DOCSLIB.ORG

Constructing Dirac Linear Fermions in Terms of Non-Linear Heisenberg Spinors

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Constructing Dirac Linear Fermions in Terms of Non-Linear Heisenberg Spinors Home Search Collections Journals About Contact us My IOPscience Constructing Dirac linear fermions in terms of non-linear Heisenberg spinors This content has been downloaded from IOPscience. Please scroll down to see the full text. 2007 EPL 80 41001 (http://iopscience.iop.org/0295-5075/80/4/41001) View the table of contents for this issue, or go to the journal homepage for more Download details: IP Address: 152.84.100.12 This content was downloaded on 04/11/2015 at 12:22 Please note that terms and conditions apply. November 2007 EPL, 80 (2007) 41001 www.epljournal.org doi: 10.1209/0295-5075/80/41001 Constructing Dirac linear fermions in terms of non-linear Heisenberg spinors M. Novello Institute of Cosmology, Relativity and Astrophysics ICRA/CBPF - Rua Dr. Xavier Sigaud 150, Urca 22290-180 Rio de Janeiro, RJ, Brazil received 14 June 2007; accepted in final form 14 September 2007 published online 17 October 2007 PACS 14.60.Pq – Neutrino mass and mixing Abstract – We show that the massive (or massless) neutrinos can be described as special states of Heisenberg nonlinear spinors. As a by-product of this decomposition a particularly attractive consequence appears: the possibility of relating the existence of only three species of mass-less neutrinos to such internal non-linear structure. At the same time it allows the possibility that neutrino oscillation can occur even for massless neutrinos. Copyright c EPLA, 2007 There are evidences that neutrino changes from one property is not exclusive for neutrinos but instead is typi- flavor to another as observed for instance in neutrino cal for any Dirac fermion (e.g., quark, electron). However oscillations found by the Super-Kamiokande Collabora- as we shall see, the decomposition of the Dirac fermion in tion [1,2]. This mix is understood as an evidence that terms of non-linear structure contains three parameters the neutrino has a small mass [3]. This has important (associated to the Heisenberg self-interaction constant) consequences not only in local laboratory experiments but that separate different classes of Dirac spinors and three also in astrophysics and even in cosmology. In a closely elements for each class that could be associated to three related path, the possibility that not only left-handed but types of particles in each class. This form of decomposition also right-handed neutrinos exist has recently attracted may appear as if we were inverting the common procedure interest, receiving a new treatment in a very imaginative and treating the simple linear case of Dirac spinor as example presented in [4] dealing with the possibility of a particular state of a more involved self-interacting neutrino superfluidity. The main idea requires the exis- nonlinear structure. This goes in the same direction as tence of an interaction between neutrinos that in the case some modern treatments in which linearity is understood of small energy and momentum can be described as a sort as a realization of a subjacent nonlinear structure. In this of Fermi process involving terms like (νν)(νν). If the ν’s vein we will examine the hypothesis that neutrinos are are the same, this interaction is nothing but an old theory special states of nonlinear Heisenberg spinors. of Heisenberg concerning self-interacting fermions [5]. The argument is based on two fundamental equations: Recent experiments [6] strongly support the idea that the linear Dirac equation of motion there are only three neutrino flavours. Based on this and µ D D iγ ∂µ Ψ − M Ψ = 0 (1) on the possibility of mixing neutrino species, it has been 1 argued [3] that neutrino flavours να are combinations of and the non linear Heisenberg theory mass eigenstates νi of mass mi through a unitary N × N µ H 5 H iγ ∂µ Ψ − 2s (A + iBγ )Ψ = 0 (2) matrix Uαi. 2 It would be interesting if we could describe all these in which the constant s has the dimension of (lenght) properties as consequences of the existence of a common and the quantities A and B are given in terms of the root for the neutrino species, e.g., if they are particular Heisenberg spinor ΨH as realizations of a unique structure. In this paper we will H develop a model of such idea and work out a unified A ≡ Ψ ΨH (3) description of the three species of neutrinos by showing 1This equation represents a self-interacting spinor field driven that they can be considered as having a common origin by a Lagrangian of the form typical of Fermi processes, e.g., µ on a more fundamental nonlinear structure. Actually such Lint = sJµJ . 