What is Majorana: Definition and 61 Discussions

The MAJORANA project (styled Majorana) is an international effort to search for neutrinoless double-beta (0νββ) decay in 76Ge. The project builds upon the work of previous experiments, notably those performed by the Heidelberg–Moscow and IGEX collaborations, which used high-purity germanium (HPGe) detectors, to study neutrinoless double-beta decay.The first stage of the project is the Majorana Demonstrator, designed to demonstrate the technique and evaluate a ton-scale experiment.
Cryostats housing up to 40 kg of natural and enriched germanium detectors are being deployed in low-background vacuum cryostats, underground (1,480 m) at the Sanford Underground Laboratory in Lead, South Dakota. Following the Demonstrator, the collaboration intends to merge with the GERDA collaboration to build a much larger experiment called LEGEND.

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  1. LCSphysicist

    Majorana Fermions: Lagrangean and equations of motion

    $$i \gamma^{\mu} \partial_{\mu} \psi = m \psi_c \\ i \gamma^{\mu} \partial_{\mu} \psi_c = m \psi $$ Where ##\psi_c = C \gamma^0 \psi^*## Show that the above equations can be obtained from the followong lagrangian $$ L = \overline{\psi} i \gamma^{\mu} \partial_{\mu} \psi - \frac{1}{2} m \left...
  2. Vanadium 50

    I Majorana Neutrinos: Different Physics than Oscillation

    [Moderator's note: Spin-off from previous thread due to topic change.] A Majorana mass term is completely different physics from a neutrino oscillating to an antineutrino.
  3. atyy

    I Majorana zero modes observed by Microsoft?

    https://arxiv.org/abs/2207.02472 InAs-Al Hybrid Devices Passing the Topological Gap Protocol "We present measurements and simulations of semiconductor-superconductor heterostructure devices that are consistent with the observation of topological superconductivity and Majorana zero modes."...
  4. F

    A Majorana representation of higher spin states

    In the article by E. Majorana "Oriented atoms in a variable magnetic field", in particular, it's considered (and solved) the problem of describing a state with spin J using 2J points on the Bloch sphere. That is, if the general state of the spin system , (1) then, according...
  5. M

    I Majorana Neutrinos: Evidence of Particle vs. Antiparticle?

    Hello! I don't know much about this topic so I am sorry if my question is silly. As far as I understand if neutrinos are Majorana particles, one consequence is that neutrinos are their own antiparticles. This can be observed, for example, in neutrinoless double beta decay. However, if we take...
  6. M

    I Majorana Mass Plot: Normal & Inverted Hierarchy

    Hello! In the attached plot, we have the Majorana mass as a function of the lightest neutrino for the normal (m1<m2<m3) and inverted (m3<m1<m2) hierarchy. Plugging in the values from the PMNS matrix in the formula for Majorana mass, I get something of the form: ##m_{\beta\beta} =...
  7. Helena Wells

    A If Neutrinos are majorana particles, does this mean lepton number is not conserved?

    If neutrinos are majorana particles does this mean that lepton number is not conserved in particle reactions? And I only noticed neutrinos are only produced when the decay of a particle to some other particles is carried by the W bosons ( weak interaction ). Is it possible the weak interaction...
  8. T

    A Majorana neutrino in matter

    For a Majorana neutrino in matter we have the equation $$(i\gamma^{\mu}\partial_{\mu}-A\gamma_{0})\nu_{L} = m\overline{\nu_{L}}.$$ A is to be considered constant. Squaring, in the ultra-relativistic limit one obtains the dispersion relation $$(E-A)^{2}-p^{2} \simeq mm^{\dagger}$$ i.e. $$p...
  9. gasar8

    Why Does the Majorana Vector Current Vanish?

    Homework Statement I am trying to show that Majorana vector current vanishes. I am following this article and I am trying to get to the very right hand side of eq. (27). Homework Equations \psi_M^C = \psi_M,\\ \psi^C_M = C \overline{\psi}_M^T,\\ C^T=-C, \hspace{1cm} C^T\gamma_{\mu}C =...
  10. YoungPhysicist

    B How could a Majorana fermion exist?

