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Leptons, quarks and hadrons Particle Physics II. Leptons, quarks · PDF filePaula Eerola Lund University 28 Leptons, quarks and hadrons Particle Physics II. Leptons, quarks and hadrons

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  • Paula Eerola Lund University 28

    Leptons, quarks and hadrons Particle Physics

    II. Leptons, quarks and hadrons

    Leptons are spin-1/2 fermions, not subject tostrong interaction

    Electron e-, muon - and tau - havecorresponding neutrinos e, and .

    Electron, muon and tau have electriccharge of -e. Neutrinos are neutral. Neutrinos have very tiny masses. For neutrinos, only weak interactions

    have been observed so far.







    Me < M < M

  • Paula Eerola Lund University 29

    Leptons, quarks and hadrons Particle Physics

    Antileptons are positron e+, positive muon andpositive tau (mu-plus and tau-plus), andantineutrinos:

    Neutrinos and antineutrinos differ by the leptonnumber. Leptons posses lepton numbers L=1 (stands for e, or ), and antileptons have L= -1.

    Lepton numbers are conserved in allinteractions.

    Neutrinos can not be directly registered by any detector,there are only indirect measurements of their properties.

    First indication of neutrino existencecame from -decays of a nucleus N:

    N(Z,A) N(Z+1,A) + e- + e

    -decay is nothing but a neutron decay:



    , +

    , +

  • Paula Eerola Lund University 30

    Leptons, quarks and hadrons Particle Physics

    n p + e- + e

    The existence of an invisibleparticle=neutrino participating in the -decay waspostulated by W. Pauli 1930, to solve the problemof apparent energy and angular momentumnon-conservation in observed reactions (if only 2particles were produced in the decay).

    Note that for the sake of the lepton numberconservation, electron must be accompanied by anelectron-type antineutrino!

    The e mass can be estimated from the electronenergy spectrum in the -decay:

    me Ee MN - me

    Current results from the tritium decay:

    3H 3He + e- + e me 3 eV/c2

    The mass is still too small to be measurable!

    New results are emerging from neutrino oscillationexperiments: if neutrinos have a non-zero mass, they

  • Paula Eerola Lund University 31

    Leptons, quarks and hadrons Particle Physics

    can mix (physical neutrinos are composed of 2 or 3neutrino types). Mixing seems to have beenobserved, best fit result for the mass difference is

    mij2 = (10-4-10-5)eV2/c4 [mij2=mi2-mj2, i=e, j=,]

    An inverse -decay also takes place:

    e + n e- + p (23)


    e + p e+ + n (24)

    However, the probability of these processes is verylow, therefore to register it one needs a very intenseflux of neutrinos

    Reines and Cowan experiment (1956)

    Using antineutrinos produced in anuclear reactor, it is possible to obtain around 2events (10) per hour.

  • Paula Eerola Lund University 32

    Leptons, quarks and hadrons Particle Physics

    To separate the signal from the background, thedelayed coincidence scheme was used: signalfrom neutron comes later than one from positron.

    (a) e interacts with p, producing n and e+

    (b) e+ annihilates with an atomic e-, produces fast softer s through the Compton effect

    (c) n captured by a Cd nucleus, releasing more s.

    Figure 13: Schematic representation of the Reines and Cowan experiment. Aqueous solution of CdCl2 used as the target (Cd used

    to capture neutrons).




    n e+





  • Paula Eerola Lund University 33

    Leptons, quarks and hadrons Particle Physics

    Muons were first observed in 1936, in cosmicrays

    Cosmic rays have two components:

    1) primaries, which are high-energy particles coming from the outer space, mostly hydrogen nuclei

    2) secondaries, the particles which are produced in collisions of primaries with nuclei in the Earth atmosphere; muons belong to this component

    Muons are 200 times heavier thanelectrons and are very penetrating particles.

    Electromagnetic properties of muon areidentical to those of electron (except the massdifference)

    Tau is the heaviest lepton, discovered in e+eannihilation experiments in 1975

    Figure 14: pair production in e+e annihilation





  • Paula Eerola Lund University 34

    Leptons, quarks and hadrons Particle Physics

    Electron is a stable particle, while muon andtau have a finite lifetime:

    = 2.2 x 10-6 s and = 2.9 x 10-13 s

    Muon decays in a purely leptonic mode:

    e + e + (25)

    Tau has a mass sufficient to decay into hadrons, butit has leptonic decay modes as well:

    e + e + (26)

    + + (27)

    Fraction of a particular decay mode withrespect to all possible decays is called branchingratio.

    Branching ratio of the process (26) is 17.84%, and of(27) -- 17.37%.

