/16/12 NNPSS 2012, Santa Fe, NM Historical Perspective

 Spin an “intrinsic property” emerges during the development of quantum mechanics;  Stern-Gerlach experiment 1922

 Spin (magnetic moment) hinted that the nucleon is not point like  Oo Stern (1933) measured the magnec moment of the proton to be

κp =1.7928

 Quantum Statistics: According to Pauli (1940) “particles of half integer spin obey Fermi-Dirac statistics and those of integer spin obey Bose-Einstein statistics.

Nature: hp://www.nature.com/milestones/milespin/index.html 7/16/12 NNPSS 2012, Santa Fe, NM outset — hence, quantum mechanics MILESTONE 13 must be incomplete. A decisive step came in 1964 when John Bell, building on the Super Bohm–Aharonov formulation in spin variables, showed that quantum mechanics makes predictions that symmetry contradict the local-realistic world outset — hence, quantum mechanics MILESTONEview of13 Einstein and do require must be incomplete. action at a distance of some sort. The way that spin is woven into the A decisive step came in 1964 Bell’s theorem has been put to the very fabric of the Universe is writ large in the standard model of when John Bell, building on the test many times since, and although Superthere is, as yet, no single experiment . In this model, Bohm–Aharonov formulation in that closes all possible loopholes, the which took shape in the 1970s and spin variables, showed that quantum weight of evidence does still favour can explain the results of all mechanics makes predictions that symmetry quantum mechanics. particle-physics experiments to contradict the local-realistic world Andreas Trabesinger, Senior Editor, date, matter (and antimatter) is view of Einstein and do require Nature Physics made of three families of quarks action at a distance of some sort. The way that spin is woven into the and leptons, which are all fermions, very fabric of the ORIGINALUniverse RESEARCH is writ PAPERS Einstein, A., The ATLAS experiment under construction at the Large Hadron Bell’s theorem has been put to the Podolsky, B. & Rosen, N. Can quantum- whereas the electromagnetic, strong Collider. Image courtesy of CERN. test many times since, and although large in the standardmechanical model description of of physical reality be and weak forces that act on these particles are particle physics. Inconsidered this model, complete? Phys. Rev. 47, 777–780 Spin Milestones Timeline According to aMILESTONES recent TIMELINENature Article. there is, as yet, no single experiment (1935) | Bohm, D. Quantum Theory Ch. XXII carried by other particles, such as photons and 1896 Zeeman effect (1) that closes all possible loopholes, the which took shape(Prentice-Hall, in the 1970s Englewood and Cliffs, New Jersey, gluons, which are all bosons. not change when bosons are replaced by weight of evidence does still favour can explain the results1951) | Bohm, of all D. & Aharonov, Y. Discussion of Despite its success, the standard model is 1922fermions, andStern–Gerlach fermions experiment are (2) replaced by experimental proof for the paradox of Einstein, 1925 The spinning (3) quantum mechanics. particle-physics experimentsRosen, and Podolsky. to Phys. Rev. 108, 1070–1076 unsatisfactory for a number of reasons. First, bosons. Andreas Trabesinger, Senior Editor, date, matter (and(1957) antimatter) | Bell, J. S. On is the Einstein Podolsky Rosen although the electromagnetic and weak forces 1928AlthoughDirac itequation is difficult (4) to explain paradox. Physics 1, 195–200 (1964) Nature Physics have been unified into a single force, a ‘grand supersymmetryQuantum magnetismthrough (5) analogies to classical made of three familiesFURTHER of REA quarksDING Bell, J. S. Bertlmann’s socks and leptons, whichand are the nature all fermions, of reality.J. Phys. 42, 41–62 (1981) | unified theory’ that brings the strong interaction 1932physics, itsIsospin consequences (6) are dramatic — it ORIGINAL RESEARCH PAPERS Einstein, A., Sauer, T. An Einstein manuscript on the EPR The ATLAS experiment under construction at the Large Hadron into the fold remains elusive. Second, the origins 1940predicts thatSpin–statistics every connection fundamental (7) particle has a Podolsky, B. & Rosen, N. Can quantum- whereas the electromagnetic,paradox for spin observables. strongStud. Hist. Philos. Collider. Image courtesy of CERN. mechanical description of physical reality be and weak forces thatMod. Phys. act 38 on, 879–887 these (2007) particles are of mass are not fully understood. Third, gravity is 1946superpartnerNuclear with magnetic half resonance a unit (8) of spin less. The considered complete? Phys. Rev. 47, 777–780 not included. electron, for instance, has a spin of a half, so its carried by other particles, such as photons and 1950s Development of magnetic devices (9) (1935) | Bohm, D. Quantum Theory Ch. XXII Moreover, there are other, less obvious superpartner (which is known as a selectron) has (Prentice-Hall, Englewood Cliffs, New Jersey, gluons, which are all bosons. not change when bosons are replaced by 1950–1951 NMR for chemical analysis (10) 1951) | Bohm, D. & Aharonov, Y. Discussion of problems with the standard model. The two zero spin. This means that the superpartner of a Despite its success, the standard model is fermions, and fermions are replaced by 1951 Einstein–Podolsky–Rosen argument in spin variables (11) experimental proof for the paradox of Einstein, natural mass scales in nature are zero and the boson is always a fermion and vice versa. unsatisfactory for a number of reasons. First, bosons. 