    Acoording to the internet, majorana fermions are particles which its antiparticle is itself. But shouldn't particles and antiparticles annihilate each other? Then how could such particle exist or being predicted?
  11. Kajagoogooooooo

    I Majorana neutrinos, sphaleron reactions, baryon asymmetry

    I`ve spent some time reading about the baryon asymmetry and the Sakharov`s conditions, and there some things I didn't exactly get: 1. Interactions out of thermal equilibrium: isn't it trivial? our universe is expanding so, of course, it out of equilibrium. 2. CP violation: I`ve read that Cronin...
  12. ohwilleke

    I B, L and Majorana Neutrinos

    Background The Standard Model conserves baryon number, which is equal to (quarks divided by three) minus (anti-quarks divided by three) and lepton number, which is equal to leptons minus antileptons, separately, except in sphaleron processes which conserve B-L, but not B or L separately. There...
  13. M

    A Majorana Lagrangian and Majorana/Dirac matrices

    In Lancaster & Burnell book, "QFT for the gifted amateur", chapter 48, it is explained that, with a special set of ##\gamma## matrices, the Majorana ones, the Dirac equation may describe a fermion which is its own antiparticle. Then, a Majorana Lagrangian is considered...
  14. smodak

    B What is the significance of a propagating Majorana mode in topological qubits?

  15. DeathbyGreen

    A Zero Energy Wavefunctions in 1D superconductor

    \bf{Setup} Hi! I am trying to derive the wavefunctions of the zero energy solutions of the Schrodinger equation in a 1D p-wave superconductor (Kitaev model). I am starting with the Hamiltonian $$ \begin{equation} H = \left[\begin{array}{cc} \epsilon_k & \Delta^{\ast}_k\\ \Delta_k & -\epsilon_k...
  16. T

    I Do Neutrinos Need to be Their Own Antiparticle for Majorana Masses to Exist?

    So we are not yet sure exactly what mechanism accounts for the neutrino masses. One possible mechanism is the seesaw mechanism. Am I correct in thinking: Majorana mass terms are born from couplings between particles and antiparticles. This violates lepton number conservation and charge...
  17. T

    I Exploring the Differences Between Dirac and Majorana Masses

    Hello, I am having a real problem trying to figure out what a Majorana mass is. The only thing I gather so far is that dirac mass is the mass that is the result of the Higgs Mechanism. What exactly is the Majorana mass, and for which particles does it exist.Thank you
  18. S

    A ##SU(2)## doublets, Majorana Fermions and Higgs

    Say ##L## and ##L^{c}## are a pair of ##SU(2)## doublets (electroweak-charge fermions) and ##N_{1}## and ##N_{1}^{c}## are a pair of neutral Majorana fermions. Say that these fermions couple to the Higgs via Yukawa coupling and have vector masses ##M_0## and ##M_1## respectively...
  19. T

    A Help with Feynman diagrams involving Majorana Fermions

    Hello everyone, I am trying to compute the ΔF=2 box diagrams in SUSY with gluinos. The relevant diagrams are the following: I want to use the Dirac formalism and NOT the Weyl one. So, the only reference that I have for Feynman rules with Majorana spinors is the old but good SUSY review from...
  20. F

    A Symplectic Majorana Spinors in 5 Dimension

    I need to know if the Symplectic Majorana spinors in 5 dimension have any advantage with respect to the Dirac spinors in 5 dimension, since they have the same number of components. For example if the Symplectic Majorana spinors have a manifested symmetry that the Dirac spinors don't have, or if...
  21. Andrea M.

    I Charge conjugation of Majorana pairs

    I was reading this article (http://arxiv.org/abs/1301.0021) about WIMP pair annihilation. At page six the author says that under charge conjugation a state of Majorana particles with orbital angular momentum ##L## and spin angular momentum ##S## take a phase ##(-1)^{L+S}##. I understand this...
  22. Andrea M.

    Pseudoscalar current of Majorana fields

    Consider a Majorana spinor $$ \Phi=\left(\begin{array}{c}\phi\\\phi^\dagger\end{array}\right) $$ and an pseudoscalar current ##\bar\Phi\gamma^5\Phi##. This term is invariant under hermitian conjugation: $$ \bar\Phi\gamma^5\Phi\to\bar\Phi\gamma^5\Phi $$ but if I exploit the two component...
  23. A

    Understanding Majorana Hamiltonian: Dot Product Notation Explained

    Can someone help me understand the Hamiltonian on the attached picture. What does the notation with the annihilation and creating operators written in a row vector exactly mean? Does it mean I should just take the dot product as written on the picture? Evidently it doesn't since this just gives...
  24. B

    Dirac and Majorana spinors for neutrinos

    Dirac description If I well understood a Dirac description for fermions is : ##\Psi_{D}=\Psi_{L}+\Psi_{R}## where ##\Psi_{L}## is the left-chiral spinor and ##\Psi_{R}## the right-chiral spinor. Each spinor, ##\Psi_{L} ## and ##\Psi_{R}## has 2 components cotrresponding to the particle and...
  25. C

    Chirality for massive neutrinos - right neutrinos - Majorana

    My question concerns the chirality vs helicity for massive neutrinos. I know that as the mass is really light we can usually approximate helicity = chirality. But I would like to consider the exact case with the mass : i.e left handed (chirality )neutrino propagates with both left and right...
  26. L

    Recent news on Ettore Majorana?

