p-p and p-air interaction data

Note

There is some difference in the ad hoc model before and after v3.0. In this page, we show data obtained by v2.106. In another page, you can see some essential points of the changes in Version 3 including those of the new Lund code.
What is here ?
We show some basic data for p-p and p-air collisions used in Cosmos.
In what form ?
Mostly in the form of EPS figures and some in tables. I chose EPS figures rather than GIF because the former will permit the user reedit the figures so that he/she can enlarge/shrink the figures, add favorite font/style labels, titles etc without degradation of quality.
Models ?
Cosmos uses Lund/Fritiof code at 5 to 500 GeV and an adhoc phenomenological model at > 500 GeV. The adhoc model borrows a lot of ideas from the UA5 phenomenological Monte Carlo code description. In versions uv2.105 or later, Gheisha code or the adhoc model can be used at 5 to 500 GeV as optional models.
What kind of data ?
All data has been obtained by using Cosmos.uv2.106
The three models are compared at 10, 100 and 500 GeV's for p-p and p-air collisions.
As basic data which is important for cosmic ray study, the x-distribution of pions + kaons, that of nucleons ( not necessarily leading particles), transvers momentum distribution of pions + kaons, multiplicity distribution of all particles.
The x distribution of pi+ vs pi-, and pi charge vs k charge.
At energies > 500 GeV, only the adhoc model data is shown at 10^12, 10^15, 10 ^18, 10^21 eV for p-p and p-air collisions.
The energy dependence of the x-distribution, log10(x) distribution, transvers momentum distribution, etc are given.
Notations.
In the figures where the three models are compared, the line histogram is by the adhoc model, square dots by Lund/Fritiof and crosses by Gheisha.
The x is defined simply by the ratio of the energy of a secondary particle to the incident proton energy in the laboratory system.
  1. 10 GeV data comparison for p-p. The number of events is 5000. Upper left: x-distribution of pions + kaons. upper right: that of nucleons. lower left: transvers momentum distribution. lower right: multiplicity distributions of all particles.
  2. 100 GeV comparison for p-p The number of events is 3000. Others are the same as in for the 10 GeV case.
  3. 500 GeV comparison for p-p The number of events is 3000. Others are the same as in for the 10 GeV case.
  4. X-distributions at 500 GeV: Pi+ vs Pi- and pi charge vs K charge. The number of events is 3000.
  5. 10 GeV comparison for p-air The number of events is 5000. At the lower right is shown a pseudo-rapidity distribution. You can convert it to dsigma/deta/sigmaInela by dividing the number by event number and multiplying by 5. Others are the same as the p-p case.
  6. 100 GeV comparison for p-air The number of events is 3000.
  7. 500 GeV comparison for p-air The number of events is 3000.
  8. Comparison of p-p and p-air pseudo-rapidity at 10, 100, 500 GeV You can convert the y-axis to dsigma/deta/sigmaInela by dividing the number by event number and multiplying by 5. Line is for p-p and dots for p-air.

Energy dependence of the adhoc model.

  1. cross-section of pp, pair, A-airas a function of lab energy (E/A in GeV).
  2. Average total multiplicity for pp and p-air collisionsas a function of lab. proton energy in eV. This is Cosmos default. Smaller multiplicity choice is possible. Approximate formulas are given in fig. which should not be used used below 10 GeV.
  3. Ratio of (K-charge/pi-charge) as a function of proton energy in eV. This is for p-p collisions, but almost no change is expected for p-air collisions.
All figures which follow contain the result of 1000 events for each of incident energies, 10^12, 10^15, 10^18 and 10^21 eV. Lines are for 10^12 eV, filled square dots for 10^15 eV, pluses for 10^18 eV and crosses for 10^21 eV. If you want to convert dN/d.. to dsigma/d../sigmaInela, you may divide the number by 1000 and further divide it by the bin width.

p-p data

  1. x and log10(x) distributions of pions + kaons The definition of x is the same as previous. You can see a gradual scale breaking feature in the fragmentation region.
  2. dN/Pt/Pt distribution (Pt: transvers momentum of pions and kaons in GeV/c) and the x-distribution of nucleons Note that the latter is NOT a leading particle x distribution but an inclusive distribution of nucleons (proton, anti-protons, neutrons, anti-neutrons). The leading particle x is expected to be almost unchanged above 10^12 eV.
  3. Pseudo-rapidity distributionof all particles.
  4. Multiplicity distribution in the form dN/dz where z is the total multiplicity divided by the average.
  5. K-charge / pi-charge values in Table
  6. Some numerical values in Table

p-air data

  1. x and log10(x) distributions of pions + kaons
  2. dN/Pt/Pt distribution (Pt: transvers momentum of pions and kaons in GeV/c) and the x-distribution of nucleons Note that the latter is NOT a leading particle x distribution but an inclusive distribution of nucleons (proton, anti-protons, neutrons, anti-neutrons).
  3. Pseudo-rapidity distributionof all particles.
  4. Multiplicity distribution in the form dN/dz where z is the total multiplicity divided by the average.
  5. Some numerical values in Table

Comarison with experimental data

Since the Lund/Fritiof code is known to give a good description of experimental data at low energies, and the ad-hoc model gives very similar results to those by the Lund/Fritiof as far as the quantities important for cosmic ray study, we expect the adhoc model can describe such experimental data. Therefore we show only a few examples here.
  1. rapidity data of pp -> pi- + X compared with the NA22 group data (Z. Phys. C-Particles and Fields, 39, 311(1988)) at 250 GeV. Circles are the experimental data. The number of simulated events is 3000.
  2. transvers momentum data of pp -> pi- + X compared with the same NA22 data. The x-axis is in Pt^2 (GeV/c)^2. The y is in dN/dPt^2. The number of simulated events is 3000. Circles are the experimental data.
  3. pseudo-rapidity distributionscompared with UA-5 data. This comparison is wrong. (At the time of tuning, UA-5 data was used incorrectly). See a new version indicated at the top
    The energies are 53, 200, 546 and 900 GeV in root s and correspond to 1.5, 21, 159 and 432 TeV lab energies. The data (circles) is non-single diffractive data (so called minimum bias data). We should be careful of this comparison, because the experimental data has some bias while the Monte-Carlo data has no such bias. Although the agreement is good, we should not rely on this agreement too much. The meaning of this data is explained by this diagram. .

    We may note that