1964 Kondo effect (12) Rosen, and Podolsky. Phys. Rev. 108, 1070–1076 The ideas and methods developed Planck mass, ~ 1019 GeV c−2. Neither photons nor Supersymmetry also plays a central role in (1957) | Bell, J. S. On the Einstein Podolsky Rosen although the electromagnetic and weak forces Although it is difficult to explain by Kondo and his fellow theorists gluons (which carry the electromagnetic and 1971theories thatSupersymmetry attempt (13) to unify the forces in the paradox. Physics 1, 195–200 (1964) have been unifiedturned into out a single to be relevant force, a to ‘grand a wide supersymmetry through analogies to classical FURTHER READING Bell, J. S. Bertlmann’s socks strong forces, respectively) have mass, but theW 1972standard modelSuperfluid helium-3with (14)gravity by treating unified theory’ thatrange brings of problems the strong that involve interaction strong physics, its consequences are dramatic — it and the nature of reality.J. Phys. 42, 41–62 (1981) | and Z bosons that are responsible for the weak 1973fundamentalMagnetic particles resonance imaging as vibrating (15) strings or Sauer, T. An Einstein manuscript on the EPR interactions between particles. As a into the fold remains elusive. Second, the origins predicts that every fundamental particle−2 has a 1975–1976 NMR for protein structure determination (16) paradox for spin observables.Stud. Hist. Philos. force have masses of about 90 GeV c . Where membranes in 10-dimensional or 11-dimensional of mass are not result,fully understood. the ‘Kondo effect’ Third, — gravity which, in is superpartner with half a unit of spin less. The Mod. Phys. 38, 879–887 (2007) does this mass scale come from? 1978spacetimes.Dilute In magnetic these semiconductors theories (17) the gravitational force not included. truth, comprises a range of phenomena electron, for instance, has a spin of a half, so its to do with collective behaviour arising This ‘hierarchy problem’ can be solved by fine- 1988is carried byGiant a magnetoresistance spin-two boson(18) called the graviton. Moreover, there are other, less obvious superpartner (which is known as a selectron) has from localized magnetic impurities tuning the model so that various quantum 1990Searching Functionalfor supersymmetric MRI (19) particles will be a problems with the standard model. The two zero spin. This means that the superpartner of a — is an active research topic today and fluctuations cancel out, although many physicists priority whenProposal the for spin Large field-effect Hadron transistor (20) Collider comes into natural mass scales in nature are zero and the boson is always a fermion and vice versa. one that still throws up surprises. are uncomfortable with this solution because 1991operation Magneticat CERN, resonance the force European microscopy (21) particle-physics The ideas and methods developed Planck mass, ~ 1019 GeV c−2. Neither photons nor someSupersymmetry parameters must also be plays fine-tuned a central to betterrole in laboratory near Geneva, in 2008. by Kondo and his fellow theorists Liesbeth Venema, Senior Editor,Nature 1996 Mesoscopic tunnelling of magnetization (22) gluons (which carry the electromagnetic and theoriesthan 1 part that in attempt 1015. However, to unify a form the forces of symmetry in the Peter Rodgers, Chief Editor, turned out to be relevant to a wide 7/16/12 NNPSS 2012, Santa Fe, NM 1997 Semiconductor spintronics (23) Nature Nanotechnology strong forces, respectively) have mass, but theW standardbetween modelfermions with and gravity bosons by called treating Zoom-zoom | Dreamstime.com range of problems that involve strong and Z bosons thatORIGINAL are responsible RESEARCH PAPERS for the Kondo, weak J. fundamentalsupersymmetry particles offers a as much vibrating more stringselegant or interactions between particles. As a ©!2008!Nature Publishing Group force have massesResistance of about minimum 90 GeV in dilute c−2 magnetic. Where alloys. membranessolution because in 10-dimensional the quantum fluctuations or 11-dimensional ORIGINAL RESEARCH PAPERS Golfand, Y. A. & Likhtman, E. P. result, the ‘Kondo effect’ — which, in Prog. Theor. Phys. 32, 37–49 (1964) | Anderson, Extension of the algebra of Poincaré group generators and viola- does this mass scaleP. W. comeA poor man’s from? derivation of scaling laws spacetimes.caused by bosons In these are theories naturally the cancelled gravitational force tion of P invariance. JETP Lett. 13, 323–326 (1971) | Neveu, A. & truth, comprises a range of phenomena This ‘hierarchyfor problem’ the Kondo problem. can be J. Phys. solved C 3, 2346–2441 by fine- isout carried by those by acaused spin-two by fermions boson called and the graviton. Schwarz, J. H. Factorizable dual model of pions. Nucl. Phys. B 31, to do with collective behaviour arising (1970) | Goldhaber-Gordon, D.et al. Kondo vice versa. 