1. Adnan Bashir, UMSNH, Mexico
QCD: A BRIDGE BETWEEN
PARTONS & HADRONS
Adnan Bashir, UMSNH, Mexico
November 2017
CINVESTAV

2. Hadron Physics & QCD Part 3: From QCD back to Hadrons:
Rutherford scattering
Nuclear structure
Form factors, radii, charge density
Electron proton scattering
Pion form factor
Proton form factor
Shrinking proton
The quark mass generation
Pseudoscalar transition form factors
Nucleon form factors to its excited states

3. Introduction The very first incidence of seeing strongly interacting
bound state was the Rutherford experiment.

4. Nuclear Sructure
An electron is a neater probe of the nuclear structure
than the alpha particles used by Rutherford.
1953 Stanford and Michigan had electron beams running at energies up to 190 MeV. Lots of new experimental data became available.
1961 Robert Hofstadter won Nobel Prize for ‘his pioneering studies of electron scattering in atomic nuclei and for his thereby achieved discoveries concerning the structure of the nucleons’.

5. Nuclear Structure Robert Hofstadter published his important work in:
Hofstadter, R., et al., Phys. Rev (1953).

6. Nuclear Structure
Form factor:

7. Nuclear Structure
Hofstadter, R., et al., Phys. Rev (1953).

8. One can use these data to extract the radius and charge density.
Nuclear Structure
ATOMIC DATA AND NUCLEAR DATA TABLES 36, (1987)
One can use these data to extract
the radius and charge density.

9. Charge Density

10. Electron Proton Scattering
In ep→ ep scattering the nature of the interaction of the virtual photon with the proton depends strongly on wavelength of the probing photon.
At very low electron energies
λ >> rp
the scattering is equivalent to
that from a point-like object:
At low electron energies
λ ~ rp
the scattering is equivalent to that from an extended charged object:

11. Electron Proton Scattering
At high electron energies
λ < rp
the wavelength is sufficiently short to resolve sub-structure. Scattering takes place from
dressed quarks.
At very high electron energies
λ << rp
the proton appears to be a sea of quarks and gluons.

12. Electron Proton Scattering
Point electron scattering from point particle:

13. Pion and Proton Form Factors
Simplest Strongly Interacting Bound States
Pion
1 form factor
Spinless particle
Proton
2 form facors
Spin ½ particle

14. QCD Equations of motion
Form Factor of a Pion
QCD Equations of motion
L. Chang, I.C. Cloët, C.D. Roberts, S.M. Schmidt, P.C. Tanday, Phys. Rev. Lett. 111, (2013)

15. Form Factor of a Pion

16. Form Factor of a Pion The most important achievements of last 7 years
Page 22: Pion electromagnetic form factor through SDES
Appears that JLab12 is within reach of first verification of a QCD hard-scattering formula

17. Proton Form Factors
F1(q2) and F2(q2) are called the nucleon form factors, or the
Dirac and Pauli form factors of the nucleon.
The point like nature of the nucleon is recovered when:
In that case, we recover the usual Feynman rule:

18. Dirac and Pauli Proton Form Factors
Thus if we us the following current
And repeat the calculation of the eP  eP scattring cross-
section, we arrive at the following Rosenbluth formula:

19. Sachs Proton Form Factors
Use the notation:
Define Sachs form factors of the nucleon as:

20. Sachs Proton Form Factors
This allows us to write:
And hence:

21. Sachs Proton Form Factors
Thus the Rosenbluth formula is:

22. Nucleon Magnetic Moments
The electric current for proton could be written as:
The following normalization
is natural:
recalling that for the electron:
 helps us fix the normalization for F2.

23. Nucleon Magnetic Moments
How do we interpret ?
Magnetic moment
Spin 0
Magnetic moment

24. Nucleon Magnetic Moments
Thus the magnetic moments for proton and neutron are
defined for q2  0:
The measured values are:

25. Proton Form Factors Recall Sachs form factors: Therefore:
GE(q2) and GM(q2) are respectively called the electric and
magnetic form factors of the nucleon.

26. Sachs Form Factors
Rosenbluth
formula:
Notation
simplification:

27. The Charge Radius The charge radii can be defined as:
J. C. Bernauer et al., PRL 105,
(2010).

28. The Lamb Shift

29. The Proton Radius

31. The Proton Radius
One goal is to repeat the scattering experiments, but
instead of shooting electrons at protons they'll shoot
muons at protons.
This project, the Muon Scattering Experiment, or MUSE,
is set to take place at the Paul Scherrer Institute in
Switzerland.
The facilities there will allow researchers to simultaneously
measure electron- and muon-scattering in one experiment.

32. The Proton Radius
 arXiv:

33. Hadron Structure Recoil Rutherford Electron Correction Scattering Spin
Modern Experiments
Large virtuality
Spin ½ Targets

34. The Quark Propagator The quark propagator:
Infrared enhancement of quark mass is a strictly non
peturbative effect. Reflection positivity  confinement!

35. Meson to * Transition Form Factor

36. Pion to * Transition Form Factor
The transition form factor:
K. Raya, L. Chang, AB, J.J. Cobos-Martinez, L.X. Gutiérrez-Guerrero, 
C.D. Roberts, P.C. Tandy, Phys. Rev. D (2016)

37. Pion to * Transition Form Factor
The transition form factor:
Belle II will have 40 times more luminosity.
Vladimir Savinov:
5th Workshop of the APS
Topical Group on Hadronic
Physics, 2013.
Precise measurements at large Q2 will provide a stringent
constraint on the pattern of chiral symmetry breaking.
K. Raya, M. Ding, AB, L. Chang, C.D. Roberts, Phys. Rev.D95 no.7, (2017)

38. c, b to * Transition Form Factor

39. , ’ to * Transition Form Factor

40. , ’ to * Transition Form Factor

41. N to *(1535) - Transition Form factors

42. N to N*(1535) - Transition Form factors

43. Conclusions The journey from a plethora of hadrons to the their
classification as isospin multiplets with a certain hyper-charge was fascinating.
Then emerged the quark model and the discovery of quarks.
Understanding the interactions between quarks led us to
QCD and the running of strong coupling.
It is substantially enhanced in the infrared and gives rise to confinement and chiral symmetry breaking.
Using QCD to predict hadronic observables is a challenge we must take up or the understanding of the Standard Model will be incomplete.