DOCSLIB.ORG

Dynamical Symmetry Breaking and Mass Generation T

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Dynamical Symmetry Breaking and Mass Generation T WDS'05 Proceedings of Contributed Papers, Part III, 436–441, 2005. ISBN 80-86732-59-2 © MATFYZPRESS Dynamical Symmetry Breaking and Mass Generation T. Brauner and J. Hoˇsek Nuclear Physics Institute, AS CR, Reˇz,ˇ Czech Republic Abstract. We give a brief review of the physics of spontaneous symmetry breaking. The field-theoretic Goldstone theorem and its consequences are emphasized. In relativistic quantum theory, the emergence of particle masses is connected with spontaneous breaking of chiral symmetry. While in the Standard model of the electroweak interaction this is achieved by the Higgs mechanism, we show on a simple model that chiral symmetry may be broken dynamically by strong Yukawa interaction. The possibility of applying our results to electroweak interactions is discussed. Introduction Understanding the origin of particle masses is one of the most challenging unsolved problems in current high-energy physics. All known elementary interactions besides gravity are described by the Standard model, which acquired its up-to-date form in late sixties through the work of Weinberg [1967] and many others. The Standard model has passed successfully all experimental probes, to which it has so far been exposed. Yet, and despite the ingenuity of its creators, it suffers from a couple of diseases that bother the minds of the world’s most prominent theorists. The presence of particle masses in the Standard model Lagrangian is prohibited by the SU(2)L × U(1)Y gauge symmetry of the electroweak interaction. To overcome this difficulty, the Higgs mechanism has been suggested which leads to spontaneous breakdown of the electroweak symmetry by condensation of a scalar Higgs field. Although this approach is formally well defined and absolutely consistent, it is rather unsatisfactory physically as it is introduced phenomenologically, that is more or less by hand. It has been a dream of many particle physicists ever since the invention of the Standard model to find a more physical, dynamical explanation for electroweak symmetry breaking, and thus the origin of particle masses. All such attempts inevitably lead to introduction of new particles and strong forces. Many of them, the first perhaps being the technicolor theory [Weinberg, 1979], introduce new strong gauge interactions, taking advantage of a rather good knowledge of quantum chromodynamics. In this contribution we present a modest attempt in a different direction. We wish to show that chiral symmetry might be broken dynamically with just the Yukawa interaction, which is already present in the Standard model Lagrangian, provided it is strong enough. The plan of the paper is following. We start with an introductory review of the physics of spontaneous symmetry breaking, emphasizing its general features and wide applications. We explain the connection to the problem of fermion masses in relativistic quantum field theory. Next we work out a simple model with Abelian chiral symmetry in order to demonstrate dynamical mass generation by means of the Yukawa interaction. Starting from general considerations of symmetry and its realization in quantum theory, we end up with the Schwinger–Dyson equations whose non-perturbative solution yields the desired masses. The extension to the Standard model, which involves a non-Abelian gauged chiral symmetry and several fermion species, is discussed in the conclusions. Spontaneous symmetry breaking Symmetry plays a key role in analyzing most physical problems. It sometimes happens that the symmetry of the equations of motion is larger than the symmetry of their particular solution. In such a case we speak of spontaneous symmetry breaking (SSB). While in classical physics this seems rather trivial, in quantum field theory SSB has far-reaching consequences. Symmetry is introduced as an invariance of the Lagrangian or the action. By the Wigner theorem, it is implemented on the Hilbert space of states by unitary operators that commute with the Hamiltonian, leading to non-trivial degeneracy of the spectrum. On the other hand, the ground state is assumed to be non-degenerate, and it must therefore be invariant under the symmetry transformations. When SSB occurs, the ground state is by definition not invariant with respect to some of the symmetry operations. There are several examples of SSB both in non-relativistic and relativistic physics. The first class, which is probably more accessible to one’s intuition, includes for example the ferromagnet. 