Nucleon-nucleon interaction at low energyInteraction between two nucleons: basic for all of nuclear physicsTraditional goal of nuclear physics: to understand properties of atomic nuclei in terms of the bare interactions between pair of nucleonsWith the advent of QCD the NN interaction became less fundamentalHowever, 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 collisionsTo 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 sectionFor 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
p cross sections
Parametrization of nucleon-nucleon cross sectionTotal cross section: total = 48 + 0.522 (ln p)2 - 4.51 (ln p)Elastic cross section:elastic = 11.9 + 0.169 (ln p)2 1.85 (ln p) + 26.9 p-1.21P 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 directionsIn diffractive scattering, nucleons loose only a small amount of energyIn 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 productionNN 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 collisionCharged 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 +, - and 0 are equally produced)
Average charged multiplicity in e+e- and pp collisionsCharged 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 multiplicityCharged multiplicity increases with s in a logarithmic wayParametrization by Thom et al. = 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 collisionsThe 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) (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/d = 3.10 (INEL= all inelastic) The ALICE Collaboration, Eur. Phys. Journal C65(2010)111The 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-diffractiveNSD: Non single-diffractive, i.e. non-diffractive + double-diffractive
Next ALICE data:pp collisions@ 2.36 TeVFirst energy ever probed beyond TevatronThe ALICE Collaboration, Eur. Phys. Journal C68(2010)89
The ALICE Collaboration, Eur. Phys. Journal C68(2010)345Recent ALICE data:pp collisions@ 7 TeV
Multiplicity distributionspp collisions
Rapidity and transverse distributions of particlesLongitudinal momentum distribution (pseudorapidity)
At lower energy gaussian shape
At higher energy a plateau is observed
ALICE results: pp@900 GeV and 2.36 TeVPseudo-rapidity distributions
Transverse momentum distributionAverage momentum of pions around 350 MeV/c
Invariant cross section exhibits an exponential shape (less steep at higher transverse momenta)
Transverse mass spectramt-scaling:Invariant cross sections of different types of particles have the same shape when plotted vs. their transverse mass
Soft particles> 1 GeV/c
Baryon energy lossIn 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)
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 .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 = yb -1i.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 2For central AA collisions: about 2 AMay 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 physicsWhere to look?A non-exhaustive list of observablesParticle multiplicitiesSlopes of transverse-mass distributionsParticle yields and ratiosRatios of momentum spectraStrangeness enhancementDilepton spectraPhoton spectraProduction of short-lived resonances
References:Wong, Chapter 3Particle Data Group