    Hi everyone, I was watching a TV programme the other day, where they talked about an Italian physicist, Ettore Majorana, who disappeared in 1938: http://en.wikipedia.org/wiki/Ettore_Majorana Apparently they've recently found evidence that he lived in Venezuela in the 50's, and that his...
  27. S

    Neutrino oscillations and Majorana Phase

    Hello Why are neutrino oscillations insensitive to Majorana phases? I'm guessing it has something to do with them being factored out the PMNS matrix using a diagonal matrix ... i.e. U_PMNS = U Diag (a1, a2, 1) Is there a point in the oscillation calculation where they always cancel due to a...
  28. jim mcnamara

    Majorana Particle Discovery: Princeton Researchers Report Direct Observation

    http://thewestsidestory.net/2014/10/05/18346/obscure-majorna-particle-discovered-encompasses-matter-antimatter/ Reports the direct observation of Majorana particles, by Princeton researchers. Is there anything substantive to this? - or is it just a Science writer getting it wrong?
  29. Matterwave

    Exploring the Nature of Neutrinos: Dirac vs Majorana

    Hi, I recently attended several lectures on the topic of neutrino astrophysics. I wanted to verify some of the fact that I gleaned for them, specifically about the Dirac vs Majorana nature of neutrinos. 1) The most basic fact first. If a neutrino is Dirac in nature, then it has 3 flavors...
  30. L

    How can majorana neutrinos still be CP violating?

    This question is probably very over-simplistic, however: if neutrinos are majorana particles, which are their own antiparticles, how could they still be CP violating? I don't understand precisely how this would work, but physicists I have spoken to said that neutrinos being majorana could...
  31. lpetrich

    Massive Majorana fermions - nontrivial gauge multiplets?

    From supersymmetry, gauge particles have superpartners, gauginos. Supersymmetry breaking will make all the gauginos massive, since none have been observed. But that has certain problems. A gauge field is a multiplet in its gauge group where each member corresponds to a generator of that...
  32. marcus

    DM candidate anapole Majorana fermion

    http://www.eurekalert.org/pub_releases/2013-06/vu-stm061013.php http://arxiv.org/abs/1211.0503 Anapole Dark Matter Chiu Man Ho, Robert J. Scherrer (Submitted on 2 Nov 2012) We consider dark matter (DM) that interacts with ordinary matter exclusively through an electromagnetic anapole, which...
  33. Mordred

    Where can I find technical papers on the Majorana particle?

    Does anyone have any good technical papers covering the Majorana particle? http://www.newscientist.com/article/mg21829160.300-nothing-to-see-the-man-who-made-a-majorana-particle.html
  34. J

    Sign of the time derivative of the Majorana Lagrangian

    Let \gamma^{\rho} \in M_{4}(\mathbb{R}) be the Majorana representation of the Dirac algebra (in spacetime signature \eta_{00} = -1), and consider the Majorana Lagrangian \mathcal{L} = \mathrm{i} \theta^{\mathrm{T}} \gamma^{0} (\gamma^{\rho} \partial_{\rho} - m) \theta, where \theta is a...
  35. P

    Question about the Majorana mass term

    The Majorana mass term is expressed from a single Weyl spinor. But I am a little confused by the expression. For example, see Eq. (2) in http://arxiv.org/pdf/hep-ph/0410370v2.pdf \mathcal{L}=\frac{1}{2}m(\chi^T\epsilon \chi+h.c.) Here \chi is the Weyl spinor and \epsilon = i\sigma^2 is...
  36. Vorde

    Discovering Majorana Fermions - A Groundbreaking Physics Find

    http://science.slashdot.org/story/12/04/13/1547242/scientists-find-long-sought-majorana-particle Is this legitimate? I tried reading the original paper but my physics skills weren't quite enough to keep up with it.
  37. B

    What Are Majorana Particles and What Are their Potential Uses?

