Deuteron and antideuteron production simulation in cosmic-ray interactions

The study of the cosmic-ray deuteron and antideuteron flux is receiving increasing attention in current astrophysics investigations. For both cases, an important contribution is expected from the nuclear interactions of primary cosmic rays with intergalactic matter. In this work, deuteron and antideuteron production from 20 to $2.6\times {10}^7\mathrm{GeV}$ beam energy in $\mathrm{p}+\mathrm{p}$ and $\mathrm{p}+\mathrm{A}$ collisions were simulated using EPOS-LHC and Geant4’s FTFP-BERT Monte Carlo models by adding an event-by-event coalescence model afterburner. These estimates depend on a single parameter ($p_0$) obtained from a fit to the data. The $p_0$ for deuterons in this wide energy range was evaluated for the first time. It was found that $p_0$ for antideuterons is not a constant at all energies as previous works suggested and, as a consequence, the antideuteron production cross section can be at least 20 times smaller in the low-collision-energy region than earlier estimations.

Figure 1

Invariant differential cross sections as a function of rapidity ($y$) are calculated with different MC models for protons (a) and antiprotons (b) in $\mathrm{p}+\mathrm{p}$ collisions at $158\mathrm{GeV}/c$. Results for two bins of transverse momentum ($p_T$) are compared with data from experiments NA49 [29] and NA61 [30].

Figure 2

Distributions of the difference between measurements and the MC generators divided by the error [see Eq. (3)] for proton production in $\mathrm{p}+\mathrm{p}$ and $\mathrm{p}+\mathrm{A}$ collisions.

Figure 3

Distributions of the difference between measurements and the MC generators divided by the error [see Eq. (3)] for antiproton production in $\mathrm{p}+\mathrm{p}$ and $\mathrm{p}+\mathrm{A}$ collisions.

Figure 4

Antiproton and antideuteron invariant differential cross sections in $\mathrm{p}+\mathrm{p}$ collisions at $70\mathrm{GeV}/c$ as function of transverse momentum ($p_T$) calculated with EPOS-LHC, FTFP-BERT and parametrizations [50, 51]. The results are compared to data [38, 39, 40] (see text for details).

Figure 5

Extracted coalescence momentum $p_0$ (symbols) for deuterons (a) and antideuterons (b) as function of the collision kinetic energy (T). Fit functions [Eqs. (4) and (5)] for EPOS-LHC (long-dashed red line) and FTFP-BERT (dashed blue line) are shown. Additionally, the $p_0$ values obtained from the analytic coalescence model and the parametrization of Korsmeier et al. are included (dashed cyan line and dots). Also, the constant value of $p_0=79\mathrm{MeV}/c$ estimated by Duperray et al. is plotted (solid magenta line).

Figure 6

Deuteron (a) and antideuteron (b) total production cross section in $\mathrm{p}+\mathrm{p}$ collisions. Deuteron (c) and antideuteron (d) total production cross section in $\mathrm{p}+\mathrm{He}$ collisions. The expected antideuteron cross section from Duperray’s parametrization has been added. In the lower panels Duperray to MC predictions in antideuteron are compared. Vertical broken lines represent antideuteron production threshold.

Figure 7

Distributions of the difference between measurements and the MC generators divided by the error [see Eq. (3)] for proton production in $\mathrm{p}+\mathrm{p}$ and $\mathrm{p}+\mathrm{A}$ collisions.

Figure 8

Distributions of the difference between measurements and the MC generators divided by the error [see Eq. (3)] for antiproton production in $\mathrm{p}+\mathrm{p}$ and $\mathrm{p}+\mathrm{A}$ collisions.

Figure 9

Distributions in two different energy regions of the difference between measurements and EPOS-LHC divided by the error [see Eq. (3)] for proton production in $\mathrm{p}+\mathrm{p}$ and $\mathrm{p}+\mathrm{A}$ collisions.

Figure 10

Distributions in two different energy regions of the difference between measurements and EPOS-LHC divided by the error [see Eq. (3)] for antiproton production in $\mathrm{p}+\mathrm{p}$ and $\mathrm{p}+\mathrm{A}$ collisions.