86–112 (1971) | Ramond, P. Dual theory for free fermions. Phys. from localized magnetic impurities tuning the modeleffect so that in a single-electron various quantum transistor. Nature Searching for supersymmetric particles will be a Rev. D 3, 2415–2418 (1971) | Wess, J. & Zumino, B. Supergauge fluctuations cancel391 out,, 156–159 although (1998) many physicists prioritySymmetry when playsthe Large a central Hadron role Colliderin physics. comes The into transformations in four dimensions. Nucl. Phys. B 70, 39–50 (1974) | — is an active research topic today and FURTHER READING Wilson, K. G. The fact that the laws of physics are, for instance, Wess, J. & Zumino, B. A Lagrangian model invariant under super- are uncomfortable with this solution because operation at CERN, the European particle-physics one that still throws up surprises. renormalization group: critical phenomena and symmetric in time (that is, they do not change gauge transformations. Phys. Lett. B 49, 52–54 (1974) some parametersthe must Kondo be problem. fine-tuned Rev. Mod. Phys. to 47 better, 773–840 laboratory near Geneva, in 2008. FURTHER READING Dimopoulos, S., Raby, S. & Wilczek, F. Liesbeth Venema, Senior Editor,Nature (1975) | Tsvelik, A. M. & Wiegmann, P. B. Exact with time) leads to the conservation of energy. Supersymmetry and the scale of unification.Phys. Rev. D 24, than 1 part in 1015. However, a form of symmetry Peter Rodgers, Chief Editor, results in the theory of magnetic alloys. Adv. These laws are also symmetric with respect to 1681–1683 (1981) | Almadi, U., de Boar, W. & Furstenau, H. Phys. 32, 453–713 (1983) | Kouwenhoven, L. & Nature Nanotechnology between fermions and bosons called space, rotation and relative motion. Initially Comparison of grand unified theories with electroweak and strong supersymmetry offersGlazman, a L.much Revival moreof the Kondo elegant effect. coupling constants measured at LEP.Phys. Lett. B 260, 447–455 ORIGINAL RESEARCH PAPERS Kondo, J. Phys. World 14(1), 33–38 (2001) explored in the early 1970s, supersymmetry is a (1991) | Greene, B.The Elegant Universe (Vintage, London, 2000) | Resistance minimum in dilute magnetic alloys. ORIGINAL RESEARCH PAPERS Golfand, Y. A. & Likhtman, E. P. solution because the quantum fluctuations less obvious kind of symmetry, which, if it exists in Kane, G. & Shifman, M. (eds)The Supersymmetric World: The Prog. Theor. Phys. 32, 37–49 (1964) | Anderson, Extension of the algebra of Poincaré group generators and viola- Beginnings of the Theory (World Scientific, Singapore, 2000) P. W. A poor man’s derivation of scaling laws caused by bosons are naturally cancelled nature,tion of P wouldinvariance. mean JETP Lett. that 13 ,the 323–326 laws (1971) of physics | Neveu, A. do & for the Kondo problem. J. Phys. C 3, 2346–2441 out by those caused by fermions and Schwarz, J. H. Factorizable dual model of pions. Nucl. Phys. B 31, (1970) | Goldhaber-Gordon, D.et al. Kondo vice versa. 86–112 (1971) | Ramond, P. Dual theory for free fermions. Phys. effect in a single-electron transistor. Nature Rev. D 3, 2415–2418 (1971) | Wess, J. & Zumino, B. Supergauge SPIN S13 391, 156–159 (1998) Symmetry playsNATURE a central MILES roleTON EinS |physics. The transformations in four dimensions. Nucl. Phys. B 70, 39–50 (1974) | MARCH 2008 | FURTHER READING Wilson, K. G. The fact that the laws of physics are, for instance, Wess, J. & Zumino, B. A Lagrangian model invariant under super- renormalization group: critical phenomena and symmetric in time (that is, they do not change gauge transformations. Phys. Lett. B 49, 52–54 (1974) the Kondo problem. Rev. Mod. Phys.47 , 773–840 FURTHER READING Dimopoulos, S., Raby, S. & Wilczek, F. (1975) | Tsvelik, A. M. & Wiegmann, P. B. Exact with time) leads to the conservation of energy. Supersymmetry and the scale of unification.Phys. Rev. D 24, results in the theory of magnetic alloys. Adv. These laws are also symmetric with respect to 1681–1683 (1981) | Almadi, U., de Boar, W. & Furstenau, H. Phys. 32, 453–713 (1983) | Kouwenhoven, L. & Comparison of grand unified theories with electroweak and strong Glazman, L. Revival of the Kondo effect. space, rotation and relative motion. Initially coupling constants measured at LEP.Phys. Lett. B 260, 447–455 Phys. World 14(1), 33–38 (2001) explored in the early 1970s, supersymmetry is a (1991) | Greene, B.The Elegant Universe (Vintage, London, 2000) | less obvious kind of symmetry, which, if it exists in Kane, G. & Shifman, M. (eds)The Supersymmetric World: The Beginnings of the Theory (World Scientific, Singapore, 2000) nature, would mean that the laws of physics do