    Published in “Science Online” 12 April 2012: “Signatures of Majorana Fermions in Hybrid Superconductor-Semiconductor Nanowire Devices” by V. Mourik, K. Zuo, S. M. Frolov, S. R. Plissard, E. P. A. M. Bakkers, and L. P. Kouwenhoven Abstract Majorana fermions are particles identical to...
  38. P

    Why do Majorana particles occur?

    Why do Majorana particles occur? For example, why is the antiparticle of photon itself?
  39. A

    How to find the Majorana matrices?

    I'm just wondering how the Majorana matrices first were found. I have only seen them immediately written down at different webpages, and never seen a derivation. Is it obvious how to transform the Dirac gamma matrices into the Majorana representation?
  40. R

    Neutrinos as majorana particles or where are left handed antineutrinos?

    Hi everyone, this has been bothering me for a while and even though I've done some light reading on this topic I am struggling to understand it. I know that theory states that we do not see left handed antineutrinos or right handed neutrinos and this is where cp violations comes from. But...
  41. R

    Majorana Propagator: Dirac vs. Majorana Equations

    The Dirac propagator (e.g. for an electron) is given by the inverse of the field equation in momentum space i.e. (\displaystyle{\not} p - m)\psi = 0, which gives: \frac{i}{(\displaystyle{\not} p - m)} = \frac{i(\displaystyle{\not} p + m)}{(p^2-m^2)}. So is the propagator for a Majorana...
  42. Z

    The Neutrino as a Majorana Particle and Ray Davis's null first experiments

    My interests are in astrophysics, so please forgive my ignorance of particle physics. I've just read Frank Close's book, "Neutrino"---excellent read, I'd recommend it---in which he points out that Ray Davis' first experiments to detect neutrinos from nuclear reactors (with no detections)...
  43. P

    When will we know whether neutrinos are Majorana fermions?

    As I understand, the answer will have to come from neutrino-less double beta decay experiments. When will these experiments reach the required sensitivity and gather enough data, to provide us with a definite answer about the nature of neutrinos?
  44. A

    The scalar partner of Majorana particle in SUSY

    For example, the right-handed sneutrino. It can decay into both (s)leptons and anti-(s)leptons, so it is also the anti-particle of itself. I wonder how it looks like mathematically. If it is the same as normal scalar field, we can still distinguish its anti-particle (the complex conjugate)...
  45. Z

    Difference Between Weyl & Majorana Spinnors

    Can anyone explain to me what is the difference between a Weyl spinnor and a Majorana spinnor? Thanks
  46. L

    Feynman rules for Majorana fields (based on Srednicki)

    Hi, So if we have an interaction Lagrangian for a Majorana field: L_1=\tfrac{1}{2} g\phi\Psi^{T}C\Psi Now looking at the path integral, I believe this must go like: Z (\eta^{T},J) ~ \exp{[\tfrac{1}{2} ig \int\,\mathrm{d}^4x (\tfrac{1}{i}\tfrac{\delta}{\delta J(x)...
  47. arivero

    So what's the deal with Majorana, Weyl, and Dirac particles in N dimensions?

    Amusingly, a search on these three words here in PF does not show a lot of postings, so I am creating this thread so you can ask all your doubts about N-dimensional Majorana, Weyl and Dirac particles, their representations, their Lagragians, masses, and whatever you have always wanted to know...
  48. L

    Majorana Path Integral: Deriving VEVs of Barred/Unbarred Fields

    Hi, By analogy with scalar field case, Srednicki leads us to Z_0 (\eta)=\int \mathcal{D}\Psi \exp{\left[i\int\,\mathrm{d}^4x (\mathcal{L}_0+\eta^{T}\psi)\right]} for a Majorana field. I was expecting something different, like maybe: Z_0 (\eta)=\int...
  49. P

    Majorana, Bartlett, Heisenberg Exchanges & Spin Interactions

    \hat{\mathbb{P}}_M\psi(\vec{r}_1,\xi_1;\vec{r}_2,\xi_2)=\psi(\vec{r}_2,\xi_1;\vec{r}_1,\xi_2) Majorana exchange \hat{\mathbb{P}}_B\psi(\vec{r}_1,\xi_1;\vec{r}_2,\xi_2)=\psi(\vec{r}_1,\xi_2;\vec{r}_2,\xi_1) Bartlett exchange...
  50. K

    Majorana particles and U(1) charges

    Hi... Recently read that neutrinos can be Majorana particles only because they are singlets under the unbroken U(1) electromagnetic.. I can understand that...Majorana means that the particle is its own antiparticle..this can't happen if it is charged, as the antiparticle should have...