Lecture 6: QCD at long distance

4( )

3s

QCDV r krr

Last week:

We discussed ep scattering ( DIS) and the evidence of quarks QED interaction between the electron and the quark at short distance Point-like constituents deduced from the x-section measurements Sum rules: Integrals over the structure functions that basically express

the conservation laws of the constituent quark quantum numbers Breaking of the Bjorken sum rule - > evidence for partons other than

the quarks present in the protons ( NOTE: direct evidence for gluons comes from 3-jet events in e+e- collisions)

Experimental determination of parton distribution functions (PDFs) for quarks, anti-quarks and gluons

Last lecture: QCD at short distance Proton-anti-proton scattering at high energy Differential x-section for

Just like in Rutherford scattering! We are able to calculate the scattering cross-

section between 2 partons usinng perturbation theory due to the running of the coupling constant ( small at short distance)

2pp jets

4

1

sin ( / 2)

d

d

DIS and pQCD

Electron-proton Scattering

(QED)

proton- anti-proton scattering -> 2 jets

(QCD)

dtd

Aaf /A

a

Abf /B

b

dDh2

d

2h

cDh1

c

1h

PDFs (fa/A,,fb/B)

At long distance

The theoretical description is much harder (s is large)

We have phenomenological models that describe certain aspects of the data

Some people say that “this is not even QCD”… But 99% of the particles produced in pp collisions

come from soft interactions => we need to deal with those

I’ll describe the classical string model of hadron production ( the pre-cursor of modern string theories) and will mention Regge theory and the dual parton model

We start with the following observations: At this point we have a picture of hadrons composed

of elementary fermions that (accurately) specify the quantum number content of the baryons and mesons. 

quarks carry an extra quantum number, color, and the interactions that couple to this quantum number, QCD, are such as to “confine” quarks and anti-quarks to color singlets with volumes of order (1 fm)3

We looked at some hadrons in their ground state – (handout 2 lectures ago) and how they decay

Not mentioned before: there are also excited states of hadrons ( just like in atoms) and they exhibit a remarkable systematic structure

Excited hadrons and Regge trajectories

Examining these closely: hadrons occur along “trajectories” in J vs mass2 space

Constant slope

Name JP m2 (GeV)2

nucleons 0.9

N(1680) 2.8

N(2220) 4.9

Name JP m2 (GeV)2

1- 0.6

3- 2.9

5- 5.5

Examples of Regge trajectories

Note: these are not the same hadrons as the tables on the previous page

The rotating string 2 massless quarks

on the end of a string of gluons

Energy density per unit length : k

The ends rotate with velocity v=c

Local velocity at radius r, v=cr/R

Mass E=m

Angular mom J

The string tension

Measure ’ from data = 0.93 GeV-2

Then find k = 0.87 GeV/fm This also comes from the mass ( ~ 1 GeV)

and radius (~ 1 fm) of the hadrons

Duality and strings

S and t channel look the same if you stretch a string between the quarks

Regge theory gives a clue on why the dual description works X-sections for elastic

and inelastic interactions are parameterized with a sqrt(s) dependence inspired by this model

String fragmentation and particle production rate: the Lund string model

Taken from a talk by Prof.

Hadronization and decays: From a talk on Pythia: a Monte-Carlo generator based on Lund model

Wit parameters tuned to data can describe both hard and soft particle production in pp collisions.

Rapidity distributions

Lund model predicts a rapidity plateau

is the proper time

0

T

kdN

dy m

Mt scaling predicted from most soft phenomenological models The data exhibits approximate mT scaling at low mT in contrast

to the power-law behavior at high-pT where hard scattering is expected to dominate

Summary

We reviewed phenomenological models of soft hadron-hadron interactions

Classical string theory and linear term in the potential describe many features of the data Rapidity distributions mT scaling

Next we will move to AA collisions and see how the collective properties of the system show up in the observed quantities