41001-p1 M. Novello and Now, the derivative of the currents yields H B ≡ iΨ γ5ΨH (4) ∂µJν − ∂ν Jµ =(a + a)[Jµ,Jν ]+(b + b)[Iµ,Iν ] The Heisenberg spinor ΨH can be depicted as a line making an angle of 45 degrees with each axis representing and ΨL and ΨR in the two-dimensional plane π generated ∂µIν − ∂ν Iµ =(a + a − b − b)[Jµ Iν − Iµ Jν ]. by left-hand and right-hand spinors as follows from the identity: Thus the condition of integrability is given by 1 1 ΨH =ΨH +ΨH = (1 + γ5)ΨH + (1 − γ5)ΨH . (5) Re(a)=Re(b). (8) L R 2 2 It is a rather long and tedious work to show that any The main outcome of the present paper is the proof combination X constructed with Ψ and for all elements of the statement that a massive or massless neutrino of the Clifford algebra, the compatibility condition that satisfies Dirac equation (1) can be described as a [∂µ,∂ν ]X = 0 is automatically fulfilled once this unique deformation of the Heisenberg spinor in the π plane. We condition (8) is satisfied. are, indeed, claiming that it is possible to write the Dirac H Let us now turn to some remarkable properties of spinor as a deformation of Ψ in the plane π given by I-spinors. µ D F H G H Lemma. The current four-vector J is irrotational. The Ψ = e Ψ + e Ψ , (6) L R same is valid for the axial-current Iµ. µ or, in other words, that the left- and the right-handed Proof. The proof that the vector J is the gradient of D F H D G H a certain scalar quantity is a simple direct consequence Dirac spinors are given by ΨL = e ΨL and ΨR = e ΨR . What are the properties of F and G in order that ΨD of its definition in terms of H-spinors. However there is satisfies eq. (1)? a further property that is worth of mention: this scalar is nothing but the norm J 2 of the current. Indeed, using The Inomata solution of Heisenberg dynamics. – equation (7), we have In [7] a particular class of solutions of Heisenberg equation was set out. The interest on this class rests on the fact that ∂µJν =(a + a)JµJν +(b + b)IµIν . (9) it directly allows one to deal with the derivatives of the This expression shows that the derivative of the four- spinor field, consequently allowing to obtain derivatives of vector current is symmetric. Multiplying eq. (9) by J µ any associated function of the spinor. Let us briefly present it follows then this class of spinors. The analysis starts by the recognition Jµ = ∂µS, (10) that it is possible to construct a sub-class of solution of Heisenberg dynamics by imposing a restrictive condition in which the scalar S is written in terms of the norm 2 ≡ µ given by J JµJ : 5 1 √ ∂µΨ= aJµ + bIµγ Ψ, (7) S = ln J 2. (11) a + a where a and b are complex numbers of dimensionality 2 Note that S = const defines a hypersurface in space- (lenght) . This is a generalization, for the non-linear case, time such that the current Jµ is not only geodesic but of a similar condition in the linear case provided by plane orthogonal to S. It follows that waves, that is, ∂µΨ=ikµ Ψ. µν 2(a+a)S A Ψ that satisfies condition (7) will be called an Inomata ∂µS∂ν Sη = e , spinor. It is immediate to prove that if Ψ satisfies this condition it satisfies automatically Heisenberg equation of or, defining the conformal metric motion if a and b aresuchthat2s = i (a − b). c ≡ 2(a+a) S This is a rather strong condition that deals with simple gµν e ηµν , derivatives instead of the scalar structure obtained by the we write contraction with γµ typical of Dirac or even for the Heisen- µν ∂µS∂ν Sg =1, (12) berg operators that appear in both equations (1) and (2). c Prior to anything one has to examine the compatibility showing that S is an eikonal in the associated conformal of such condition which concerns all quantities that can space. be constructed with such spinors. It is a remarkable result Lemma. The two four-vectors Jµ and Iµ constitute that, in order that the restrictive condition eq. (7) be inte- a basis for vectors constructed by the derivative ∂µ grable, constants a and b must satisfy a unique constraint operating on functionals of Ψ. given by Re(a) − Re(b)=0. Proof. It is enough to show that this assertion is true Indeed, we have for the scalars A and B. Indeed, we have 5 [∂µ,∂ν ]Ψ= a∂[µ Jν] + b∂[µ Iν] γ Ψ. ∂µ A =(a + a) AJµ +(b − b) iB Iµ (13) 41001-p2 Constructing Dirac linear fermions in terms of non-linear Heisenberg spinors and Multiplying these expressions by iγµ it follows that ΨD ∂µ B =(a + a) BJµ +(b − b) iAIµ.