NATURE MILESTONES | SPIN MARCH 2008 | S13 Nucleon Spin; Why should we / you care?

 Has been a laboratory for (QCD) the theory of strong interacons in the last 30 years ➥ Example: Test of the Bjorken Sum Rule, described by Feynman as one that would have a decisive influence on the future of high- energy physics

 The nucleon is a strongly interacng many body confined system

 Turns out to be an important window into QCD dynamics too

7/16/12 NNPSS 2012, Santa Fe, NM Force carriers (Fields) and maer constuents within the Standard Model

7/16/12 NNPSS 2012, Santa Fe, NM Nucleon Mass- Where does it come from?

 Naive expectaon ➥ quark masses (current quarks not constuent quarks) but not enough to generate the proton mass  Ji’s Decomposion of the proton mass X. Ji PRL 74 (1995) 1071 Trace 20% Gluon Anomaly Energy 29% Quark Quark Energy 17% Mass  Lace QCD: 34% Current quark mass Grows into a constuent quark mass

Gluon dynamics dominates The mass of QCD bound states 7/16/12 NNPSS 2012, Santa Fe, NM Quantum Chromodynamics (QCD)

7/16/12 NNPSS 2012, Santa Fe, NM Courtesy of J. W. Qiu The Science Problem in relaon to Nucleon Structure?

Quantum Chromodynamics (QCD) and confinement

What do we know? QCD works well in the perturbave (weak) regime Many experimental tests led to this conclusion

But Confinement in QCD is still a puzzle and among the 10 top problems in Physics! (Gross, Witten,.…) Strings 2000

Lace QCD, AdS/CFT correspondence…….?!

AdS/CFT: an de Sier/Conformal field theory

7/16/12 NNPSS 2012, Santa Fe, NM 7. What are the fundamental degrees of freedom of M-theory (the theory whose low-energy limit is eleven-dimensional supergravity and which subsumes the five consistent superstring theories) and does the theory describe Nature? Louise Dolan, University of North Carolina, Chapel Hill Annamaria Sinkovics, Spinoza Institute Billy & Linda Rose, San Antonio College

8. What is the resolution of the black hole information paradox? Tibra Ali, Department of Applied Mathematics and Theoretical Physics, Cambridge Samir Mathur, Ohio State University

