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Probing the Minimal Length Scale by Precision Tests of the Muon G − 2
Physics Letters B 584 (2004) 109–113 www.elsevier.com/locate/physletb Probing the minimal length scale by precision tests of the muon g − 2 U. Harbach, S. Hossenfelder, M. Bleicher, H. Stöcker Institut für Theoretische Physik, J.W. Goethe-Universität, Robert-Mayer-Str. 8-10, 60054 Frankfurt am Main, Germany Received 25 November 2003; received in revised form 20 January 2004; accepted 21 January 2004 Editor: P.V. Landshoff Abstract Modifications of the gyromagnetic moment of electrons and muons due to a minimal length scale combined with a modified fundamental scale Mf are explored. First-order deviations from the theoretical SM value for g − 2 due to these string theory- motivated effects are derived. Constraints for the fundamental scale Mf are given. 2004 Elsevier B.V. All rights reserved. String theory suggests the existence of a minimum • the need for a higher-dimensional space–time and length scale. An exciting quantum mechanical impli- • the existence of a minimal length scale. cation of this feature is a modification of the uncer- tainty principle. In perturbative string theory [1,2], Naturally, this minimum length uncertainty is re- the feature of a fundamental minimal length scale lated to a modification of the standard commutation arises from the fact that strings cannot probe dis- relations between position and momentum [6,7]. Ap- tances smaller than the string scale. If the energy of plication of this is of high interest for quantum fluc- a string reaches the Planck mass mp, excitations of the tuations in the early universe and inflation [8–16]. string can occur and cause a non-zero extension [3]. -
An Introduction to Effective Field Theory
An Introduction to Effective Field Theory Thinking Effectively About Hierarchies of Scale c C.P. BURGESS i Preface It is an everyday fact of life that Nature comes to us with a variety of scales: from quarks, nuclei and atoms through planets, stars and galaxies up to the overall Universal large-scale structure. Science progresses because we can understand each of these on its own terms, and need not understand all scales at once. This is possible because of a basic fact of Nature: most of the details of small distance physics are irrelevant for the description of longer-distance phenomena. Our description of Nature’s laws use quantum field theories, which share this property that short distances mostly decouple from larger ones. E↵ective Field Theories (EFTs) are the tools developed over the years to show why it does. These tools have immense practical value: knowing which scales are important and why the rest decouple allows hierarchies of scale to be used to simplify the description of many systems. This book provides an introduction to these tools, and to emphasize their great generality illustrates them using applications from many parts of physics: relativistic and nonrelativistic; few- body and many-body. The book is broadly appropriate for an introductory graduate course, though some topics could be done in an upper-level course for advanced undergraduates. It should interest physicists interested in learning these techniques for practical purposes as well as those who enjoy the beauty of the unified picture of physics that emerges. It is to emphasize this unity that a broad selection of applications is examined, although this also means no one topic is explored in as much depth as it deserves. -
Astro 282: Problem Set 1 1 Problem 1: Natural Units
Astro 282: Problem Set 1 Due April 7 1 Problem 1: Natural Units Cosmologists and particle physicists like to suppress units by setting the fundamental constants c,h ¯, kB to unity so that there is one fundamental unit. Structure formation cosmologists generally prefer Mpc as a unit of length, time, inverse energy, inverse temperature. Early universe people use GeV. Familiarize yourself with the elimination and restoration of units in the cosmological context. Here are some fundamental constants of nature Planck’s constant ¯h = 1.0546 × 10−27 cm2 g s−1 Speed of light c = 2.9979 × 1010 cm s−1 −16 −1 Boltzmann’s constant kB = 1.3807 × 10 erg K Fine structure constant α = 1/137.036 Gravitational constant G = 6.6720 × 10−8 cm3 g−1 s−2 Stefan-Boltzmann constant σ = a/4 = π2/60 a = 7.5646 × 10−15 erg cm−3K−4 2 2 −25 2 Thomson cross section σT = 8πα /3me = 6.6524 × 10 cm Electron mass me = 0.5110 MeV Neutron mass mn = 939.566 MeV Proton mass mp = 938.272 MeV −1/2 19 Planck mass mpl = G = 1.221 × 10 GeV and here are some unit conversions: 1 s = 9.7157 × 10−15 Mpc 1 yr = 3.1558 × 107 s 1 Mpc = 3.0856 × 1024 cm 1 AU = 1.4960 × 1013 cm 1 K = 8.6170 × 10−5 eV 33 1 M = 1.989 × 10 g 1 GeV = 1.6022 × 10−3 erg = 1.7827 × 10−24 g = (1.9733 × 10−14 cm)−1 = (6.5821 × 10−25 s)−1 −1 −1 • Define the Hubble constant as H0 = 100hkm s Mpc where h is a dimensionless number observed to be −1 −1 h ≈ 0.7. -