Load more

Recommended publications
  • Effective Dirac Equations in Honeycomb Structures
    Effective Dirac equations in honeycomb structures Effective Dirac equations in honeycomb structures Young Researchers Seminar, CERMICS, Ecole des Ponts ParisTech William Borrelli CEREMADE, Universit´eParis Dauphine 11 April 2018 It is self-adjoint on L2(R2; C2) and the spectrum is given by σ(D0) = R; σ(D) = (−∞; −m] [ [m; +1) The domain of the operator and form domain are H1(R2; C2) and 1 2 2 H 2 (R ; C ), respectively. Remark The negative spectrum is associated with antiparticles, in relativistic theories. Effective Dirac equations in honeycomb structures Dirac in 2D The 2D Dirac operator The 2D Dirac operator is defined as D = D0 +mσ3 = −i(σ1@1 + σ2@2) + mσ3: (1) where σk are the Pauli matrices and m ≥ 0 is the mass of the particle. It acts on C2-valued spinors. The domain of the operator and form domain are H1(R2; C2) and 1 2 2 H 2 (R ; C ), respectively. Remark The negative spectrum is associated with antiparticles, in relativistic theories. Effective Dirac equations in honeycomb structures Dirac in 2D The 2D Dirac operator The 2D Dirac operator is defined as D = D0 +mσ3 = −i(σ1@1 + σ2@2) + mσ3: (1) where σk are the Pauli matrices and m ≥ 0 is the mass of the particle. It acts on C2-valued spinors. It is self-adjoint on L2(R2; C2) and the spectrum is given by σ(D0) = R; σ(D) = (−∞; −m] [ [m; +1) Effective Dirac equations in honeycomb structures Dirac in 2D The 2D Dirac operator The 2D Dirac operator is defined as D = D0 +mσ3 = −i(σ1@1 + σ2@2) + mσ3: (1) where σk are the Pauli matrices and m ≥ 0 is the mass of the particle.
    [Show full text]
  • 2 Lecture 1: Spinors, Their Properties and Spinor Prodcuts
    2 Lecture 1: spinors, their properties and spinor prodcuts Consider a theory of a single massless Dirac fermion . The Lagrangian is = ¯ i@ˆ . (2.1) L ⇣ ⌘ The Dirac equation is i@ˆ =0, (2.2) which, in momentum space becomes pUˆ (p)=0, pVˆ (p)=0, (2.3) depending on whether we take positive-energy(particle) or negative-energy (anti-particle) solutions of the Dirac equation. Therefore, in the massless case no di↵erence appears in equations for paprticles and anti-particles. Finding one solution is therefore sufficient. The algebra is simplified if we take γ matrices in Weyl repreentation where µ µ 0 σ γ = µ . (2.4) " σ¯ 0 # and σµ =(1,~σ) andσ ¯µ =(1, ~ ). The Pauli matrices are − 01 0 i 10 σ = ,σ= − ,σ= . (2.5) 1 10 2 i 0 3 0 1 " # " # " − # The matrix γ5 is taken to be 10 γ5 = − . (2.6) " 01# We can use the matrix γ5 to construct projection operators on to upper and lower parts of the four-component spinors U and V . The projection operators are 1 γ 1+γ Pˆ = − 5 , Pˆ = 5 . (2.7) L 2 R 2 Let us write u (p) U(p)= L , (2.8) uR(p) ! where uL(p) and uR(p) are two-component spinors. Since µ 0 pµσ pˆ = µ , (2.9) " pµσ¯ 0(p) # andpU ˆ (p) = 0, the two-component spinors satisfy the following (Weyl) equations µ µ pµσ uR(p)=0,pµσ¯ uL(p)=0. (2.10) –3– Suppose that we have a left handed spinor uL(p) that satisfies the Weyl equation.