436 BRAUNER AND HOSEK:ˇ DYNAMICAL SYMMETRY BREAKING AND MASS GENERATION There, the Hamiltonian is invariant under rotations of electron spins. In the ground state, however, the spins of all electrons are aligned, breaking the full rotation SO(3) group down to the SO(2) subgroup of rotations about the axis of spontaneous magnetization, which constitutes the order parameter for the phase transition to the ferromagnetic state. The direction of the magnetization is arbitrary and is induced by some random external perturbation that slightly breaks the rotation symmetry. Other non-relativistic examples are the superconductor, where the broken symmetry is the electro- magnetic gauge invariance, or even any crystallic solid, where full translation symmetry is broken by the crystal lattice down to some discrete subgroup. Relativistic, especially particle physics offers a variety of examples of SSB, e.g. the gauge SU(2)L U(1)Y invariance of the electroweak interaction and its exten- × sions to larger symmetry groups in models of grand unification, or the color SU(3)c in superconducting phases of quantum chromodynamics. The experience gained from the above listed examples may be summarized in the observation that SSB is always characterized by the existence of an order parameter. This can acquire various values, which are formally connected by the broken symmetry transformations. There are therefore several degenerate ground states, each specified by the particular value of the order parameter. This is the intuitive picture of SSB. Formally, however, the broken symmetry is not implemented on the Hilbert space by unitary operators and thus is not manifested in the degeneracy of the spectrum. As a consequence, different ground states are not connected by a unitary transformation. They are unitarily inequivalent and the Hilbert spaces built above them are completely orthogonal — they represent different worlds with different values of the order parameter. Chiral symmetry We shall now in more detail comment on the connection of SSB and fermion mass generation. The 1 Lagrangian of a free relativistic spin- 2 (Dirac) fermion contains two separate pieces for the left- and right- handed chiral components of the Dirac field, 0 = ψ¯Ri∂ψ/ R + ψ¯Li∂ψ/ L. It is invariant under independent L phase transformations of the left and right fields, that is the Abelian chiral group U(1)R U(1)L. × Now the Dirac mass term, δ m = m(ψ¯RψL + ψ¯LψR), intertwines the left and right fields so that they can no more be rephased independently.L − The mass term is invariant only under the diagonal vector U(1)V . It follows that non-zero Dirac masses can arise in a chirally-invariant theory only after the chiral symmetry has been spontaneously broken. The mass m itself is the order parameter here. The ground state is chosen so that m is real and positive and corresponds directly to the physical mass of the particle. Goldstone theorem The Goldstone theorem [Goldstone et al., 1962] is one of a few exact and general results in quantum field theory, and is the starting point for any consideration about broken symmetry. It states that whenever a continuous symmetry is spontaneously broken, there is an excitation branch in the spectrum of the theory (the Nambu–Goldstone mode) for which E(k) 0 as k 0. For Lorentz-invariant theories, this statement considera→bly simplifies:→ the Nambu–Goldstone (NG) mode is a spinless particle with zero mass. It also holds that the number of NG bosons is equal to the number of broken symmetry generators. For non-relativistic systems the NG boson counting is more complicated [Nielsen and Chadha, 1976]. It turns out that the number of NG bosons may be smaller than the number of broken generators provided some of the symmetry generators develops non-zero density in the ground state. This is the case for the ferromagnet mentioned before — there are two broken generators, but a single NG mode, the magnon. Before concluding the review part of the contribution we note that there are also symmetries that are not exact, e.g. the chiral SU(3)R SU(3)L symmetry of quantum chromodynamics, which is slightly broken by u, d, and s quark masses.× When such a symmetry is spontaneously broken, one naturally expects a nearly massless particle (the pseudo-Nambu–Goldstone boson) to appear. However, no theorem analogous to Goldstone’s exists for approximate symmetries. Abelian model of chiral symmetry breaking Now we shall introduce our model for dynamical breaking of chiral symmetry. We shall give a brief description and summarize the results, full details may be found in our recent paper [Brauner and Hoˇsek, 2005]. Trying to keep the idea as simple as possible, we consider the theory of a complex scalar field φ with mass M and two massless Dirac fermions ψ1,2, coupled by the Yukawa interaction Yukawa = y1 ψ¯1Lψ1Rφ + ψ¯1Rψ1Lφ† + y2 ψ¯2Rψ2Lφ + ψ¯2Lψ2Rφ† . (1) L 437 BRAUNER AND HOSEK:ˇ DYNAMICAL SYMMETRY BREAKING AND MASS GENERATION A curious reader might wonder why we include two different fermion species. The reason is that with just one fermion our model would suffer from an axial anomaly. This is no problem as long as the anomalous symmetry is global, as it actually is in our case. However, as we already mentioned above, our ultimate goal is to apply the same idea to electroweak symmetry breaking. For a gauge invariance the anomaly would be a disaster, and we therefore choose to remove it from the very beginning.
