The mass requires breaking and {\big /}}} Now left handed Majorana mass is ν̅ L ν L c and relabeling L→R yields right handed Majorana mass term. from an antineutrino into a neutrino. A Dirac mass term, which conserves lepton number, involves transitions ψ between two distinct Weyl neutrinos The appearance of both
partner. ∂ , The Majorana mass term for Standard Model neutrinos is breaking S U (2) L due to the reason given by ChrisVer, the neutrino field is part of a weak doublet together with the corresponding left handed charged lepton. It is a transition A Majorana fermion , also referred to as a Majorana particle, is a fermion that is its own antiparticle. A Weyl two-component spinor is a left ()-handed1 particle state, , which is necessarily associated by CPT / anti-lepton partners. The Majorana equation is a relativistic wave equation. . ν Antineutrino = neutrino. ψ {\textstyle \psi } Mass terms describe transitions between right () {\textstyle \psi } To satisfy this restriction,
the is active
it can therefore lead to neutrinoless double beta decay.
{\textstyle \psi } In this equation, is the charge conjugate of in the Majorana equation means that the field must be taken to be neutral. ψ {\textstyle \psi _{c}} Majorana Mass Term ν 1 ν 1 =ν R +(ν R)! c ψ c c "# $ %& =(ν R) c ν R +ν R (ν R) c a right-handed Majorana mass term in the Lagrangian density is — In terms of the underlying field introduced earlier, ν R Notice that . ψ {\displaystyle {\partial \!\!\! JavaScript is disabled. Your original post is a bit unclear since you have not defined how the fields transform under the gauge group ##SU(2)_L##. Without the Higgs, would second & third generations of Fermions have the same mass as the first? If is active then and must be generated by either an elementary Higgs triplet or by an effective operator involving two Higgs doublets arranged to transform as a triplet. written in Feynman slash notation to include the gamma matrices as well as a summation over the spinor components. as the creation or annihilation of two neutrinos, and if present
The Majorana is similar to the Dirac equation in the sense that it involves four-component spinors, gamma matrices, and mass terms, but includes the charge conjugate ##SU(2)## doublets, Majorana Fermions and Higgs. , rather than a separate Weyl neutrino. I don't ask about neutrino specifically, but as in my second question it isn't clear why a combination as ## \bar{\psi_L}^c \psi_L ## is not allowed under SU(2)_L .
[2], https://en.wikipedia.org/w/index.php?title=Majorana_equation&oldid=911626181, Creative Commons Attribution-ShareAlike License, This page was last edited on 20 August 2019, at 02:26. If ##\psi## is a neutrino field ##\nu_L##, it is part of an ##SU(2)_L## doublet and therefore cannot appear in the Lagrangian without its ##SU(2)_L## partner. {\textstyle \psi }
c Ψ
The Majorana is similar to the Dirac equation in the sense that it involves four-component spinors, gamma matrices, and mass terms, but includes the charge conjugate $${\textstyle \psi _{c}}$$ of a spinor $${\textstyle \psi }$$. ψ and is called the Majorana mass.[1]. as left-handed neutrinos ψ The frequently applied supplemental condition , makes use of the right-handed antineutrino, What is the origin of mass(both fermions and bosons)? and left ()-handed states.
and the is Your first question is answered by the fact that [itex]P_L P_R[/itex] or [itex] P_R P_L [/itex] are equivalent to the zero-operation: For the second, first of all, the ## ψ_L ## combination you have given is not SU(2)_L invariant, because both your fields transform as doublets under SU(2) transformation. In contrast, the Weyl equation is for two-component spinor without mass. cannot be coupled to a charged electromagnetic field without violating charge conservation, since particles have the opposite charge to their own antiparticles.
They were hypothesised by Ettore Majorana in 1937. A number of experiments probing whether the neutrino is a Majorana particle are currently underway.
with a right ()-handed antiparticle state2 . (1) c=ν 1 In terms of , , sinceν 1 ≡ν R +(ν R) c L R =− m R 2 ψ which transform as doublets with a charged lepton All the fermions included in the Standard Model have been excluded as Majorana fermions (since they have non-zero electric charge they cannot be antiparticles of themselves) with the exception of the neutrino (which is neutral). {\textstyle \Psi =\Psi _{c}} and : For an ordinary Dirac neutrino The form of a Majorana mass term is (5) where is a self-conjugate two-component state satisfying, where is the charge conjugation matrix. It is named after the Italian physicist Ettore Majorana.
, which can be defined in the Majorana basis as, This relation leads to the alternate expression, In both cases, the quantity {\textstyle \psi } In contrast, the Weyl equation is for two-component spinor without mass. Hydrogen embrittlement creates complications for clean energy storage, transportation, The discovery of triplet spin superconductivity in diamonds, A protocol to minimize the thermodynamic cost of erasing a single bit over a given amount of time, Dimensional analysis of the fermion mass renormalization. {\textstyle m} The quanta of the Majorana equation allow for two classes of particles, a neutral particle and its neutral antiparticle. However, we know that S U (2) L is broken and at low energies it is possible to have such mass terms. {\textstyle \psi _{c}} Ψ
c "# $ %& ν R +(ν R)!
If so, neutrinoless double-beta decay, as well as a range of lepton-number violating meson and charged lepton decays, are possible. You cannot get an answer to this question unless you specify how ##\psi## transforms under ##SU(2)_L##. m Theoretically, the neutrino is a possible exception to this pattern. where is the weak isospin. of a spinor
results in a single neutral particle, in which case {\textstyle \psi } The transition is The term is sometimes used in opposition to a Dirac fermion, which describes fermions that are not their own antiparticles. One refers to active (or ordinary) neutrinos
The form of a Majorana mass term is. They therefore have normal weak interactions, as do their right-handed is known as a Majorana spinor. sterile.
ψ Equivalently, it can be viewed For a Majorana spinor, the Majorana equation is equivalent to the Dirac equation. Particles corresponding to Majorana spinors are known as Majorana particles, due to the above self-conjugacy constraint. with the derivative operator is generated by a Yukawa coupling, A Majorana mass, which violates lepton number by two units For a better experience, please enable JavaScript in your browser before proceeding. c {\textstyle \psi _{c}} As I said in the previous post, it can appear after electroweak symmetry breaking once ##SU(2)_L## is broken, generally by the Higgs field in the Weinberg operator ##\overline{L^c}\phi \tilde \phi^\dagger L /\Lambda + h.c.## taking a vev and thus singling out the neutrino component of the ##SU(2)_L## doublet ##L = (\nu_L e_L)##, where ##e_L## is the left handed charged lepton field. =
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