    [Show full text]
  • The Bound States of Dirac Equation with a Scalar Potential
    THE BOUND STATES OF DIRAC EQUATION WITH A SCALAR POTENTIAL BY VATSAL DWIVEDI THESIS Submitted in partial fulfillment of the requirements for the degree of Master of Science in Applied Mathematics in the Graduate College of the University of Illinois at Urbana-Champaign, 2015 Urbana, Illinois Adviser: Professor Jared Bronski Abstract We study the bound states of the 1 + 1 dimensional Dirac equation with a scalar potential, which can also be interpreted as a position dependent \mass", analytically as well as numerically. We derive a Pr¨ufer-like representation for the Dirac equation, which can be used to derive a condition for the existence of bound states in terms of the fixed point of the nonlinear Pr¨uferequation for the angle variable. Another condition was derived by interpreting the Dirac equation as a Hamiltonian flow on R4 and a shooting argument for the induced flow on the space of Lagrangian planes of R4, following a similar calculation by Jones (Ergodic Theor Dyn Syst, 8 (1988) 119-138). The two conditions are shown to be equivalent, and used to compute the bound states analytically and numerically, as well as to derive a Calogero-like upper bound on the number of bound states. The analytic computations are also compared to the bound states computed using techniques from supersymmetric quantum mechanics. ii Acknowledgments In the eternity that is the grad school, this project has been what one might call an impulsive endeavor. In the 6 months from its inception to its conclusion, it has, without doubt, greatly benefited from quite a few individuals, as well as entities, around me, to whom I owe my sincere regards and gratitude.
    [Show full text]
  • Introduction to Supersymmetry
    Introduction to Supersymmetry Pre-SUSY Summer School Corpus Christi, Texas May 15-18, 2019 Stephen P. Martin Northern Illinois University [email protected] 1 Topics: Why: Motivation for supersymmetry (SUSY) • What: SUSY Lagrangians, SUSY breaking and the Minimal • Supersymmetric Standard Model, superpartner decays Who: Sorry, not covered. • For some more details and a slightly better attempt at proper referencing: A supersymmetry primer, hep-ph/9709356, version 7, January 2016 • TASI 2011 lectures notes: two-component fermion notation and • supersymmetry, arXiv:1205.4076. If you find corrections, please do let me know! 2 Lecture 1: Motivation and Introduction to Supersymmetry Motivation: The Hierarchy Problem • Supermultiplets • Particle content of the Minimal Supersymmetric Standard Model • (MSSM) Need for “soft” breaking of supersymmetry • The Wess-Zumino Model • 3 People have cited many reasons why extensions of the Standard Model might involve supersymmetry (SUSY). Some of them are: A possible cold dark matter particle • A light Higgs boson, M = 125 GeV • h Unification of gauge couplings • Mathematical elegance, beauty • ⋆ “What does that even mean? No such thing!” – Some modern pundits ⋆ “We beg to differ.” – Einstein, Dirac, . However, for me, the single compelling reason is: The Hierarchy Problem • 4 An analogy: Coulomb self-energy correction to the electron’s mass A point-like electron would have an infinite classical electrostatic energy. Instead, suppose the electron is a solid sphere of uniform charge density and radius R. An undergraduate problem gives: 3e2 ∆ECoulomb = 20πǫ0R 2 Interpreting this as a correction ∆me = ∆ECoulomb/c to the electron mass: 15 0.86 10− meters m = m + (1 MeV/c2) × .
    [Show full text]
  • Spin-1/2 Fermions in Quantum Field Theory
    Spin-1/2 fermions in quantum field theory µ First, recall that 4-vectors transform under Lorentz transformations, Λ ν, as p′ µ = Λµ pν, where Λ SO(3,1) satisfies Λµ g Λρ = g .∗ A Lorentz ν ∈ ν µρ λ νλ transformation corresponds to a rotation by θ about an axis nˆ [θ~ θnˆ] and ≡ a boost, ζ~ = vˆ tanh−1 ~v , where ~v is the corresponding velocity. Under the | | same Lorentz transformation, a generic field transforms as: ′ ′ Φ (x )= MR(Λ)Φ(x) , where M exp iθ~·J~ iζ~·K~ are N N representation matrices of R ≡ − − × 1 1 the Lorentz group. Defining J~+ (J~ + iK~ ) and J~− (J~ iK~ ), ≡ 2 ≡ 2 − i j ijk k i j [J± , J±]= iǫ J± , [J± , J∓] = 0 . Thus, the representations of the Lorentz algebra are characterized by (j1,j2), 1 1 where the ji are half-integers. (0, 0) is a scalar and (2, 2) is a four-vector. Of 1 1 interest to us here are the spinor representations (2, 0) and (0, 2). ∗ In our conventions, gµν = diag(1 , −1 , −1 , −1). (1, 0): M = exp i θ~·~σ 1ζ~·~σ , butalso (M −1)T = iσ2M(iσ2)−1 2 −2 − 2 (0, 1): [M −1]† = exp i θ~·~σ + 1ζ~·~σ , butalso M ∗ = iσ2[M −1]†(iσ2)−1 2 −2 2 since (iσ2)~σ(iσ2)−1 = ~σ∗ = ~σT − − Transformation laws of 2-component fields ′ β ξα = Mα ξβ , ′ α −1 T α β ξ = [(M ) ] β ξ , ′† α˙ −1 † α˙ † β˙ ξ = [(M ) ] β˙ ξ , ˙ ξ′† =[M ∗] βξ† .