Small Angle Scattering in Neutron Imaging—A Review
Journal of Imaging Review Small Angle Scattering in Neutron Imaging—A Review Markus Strobl 1,2,*,†, Ralph P. Harti 1,†, Christian Grünzweig 1,†, Robin Woracek 3,† and Jeroen Plomp 4,† 1 Paul Scherrer Institut, PSI Aarebrücke, 5232 Villigen, Switzerland; [email protected] (R.P.H.); [email protected] (C.G.) 2 Niels Bohr Institute, University of Copenhagen, Copenhagen 1165, Denmark 3 European Spallation Source ERIC, 225 92 Lund, Sweden; [email protected] 4 Department of Radiation Science and Technology, Technical University Delft, 2628 Delft, The Netherlands; [email protected] * Correspondence: [email protected]; Tel.: +41-56-310-5941 † These authors contributed equally to this work. Received: 6 November 2017; Accepted: 8 December 2017; Published: 13 December 2017 Abstract: Conventional neutron imaging utilizes the beam attenuation caused by scattering and absorption through the materials constituting an object in order to investigate its macroscopic inner structure. Small angle scattering has basically no impact on such images under the geometrical conditions applied. Nevertheless, in recent years different experimental methods have been developed in neutron imaging, which enable to not only generate contrast based on neutrons scattered to very small angles, but to map and quantify small angle scattering with the spatial resolution of neutron imaging. This enables neutron imaging to access length scales which are not directly resolved in real space and to investigate bulk structures and processes spanning multiple length scales from centimeters to tens of nanometers. Keywords: neutron imaging; neutron scattering; small angle scattering; dark-field imaging 1. Introduction The largest and maybe also broadest length scales that are probed with neutrons are the domains of small angle neutron scattering (SANS) and imaging. -
Arxiv:1901.04741V2 [Hep-Th] 15 Feb 2019 2
Quantum scale symmetry C. Wetterich [email protected] Universität Heidelberg, Institut für Theoretische Physik, Philosophenweg 16, D-69120 Heidelberg Quantum scale symmetry is the realization of scale invariance in a quantum field theory. No parameters with dimension of length or mass are present in the quantum effective action. Quantum scale symmetry is generated by quantum fluctuations via the presence of fixed points for running couplings. As for any global symmetry, the ground state or cosmological state may be scale invariant or not. Spontaneous breaking of scale symmetry leads to massive particles and predicts a massless Goldstone boson. A massless particle spectrum follows from scale symmetry of the effective action only if the ground state is scale symmetric. Approximate scale symmetry close to a fixed point leads to important predictions for observations in various areas of fundamental physics. We review consequences of scale symmetry for particle physics, quantum gravity and cosmology. For particle physics, scale symmetry is closely linked to the tiny ratio between the Fermi scale of weak interactions and the Planck scale for gravity. For quantum gravity, scale symmetry is associated to the ultraviolet fixed point which allows for a non-perturbatively renormalizable quantum field theory for all known interactions. The interplay between gravity and particle physics at this fixed point permits to predict couplings of the standard model or other “effective low energy models” for momenta below the Planck mass. In particular, quantum gravity determines the ratio of Higgs boson mass and top quark mass. In cosmology, approximate scale symmetry explains the almost scale-invariant primordial fluctuation spectrum which is at the origin of all structures in the universe. -
