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particle decay wikipedia jump to content main menu main menu move to sidebar hide navigation main page contents current events random article about wikipedia contact us contribute help learn to edit community portal recent changes upload file special pages search search appearance donate create account log in personal tools donate create account log in contents move to sidebar hide top 1 probability of survival and particle lifetime toggle probability of survival and particle lifetime subsection 1 1 table of some elementary and composite particle lifetimes 2 decay rate 3 two body decay toggle two body decay subsection 3 1 decay rate 3 2 from two different frames 4 complex mass and decay rate 5 see also 6 notes 7 external links toggle the table of contents particle decay 16 languages العربية čeština español فارسی français हिन्दी bahasa indonesia italiano 日本語 русский தமிழ் tagalog türkçe українська tiếng việt 中文 edit links article talk english read edit view history tools tools move to sidebar hide actions read edit view history general what links here related changes upload file permanent link page information cite this page get shortened url switch to legacy parser print export download as pdf printable version in other projects wikidata item appearance move to sidebar hide from wikipedia the free encyclopedia spontaneous breakdown of an unstable subatomic particle into other particles in particle physics particle decay is the spontaneous process of one unstable 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 of the system must be conserved a particle is unstable if there is at least one allowed final state that it can decay into unstable particles will often have multiple ways of decaying each with its own associated probability decays are mediated by one or several 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 in which an unstable atomic nucleus is transformed into a lighter nucleus accompanied by the emission of particles or radiation although the two are conceptually similar and are often described using the same terminology probability of survival and particle lifetime edit particle decay is a poisson process and hence the probability that a particle survives for time t before decaying the survival function is given by an exponential distribution whose time constant depends on the particle s velocity p t exp t γ τ displaystyle p t exp left frac t gamma tau right where τ displaystyle tau is the mean lifetime of the particle when at rest and γ 1 1 v 2 c 2 displaystyle gamma tfrac 1 sqrt 1 frac v 2 c 2 is the lorentz factor of the particle table of some elementary and composite particle lifetimes edit all data are from the particle data group type name symbol mass mev mean lifetime lepton electron positron 1 e e displaystyle mathrm e mathrm e 0 511 6 6 10 28 years muon antimuon μ μ displaystyle mathrm mu mathrm mu 105 7 2 2 10 6 seconds tau lepton antitau τ τ displaystyle mathrm tau mathrm tau 1777 2 9 10 13 seconds meson neutral pion π 0 displaystyle mathrm pi 0 135 8 4 10 17 seconds charged pion π π displaystyle mathrm pi mathrm pi 139 6 2 6 10 8 seconds baryon proton antiproton 2 3 p p displaystyle mathrm p mathrm p 938 2 1 67 10 34 years neutron antineutron n n displaystyle mathrm n mathrm bar n 939 6 885 7 seconds boson w boson w w displaystyle mathrm w mathrm w 80400 10 26 seconds z boson z 0 displaystyle mathrm z 0 91000 10 26 seconds decay rate edit this section uses natural units where c ℏ 1 displaystyle c hbar 1 the lifetime of a particle is given by the inverse of its decay rate γ the probability per unit time that the particle will decay for a particle of a mass m and four momentum p decaying into particles with momenta p i the differential decay rate is given by the general formula expressing fermi s golden rule d γ n s m 2 2 m d φ n p p 1 p 2 p n displaystyle d gamma _ n frac s left mathcal m right 2 2m d phi _ n p p_ 1 p_ 2 dots p_ n where n is the number of particles created by the decay of the original s is a combinatorial factor to account for indistinguishable final states see below m displaystyle mathcal m is the invariant matrix element or amplitude connecting the initial state to the final state usually calculated using feynman diagrams d φ n displaystyle d phi _ n is an element of the phase space and p i is the four momentum of particle i the factor s is given by s j 1 m 1 k j displaystyle s prod _ j 1 m frac 1 k_ j where m is the number of sets of indistinguishable particles in the final state and k j is the number of particles of type j so that j 1 m k j n displaystyle sum _ j 1 m k_ j n the phase space can be determined from d φ n p p 1 p 2 p n 2 π 4 δ 4 p i 1 n p i i 1 n d 3 p i 2 2 π 3 e i displaystyle 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 δ 4 displaystyle delta 4 is a four dimensional dirac delta function p i displaystyle vec p _ i is the three momentum of particle i and e i displaystyle e_ i is the energy of particle 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 for each mode is given by its decay rate divided by the full decay rate two body decay edit this section uses natural units where c ℏ 1 displaystyle c hbar 1 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 while in the lab frame the parent particle is probably moving at a speed close to the speed of light so the two emitted particles would come out at angles different from those in the center of momentum frame decay rate edit say a parent particle of mass m decays into two particles labeled 1 and 2 in the rest frame of the parent particle p 1 p 2 m 2 m 1 m 2 2 m 2 m 1 m 2 2 2 m displaystyle 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 be conserved in the decay i e m 0 e 1 p 1 e 2 p 2 displaystyle m vec 0 e_ 1 vec p _ 1 e_ 2 vec p _ 2 also in spherical coordinates d 3 p p 2 d p d ϕ d cos θ displaystyle 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 p 2 displaystyle d 3 vec p _ 2 and d p 1 displaystyle 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 γ m 2 32 π 2 p 1 m 2 d ϕ 1 d cos θ 1 displaystyle 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 edit 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 θ sin θ γ β β cos θ displaystyle tan theta frac sin theta gamma left beta beta cos theta right complex mass and decay rate edit further information resonance atomic particle and molecular resonance and resonance particle physics this section uses natural units where c ℏ 1 displaystyle c hbar 1 the mass of an unstable particle is formally a complex number with the real part being its mass in the usual sense and the imaginary part being its decay rate in natural units when the imaginary part is large compared to the real part the particle is usually thought of as a resonance more than a particle this is because in quantum field theory a particle of mass m a 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 1 m displaystyle tfrac 1 m according to the uncertainty principle for a particle of mass m i γ displaystyle m i gamma the particle can travel for time 1 m displaystyle tfrac 1 m but decays after time of order of 1 γ displaystyle tfrac 1 gamma if γ m displaystyle gamma m then the particle usually decays before it completes its travel 4 see also edit relativistic breit wigner distribution particle physics particle radiation list of particles weak interaction notes edit electron lifetime is at least 66 000 yottayears physics world 9 december 2015 bajc borut hisano junji kuwahara takumi omura yuji 2016 threshold corrections to dimension six proton decay operators in non minimal susy su 5 guts nuclear physics b 910 1 22 arxiv 1603 03568 bibcode 2016nuphb 910 1b doi 10 1016 j nuclphysb 2016 06 017 s2cid 119212168 how certain are we that protons don t decay forbes the particle adventures external links edit j d jackson 2004 kinematics pdf particle data group archived from the original pdf on 2014 11 21 retrieved 2006 11 26 see page 2 particle data group the particle adventure particle data group lawrence berkeley national laboratory retrieved from https en wikipedia org w index php title particle_decay oldid 1343007413 category particle physics hidden categories articles with short description short description is different from wikidata this page was last edited on 11 march 2026 at 19 03 utc page was rendered with parsoid text is available under the creative commons attribution sharealike 4 0 license additional terms may apply by using this site you agree to the terms of use and privacy policy wikipedia is a registered trademark of the wikimedia foundation inc a non profit organization privacy policy about wikipedia disclaimers contact wikipedia legal safety contacts code of conduct developers statistics cookie statement mobile view search search toggle the table of contents particle decay 16 languages add topic