Skip to main content
replaced http://physics.stackexchange.com/ with https://physics.stackexchange.com/
Source Link

Charged particles can't have Majorana masses of any type because they would violate the charge conservation law. The Majorana mass is really a term that is converting a particle into its antiparticle. It implies that the particle must be considered "physically indistinguishable" from its antiparticle.

The Majorana mass term violates the lepton number or its generalization – the number of "particles minus antiparticles" – by $\Delta L = \pm 2$. It has the form $$ m \eta_A \eta_B \epsilon^{AB} + \text{complex conjugate terms} $$ where the first term contains no complex conjugation of any factor, so it creates two equal particles (or annihilates two equal particles; or annihilates a particle and creates an antiparticle, or vice versa).

That's clearly impossible for particles that carry a nonzero conserved additive charge such as the electric charge. Only neutral fermions – in the Standard Model, only the neutrinos – may have a Majorana mass term.

And because in the Standard Model, the visible left-handed neutrino is a component of a doublet with the charged particle that prohibits the Majorana term, as I just argued, the neutrino Majorana mass can't be there at a tree levelneutrino Majorana mass can't be there at a tree level, either. It has to be generated as an effective interaction.

Charged particles can't have Majorana masses of any type because they would violate the charge conservation law. The Majorana mass is really a term that is converting a particle into its antiparticle. It implies that the particle must be considered "physically indistinguishable" from its antiparticle.

The Majorana mass term violates the lepton number or its generalization – the number of "particles minus antiparticles" – by $\Delta L = \pm 2$. It has the form $$ m \eta_A \eta_B \epsilon^{AB} + \text{complex conjugate terms} $$ where the first term contains no complex conjugation of any factor, so it creates two equal particles (or annihilates two equal particles; or annihilates a particle and creates an antiparticle, or vice versa).

That's clearly impossible for particles that carry a nonzero conserved additive charge such as the electric charge. Only neutral fermions – in the Standard Model, only the neutrinos – may have a Majorana mass term.

And because in the Standard Model, the visible left-handed neutrino is a component of a doublet with the charged particle that prohibits the Majorana term, as I just argued, the neutrino Majorana mass can't be there at a tree level, either. It has to be generated as an effective interaction.

Charged particles can't have Majorana masses of any type because they would violate the charge conservation law. The Majorana mass is really a term that is converting a particle into its antiparticle. It implies that the particle must be considered "physically indistinguishable" from its antiparticle.

The Majorana mass term violates the lepton number or its generalization – the number of "particles minus antiparticles" – by $\Delta L = \pm 2$. It has the form $$ m \eta_A \eta_B \epsilon^{AB} + \text{complex conjugate terms} $$ where the first term contains no complex conjugation of any factor, so it creates two equal particles (or annihilates two equal particles; or annihilates a particle and creates an antiparticle, or vice versa).

That's clearly impossible for particles that carry a nonzero conserved additive charge such as the electric charge. Only neutral fermions – in the Standard Model, only the neutrinos – may have a Majorana mass term.

And because in the Standard Model, the visible left-handed neutrino is a component of a doublet with the charged particle that prohibits the Majorana term, as I just argued, the neutrino Majorana mass can't be there at a tree level, either. It has to be generated as an effective interaction.

added 70 characters in body
Source Link
Luboš Motl
  • 181.3k
  • 15
  • 413
  • 643

Charged particles can't have Majorana masses of any type because they would violate the charge conservation law. The Majorana mass is really a term that is converting a particle into its antiparticle. It implies that the particle must be considered "physically indistinguishable" from its antiparticle.

The Majorana mass term violates the lepton number or its generalization – the number of "particles minus antiparticles" – by $\Delta L = \pm 2$. It has the form $$ m \eta_A \eta_B \epsilon^{AB} + \text{complex conjugate terms} $$ where the first term contains no complex conjugation of any factor, so it creates two equal particles (or annihilates two equal particlesparticles; or annihilates a particle and creates an antiparticle, or vice versa).

That's clearly impossible for particles that carry a nonzero conserved additive charge such as the electric charge. Only neutral fermions – in the Standard Model, only the neutrinos – may have a Majorana mass term.

And because in the Standard Model, the visible left-handed neutrino is a component of a doublet with the charged particle that prohibits the Majorana term, as I just argued, the neutrino Majorana mass can't be there at a tree levelneutrino Majorana mass can't be there at a tree level, either. It has to be generated as an effective interaction.

Charged particles can't have Majorana masses of any type because they would violate the charge conservation law. The Majorana mass is really a term that is converting a particle into its antiparticle. It implies that the particle must be considered "physically indistinguishable" from its antiparticle.

The Majorana mass term violates the lepton number or its generalization – the number of "particles minus antiparticles" – by $\Delta L = \pm 2$. It has the form $$ m \eta_A \eta_B \epsilon^{AB} + \text{complex conjugate terms} $$ where the first term contains no complex conjugation of any factor, so it creates two equal particles (or annihilates two equal particles).

That's clearly impossible for particles that carry a nonzero conserved additive charge such as the electric charge. Only neutral fermions – in the Standard Model, only the neutrinos – may have a Majorana mass term.

And because in the Standard Model, the visible left-handed neutrino is a component of a doublet with the charged particle that prohibits the Majorana term, as I just argued, the neutrino Majorana mass can't be there at a tree level, either. It has to be generated as an effective interaction.

Charged particles can't have Majorana masses of any type because they would violate the charge conservation law. The Majorana mass is really a term that is converting a particle into its antiparticle. It implies that the particle must be considered "physically indistinguishable" from its antiparticle.

The Majorana mass term violates the lepton number or its generalization – the number of "particles minus antiparticles" – by $\Delta L = \pm 2$. It has the form $$ m \eta_A \eta_B \epsilon^{AB} + \text{complex conjugate terms} $$ where the first term contains no complex conjugation of any factor, so it creates two equal particles (or annihilates two equal particles; or annihilates a particle and creates an antiparticle, or vice versa).

That's clearly impossible for particles that carry a nonzero conserved additive charge such as the electric charge. Only neutral fermions – in the Standard Model, only the neutrinos – may have a Majorana mass term.

And because in the Standard Model, the visible left-handed neutrino is a component of a doublet with the charged particle that prohibits the Majorana term, as I just argued, the neutrino Majorana mass can't be there at a tree level, either. It has to be generated as an effective interaction.

Source Link
Luboš Motl
  • 181.3k
  • 15
  • 413
  • 643

Charged particles can't have Majorana masses of any type because they would violate the charge conservation law. The Majorana mass is really a term that is converting a particle into its antiparticle. It implies that the particle must be considered "physically indistinguishable" from its antiparticle.

The Majorana mass term violates the lepton number or its generalization – the number of "particles minus antiparticles" – by $\Delta L = \pm 2$. It has the form $$ m \eta_A \eta_B \epsilon^{AB} + \text{complex conjugate terms} $$ where the first term contains no complex conjugation of any factor, so it creates two equal particles (or annihilates two equal particles).

That's clearly impossible for particles that carry a nonzero conserved additive charge such as the electric charge. Only neutral fermions – in the Standard Model, only the neutrinos – may have a Majorana mass term.

And because in the Standard Model, the visible left-handed neutrino is a component of a doublet with the charged particle that prohibits the Majorana term, as I just argued, the neutrino Majorana mass can't be there at a tree level, either. It has to be generated as an effective interaction.