Minimal Length Scale Scenarios for Quantum Gravity
Living Rev. Relativity, 16, (2013), 2 LIVINGREVIEWS http://www.livingreviews.org/lrr-2013-2 doi:10.12942/lrr-2013-2 in relativity Minimal Length Scale Scenarios for Quantum Gravity Sabine Hossenfelder Nordita Roslagstullsbacken 23 106 91 Stockholm Sweden email: [email protected] Accepted: 11 October 2012 Published: 29 January 2013 Abstract We review the question of whether the fundamental laws of nature limit our ability to probe arbitrarily short distances. First, we examine what insights can be gained from thought experiments for probes of shortest distances, and summarize what can be learned from different approaches to a theory of quantum gravity. Then we discuss some models that have been developed to implement a minimal length scale in quantum mechanics and quantum field theory. These models have entered the literature as the generalized uncertainty principle or the modified dispersion relation, and have allowed the study of the effects of a minimal length scale in quantum mechanics, quantum electrodynamics, thermodynamics, black-hole physics and cosmology. Finally, we touch upon the question of ways to circumvent the manifestation of a minimal length scale in short-distance physics. Keywords: minimal length, quantum gravity, generalized uncertainty principle This review is licensed under a Creative Commons Attribution-Non-Commercial 3.0 Germany License. http://creativecommons.org/licenses/by-nc/3.0/de/ Imprint / Terms of Use Living Reviews in Relativity is a peer reviewed open access journal published by the Max Planck Institute for Gravitational Physics, Am M¨uhlenberg 1, 14476 Potsdam, Germany. ISSN 1433-8351. This review is licensed under a Creative Commons Attribution-Non-Commercial 3.0 Germany License: http://creativecommons.org/licenses/by-nc/3.0/de/. -
Natural Length Scale from Cosmological Holographic Principle Matches Proton
Natural Length Scale from Cosmological Holographic Principle Matches Proton Simon WW Manley [email protected] Abstract A natural unit of length, determined by applying the Holographic Principle to the Hubble sphere, matches the diameter of the proton, the smallest relevant size in nature. Unlike traditional Large Numbers coincidences, which are accurate only to order of magnitude, this agreement is precise. Introduction This brief Note discusses the natural length scale implied by the restriction on the information density of a region under the Holographic Principle. 3 1/2 -35 The Planck length, lP = (hG/2πc ) = 1.616×10 m, is 20 orders of magnitude smaller than the atomic nucleus. Mathematically, this is trivial, following from the weakness of gravity. But from an informational perspective, it seems deeply disturbing. If we naïvely consider the world to be about as rich in information as a discrete 3-dimensional lattice of spacing lP, reality appears to be severely over-specified. Since John Archibald Wheeler’s promotion of the epigrammatic “It from Bit” hypothesis [Wheeler, 1989], the physics community has become increasingly committed to the concept of information being the deep foundation underlying quantum mechanics [Zeilinger, 1999]. This visionary idea was recently given a rigorous mathematical formulation by Chiribella and colleagues [2011]. The relationship of information to geometry was first made explicit in black hole 2 thermodynamics, where each bit requires an area of 4 lP on the event horizon [Bekenstein, 1973]. The universality of this relationship, implying dimensional reduction in quantum gravity, was first proposed by ’t Hooft [1993], and through work of Thorn and Susskind, refined into a Holographic Principle [Susskind, 1994]. -
Redalyc.A Local Non-Abelian Gauge Invariant Action Stemming from The
