Primordial nucleosynthesis and hadronic decay of a massive particle with a relatively short lifetime

TL;DR

This work analyzes how late-time hadronic decays of a long-lived particle X during the BBN epoch (approximately $t$ in the range $10^{-2}$--$10^{2}$ s) can dramatically alter light-element abundances by injecting hadrons that thermalize electromagnetically and subsequently inter-convert background protons and neutrons via strong interactions, thereby increasing the neutron-to-proton ratio and ${}^4\text{He}$ production. The authors model hadron fragmentation with the JETSET $7.4$ Monte Carlo, incorporate updated hadron–nucleon cross sections, and perform a Monte Carlo error analysis to derive robust bounds in the $(m_X,\tau_X,B_h,n_X/s)$ parameter space for $m_X\sim 10$ GeV--$10$ TeV and plausible $\eta$ values. They solve the hadron-injection Boltzmann-like evolution with $\frac{dn_N}{dt}+3Hn_N = [dn_N/dt]_{\rm weak} - B_h\Gamma_X n_X (K_{N\to N'} - K_{N'\to N})$, use $K_{N\to N'} = \sum_{H_i}\tfrac{N_{\rm jet}}{2}N^{H_i}R^{H_i}_{N\to N'}$, and find that hadronic decays tend to increase ${}^4\text{He}$ and, at longer lifetimes, modify deuterium as well, yielding 95% CL bounds that constrain reheating temperature in gravitino scenarios. The study highlights the importance of hadronization modeling in early-universe constraints and notes planned work to include hadro-dissociation effects for longer lifetimes.

Abstract

In this paper we consider the effects on big bang nucleosynthesis (BBN) of the hadronic decay of a long-lived massive particle. If high-energy hadrons are emitted near the BBN epoch ($t \sim 10^{-2}$ -- $10^2 \sec$), they extraordinarily inter-convert the background nucleons each other even after the freeze-out time of the neutron to proton ratio. Then, produced light element abundances are changed, and that may result in a significant discrepancy between standard BBN and observations. Especially on the theoretical side, now we can obtain a lot of experimental data of hadrons and simulate the hadronic decay process executing the numerical code of the hadron fragmentation even in the high energy region where we have no experimental data. Using the light element abundances computed in the hadron-injection scenario, we derive a constraint on properties of such a particle by comparing our theoretical results with observations.

Figures (14)

• Figure 1: Plot of $\chi^2$ as a function of baryon to photon ratio ($\eta = n_B/n_{\gamma}$). The solid line (dashed line) represents the case of low D (high D).
• Figure 2: Plot of the averaged charged-particle multiplicity $\langle N_{\rm ch}\rangle$. This represents the total number of the charged hadrons emitted per $e^+ e^-$ annihilation and per two hadron jets as a function of $\sqrt{s}$ (= 2 $E_{\rm jet}$), where $\sqrt{s}$ denotes the center of mass energy, and $E_{\rm jet}$ is the energy per one hadron jet. The solid line denotes the value obtained by using the JETSET 7.4 Monte Carlo event generator. The filled circle denotes the data points of $e^+ e^-$ collider experiments. Error is quadratically added for the statistical and systematic one. Here $\langle N_{\rm ch}\rangle$ is defined as the value after both $K_S$ and $\Lambda^0$ had completely finished to decay.
• Figure 3: Plot of the spectrum of the produced mesons ($\pi^+$ + $\pi^-$, $K^+$ + $K^-$, and $K^0_L$) as a function of the kinetic energy $E_{\rm kin}$. This is the case that the center of mass energy is $\sqrt{s} = 91.2$ GeV which corresponds to the $Z^0$ resonance. They are computed by using the JETSET 7.4 Monte Carlo event generator.
• Figure 4: Plot of the spectrum of the produced baryons ((a) $n + {\overline{n}}$ and (b) $p + {\overline{p}}$) as a function of the kinetic energy $E_{\rm kin}$. This is the case that the center of mass energy is $\sqrt{s} = 91.2$ GeV which corresponds to the $Z^0$ resonance. They are computed by using the JETSET 7.4 Monte Carlo event generator.
• Figure 5: Plot of the averaged number of the produced hadrons as a function of $2 E_{\rm jet} (=\sqrt{s})$, where $E_{\rm jet}$ denotes the energy of one hadron jet. The number is defined by the value per two hadron jets. $\langle N_{\rm ch}\rangle$ denotes the averaged charged-particle multiplicity (thick solid line). The number is obtained by summing up the energy distribution. The dotted line is $\pi^+ + \pi^-$, the short dashed line is $K^+ +K^-$, the thin solid line is $K^0_L$, the dot-dashed line is $p + {\overline{p}}$, and the long dashed line is $n + {\overline{n}}$. They are computed by using the JETSET 7.4 Monte Carlo event generator.