Load more

Recommended publications
  • Conformal Symmetry in Field Theory and in Quantum Gravity
    universe Review Conformal Symmetry in Field Theory and in Quantum Gravity Lesław Rachwał Instituto de Física, Universidade de Brasília, Brasília DF 70910-900, Brazil; [email protected] Received: 29 August 2018; Accepted: 9 November 2018; Published: 15 November 2018 Abstract: Conformal symmetry always played an important role in field theory (both quantum and classical) and in gravity. We present construction of quantum conformal gravity and discuss its features regarding scattering amplitudes and quantum effective action. First, the long and complicated story of UV-divergences is recalled. With the development of UV-finite higher derivative (or non-local) gravitational theory, all problems with infinities and spacetime singularities might be completely solved. Moreover, the non-local quantum conformal theory reveals itself to be ghost-free, so the unitarity of the theory should be safe. After the construction of UV-finite theory, we focused on making it manifestly conformally invariant using the dilaton trick. We also argue that in this class of theories conformal anomaly can be taken to vanish by fine-tuning the couplings. As applications of this theory, the constraints of the conformal symmetry on the form of the effective action and on the scattering amplitudes are shown. We also remark about the preservation of the unitarity bound for scattering. Finally, the old model of conformal supergravity by Fradkin and Tseytlin is briefly presented. Keywords: quantum gravity; conformal gravity; quantum field theory; non-local gravity; super- renormalizable gravity; UV-finite gravity; conformal anomaly; scattering amplitudes; conformal symmetry; conformal supergravity 1. Introduction From the beginning of research on theories enjoying invariance under local spacetime-dependent transformations, conformal symmetry played a pivotal role—first introduced by Weyl related changes of meters to measure distances (and also due to relativity changes of periods of clocks to measure time intervals).
    [Show full text]
  • Neutrino Mass Models: a Road Map
    Neutrino Mass Models: a road map S.F.King School of Physics and Astronomy, University of Southampton, Southampton SO17 1BJ, UK E-mail: [email protected] Abstract. In this talk we survey some of the recent promising developments in the search for the theory behind neutrino mass and mixing, and indeed all fermion masses and mixing. The talk is organized in terms of a neutrino mass models road map according to which the answers to experimental questions provide sign posts to guide us through the maze of theoretical models eventually towards a complete theory of flavour and uni¯cation. 1. Introduction It has been one of the long standing goals of theories of particle physics beyond the Standard Model (SM) to predict quark and lepton masses and mixings. With the discovery of neutrino mass and mixing, this quest has received a massive impetus. Indeed, perhaps the greatest advance in particle physics over the past decade has been the discovery of neutrino mass and mixing involving two large mixing angles commonly known as the atmospheric angle θ23 and the solar angle θ12, while the remaining mixing angle θ13, although unmeasured, is constrained to be relatively small [1]. The largeness of the two large lepton mixing angles contrasts sharply with the smallness of the quark mixing angles, and this observation, together with the smallness of neutrino masses, provides new and tantalizing clues in the search for the origin of quark and lepton flavour. However, before trying to address such questions, it is worth recalling why neutrino mass forces us to go beyond the SM.