    Note: lepton numbers are conserved in all reactionsever observed

  • Paula Eerola Lund University 35

    Leptons, quarks and hadrons Particle Physics

    Important assumptions:

    1) Weak interactions of leptons are identical, just like electromagnetic ones (universality of weak interactions)

    2) One can neglect final state lepton masses for many basic calculations

    The decay rate of a muon is given by expression:


    where =B/, =muon lifetime, B=branching ratio,and GF is the Fermi constant.

    Substituting m with m in (28), one obtains decayrates of tau leptonic decays. Since only m appearsin (28), decay rates are equal for processes (26) and(27). It explains why branching ratios of theseprocesses have very close values.

    Using the decay rate, the lifetime of a lepton is:

    - e- e + +( )GF

    2 m5


  • Paula Eerola Lund University 36

    Leptons, quarks and hadrons Particle Physics


    Here l stands for or . Since muons have basicallyonly one decay mode, B=1 in their case. Usingexperimental values of B and formula (28), oneobtains the ratio of muon and tau lifetimes:

    This again is in a very good agreement withindependent experimental measurements

    Universality of lepton interactions is proved to agreat extent. That means that there is basically nodifference between lepton generations, apart of themass and the lepton numbers.

    lB l- e-el( )

    l- e-el( )-------------------------------------=

    ----- 0,178

    mm------- 5

    1,3 710

  • Paula Eerola Lund University 37

    Leptons, quarks and hadrons Particle Physics

    Quarks are spin-1/2 fermions, subject to allinteractions. Quarks have fractional electriccharges.

    Quarks and their bound states are the only particles whichinteract strongly.

    Some historical background:

    Proton and neutron (nucleons) wereknown to interact strongly.

    In 1947, in cosmic rays, new heavyparticles were detected (hadrons).

    By 1960s, in accelerator experiments,many dozens of hadrons were discovered

    An urge to find a kind of periodicsystem lead to the Eightfold Way classification,invented by Gell-Mann and Neeman in 1961,based on the SU(3) symmetry group anddescribing hadrons in terms of building blocks.

    In 1964, Gell-Mann invented quarks asthe building blocks (and Zweig invented aces).

  • Paula Eerola Lund University 38

    Leptons, quarks and hadrons Particle Physics

    The quark model: baryons and antibaryons arebound states of three quarks, and mesons arebound states of a quark and antiquark.

    Hadrons = baryons and mesons.Like leptons, quarks occur in three generations:

    Corresponding antiquarks are:


    Symbol Charge (units of e)Mass

    Down d -1/3 5-8.5 MeV/c2

    Up u +2/3 1.5-4.5 MeV/c2


    , cs

    , tb


    , sc

    , bt

  • Paula Eerola Lund University 39

    Leptons, quarks and hadrons Particle Physics

    Free quarks can never be observedThere is an elegant explanation for this:

    Every quark possesses a new quantumnumber: the colour. There are three differentcolours, thus each quark can have three distinctcolour states. Colours are called red (R), green (G)and blue (B).

    Coloured objects can not appear as freeparticles.

    Therefore quarks must confine into colourlesshadrons.

    Colourless combinations: 3 colour states RGB

    Strange s -1/3 80-155 MeV/c2

    Charmed c +2/3 1.0-1.4 GeV/c2

    Bottom b -1/3 4.0-4.5 GeV/c2

    Top t +2/3 174 GeV/c2


    Symbol Charge (units of e)Mass

  • Paula Eerola Lund University 40

    Leptons, quarks and hadrons Particle Physics

    (RGB), or colour-anticolour (RR, GG, BB, andtheir linear combinations).

    Baryons are bound states of three quarks of differentcolours. Mesons consist of colour-anticolour quarkpairs.

    s-, c-, b- and top quarks have their own quantum

    numbers: strangeness , charm , beauty and truth. These quantum numbers are conserved in strong

    and e.m. interactions, but not in weak ones.

    Some examples of baryons:

    Quark quantum numbers are defined as: S= -1 for

    s-quark, S=1 for s; C=1 for c-quark; = -1 forb-quark, T=1 for t-quark.

    The top-quark has a very short lifetime, so it doesnt




    (units of e) S C

    p 0.938 uud 1 0 0 0

    n 0.940 udd 0 0 0 0

    1.116 uds 0 -1 0 0

    c 2.285 udc 1 0 1 0

    S C BT



  • Paula Eerola Lund University 41

    Leptons, quarks and hadrons Particle Physics

    form hadrons before decaying T=0 for all hadrons.

    Quark numbers for u- and d-quarks have no name,but just like the other flavours, they are conserved instrong and electromagnetic interactions.

    Baryons are assigned own

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