Singular Charge Density at the Center of the Pion?

Transcription

1 Singular Charge Density at the Center of the Pion? Gerald A. Miller University of Washington arxive: INT program Jlab-12 Fall 09

2 Why study the pion? Nearly massless excitation of QCD vacuum Spontaneous symmetry breaking Carrier of longest ranged strong force Jlab experiments to measure form factor!! Lattice QCD calculations

3 Outline 1. How to interpret form factor? 2. Use of infinite momentum Drell-Yan frame to extract model independent information 3. Interpretation of existing form factor data 4. Central charge density may be singularpqcd predicts singular charge densityneed more experiments, higher Q 2 to find out

4 Pion form factor Pion to pion matrix element of electromagnetic current operator What does F π measure? One interpretation Fourier transform of charge density

5 Fourier transform of charge density Interpretation is not right Correct non-relativistic: wave function invariant under Galilean transformation Relativistic : wave function is frame dependent, initial and final states differ Final wave - function is boosted from initial Pion is moving at relativistic speed before, after or both

6 Light cone coordinates/infinite momentum frame perp

7 Relativistic formalismkinematic subgroup of Poincare Lorentz transformation transverse velocity v k - such that k 2 not changed Just like non-relativistic with k + as mass, take momentum transfer in perp direction, then density is 2 Dimensional Fourier Trans

8 Absent in a Drell-Yan IMF From Marc Vanderhaeghen

9 π π q= q transverse charge densitycoordinate space derviation

10 JLab Fπ collaboration

11 Monopole form factor Monopole not realistic?

12 Perturbative QCD Also singular

13 3D FT of Fπ Non-relativistic & Dirac

14 What about f π (weak decay constant)? Chiral quark models e.g. NJL Evaluate triangle graph to get form factor Renormalization Predict monopole form factor Singular transverse charge density structure functions ok f π is reproduced, not infinite Broniowksi, Arriola, Golec-Biernat arxive:

15 Relativistic light front constituent quark models Coester, Miller Frederico, Hwang PRD64, Cut off triangle graph with wave function Form factor falls faster than monopole Fits available data

16 Singular vs non-singular monopole rel c q m

17 Summary Monopole, pqcd, many quark models predict singular transverse density Singular densities known in atomic physics Maybe singularity happens here Relativistic constituent quark models predict non-singular Need experiments to find out,

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19 Nucleon Transverse charge density BBBA Kelly Negative

20 Negative F 1 means central density negative GeV 2

21 Neutron Interpretation needed ρ Why? What? How? Combine elastic and deep inelastic scattering information. Generalized parton distribution b

22 relate:high x, high Q 2, low b

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24 Input distribution x Neutron- d v dominates at high x (b=0)????

25 Proton- connect x and b x<0.1 high x-low b x>.5

26 Neutron charge distribution vs x x<0.1 u x>0.5 d high x: d dominates at small b

27 d dominates at high x, low b Total neutron charge distribution x<0.23 total x>0.23

28 Neutron ρ(b,x) x=0.1 x=0.3 x=0.5 d dominates at high x, low b

29 Center of the Neutron Burkardt

30 width in B rel ~independent of x

31 Summary Gpd s imply that charge density at the center of neutron is dominated by d quarks.

32 Expectations- Jlab Pre Jlab G E /G M QF 2 /F 1 QF 2 /F 1 G E /G M Q 2 Q 2 Proton

33 Impulse Approximation 1995 g Frank, Jennings, Miller 95 Correct wave function includes PQCD, Feynman mechanisms

34 QCD the fundamental theory of the strong interaction QCD Lagrangian: quarks and gluons QCD works at high energy/momentum transfer but difficult to evaluate at low energies when the interaction is strong. HOW does QCD work?.

35 Ratio of Pauli to Dirac Form Factors 1995 theory, data 2000

36 Why study the nucleon? We are made of neutrons & protons those made of quarks, gluons, QCD UNDERSTAND CONFINEMENT How does the nucleon stick together when struck by photon? Where is charge and magnetization density located? Origin of angular momentum? What is the shape of the proton?

37 How to tell how big something is? Look Proton P+q e Non rel form factor -old q e Proton P Structure factor

38 Electron scattering from a nucleon j =<e g e > J =<p p> Nucleon vertex: i p, p' F ( Q2 ) F ( Q2 g ) 1 2M 2 Dirac Pauli Deep inelastic scattering 1990 Nobel Prize Cross section for scattering from a point-like object G E, G M Sachs Form factors describing nucleon shape/structure 1961 Nobel Prize

39 Relativistic Model Explanation

40 Model exists lower components of Dirac spinor orbital angular momentum shape of proton?? Wigner Eckart no quadrupole moment spin dependent densities SDD non-relativistic example

41 Spin Crisis Proton Spin (total angular momentum) is ~/2 Experiments show quarks carry only 30 % three ideasu,d quarks surrounded by s s gluons carry angular momentum quarks carry orbital angular momentum

42 s r

43 Shapes of the proton three vectors n, K, S MODEL, HOW TO MEASURE?

44 Shapes of the proton Relate spin dependent density SDD to experiment

45 Field theoretic SDD Probability to have momentum K, and spin direction n Matrix elements depend on three vectors n, K, S

46 Transverse Momentum Distributions TMDs x=k + /P + + =t+z=0 Mulders & Tangerman 96 z + c t=0; ξ + =0 Light cone correlation function

47 Relate SDD to TMD SDD depend on K x, K y, K z correlation function & equal time TMD depend on x, K x, K y & + =0 =t+z correlation function Integrate SDD over K z! t=0,z=0 Integrate TMD over x! - =0, t=0,z=0 Result :non-spherical nature of proton related to h 1T

48 Transverse spin-dependent densities n n S

49 Cross section has term proportional to cos 3 B er Mulders 98 Measure :e, p e, X S T e e g

50 Summary of SDD SDD are closely related to TMD s If h 1T? is not 0, proton is not round. Experiment can show proton ain t round. The Proton

51 Spin density operator: d(r-r p ). n Canted ferromagnetic structure of UNiGe high magnetic fields PRB65, Neutron magnetic scattering Neutron, B, crystal

52 Neutron Interpretation b ? - at short distance? Central quark density reduced by orbital ang. momentum OAM?

53 Relate SDD to TMD SDD depend on K x, K y, K z correlation function & equal time TMD depend on x, K x, K y & + =0 =t+z correlation function Integrate SDD over K z --> t=0,z=0 Integrate TMD over x! =0, t=0,z=0 Result :non-spherical nature of proton related to h 1T?

54 proton e.m. form factor : status green : Rosenbluth data (SLAC, JLab) Pun05 Gay02 JLab/HallA recoil pol. data new MAMI/A1 data up to Q GeV 2 new JLab/HallC recoil pol. exp. (spring 2008) : extension up to Q GeV 2

55 neutron e.m. form factor : status MAMI JLab/HallC JLab/CLAS JLab/HallA new MIT-Bates (BLAST) data for both p and n at low Q 2 new JLab/HallA double pol. exp. (spring 07) : extension up to Q GeV 2 completed

56 n p - TTM 4 r 2 n (r) One gluon exchange also gives positive central charge density Need model independent way to answer

57 Transverse Momentum Distributions TMDs x=k + /P + Mulders & Tangerman 96 i+ g 5» g + i» g 0 i