    [Show full text]
  • Quantum Gravity from the QFT Perspective
    Quantum Gravity from the QFT perspective Ilya L. Shapiro Universidade Federal de Juiz de Fora, MG, Brazil Partial support: CNPq, FAPEMIG ICTP-SAIFR/IFT-UNESP – 1-5 April, 2019 Ilya Shapiro, Quantum Gravity from the QFT perspective April - 2019 Lecture 5. Advances topics in QG Induced gravity concept. • Effective QG: general idea. • Effective QG as effective QFT. • Where we are with QG?. • Bibliography S.L. Adler, Rev. Mod. Phys. 54 (1982) 729. S. Weinberg, Effective Field Theory, Past and Future. arXive:0908.1964[hep-th]; J.F. Donoghue, The effective field theory treatment of quantum gravity. arXive:1209.3511[gr-qc]; I.Sh., Polemic notes on IR perturbative quantum gravity. arXiv:0812.3521 [hep-th]. Ilya Shapiro, Quantum Gravity from the QFT perspective April - 2019 I. Induced gravity. The idea of induced gravity is simple, while its realization may be quite non-trivial, depending on the theory. In any case, the induced gravity concept is something absolutely necessary if we consider an interaction of gravity with matter and quantum theory concepts. I. Induced gravity from cut-off Original simplest version. Ya.B. Zeldovich, Sov. Phys. Dokl. 6 (1967) 883. A.D. Sakharov, Sov. Phys. Dokl. 12 (1968) 1040. Strong version of induced gravity is like that: Suppose that the metric has no pre-determined equations of motion. These equations result from the interaction to matter. Main advantage: Since gravity is not fundamental, but induced interaction, there is no need to quantize metric. Ilya Shapiro, Quantum Gravity from the QFT perspective April - 2019 And we already know that the semiclassical approach has no problems with renormalizability! Suppose we have a theory of quantum matter fields Φ = (ϕ, ψ, Aµ) interacting to the metric gµν .
    [Show full text]
  • A Fermi National Accelerator Laboratory
    a Fermi National Accelerator Laboratory FERMILAB-Pub-83/l&THY January, 1983 Composite Model with Confining SU(N) x SU(2)L x SU(2)K Hypercolor Carl H. Albright Fermi National Accelerator Laboratory P.O. Box 500, Batavia, Illinois 60510 and Department of Physics, Northern Illinois University* DeKalb, Illinois 60115 ABSTRACT A model of composite quarks and leptons is constructed with confining SU(N) x SU(2jL x SU(2)R hypercolor interactions such that only standard quark and lepton families appear in global SU(2)L x SU(2)K doublets. Several generations are admitted by the anomaly-matching conditions and labeled by a discrete axial symmetry. The SU(N) interactions are N independent and play the role Of technicolor. Three conserved U(l)" charges identified with Q, B - L and B + L prohibit qqq + Lc transitions. 3 Oparatrd by Unlvsrsitiae Research Association Inc. under contract with the United States Department of Energy -2- FERMILAB-Pub-83/16-THY With little or no support from the experimental realm, an extensive literature fl on the subject of composite quarks and leptons has emerged over the past few years. Many of the papers are based on the pioneering work of 't Hooft who formulated several criteria which composite models should satisfy in order to explain why quarks and leptons are nearly massless on the large energy scale where the hypercolor forces become sufficiently strong to bind the massless preons together. General searches for candidate preon models have been carried out, or specfific models themselves have been proposed, in which the fundamental preons are either all spinors or spinors and scalars and the weak gauge fields are either fundamental or composite.
    [Show full text]
  • Spontaneous Symmetry Breaking and Mass Generation As Built-In Phenomena in Logarithmic Nonlinear Quantum Theory
    Vol. 42 (2011) ACTA PHYSICA POLONICA B No 2 SPONTANEOUS SYMMETRY BREAKING AND MASS GENERATION AS BUILT-IN PHENOMENA IN LOGARITHMIC NONLINEAR QUANTUM THEORY Konstantin G. Zloshchastiev Department of Physics and Center for Theoretical Physics University of the Witwatersrand Johannesburg, 2050, South Africa (Received September 29, 2010; revised version received November 3, 2010; final version received December 7, 2010) Our primary task is to demonstrate that the logarithmic nonlinearity in the quantum wave equation can cause the spontaneous symmetry break- ing and mass generation phenomena on its own, at least in principle. To achieve this goal, we view the physical vacuum as a kind of the funda- mental Bose–Einstein condensate embedded into the fictitious Euclidean space. The relation of such description to that of the physical (relativis- tic) observer is established via the fluid/gravity correspondence map, the related issues, such as the induced gravity and scalar field, relativistic pos- tulates, Mach’s principle and cosmology, are discussed. For estimate the values of the generated masses of the otherwise massless particles such as the photon, we propose few simple models which take into account small vacuum fluctuations. It turns out that the photon’s mass can be naturally expressed in terms of the elementary electrical charge and the extensive length parameter of the nonlinearity. Finally, we outline the topological properties of the logarithmic theory and corresponding solitonic solutions. DOI:10.5506/APhysPolB.42.261 PACS numbers: 11.15.Ex, 11.30.Qc, 04.60.Bc, 03.65.Pm 1. Introduction Current observational data in astrophysics are probing a regime of de- partures from classical relativity with sensitivities that are relevant for the study of the quantum-gravity problem [1,2].