9. What physics explains the enormous disparity between the gravitational scale and the typical mass scale of the elementary particles? Matt Strassler, Institute for Advanced Study, Princeton

10. Can we quantitatively understand quark and gluon confinement in Quantum Chromodynamics and the existence of a mass gap? Igor Klebanov, Princeton University Oyvind Tafjord, McGill University

These ten questions were presented by David Gross at the closing of the conference on Saturday July 15, 2000.7/16/12 NNPSS 2012, Santa Fe, NM Listen to Prof. Gross's presentation of the problems. See also:

CMI Millennium Prize Problems, the Clay Mathematics Institute The Mathematical Problems of David Hilbert, David E. Joyce David Hilbert, the MacTutor History of Mathematics archive Unanswered Questions in Physics, Queen's University, Belfast

Return to the Strings 2000 Home Page...

Last modified: Sat Mar 10 16:53:12 EST 2001 [email protected]

2 of 2 9/26/09 11:00 AM QCD: asymptoc freedom Gross,Wilczek, Politzer

Coupling grows weaker with increasing momentum transfer (shorter distances) 7/16/12 NNPSS 2012, Santa Fe, NM Resolution of the probe and scale of the theory tools Models

0 1 10 ∞ χPT Q2 OPE pQCD Lattice QCD

 χ PT: Chiral Perturbaon theory OPE : Operator Product expansion p-QCD : pertubave Quantum Chromodynamic Lace QCD

7/16/12 NNPSS 2012, Santa Fe, NM Nucleon Spin  In QCD- the Nucleon Spin is a window into a complex nucleon state 1 1 S(µ)= P, S Jˆz(µ) P, S = J (µ)+J (µ)= Σ(µ)+L (µ)+J (µ) ￿ | f | ￿ 2 ≡ q g 2 q g ￿f 1 S(µ)= µ 2 ⇒∞ 1  In a Quark Model S p S p = ,S= S p ≡￿ ↑ | | ↑￿ 2 i i 1 ￿ p = [u u d 2 u u d +perm.] | ↑￿ ￿18 ↑ ↓ ↑− ↑ ↑ ↓  Asymptoc Limit Ji 1 3Nf 1 1 16 1 Jq(µ ) Jg(µ ) →∞ ⇒ 2 16 + 3Nf ∼ 4 →∞ ⇒ 2 16 + 3Nf ∼ 4  Spin Structure? Role of partons’ intrinsic spin vs partons’ dynamical moon

7/16/12 NNPSS 2012, Santa Fe, NM Studying the structure of How?

 Rutherford tradion of scaering experiments

 Using a super high resoluon transmission electron (lepton) microscopes SLAC, CERN, DESY, Jefferson Lab

 Using hadronic probes RHIC

7/16/12 NNPSS 2012, Santa Fe, NM Experimental tools to invesgate Spin by Scaering

 Use of lepton or hadron beams to scaer on the nucleon ➥ Polarized beams of e-, e+, μ+, μ-, p  Use of proton and nuclei targets that are polarized Rutherford, ➥ 3 Targets in many cases are polarized p, D, NH3, ND3, He,) 1908, Chem. N.P.

 Electromagnec probe as a microscope: Compton scaering, real and virtual

➥ Exclusive, semi-inclusive or inclusive (elasc scaering, inelasc scaering)

￿￿￿￿ l l￿ ￿￿￿￿ l￿ l￿ l l X ￿￿￿￿

p p p ￿￿￿￿p￿ p p￿ Compton, 7/16/12 NNPSS 2012, Santa Fe, NM 1927, Phys. N.P. How to get Informaon about the nucleon structure in terms of the constuents, quarks and gluons? Proton Mass:  1.672 621 71(29) × 10−27 kg Elasc scaering 938.272 029(80) MeV/c2 ➥ Charge distribuon Electric Charge: 1.602 176 53(14) × 10−19 C ➥ Magnezaon distribuon Diameter: About 1.6×10−15 m Spin: 1/2  Quark Composition: Deep Inelasc Scaering (DIS) 1 down, 2 up ➥ Inclusive DIS: detect scaered lepton ➥ Semi-inclusive DIS: detect scaered lepton + one leading hadron (pion, kaon,..) ➪ Momentum distribuon among the different constuents ➪ Spin distribuon among the different constuents

