# Particle decay > Mediated Wiki article. Canonical URL: https://mediated.wiki/source/Particle_decay > Markdown URL: https://mediated.wiki/source/Particle_decay.md > Source: https://en.wikipedia.org/wiki/Particle_decay > Source revision: 1343007413 > License: Creative Commons Attribution-ShareAlike 4.0 International (https://creativecommons.org/licenses/by-sa/4.0/) {{Short description|Spontaneous breakdown of an unstable subatomic particle into other particles}} In [particle physics](/source/particle_physics), '''particle decay''' is the [spontaneous process](/source/spontaneous_process) of one unstable [subatomic particle](/source/subatomic_particle) transforming into multiple other particles. The particles created in this process (the ''final state'') must each be less massive than the original, although the [total mass](/source/Mass_in_special_relativity) of the system must be conserved. A particle is unstable if there is at least one [allowed](/source/conservation_law) final state that it can decay into. Unstable particles will often have multiple ways of decaying, each with its own [associated probability](/source/branching_fraction). Decays are mediated by one or several [fundamental forces](/source/fundamental_forces). The particles in the final state may themselves be unstable and subject to further decay. The term is typically distinct from [radioactive decay](/source/radioactive_decay), in which an unstable [atomic nucleus](/source/atomic_nucleus) is transformed into a lighter nucleus accompanied by the emission of particles or [radiation](/source/radiation), although the two are conceptually similar and are often described using the same terminology. ==Probability of survival and particle lifetime== Particle decay is a [Poisson process](/source/Poisson_process), and hence the probability that a particle survives for time {{mvar|t}} before decaying (the [survival function](/source/survival_function)) is given by an [exponential distribution](/source/exponential_distribution) whose [time constant](/source/time_constant) depends on the particle's velocity: P(t) = \exp\left(-\frac{t}{\gamma \tau}\right) :where ::\tau is the mean lifetime of the particle (when at rest), and ::\gamma = \tfrac{1}{\sqrt{1-\frac{v^2}{c^2}}} is the [Lorentz factor](/source/Lorentz_factor) of the particle. ===Table of some elementary and composite particle lifetimes=== All data are from the [Particle Data Group](/source/Particle_Data_Group). {| class=wikitable style="text-align: center;" !Type !Name !Symbol ![Mass](/source/Mass) ([MeV](/source/MeV)) !Mean lifetime |- |rowspan="3" | Lepton |[Electron](/source/Electron) / [Positron](/source/Positron){{cite web |url=https://physicsworld.com/a/electron-lifetime-is-at-least-66000-yottayears/ |title=Electron lifetime is at least 66,000 yottayears – Physics World |date=9 December 2015 }} |\mathrm{e}^- \, / \, \mathrm{e}^+ |0.511 |>6.6{{x10^|28}} years |- |[Muon](/source/Muon) / Antimuon |\mathrm{\mu}^- \, / \, \mathrm{\mu}^+ |105.7 |2.2{{x10^|-6}} seconds |- |[Tau lepton](/source/Tau_lepton) / Antitau |\mathrm{\tau}^- \, / \, \mathrm{\tau}^+ |1777 |2.9{{x10^|-13}} seconds |- |rowspan="2" | Meson |Neutral [Pion](/source/Pion) | \mathrm{\pi}^0\, |135 |8.4{{x10^|-17}} seconds |- |Charged [Pion](/source/Pion) | \mathrm{\pi}^+ \, / \, \mathrm{\pi}^- |139.6 |2.6{{x10^|-8}} seconds |- |rowspan="2" | Baryon |[Proton](/source/Proton) / [Antiproton](/source/Antiproton){{cite journal |title=Threshold corrections to dimension-six proton decay operators in non-minimal SUSY SU (5) GUTs |year=2016 |doi=10.1016/j.nuclphysb.2016.06.017 |arxiv=1603.03568 |last1=Bajc |first1=Borut |last2=Hisano |first2=Junji |last3=Kuwahara |first3=Takumi |last4=Omura |first4=Yuji |journal=Nuclear Physics B |volume=910 |pages=1–22 |bibcode=2016NuPhB.910....1B |s2cid=119212168 }}{{cite web |url=https://www.forbes.com/sites/startswithabang/2020/01/03/how-certain-are-we-that-protons-dont-decay/ |title=How Certain Are We That Protons Don't Decay? |website=[Forbes](/source/Forbes) }} | \mathrm{p}^+ \, / \, \mathrm{p}^- |938.2 |1.67{{x10^|34}} years |- |[Neutron](/source/Neutron) / [Antineutron](/source/Antineutron) | \mathrm{n} \, / \, \mathrm{\bar{n}} |939.6 |885.7 seconds |- |rowspan="2" | Boson |[W boson](/source/W_and_Z_bosons) | \mathrm{W}^+ \, / \, \mathrm{W}^- |80400 |{{10^|-26}} seconds |- |[Z boson](/source/W_and_Z_bosons) | \mathrm{Z}^0 \, |91000 |{{10^|-26}} seconds |} ==Decay rate== This section uses [natural units](/source/natural_units), where c=\hbar=1. \, The lifetime of a particle is given by the inverse of its decay rate, {{math|Γ}}, the probability per unit time that the particle will decay. For a particle of a mass {{mvar|M}} and [four-momentum](/source/four-momentum) {{mvar|P}} decaying into particles with momenta {{mvar|p{{sub|i}}}}, the differential decay rate is given by the general formula (expressing [Fermi's golden rule](/source/Fermi's_golden_rule)) d \Gamma_n = \frac{S \left|\mathcal{M} \right|^2}{2M} d \Phi_n (P; p_1, p_2,\dots, p_n) \, :where ::{{mvar|n}} is the number of particles created by the decay of the original, ::{{mvar|S}} is a combinatorial factor to account for indistinguishable final states (see below), ::\mathcal{M}\, is the ''invariant matrix element'' or [amplitude](/source/Probability_amplitude) connecting the initial state to the final state (usually calculated using [Feynman diagrams](/source/Feynman_diagrams)), ::d\Phi_n \, is an element of the [phase space](/source/phase_space), and ::{{mvar|p{{sub|i}}}} is the [four-momentum](/source/four-momentum) of particle {{mvar|i}}. The factor {{mvar|S}} is given by S = \prod_{j=1}^m \frac{1}{k_j!}\, :where ::{{mvar|m}} is the number of sets of indistinguishable particles in the final state, and ::{{mvar|k{{sub|j}}}} is the number of particles of type {{mvar|j}}, so that \sum_{j=1}^m k_j = n \,. The phase space can be determined from d \Phi_n (P; p_1, p_2,\dots, p_n) = (2\pi)^4 \delta^4\left(P - \sum_{i=1}^n p_i\right) \prod_{i=1}^n \frac{d^3 \vec{p}_i}{2(2\pi)^3 E_i} :where ::\delta^4 \, is a four-dimensional [Dirac delta function](/source/Dirac_delta_function), ::\vec{p}_i \, is the (three-)momentum of particle {{mvar|i}}, and ::E_i \, is the energy of particle {{mvar|i}}. One may integrate over the phase space to obtain the total decay rate for the specified final state. If a particle has multiple decay branches or ''modes'' with different final states, its full decay rate is obtained by summing the decay rates for all branches. The [branching ratio](/source/branching_ratio) for each mode is given by its decay rate divided by the full decay rate. ==Two-body decay== This section uses [natural units](/source/natural_units), where c=\hbar=1. \, {{multiple image | align = right | image1 = 2-body Particle Decay-CoM.svg | width1 = 140 | alt1 = | caption1 = In the '''Center of Momentum Frame''', the decay of a particle into two equal mass particles results in them being emitted with an angle of 180° between them. | image2 = 2-body Particle Decay-Lab.svg | width2 = 160 | alt2 = | caption2 = ...while in the '''Lab Frame''' the parent particle is probably moving at a speed close to the [speed of light](/source/speed_of_light) so the two emitted particles would come out at angles different from those in the center of momentum frame. | footer = }} ===Decay rate=== Say a parent particle of mass {{mvar|M}} decays into two particles, labeled '''1''' and '''2'''. In the rest frame of the parent particle, |\vec{p}_1| = |\vec{p}_2| = \frac{ \sqrt{[M^2 - (m_1 + m_2)^2][M^2 - (m_1 - m_2)^2]} }{2M}, \, which is obtained by requiring that [four-momentum](/source/four-momentum) be conserved in the decay, i.e. (M, \vec{0}) = (E_1, \vec{p}_1) + (E_2, \vec{p}_2).