    [Show full text]
  • Arxiv:1003.1912V2 [Hep-Ph] 30 Jun 2010 Fermion and Complex Vector Boson Dark Matter Are Also Disfavored, Except for Very Specific Choices of Quantum Numbers
    Preprint typeset in JHEP style - HYPER VERSION UMD-PP-10-004 RUNHETC-2010-07 A Classification of Dark Matter Candidates with Primarily Spin-Dependent Interactions with Matter Prateek Agrawal Maryland Center for Fundamental Physics, Department of Physics, University of Maryland, College Park, MD 20742 Zackaria Chacko Maryland Center for Fundamental Physics, Department of Physics, University of Maryland, College Park, MD 20742 Can Kilic Department of Physics and Astronomy, Rutgers University, Piscataway NJ 08854 Rashmish K. Mishra Maryland Center for Fundamental Physics, Department of Physics, University of Maryland, College Park, MD 20742 Abstract: We perform a model-independent classification of Weakly Interacting Massive Particle (WIMP) dark matter candidates that have the property that their scattering off nucleons is dominated by spin-dependent interactions. We study renormalizable theories where the scattering of dark matter is elastic and arises at tree-level. We show that if the WIMP-nucleon cross section is dominated by spin-dependent interactions the natural dark matter candidates are either Majorana fermions or real vector bosons, so that the dark matter particle is its own anti-particle. In such a scenario, scalar dark matter is disfavored. Dirac arXiv:1003.1912v2 [hep-ph] 30 Jun 2010 fermion and complex vector boson dark matter are also disfavored, except for very specific choices of quantum numbers. We further establish that any such theory must contain either new particles close to the weak scale with Standard Model quantum numbers, or alternatively, a Z0 gauge boson with mass at or below the TeV scale. In the region of parameter space that is of interest to current direct detection experiments, these particles naturally lie in a mass range that is kinematically accessible to the Large Hadron Collider (LHC).
    [Show full text]
  • Arxiv:1702.04624V3 [Cond-Mat.Str-El]
    Type-III and IV interacting Weyl points J. Nissinen1 and G.E. Volovik1, 2 1Low Temperature Laboratory, Aalto University, P.O. Box 15100, FI-00076 Aalto, Finland 2Landau Institute for Theoretical Physics, acad. Semyonov av., 1a, 142432, Chernogolovka, Russia (Dated: July 7, 2017) 3+1-dimensional Weyl fermions in interacting systems are described by effective quasi-relativistic µ Green’s functions parametrized by a 16 element matrix eα in an expansion around the Weyl point. µ The matrix eα can be naturally identified as an effective tetrad field for the fermions. The corre- spondence between the tetrad field and an effective quasi-relativistic metric gµν governing the Weyl fermions allows for the possibility to simulate different classes of metric fields emerging in general relativity in interacting Weyl semimetals. According to this correspondence, there can be four types 00 of Weyl fermions, depending on the signs of the components g and g00 of the effective metric. In addition to the conventional type-I fermions with a tilted Weyl cone and type-II fermions with an 00 overtilted Weyl cone for g > 0 and respectively g00 > 0 or g00 < 0, we find additional “type-III” 00 and “type-IV” Weyl fermions with instabilities (complex frequencies) for g < 0 and g00 > 0 or g00 < 0, respectively. While the type-I and type-II Weyl points allow us to simulate the black hole event horizon at an interface where g00 changes sign, the type-III Weyl point leads to effective spacetimes with closed timelike curves. PACS numbers: I. INTRODUCTION Weyl fermions1 are massless fermions whose masslessness (gaplessness) is topologically protected2–5.
