Why EM and weak interaction are unified

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SUMMARY

The discussion centers on the unification of electromagnetic (EM) and weak interactions within the framework of the electroweak theory, specifically the ##SU(2)\otimes U(1)## model. While both interactions stem from this theory, they do not unify in the sense required by Grand Unified Theories (GUTs), as they maintain independent gauge groups and couplings. The weak interaction's coupling constant behaves differently at low energies compared to the EM interaction, leading to the perception of weakness. The discussion highlights the ambition of GUTs to derive the Standard Model's gauge groups from a single gauge group.

PREREQUISITES
  • Understanding of electroweak theory and its components, specifically ##SU(2)\otimes U(1)##.
  • Knowledge of coupling constants and their role in particle interactions.
  • Familiarity with Grand Unified Theories (GUTs) and their objectives.
  • Basic grasp of particle physics, particularly the Standard Model.
NEXT STEPS
  • Research the implications of gauge group unification in Grand Unified Theories (GUTs).
  • Study the mathematical framework of electroweak theory and its gauge groups.
  • Examine the behavior of coupling constants at different energy scales in particle physics.
  • Explore the differences between weak and electromagnetic interactions in detail.
USEFUL FOR

Physicists, students of particle physics, and anyone interested in the theoretical foundations of the Standard Model and the unification of fundamental forces.

karlzr
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In SM, people say the ##SU(2)\otimes U(1)## theory unify the EM and weak interaction. I understand that the two interactions both originate from the electroweak theory in a mixed way. But does this mean they are unified? Since when we talk about unification like GUT, we require the couplings run to the same value at a high unification scale. I don't see it in electroweak theory. So how should we interpret the difference?
 
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Yes, you can justifiably complain that the electroweak theory does not really unify anything since it still has two independent gauge groups, SU(2) and U(1), with independent couplings. Ideally we might have hoped that both forces would arise from a single gauge group. GUTs are more ambitious and seek to derive the SU(3), SU(2), and U(1) of the Standard Model from a single gauge group.
 
The weak and EM couplings are the same alpha=1/137. However the weak interaction depends on
alpha/(M_W^2+Q^2), while EM is alpha/Q^2, so the weak looks weak at low energies.
 

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