\, Also, in spherical coordinates, d^3 \vec{p} = |\vec{p}\,|^2\, d|\vec{p}\,|\, d\phi\, d\left(\cos \theta \right). \, Using the delta function to perform the d^3 \vec{p}_2 and d|\vec{p}_1|\, integrals in the phase-space for a two-body final state, one finds that the decay rate in the rest frame of the parent particle is d\Gamma = \frac{ \left| \mathcal{M} \right|^2}{32 \pi^2} \frac{|\vec{p}_1|}{M^2}\, d\phi_1\, d\left( \cos \theta_1 \right). \, ===From two different frames=== The angle of an emitted particle in the lab frame is related to the angle it has emitted in the center of momentum frame by the equation \tan{\theta'} = \frac{\sin{\theta}}{\gamma \left(\beta / \beta' + \cos{\theta} \right)} ==Complex mass and decay rate== {{further|Resonance#Atomic, particle, and molecular resonance| Resonance (particle physics)}} This section uses [natural units](/source/natural_units), where c=\hbar=1. \, The mass of an unstable particle is formally a [complex number](/source/complex_number), with the real part being its mass in the usual sense, and the imaginary part being its decay rate in [natural units](/source/natural_units). When the imaginary part is large compared to the real part, the particle is usually thought of as a [resonance](/source/Resonance_(particle_physics)) more than a particle. This is because in [quantum field theory](/source/quantum_field_theory) a particle of mass {{mvar|M}} (a [real number](/source/real_number)) is often exchanged between two other particles when there is not enough energy to create it, if the time to travel between these other particles is short enough, of order \tfrac{1}{M}, according to the [uncertainty principle](/source/uncertainty_principle). For a particle of mass M + i\Gamma, the particle can travel for time \tfrac{1}{M}, but decays after time of order of \tfrac{1}{\Gamma}. If \Gamma > M then the particle usually decays before it completes its travel.[https://particleadventure.org/mediator.html "The Particle Adventures"] ==See also== *[Relativistic Breit-Wigner distribution](/source/Relativistic_Breit-Wigner_distribution) *[Particle physics](/source/Particle_physics) *[Particle radiation](/source/Particle_radiation) *[List of particles](/source/List_of_particles) *[Weak interaction](/source/Weak_interaction) ==Notes== {{Reflist}} ==External links== *{{cite journal|author=J. D. Jackson|author-link=John David Jackson (physicist)|title=Kinematics|journal=[Particle Data Group](/source/Particle_Data_Group)|year=2004|url=http://pdg.lbl.gov/2005/reviews/kinemarpp.pdf|access-date=2006-11-26|archive-url=https://web.archive.org/web/20141121115205/http://pdg.lbl.gov/2005/reviews/kinemarpp.pdf|archive-date=2014-11-21|url-status=dead}} (See page 2). *[http://pdg.lbl.gov/ Particle Data Group]. *"[https://web.archive.org/web/20190719141632/http://particleadventure.org/ The Particle Adventure]" [Particle Data Group](/source/Particle_Data_Group), Lawrence Berkeley National Laboratory. Category:Particle physics --- Adapted from the Wikipedia article [Particle decay](https://en.wikipedia.org/wiki/Particle_decay) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Particle_decay?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.