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

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

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

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’.

Nuclear Structure Robert Hofstadter published his important work in: Hofstadter, R., et al., Phys. Rev. 92 978 (1953).

Nuclear Structure Form factor:

Nuclear Structure Hofstadter, R., et al., Phys. Rev. 92 978 (1953).

One can use these data to extract the radius and charge density. Nuclear Structure ATOMIC DATA AND NUCLEAR DATA TABLES 36,495536 (1987) One can use these data to extract the radius and charge density.

Charge Density

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:

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.

Electron Proton Scattering Point electron scattering from point particle:

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

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, 14 141802 (2013)

Form Factor of a Pion

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

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:

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:

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

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

Sachs Proton Form Factors Thus the Rosenbluth formula is:

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.

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

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

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.

Sachs Form Factors Rosenbluth formula: Notation simplification:

The Charge Radius The charge radii can be defined as: J. C. Bernauer et al., PRL 105, 242001 (2010).

The Lamb Shift

The Proton Radius

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.

The Proton Radius  arXiv:1702.01189

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

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

Meson to * Transition Form Factor

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. D93 074017 (2016)

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, 074014 (2017)

c, b to * Transition Form Factor

, ’ to * Transition Form Factor

, ’ to * Transition Form Factor

N to *(1535) - Transition Form factors

N to N*(1535) - Transition Form factors

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.