    [Show full text]
  • Magnetic Moment (G-2) and New Physics
    Magnetic moment (g − 2)µ and new physics Dominik Stöckinger Dresden Lepton Moments, July 2010 Dominik Stöckinger Magnetic moment (g − 2)µ and new physics Introduction exp SM A3σ deviation for aµ − aµ has been established! Currently: exp SM −11 aµ − aµ = (255 ± 63 ± 49) × 10 Expected with new Fermilab exp. (and th. progress): exp SM −11 aµ − aµ = (?? ± 16 ± 30) × 10 Which types of physics beyond the SM could explain this? What is the impact of aµ on physics beyond the SM? Dominik Stöckinger Magnetic moment (g − 2)µ and new physics Outline 1 Introduction 2 Different types of new physics 3 aµ, parameter measurements and model discrimination SUSY could explain the deviation Littlest Higgs (T-parity) cannot explain the deviation Randall-Sundrum models could explain the deviation 4 Conclusions Dominik Stöckinger Magnetic moment (g − 2)µ and new physics Introduction Outline 1 Introduction 2 Different types of new physics 3 aµ, parameter measurements and model discrimination SUSY could explain the deviation Littlest Higgs (T-parity) cannot explain the deviation Randall-Sundrum models could explain the deviation 4 Conclusions Dominik Stöckinger Magnetic moment (g − 2)µ and new physics Introduction Muon magnetic moment Quantum field theory: Operator: aµ µ¯ σ qνµ mµ L µν R CP-, Flavour-conserving, chirality-flipping, loop-induced 2 Heavy particles contribute ∝ mµ Mheavy Sensitive to all SM interactions Sensitive to TeV-scale new physics in a unique way Dominik Stöckinger Magnetic moment (g − 2)µ and new physics Introduction Why new physics? Big questions EWSB, Higgs, mass generation? hierarchy MPl/MW ? Naturalness? Unification of the Coupling Constants in the SM and the minimal MSSM i i α 60 α 60 1/α 1/ 1/ 1 MSSM 50 50 40 40 α 1/ 2 30 30 20 20 10 10 α 1/ 3 0 0 0 5 10 15 0 5 10 15 10log Q 10log Q dark matter? Grand Unification? .
    [Show full text]
  • Hep-Ph/9703242
    LMU–02/97 The Symmetry and the Problem of Mass Generation Harald Fritzsch Sektion Physik, Ludwig–Maximilians–Universit¨at Munchen,¨ Theresienstrasse 37, 80333 Munchen,¨ Germany (E–Mail: [email protected]–muenchen.de) Abstract The mass problem in particle physics and its impact for other fields is discussed. While the problem of the nuclear masses has been resolved within the QCD framework, many parameters of the “Standard Model” are related to the fermion sector. The origin of the fermion masses remains unresolved. We discuss attempts to explain the observed hierarchical features of the mass spectrum by a symmetry, relating the mass eigenvalues to the flavor mixing angles. Invited plenary talk given at the XXI International Colloquium on Group Theoretical Methods in Physics (Goslar, Germany, July 1996)” arXiv:hep-ph/9703242v1 5 Mar 1997 Towards the end of the last century the electron was discovered. In retrospect this discovery marked the beginning of a remarkable development, which eventually led to the emergence of the “Standard Model of Fundamental Particles and Forces” in the 70ies. According to the latter all the visible matter in the universe is composed of fundamental objects of two different categories – leptons (among them the electron) and quarks. The latter do not exist as free particles, but are bound among each other to form the protons and neutrons, the building blocks of the atomic nuclei. Symmetries have played a decisive role in this development, especially at the beginning, and group theory became since the sixties an essential tool of the particle physicists. They learned move than any other scientists that symmetry is the poetry of nature, and group theory its language.