Brazilian Journal of Physics ISSN: 0103-9733 [email protected] Sociedade Brasileira de Física Brasil Dudal, D.; Capri, M. A. L.; Gracey, J. A.; Lemes, V. E. R.; Sobreiro, R. F.; Sorella, S. P.; Verschelde, H. A Local Non-Abelian Gauge Invariant Action Stemming from the Nonlocal Operator F(D2)-1F Brazilian Journal of Physics, vol. 37, núm. 1B, march, 2007, pp. 232-238 Sociedade Brasileira de Física Sâo Paulo, Brasil Available in: http://www.redalyc.org/articulo.oa?id=46437212 How to cite Complete issue Scientific Information System More information about this article Network of Scientific Journals from Latin America, the Caribbean, Spain and Portugal Journal's homepage in redalyc.org Non-profit academic project, developed under the open access initiative 232 Brazilian Journal of Physics, vol. 37, no. 1B, March, 2007 A Local Non-Abelian Gauge Invariant Action Stemming from the 2 ¡1 Nonlocal Operator Fµn(D ) Fµn D. Dudala,¤ M. A. L. Caprib, J. A. Graceyc, V. E. R. Lemesb, R. F. Sobreirob, S. P. Sorellab,† and H. Verscheldea a Ghent University Department of Mathematical Physics and Astronomy, Krijgslaan 281-S9, B-9000 Gent, Belgium b UERJ - Universidade do Estado do Rio de Janeiro, Rua Sao˜ Francisco Xavier 524, 20550-013 Maracana,˜ Rio de Janeiro, Brazil c Theoretical Physics Division, Department of Mathematical Sciences, University of Liverpool, P.O. Box 147, Liverpool, L69 3BX, United Kingdom (Received on 12 September, 2006) 2 ¡1 We report on the nonlocal gauge invariant operator of dimension two, Fµn(D ) Fµn. We are able to localize this operator by introducing a suitable set of (anti)commuting antisymmetric tensor fields. -
Jhep11(2016)024
Published for SISSA by Springer Received: June 27, 2016 Revised: September 1, 2016 Accepted: October 16, 2016 Published: November 7, 2016 Massless and massive higher spins from anti-de Sitter space waveguide JHEP11(2016)024 Seungho Gwak,a Jaewon Kima and Soo-Jong Reya;b aSchool of Physics and Astronomy & Center for Theoretical Physics, Seoul National University, Seoul 08826, Korea bFields, Gravity & Strings, Center for Theoretical Physics of the Universe, Institute for Basic Sciences, Daejeon 34047, Korea E-mail: [email protected] Abstract: Understanding Higgs mechanism for higher-spin gauge fields is an outstanding open problem. We investigate this problem in the context of Kaluza-Klein compactifica- tion. Starting from a free massless higher-spin field in (d + 2)-dimensional anti-de Sitter space and compactifying over a finite angular wedge, we obtain an infinite tower of heavy, light and massless higher-spin fields in (d + 1)-dimensional anti-de Sitter space. All mas- sive higher-spin fields are described gauge invariantly in terms of Stueckelberg fields. The spectrum depends on the boundary conditions imposed at both ends of the wedges. We ob- served that higher-derivative boundary condition is inevitable for spin greater than three. For some higher-derivative boundary conditions, equivalently, spectrum-dependent bound- ary conditions, we get a non-unitary representation of partially-massless higher-spin fields of varying depth. We present intuitive picture which higher-derivative boundary conditions yield non-unitary system in terms of boundary action. We argue that isotropic Lifshitz in- terfaces in O(N) Heisenberg magnet or O(N) Gross-Neveu model provides the holographic dual conformal field theory and propose experimental test of (inverse) Higgs mechanism for massive and partially massless higher-spin fields. -
Arxiv:1411.4673V1 [Hep-Ph] 17 Nov 2014 E Unn Coupling Running QED Scru S Considerable and Challenge
Attempts at a determination of the fine-structure constant from first principles: A brief historical overview U. D. Jentschura1, 2 and I. N´andori2 1Department of Physics, Missouri University of Science and Technology, Rolla, Missouri 65409-0640, USA 2MTA–DE Particle Physics Research Group, P.O.Box 51, H–4001 Debrecen, Hungary It has been a notably elusive task to find a remotely sensical ansatz for a calculation of Sommer- feld’s electrodynamic fine-structure constant αQED ≈ 1/137.036 based on first principles. However, this has not prevented a number of researchers to invest considerable effort into the problem, despite the formidable challenges, and a number of attempts have been recorded in the literature. Here, we review a possible approach based on the quantum electrodynamic (QED) β function, and on algebraic identities relating αQED to invariant properties of “internal” symmetry groups, as well as attempts to relate the strength of the electromagnetic interaction to the natural cutoff scale for other gauge theories. Conjectures based on both classical as well as quantum-field theoretical considerations are discussed. We point out apparent strengths and weaknesses of the most promi- nent attempts that were recorded