    [Show full text]
  • An Effective Theory of Dirac Dark Matter
    SLAC-PUB-13482 An Effective Theory of Dirac Dark Matter Roni Harnik1 and Graham D. Kribs2 1SITP, Physics Department, Stanford University, Stanford, CA 94305 and SLAC, Stanford University, Menlo Park, CA 94025 2Department of Physics and Institute of Theoretical Science, University of Oregon, Eugene, OR 97403 (Dated: October 31, 2008) A stable Dirac fermion with four-fermion interactions to leptons suppressed by a scale Λ ∼ 1 TeV is shown to provide a viable candidate for dark matter. The thermal relic abundance matches cosmology, while nuclear recoil direct detection bounds are automatically avoided in the absence of (large) couplings to quarks. The annihilation cross section in the early Universe is the same as the annihilation in our galactic neighborhood. This allows Dirac fermion dark matter to naturally explain the positron ratio excess observed by PAMELA with a minimal boost factor, given present astrophysical uncertainties. We use the Galprop program for propagation of signal and background; we discuss in detail the uncertainties resulting from the propagation parameters and, more impor- tantly, the injected spectra. Fermi/GLAST has an opportunity to see a feature in the gamma-ray spectrum at the mass of the Dirac fermion. The excess observed by ATIC/PPB-BETS may also be explained with Dirac dark matter that is heavy. A supersymmetric model with a Dirac bino provides a viable UV model of the effective theory. The dominance of the leptonic operators, and thus the observation of an excess in positrons and not in anti-protons, is naturally explained by the large hypercharge and low mass of sleptons as compared with squarks.
    [Show full text]
  • Majorana Fermions As Emergent Quasiparticles
    Majorana fermions as emergent quasiparticles Abhisek Sahu1 1Department of Physics and Astronomy, University of British Columbia, Vancouver, B.C., V6T 1Z1, Canada (Dated: December 19, 2020) Majorana fermions are a special type of fermion predicted by the Dirac’s equation that are their own antiparticles. Currently they have rapidly gained interest in condensed matter physics as emergent quasiparticles in certain systems like topological superconductors. In this article, we review the theory of Majorana fermions starting from the Dirac equation. Then we discuss using Bogoliubov-deGennes formalism how Superconductors form ideal hunting grounds for Majorana particles and introduce the notion of Majorana zero modes. Finally we discuss the Kitaev model- a paradigmatic model to look for unpaired Majorana zero modes. I. INTRODUCTION II. WHAT ARE MAJORANA FERMIONS? In this section, we briefly review how Majorana In 1928 developed the wave equation that describes fermions come about from Dirac’s equations. The relativistic spin 1=2 particles. The solutions of this Dirac equation for a free particle 1is equation are complex valued four component spinors µ which can be interpreted as a spin 1=2 particle- (iγ @µ − m)Ψ(x) = 0 (1) antiparticle pair. It was Etorre Majorana’s insight to T look for a completely real set of solutions for the Dirac Where Ψ(x) = ( 1; 2; 3; 4) is a four-component µ equation in order to create a symmetric theory of par- spinor field and γ are 4 × 4 matrices satisfying the ticles and anti-particles. As a result in the year 1937 following algebra: he introduced the notion of fermions which are their µ ν µν y own anti-particles; known today as Majorana fermions fγ ; γ g = 2η ; γ0γµγ0 = γµ: (2) [1].