    [Show full text]
  • Spontaneous Symmetry Breaking in the Higgs Mechanism
    Spontaneous symmetry breaking in the Higgs mechanism August 2012 Abstract The Higgs mechanism is very powerful: it furnishes a description of the elec- troweak theory in the Standard Model which has a convincing experimental ver- ification. But although the Higgs mechanism had been applied successfully, the conceptual background is not clear. The Higgs mechanism is often presented as spontaneous breaking of a local gauge symmetry. But a local gauge symmetry is rooted in redundancy of description: gauge transformations connect states that cannot be physically distinguished. A gauge symmetry is therefore not a sym- metry of nature, but of our description of nature. The spontaneous breaking of such a symmetry cannot be expected to have physical e↵ects since asymmetries are not reflected in the physics. If spontaneous gauge symmetry breaking cannot have physical e↵ects, this causes conceptual problems for the Higgs mechanism, if taken to be described as spontaneous gauge symmetry breaking. In a gauge invariant theory, gauge fixing is necessary to retrieve the physics from the theory. This means that also in a theory with spontaneous gauge sym- metry breaking, a gauge should be fixed. But gauge fixing itself breaks the gauge symmetry, and thereby obscures the spontaneous breaking of the symmetry. It suggests that spontaneous gauge symmetry breaking is not part of the physics, but an unphysical artifact of the redundancy in description. However, the Higgs mechanism can be formulated in a gauge independent way, without spontaneous symmetry breaking. The same outcome as in the account with spontaneous symmetry breaking is obtained. It is concluded that even though spontaneous gauge symmetry breaking cannot have physical consequences, the Higgs mechanism is not in conceptual danger.
    [Show full text]
  • Resolving Cosmological Singularity Problem in Logarithmic Superfluid Theory of Physical Vacuum
    XXI International Meeting of Physical Interpretations of Relativity Theory IOP Publishing Journal of Physics: Conference Series 1557 (2020) 012038 doi:10.1088/1742-6596/1557/1/012038 Resolving cosmological singularity problem in logarithmic superfluid theory of physical vacuum K G Zloshchastiev Institute of Systems Science, Durban University of Technology, Durban, South Africa E-mail: [email protected] Abstract. A paradigm of the physical vacuum as a non-trivial quantum object, such as superfluid, opens an entirely new prospective upon origins and interpretations of Lorentz symmetry and spacetime, black holes, cosmological evolution and singularities. Using the logarithmic superfluid model, one can formulate a post-relativistic theory of superfluid vacuum, which is not only essentially quantum but also successfully recovers special and general relativity in the \phononic" (low-momenta) limit. Thus, it represents spacetime as an induced observer- dependent phenomenon. We focus on the cosmological aspects of the logarithmic superfluid vacuum theory and show how can the related singularity problem be resolved in this approach. 1. Introduction It is a general consensus now that the physical vacuum, or a non-removable background, is a nontrivial object whose properties' studies are of utmost importance, because it affects the most fundamental notions our physics is based upon, such as space, time, matter, field, and fundamental symmetries. An internal structure of physical vacuum is still a subject of debates based on different views and approaches, which generally agree on the main paradigm, but differ in details; some introduction can be found in monographs by Volovik and Huang [1, 2]. It is probably Dirac who can be regarded as a forerunner of the superfluid vacuum theory (SVT).
    [Show full text]
  • Neutrino Masses and the Structure of the Weak Gauge Boson
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by CERN Document Server Neutrino masses and the structure of the weak gauge boson V.N.Yershov University College London, Mullard Space Science Laboratory, Holmbury St.Mary, Dorking RH5 6NT, United Kingdom E-mail: [email protected] Abstract. The problem of neutrino masses is discussed. It is assumed that the electron 0 neutrino mass is related to the structures and masses of the W ± and Z bosons. Using a composite model of fermions (described by the author elsewhere), it is shown that the massless 0 neutrino is not consistent with the high values of the experimental masses of W ± and Z . Consistency can be achieved on the assumption that the electron-neutrino has a mass of about 4.5 meV. Masses of the muon- and tau-neutrinos are also estimated. PACS numbers: 11.30.Na, 12.60.Rc, 14.60.St, 14.70.Fm, 14.70.Hp 1. Introduction The results of recent observations of atmospheric and solar neutrinos aimed at testing the hypothesis of the neutrino flavour oscillations [1, 2] indicate that neutrinos are massive. Although a very small, but non-zero neutrino mass, can be a key to new physics underlying the Standard Model of particle physics [3]. The Standard Model consider all three neutrinos (νe, νµ,andντ ) to be massless. Thus, observations show that the Standard Model needs some corrections or extensions. So far, many models have been proposed in order to explain possible mechanisms for the neutrino mass generation [4]-[9], and many experiments have been carried out for measuring this mass.
