Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

I How does SU(5) explain proton-electron charge equivalence?

  1. Apr 19, 2016 #1
    Hi,

    In my notes it says that SU(5) operates on a five component vector. Fine. But the example given is (d d d e v)

    ie. electron, neutrino and 3 down quarks (one for each colour) it says this explains why the proton charge is the equal and opposite to the electrons but why?

    A proton is uud not ddd.

    Thanks.
     
  2. jcsd
  3. Apr 20, 2016 #2

    haushofer

    User Avatar
    Science Advisor

    Q(up) = Q(down) + 1. See e.g. chapter VII of Zee's QFT.
     
  4. May 30, 2016 #3
    Strictly speaking, the SU(5) GUT breaks into the unbroken Standard Model, and its multiplets have weak-isospin and weak-hypercharge degrees of freedom. Standard-Model breaking then makes electric charge out of them.

    Q = I3 + Y
    (electric charge) = (projected weak isospin) + (weak hypercharge)

    Here are the Standard Model's unbroken elementary-fermion multiplets with (QCD, weak isospin, weak hypercharge) values. A c means charge conjugate:
    • L (left-handed electron, neutrino): (1, 2, -1/2) -- Lc: (1, 2, 1/2)
    • E (right-handed electron): (1,1,-1) -- Ec: (1,1,1)
    • N (right-handed neutrino): (1,1,0) -- Nc: (1,1,0)
    • Q (left-handed up, down quarks): (3,2,1/6) -- Qc: (3*,2,-1/6)
    • U (right-handed up quark): (3,1,2/3) -- Uc: (3*,1,-2/3)
    • D (right-handed down quark: (3,1,-1/3) -- Dc: (3*,1,1/3)

    Here is where they are in the Georgi-Glashow SU(5) model (multiplet number, chirality, indices in asymmetric tensor,):
    • 1L (0): Nc
    • 5R (1): D + Lc
    • 10L (2): Q + Uc + Ec
    • 10R (3): Qc + U + E
    • 5L (4): Dc + L
    • 1R (5): N
    In all of these multiplets, the weak-hypercharge values add up to 0. That's because the weak hypercharge is derived from a SU(5) operator, and SU(N) operators are traceless (diagonal components adding to 0). One can show that these are the only WHC values that are consistent with SU(5), to within a multiplicative factor.

    This is what makes the up quark charged +2/3, the down quark charged -1/3, the neutrino charged 0, and the electron charge -1. Since quarks are confined as multiples of 3, antiquarks being negative quarks, that means that hadrons all have integer charges, just like the electron.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: How does SU(5) explain proton-electron charge equivalence?
  1. Flipped-SU(5) intro? (Replies: 4)

  2. SU(5) subgroups (Replies: 4)

Loading...