in the literature. This includes possible connections to scaling properties of the Einstein–Maxwell Lagrangian which describes gravitational and electromagnetic interactions on curved space-times. Alternative approaches inspired by string theory are also dis- cussed. A conceivable variation of the fine-structure constant with time would suggest a connection of αQED to global structures of the Universe, which in turn are largely determined by gravitational interactions. PACS: 12.20.Ds (Quantum electrodynamics — specific calculations) ; 11.25.Tq (Gauge field theories) ; 11.15.Bt (General properties of perturbation theory) ; 04.60.Cf (Gravitational aspects of string theory) ; 06.20.Jr (Determination of fundamental constants) . -
Universality of the Chern-Simons Diffusion Rate
PHYSICAL REVIEW D 98, 106023 (2018) Universality of the Chern-Simons diffusion rate † ‡ Francesco Bigazzi,1,* Aldo L. Cotrone,1,2, and Flavio Porri1,2, 1INFN, Sezione di Firenze, Via G. Sansone 1, I-50019 Sesto Fiorentino (Firenze), Italy 2Dipartimento di Fisica e Astronomia, Universit`a di Firenze, Via G. Sansone 1, I-50019 Sesto Fiorentino (Firenze), Italy (Received 20 August 2018; published 27 November 2018) We prove the universality of the Chern-Simons diffusion rate—a crucial observable for the chiral magnetic effect—in a large class of planar strongly correlated gauge theories with dual string description. When the effects of anomalies are suppressed, the diffusion rate is simply given in terms of temperature, entropy density and gauge coupling, with a universal numerical coefficient. We show that this result holds, in fact, for all the top-down holographic models where the calculation has been performed in the past, even in the presence of magnetic fields and anisotropy. We also extend the check to further well-known models for which the same computation was lacking. Finally we point out some subtleties related to the definition of the Chern-Simons diffusion rate in the presence of anomalies. In this case, the usual definition of the rate—a late time limit of the imaginary part of the retarded correlator of the topological charge density—would give an exactly vanishing result, due to its relation with a nonconserved charge correlator. We confirm this observation by explicit holographic computations on generic isotropic black hole backgrounds. Nevertheless, a nontrivial Chern- Simons relaxation time can in principle be extracted from a quasinormal mode calculation. -
1 Scale-Relativistic Estimate of the Fine Structure Constant
1 Scale-Relativistic Estimate of the Fine Structure Constant Laurent Nottale CNRS, DAEC, Observatoire de Paris-Meudon, 92195 Meudon Cedex, France Abstract. The low energy value of the fine structure constant is theoretically estimated to within 1‰ of its observed value in the framework of the theory of scale relativity, in which the Planck length-scale is reinterpreted as a lowest, limiting, unpassable length, invariant under dilatations. This estimate is performed by using the renormalization group equations to evolve the QED coupling constant from infinite energy, where the bare mean electroweak coupling is assumed to reach its “natural” value 1/4π2, down to the electron energy. A consequence of this calculation is that the number of Higgs boson doublets is predicted to be NH = 1. Completed: 28 December 1992 Revised: 14 April 1993 2 1. Introduction Present high energy physics seems to be faced with several unsolved fundamental problems, among which: (i) the problem of divergences of self-energies and charges in QED; (ii) the nature of the Planck scale; (iii) the origin and values of universal scales, such as the Electroweak and GUT scales; (iv) the values of coupling constants. These problems are clearly related with one another. Indeed, consider in particular the question of the theoretical understanding of the coupling constant values which we address in the present letter. Once it was realized that vacuum polarization by virtual particle-antiparticle pairs resulted in a screening of bare charges, it became clear that the most straighforward programme for theoretically predicting the low energy value of the electromagnetic coupling (i.e., the fine structure constant) was to derive it from its “bare” (infinite energy) value and from its variation with scale.