    [Show full text]
  • Physics of Neutrino Mass
    SLAC Summer Institute on Particle Physics (SSI04), Aug. 2-13, 2004 Physics of Neutrino Mass Rabindra N. Mohapatra Department of Physics, University of Maryland, College Park, MD-20742, USA Recent discoveries in the field of neutrino oscillations have provided a unique window into physics beyond the standard model. In this lecture, I summarize how well we understand the various observations, what they tell us about the nature of new physics and what we are likely to learn as some of the planned experiments are carried out. 1. INTRODUCTION For a long time, it was believed that neutrinos are massless, spin half particles, making them drastically different from their other standard model spin half cousins such as the charged leptons (e, µ, τ) and the quarks (u, d, s, c, t, b), which are known to have mass. In fact the masslessness of the neutrino was considered so sacred in the 1950s and 1960s that the fundamental law of weak interaction physics, the successful V-A theory for charged current weak processes was considered to be intimately linked to this fact. During the past decade, however, there have been a number of very exciting observations involving neutrinos emitted in the process of solar burning, produced during collision of cosmic rays in the atmosphere as well as those produced in terrestrial sources such as reactors and accelerators that have conclusively established that neutrinos not only have mass but they also mix among themselves, like their counterparts (e, µ, τ) and quarks, leading to the phenomenon of neutrino oscillations. The detailed results of these experiments and their interpretation have led to quantitative conclusions about the masses and the mixings, that have been discussed in other lectures[1].
    [Show full text]
  • Effective Field Theory Analysis of Composite Higgsino-Like and Wino
    Prepared for submission to JHEP Effective field theory analysis of composite higgsino-like and wino-like thermal relic dark matter Ben Geytenbeeka and Ben Gripaiosa aCavendish Laboratory, J.J. Thomson Avenue, Cambridge, CB3 0HE, United Kingdom E-mail: [email protected], [email protected] Abstract: We study the effective field theory (including operators up to dimension five) of models in which dark matter is composite, consisting of either an electroweak doublet Dirac fermion (‘higgsino-like dark matter’) or an electroweak triplet Majorana fermion (‘wino-like dark matter’). Some of the dimension-five operators in the former case cause mass splittings between the neutralino and chargino states, leading to a depleted rate of coannihilations and viable thermal relic dark matter with masses of the order of tens to hundreds of GeV rather than the usual pure higgsino thermal relic mass of 1 TeV. No such effects are found in the latter case (where the usual thermal relic mass is 3 TeV). Other operators, present for both wino- and higgsino-like dark matter, correspond to inelastic electromagnetic dipole moment interactions and annihilation through these can lead to viable models with dark matter masses up by an order of magnitude compared to the usual values. arXiv:2011.06025v1 [hep-ph] 11 Nov 2020 Contents 1 Introduction 1 2 Models 3 2.1 Doublet models (higgsinos) 3 2.2 Triplet models (winos) 7 3 Relic density 8 3.1 Higgsino electric dipole interactions 10 3.2 Higgsino magnetic dipole interaction via W 10 3.3 Higgs-higgsino interaction with neutralino mass splitting 12 3.4 Higgs-higgsino interaction without neutralino mass splitting 14 3.5 Wino inelastic magnetic dipole 15 3.6 Wino-Higgs interaction 16 4 Discussion 16 1 Introduction The existence and identity of the dark matter in the universe have long been major issues in astronomy and particle physics [1].
    [Show full text]
  • Laser-Driving of Semimetals Allows Creating Novel Quasiparticle States 17 January 2017, by Mg
    Laser-driving of semimetals allows creating novel quasiparticle states 17 January 2017, by Mg ultrafast switching of material properties. The findings are published online in the journal Nature Communications today. In the standard model of particle physics, the fundamental particles that make up all matter around us – electrons and quarks – are so-called fermions, named after the famous Italian physicist Enrico Fermi. Quantum theory predicts that elementary fermions could exist as three different kinds: Dirac, Weyl, and Majorana fermions, named after Paul Dirac, Hermann Weyl, and Ettore Majorana. However, despite being predicted almost a hundred years ago, of these three kinds of particles only Dirac fermions have been observed as elementary particles in nature so far. With the discovery of graphene in 2004, however, it was realized that the behaviour of relativistic free Dancing Weyl cones: When excited by tailored laser particles could be observed in the electronic pulses (white spiral), the cones in a Dirac fermion material dance on a path (8-shape) that can be properties of materials. This sparked the search for controlled by the laser light. This turns a Dirac material materials where these fundamental particles could into a Weyl material, changing the nature of the be observed and only last year the first materials quasiparticles in it. One of the cones hosts right-handed hosting Weyl fermions were discovered. While any Weyl fermions; the other cone hosts left-handed ones. known material only hosts one kind of these Credit: Joerg M. Harms/MPSD fermions in its equilibrium state, in the present work it is demonstrated how one can transform the fermion nature within specific materials by using tailored light pulses.
    [Show full text]