7/16/12 NNPSS 2012, Santa Fe, NM Some Tools to Study Nucleon Structure and understand QCD Generalized Parton Distribuons Transverse Momentum Distribuons (GPDs) Since 1998 Inclusive (TMDs) Since 2002 Sum rules and polarizabilies Exclusive reacons Semi-Inclusive DIS

Elasc form factors Distribuons and Deep Virtual Compton Fragmentaon funcons Scaering QCD Deep Virtual Meson Producon Beyond the standard Electroweak Model/or a probe to Physics/probe hadronic systems

GPDs and TMDs in Nuclei Exclusive Semi-inclusive Inial and final medium effects

7/16/12 NNPSS 2012, Santa Fe, NM Rutherford scattering

NNPSS 2012, Santa Fe, NM 7/16/12 Finite size of proton

 Rutherford (elastic) scattering with Hofstadter

NNPSS 2012, Santa Fe, NM 7/16/12 Deep Inelastic Scattering

Friedman Kendall Taylor

Bjorken Scaling: Q2Infinity Feynman Parton Model

7/16/12 NNPSS 2012, Santa Fe, NM Feynman Inclusive lepton scaering The one photon exchange approximation   e = (E,k ) e '= (E',k ') W 2 = M 2 + 2Mν − Q2 θ 2 2 2 ⎛ θ ⎞  Q = −q = 4EE' sin ⎜ ⎟ q = (ν,q ) ⎝ 2⎠ Q2 x = 2Mν  W p = (M,0)

Leptonic tensor:

Hadronic Tensor:

7/16/12 NNPSS 2012, Santa Fe, NM Quantum Electrodynamics

Feynman diagrams Matrix element Fermi’s Golden Rule

Cross secon Transion probability

Example of inclusive electron scattering

7/16/12 NNPSS 2012, Santa Fe, NM Nucleus/nucleon response to electromagnec scaering

Nuclear Response funcon R(Q2,ν)

Giant Resonance

Δ N*

Q2 = 0 n 50 MeV 300 MeV Total photo-absorption Elasc Δ

N* Deep Inelasc Quasi “EMC” Nucleus Elasc Lepton scattering

Elasc Δ N* Deep Inelasc “QUARKS”

Q2 Proton x = Q2/2Mν Lepton scattering x = 1

7/16/12 NNPSS 2012, Santa Fe, NM Inclusive lepton scaering (connued)

 The symmetric part of the tensor is written in terms of two spin- 2 2 independent structure functions W1 (x,Q ) and W2(x,Q ):

 The antisymmetric part of the tensor is similarely written in terms of 2 2 two spin dependent structure functions G1 (x,Q ) and G2 (x,Q )

 This decomposition is possible because the form of the tensor is constrained to be invariant under parity and time reversal. It must be hermitian; and satisfy current conservation;

7/16/12 NNPSS 2012, Santa Fe, NM Inclusive electron scaering cross secons

Unpolarized beam and target

Longitudinally polarized target and longitudinally polarized beam

-

Transversely polarized target and longitudinally polarized beam

-

7/16/12 NNPSS 2012, Santa Fe, NM Virtual Photoabsorpon Cross Secon

Polarizaon vectors

Compton scaering amplitude

7/16/12 NNPSS 2012, Santa Fe, NM Virtual Photoabsorpon Cross Secon

The unpolarized differenal deep inelasc cross secon can be expressed in terms of the virtual photo-absorpon cross secons

7/16/12 NNPSS 2012, Santa Fe, NM Scaling of structure funcons

First measurements of the unpolarized cross secon show that at large Q2 the cross secon was independent of Q2

At large Q2 and large ν but finite x the structure funcons depend only one variable, x

The typical notaon found in many papers is to write the cross secons in terms of

7/16/12 NNPSS 2012, Santa Fe, NM SLAC

End Staon A

7/16/12 NNPSS 2012, Santa Fe, NM SLAC End Staon A Spectrometers

20 GeV maximum momentum spect. 8 GeV maximum momentum spect.

7/16/12 NNPSS 2012, Santa Fe, NM Scaling of F2 Structure Funcon

F2=

x = 0.25

Figure from: H. W. Kendall, Rev. Mod. Phys. 63 (1991) 597

1990 Nobel Prize J. I. Friedman, H. W. Kendall and R. E. Taylor

7/16/12 NNPSS 2012, Santa Fe, NM Modern era: HERA

Unpolarized beam and target Scaling violaon due to QCD evoluon

7/16/12 NNPSS 2012, Santa Fe, NM