Figure 11

Double differential cross sections from MC models compared to data of protons and deuterons produced in $\mathrm{p}+\mathrm{p}$ collisions at $19\mathrm{GeV}/c$ [36].

Figure 12

Double differential cross sections from MC models and Duperray’s parametrization (pink line) compared to data of antiprotons produced in $\mathrm{p}+\mathrm{Be}$ collisions at $19.2\mathrm{GeV}/c$ [35].

Figure 13

Double differential cross sections from MC models compared to data of protons and deuterons produced in $\mathrm{p}+\mathrm{p}$ collisions at $24\mathrm{GeV}/c$ [36].

Figure 14

Double differential momentum distribution from MC models compared to data of protons produced in $\mathrm{p}+\mathrm{C}$ collisions at $31\mathrm{GeV}/c$ [37].

Figure 15

Invariant differential cross section for protons and deuterons produced in $\mathrm{p}+\mathrm{p}$ collisions at $70\mathrm{GeV}/c$. Data taken from [38, 39, 40].

Figure 16

Invariant differential cross section for protons and deuteron produced in $\mathrm{p}+\mathrm{Be}$ collisions at $70\mathrm{GeV}/c$. Data taken from [40].

Figure 17

Invariant differential cross section for antiprotons and antideuterons produced in $\mathrm{p}+\mathrm{Be}$ collisions at $70\mathrm{GeV}/c$. Data taken from [40].

Figure 18

Invariant differential cross section for protons produced in $\mathrm{p}+\mathrm{p}$ collisions at $158\mathrm{GeV}/c$. Data taken from [29].

Figure 19

Invariant differential cross section for antiprotons produced in $\mathrm{p}+\mathrm{C}$ collisions at $158\mathrm{GeV}/c$. Data taken from [42].

Figure 20

Invariant differential cross section for protons and deuteron produced in $\mathrm{p}+\mathrm{Be}$ collisions at $200\mathrm{GeV}/c$. Data taken from [43, 53].

Figure 21

Invariant differential cross section for antiprotons and antideuterons produced in $\mathrm{p}+\mathrm{Be}$ collisions at $200\mathrm{GeV}/c$. Data taken from [43, 53].

Figure 22

Invariant differential cross section for protons and deuterons produced in $\mathrm{p}+\mathrm{Be}$ collisions at $300\mathrm{GeV}/c$. Data taken from [45, 46].

Figure 23

Invariant differential cross section for antiprotons and antideuterons produced in $\mathrm{p}+\mathrm{Be}$ collisions at $300\mathrm{GeV}/c$. Data taken from [45, 46].

Figure 24

Invariant differential cross section for protons and deuteron produced in $\mathrm{p}+\mathrm{p}$ collisions at $\sqrt{s}=53\mathrm{GeV}$. Data taken from [47, 56].

Figure 25

Invariant differential cross section for antiprotons and antideuterons produced in $\mathrm{p}+\mathrm{p}$ collisions at $\sqrt{s}=53\mathrm{GeV}$. Data taken from [47, 54, 55].

Figure 26

Differential cross section for antiprotons produced in $\mathrm{p}+\mathrm{He}$ collisions at $\sqrt{s_{NN}}=110\mathrm{GeV}$. Data taken from [48].

Figure 27

Invariant differential cross section for protons and deuteron produced in $\mathrm{p}+\mathrm{p}$ collisions at $\sqrt{s}=900\mathrm{GeV}$. Data taken from [49, 52, 57].

Figure 28

Invariant differential momentum distribution for antiprotons and antideuterons produced in $\mathrm{p}+\mathrm{p}$ collisions at $\sqrt{s}=900\mathrm{GeV}$. Data taken from [49, 52, 57].

Figure 29

Extracted coalescence momentum $p_0^{\prime }$ (symbols) for deuterons (a) and antideuterons (b) as a function of the collision kinetic energy (T). Fit functions [Eqs. (4) and (5)] for EPOS-LHC (long-dashed red line) and FTFP-BERT (dashed blue line) are shown.