    [Show full text]
  • Mass Generation Via the Higgs Boson and the Quark Condensate of the QCD Vacuum
    Pramana – J. Phys. (2016) 87: 44 c Indian Academy of Sciences DOI 10.1007/s12043-016-1256-0 Mass generation via the Higgs boson and the quark condensate of the QCD vacuum MARTIN SCHUMACHER II. Physikalisches Institut der Universität Göttingen, Friedrich-Hund-Platz 1, D-37077 Göttingen, Germany E-mail: [email protected] Published online 24 August 2016 Abstract. The Higgs boson, recently discovered with a mass of 125.7 GeV is known to mediate the masses of elementary particles, but only 2% of the mass of the nucleon. Extending a previous investigation (Schumacher, Ann. Phys. (Berlin) 526, 215 (2014)) and including the strange-quark sector, hadron masses are derived from the quark condensate of the QCD vacuum and from the effects of the Higgs boson. These calculations include the π meson, the nucleon and the scalar mesons σ(600), κ(800), a0(980), f0(980) and f0(1370). The predicted second σ meson, σ (1344) =|ss¯, is investigated and identified with the f0(1370) meson. An outlook is given on the hyperons , 0,± and 0,−. Keywords. Higgs boson; sigma meson; mass generation; quark condensate. PACS Nos 12.15.y; 12.38.Lg; 13.60.Fz; 14.20.Jn 1. Introduction adds a small additional part to the total constituent- quark mass leading to mu = 331 MeV and md = In the Standard Model, the masses of elementary parti- 335 MeV for the up- and down-quark, respectively [9]. cles arise from the Higgs field acting on the originally These constituent quarks are the building blocks of the massless particles. When applied to the visible matter nucleon in a similar way as the nucleons are in the case of the Universe, this explanation remains unsatisfac- of nuclei.
    [Show full text]
  • An Alternative to Dark Matter and Dark Energy: Scale-Dependent Gravity in Superfluid Vacuum Theory
    universe Article An Alternative to Dark Matter and Dark Energy: Scale-Dependent Gravity in Superfluid Vacuum Theory Konstantin G. Zloshchastiev Institute of Systems Science, Durban University of Technology, P.O. Box 1334, Durban 4000, South Africa; [email protected] Received: 29 August 2020; Accepted: 10 October 2020; Published: 15 October 2020 Abstract: We derive an effective gravitational potential, induced by the quantum wavefunction of a physical vacuum of a self-gravitating configuration, while the vacuum itself is viewed as the superfluid described by the logarithmic quantum wave equation. We determine that gravity has a multiple-scale pattern, to such an extent that one can distinguish sub-Newtonian, Newtonian, galactic, extragalactic and cosmological terms. The last of these dominates at the largest length scale of the model, where superfluid vacuum induces an asymptotically Friedmann–Lemaître–Robertson–Walker-type spacetime, which provides an explanation for the accelerating expansion of the Universe. The model describes different types of expansion mechanisms, which could explain the discrepancy between measurements of the Hubble constant using different methods. On a galactic scale, our model explains the non-Keplerian behaviour of galactic rotation curves, and also why their profiles can vary depending on the galaxy. It also makes a number of predictions about the behaviour of gravity at larger galactic and extragalactic scales. We demonstrate how the behaviour of rotation curves varies with distance from a gravitating center, growing from an inner galactic scale towards a metagalactic scale: A squared orbital velocity’s profile crosses over from Keplerian to flat, and then to non-flat. The asymptotic non-flat regime is thus expected to be seen in the outer regions of large spiral galaxies.
    [Show full text]