Nucleon-Nucleon collisions

Nucleon-nucleon interaction at low energy

Interaction between two nucleons: basic for all of nuclear physics

Traditional goal of nuclear physics: to understand properties of atomic nuclei in terms of the bare interactions between pair of nucleons

With the advent of QCD the NN interaction became less fundamental

However, still two reasons for its importance:

● In nuclear structure and low energy nucleus-nucleus collisions, nucleons are still considered to be elementary particles

● In high energy heavy ion collisions, NN collisions constitute a reference point for complex systems

A reference for the NN interaction at low energy

Nucleon-nucleon data provide information to nucleus-nucleus collisions

To what extent is the longitudinal kinetic energy dissipated by the collisions into other degree of freedoms?

Is the longitudinal energy dissipated in nucleus-nucleus collisions high enough to allow for QGP formation?

Are exotic behaviours of QGP expected from nucleon-nucleon extrapolations?

Nucleon-nucleon total cross section

For 3 GeV < √s < 100 GeV: about 40 mbarn

Elastic ( about 10 mbarn) + inelastic (about 30 mbarn)

Inelastic processes create particles

pp cross sections

pp cross sections

pd, pn, np cross sections

π p cross sections

Parametrization of nucleon-nucleon cross section

Total cross section:

σtotal = 48 + 0.522 (ln p)2 - 4.51 (ln p)

Elastic cross section:

σelastic = 11.9 + 0.169 (ln p)2 – 1.85 (ln p) + 26.9 p-

1.21

P in GeV/c

Diffractive processes:

One nucleon is considered as a region of absorption and the interference of the scattering amplitudes from different impact parameters produces a diffractive pattern in the very forward/backward directions

In diffractive scattering, nucleons loose only a small amount of energy

In a non-diffractive inelastic event, colliding nucleons loose a large fraction of their energy and a large number of particles is produced.

Separation of diffractive and non diffractive component is difficult. The diffractive component is about 10 %.

Particle production

NN collisions produce particles. Most of them (80-90 %) are pions, the rest are mainly kaons, baryons and antibaryons.

Multiplicity: total number of particles produced in the collision

Charged multiplicity: total number of charged particles produced

Quite often, only the charged multiplicity is measured, and the multiplicity is only inferred

(for instance neutral pions are not detected, and it is assumed that π+, π- and π0 are equally produced)

Average charged multiplicity in e+e- and pp collisions

Charged multiplicity in pp collisions is lower than in e+e- collisions, since only about half of the c.m. energy is used to produce particles

Parametrization of multiplicity

Charged multiplicity increases with √s in a logarithmic way

Parametrization by Thomé et al.

<Nch> = 0.88 + 0.44 (ln s) + 0.118 (ln s)2

Understanding the multiplicity in pp collisions is a prerequisite to study the multiplicity in AA collisions

The inclusive hadron rapidity density in the process pp -> h X is:

The hadron rapidity density grows with √s and can be parametrized in several ways at y=0 (i.e. at mid-rapidity):

(dN/dy)ch = 0.96 + 0.046 ln √s + 0.049 ln2 √s

(dN/dy)ch = 2.5 - 0.50 ln √s + 0.092 ln2 √s

(dN/dy)ch = 0.6 ln (√s /1.88)

σ(s) = pp inelastic cross section

Facility Energy (c.m.) Charged-particle rapidity density

SPS 20 GeV about 2

RHIC 200 GeV about 2.5

LHC up to 14 TeV ??

Starting from November 2009 we have new data from LHC!

The first ALICE data on charged particle rapidity density in pp collisions @ 900 GeV (Nov.2009)

dN_charged/dη = 3.10 (INEL= all inelastic)

The ALICE Collaboration,

Eur. Phys. Journal C65(2010)111

The first LHC

publication

Classification of pp inelastic collisions:

If one (two) beam particles are excited to a high mass state, the process is single (double) diffractive, otherwise is non-diffractive

INEL: Sum of non-diffractive, single diffractive and double-diffractive

NSD: Non single-diffractive, i.e. non-diffractive + double-diffractive

Next ALICE data:

pp collisions@ 2.36 TeV

First energy ever probed beyond Tevatron

The ALICE Collaboration,

Eur. Phys. Journal C68(2010)89

The ALICE Collaboration,

Eur. Phys. Journal C68(2010)345

Recent ALICE data:

pp collisions@ 7 TeV

Multiplicity distributions

pp collisions

Rapidity and transverse distributions of particles

Longitudinal momentum distribution (pseudorapidity)

At lower energy gaussian shape

At higher energy a plateau is observed

ALICE results: pp@900 GeV and 2.36 TeV

Pseudo-rapidity distributions

Transverse momentum distribution

Average momentum of pions around 350 MeV/c

Invariant cross section exhibits an exponential shape (less steep at higher transverse momenta)

Transverse mass spectra

mt-scaling:

Invariant cross sections of different types of particles have the same shape when plotted vs. their transverse mass

Soft particles

<< 1 GeV/c

Hard particles

>> 1 GeV/c

Baryon energy loss

In a NN collision, an incident projectile nucleon loses a non-negligible fraction of its light-cone momentum. The degree of inelasticity may be characterized by the forward light-cone

light-cone momentum of the detected baryon

light cone momentum of the incident parent baryon

(See Wong, Chapter 2)

x =

The shape of the pt-distribution depends on the baryon energy loss. For pp collisions with x close to 1, the invariant cross section has an almost exponential shape.For collisions with x very small, the shape is close to a gaussian.

However, the average pt value is almost the same in the two cases.

The shape of the x-distribution is nearly independent of the incident energy

Except for x close to 1, the distribution is nearly flat. After an inelastic NN collision, there is the same probability to find the nucleon with x between 0 and 1. The average value is ½.This means that on average, about half of the initial light-cone momentum is lost.

It can be shown that the average rapidity after a pp inelastic collision is

<y> = yb -1

i.e. on the average the incident proton loses about one unit of rapidity in a pp inelastic collision.

In nucleus-nucleus collisions, nucleons from one nucleus suffer many inelastic collisions with nucleons from the other nucleus.

In multiple-collisions processes, the loss of incident energy and momentum can be large (stopping)

Energy loss and particle production are related

Baryon energy loss

To search for new effects when going from pp collisions to AA collisions, the multiplicity may be compared with the number of participants

For pp collisions: No. of participants is about 2

For central AA collisions: about 2 A

May be estimated from geometrical models as a function of the impact parameter

Interesting result:

in pp collisions at √s=200 GeV: 2.5/participant

in AA collisions at √s=200 GeV: 3.8/participant

A few remarks concerning the comparison between theoretically and experimentally multiplicities:

-Experiments measure usually the charged multiplicity, theory predicts the total

- Experiments usually measure the pseudo-rapidity distributions, theory evaluates the rapidity

- Central collisions are not exactly defined

- Experiments probe the final state, theory often predicts the formation stage, which is modified during the system evolution

Proton-proton measurements as a reference for heavy ion physics

Where to look?

A non-exhaustive list of observables

Particle multiplicities

Slopes of transverse-mass distributions

Particle yields and ratios

Ratios of momentum spectra

Strangeness enhancement

Dilepton spectra

Photon spectra

Production of short-lived resonances

References:

Wong, Chapter 3

Particle Data Group