Proton-proton cross section

Full text


Lecture 6

The advent of small accelerators in late 1950ties allowed to shoot e.g., electron at a specific energy onto a target rich in proton and detect the rate as function

of beam momentum. Many universities in US had small accelerator in their basements. This led to first observations of “resonances” – excited states of the proton that after short time decayed to a proton and additional particles – typically pions.

The lifetime of such excited states was related to width of the bump in the rate of events With beam energy directly related to the invariant mass of the particle. About 30 such states have been seen and the angular distributions of the final state particles allowed to determine the spin of the parent.

In 1960ties larger, proton accelerators capable of higher energies allowed to select fast secondaries of the proton-proton collision – mostly pions – into mono-energetic beams.


• These resonances are formed by the absorption of the energy imparted

by the beam particle to the nucleon (proton or neutron) - formation mechanism. They decay into the final state of nucleon and one

or more pions.

• That means that such resonances can be searched for also among

the multi-particle final states in high energy collisions - time reversal.

They should show up as bumps in the distributions of invariant mass of two, three and more particles.

• As a result the number of discovered resonances exploded.

There are over a thousand known states. Many studied with high precision.

• The listings, tables, reviews etc are collected in Particle Data Tables


E2 = (mc2)2 +(pc)2


mc2 - invariant mass

independent of reference frame

Resonance states



• The development of electron-positron colliders in 1970-80ties led to much improved precision of all measurements.

• The electron and positron beams can be energy tuned with high precision.

• Anything observed in the final state comes from decays of the virtual photon. There is no baryon (proton or neutron) in the initial state, but the photon couple to anything with charge. -> lots of cleanly measured new resonances.


cross-section for e+e- annihilation into hadrons


Mass of the resonance is not well determined. It has a width that is inversely proportional to the lifetime.

A typical parameters can be seen for one of the common resonance ρ0(770) that decays to two pi mesons

mass (central value) m = 775.49


0.34 MeV Width Γ = 149.1


0.8 MeV

Branching fraction ρ


π+ π- Γ


10 -8 10 -7 10 -6 10 -5 10 -4 10 -3 10 -2 1 10 102 10 -1 1 10 102 103 1 10 102


Antiparticle – a particle with the same mass but opposite charge or magnetic property


•γ - gamma conversion – creation of electron + positron pair •antiproton observed as secondary negative particle with mass

equal to that of a proton, can be produced in p-p collisions

•π mesons of opposite charges produced in collisions

•resonance states of opposite charge observed in scattering

and in collisions resulting in multi-particle production Problem with neutral particles:

No opposite charge - eg, πo, η

Explanation given by the Quark Model:


Antiproton discovery (1955)

Threshold energy for antiproton ( p ) production in proton – proton collisions

Baryon number conservation -> simultaneous production of p and p (or p and n)

p p p p p p + ® + + +

Example: Threshold energy ~ 6 GeV

Bevatron”: 6 GeV

proton synchrotron in Berkeley § build a beam line for 1.19 GeV/c momentum

§ select negatively charged particles (mostly π–)

§ reject fast π– by Čerenkov effect: light emission

in transparent medium if particle velocity v > c / n (n: refraction index) – antiprotons have v < c / n -> no Čerenkov light

§ measure time of flight between counters S1 and S2 (12 m path): 40 ns for π , 51 ns for antiprotons

For fixed momentum, time of flight gives particle velocity, hence particle mass



Momentum measurement in magnetic field

p (GeV/c) = 0.3 B (Tesla) × ρ (curvature, m-1) ρ = 1/R

Only one particle observed – production of second proton is implied by conservation law


Example of antiproton annihilation at rest in a liquid hydrogen bubble chamber



Late 1940’s: discovery of a variety of heavier mesons (K – mesons) and baryons (“hyperons”) – studied in detail in the 1950’s at the new high-energy

proton synchrotrons (the 3 GeV “cosmotron” at the Brookhaven National Lab and the 6 GeV Bevatron at Berkeley)

Examples of mass values

Mesons (spin = 0): m(K±) = 493.68 MeV/c2 ; m(K°) = 497.67 MeV/c2 Hyperons (spin = ½): m(Λ) = 1115.7 MeV/c2 ; m(Σ±) = 1189.4 MeV/c2

m(Ξ°) = 1314.8 MeV/c2; m(X ) = 1321.3 MeV/c2 Properties

§ Abundant production in proton – nucleus , p – nucleus collisions

§ Production cross-section typical of strong interactions (σ > 10-27 cm2)

§ Production in pairs (example: p– + p à K° + Λ ; K– + p à Ξ + K+ )

§ Decay to lighter particles with mean life values 10–8 – 10–10 s (as expected for a weak decay)

Examples of decay modes

K± àπ± π° ; K± à π± π+π– ; K± à π± π°π° ; K° à π+π– ; K° à ππ° Λ à p π– ; Λ à n π° ; Σ+ à p π° ; Σ+ à n π+ ; Σ+ à n π– ; . . .

Ξ àΛπ ; Ξ° à Λπ°






Related subjects :