The Hierarchy Problem and Other Short-Comings of the Standard Model (SM)
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Symmetry and Gravity
universe Article Making a Quantum Universe: Symmetry and Gravity Houri Ziaeepour 1,2 1 Institut UTINAM, CNRS UMR 6213, Observatoire de Besançon, Université de Franche Compté, 41 bis ave. de l’Observatoire, BP 1615, 25010 Besançon, France; [email protected] or [email protected] 2 Mullard Space Science Laboratory, University College London, Holmbury St. Mary, Dorking GU5 6NT, UK Received: 05 September 2020; Accepted: 17 October 2020; Published: 23 October 2020 Abstract: So far, none of attempts to quantize gravity has led to a satisfactory model that not only describe gravity in the realm of a quantum world, but also its relation to elementary particles and other fundamental forces. Here, we outline the preliminary results for a model of quantum universe, in which gravity is fundamentally and by construction quantic. The model is based on three well motivated assumptions with compelling observational and theoretical evidence: quantum mechanics is valid at all scales; quantum systems are described by their symmetries; universe has infinite independent degrees of freedom. The last assumption means that the Hilbert space of the Universe has SUpN Ñ 8q – area preserving Diff.pS2q symmetry, which is parameterized by two angular variables. We show that, in the absence of a background spacetime, this Universe is trivial and static. Nonetheless, quantum fluctuations break the symmetry and divide the Universe to subsystems. When a subsystem is singled out as reference—observer—and another as clock, two more continuous parameters arise, which can be interpreted as distance and time. We identify the classical spacetime with parameter space of the Hilbert space of the Universe. -
Consequences of Kaluza-Klein Covariance
CONSEQUENCES OF KALUZA-KLEIN COVARIANCE Paul S. Wesson Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada Space-Time-Matter Consortium, http://astro.uwaterloo.ca/~wesson PACs: 11.10Kk, 11.25Mj, 0.45-h, 04.20Cv, 98.80Es Key Words: Classical Mechanics, Quantum Mechanics, Gravity, Relativity, Higher Di- mensions Addresses: Mail to Waterloo above; email: [email protected] Abstract The group of coordinate transformations for 5D noncompact Kaluza-Klein theory is broader than the 4D group for Einstein’s general relativity. Therefore, a 4D quantity can take on different forms depending on the choice for the 5D coordinates. We illustrate this by deriving the physical consequences for several forms of the canonical metric, where the fifth coordinate is altered by a translation, an inversion and a change from spacelike to timelike. These cause, respectively, the 4D cosmological ‘constant’ to be- come dependent on the fifth coordinate, the rest mass of a test particle to become measured by its Compton wavelength, and the dynamics to become wave-mechanical with a small mass quantum. These consequences of 5D covariance – whether viewed as positive or negative – help to determine the viability of current attempts to unify gravity with the interactions of particles. 1. Introduction Covariance, or the ability to change coordinates while not affecting the validity of the equations, is an essential property of any modern field theory. It is one of the found- ing principles for Einstein’s theory of gravitation, general relativity. However, that theory is four-dimensional, whereas many theories which seek to unify gravitation with the interactions of particles use higher-dimensional spaces. -
Naturalness and New Approaches to the Hierarchy Problem
Naturalness and New Approaches to the Hierarchy Problem PiTP 2017 Nathaniel Craig Department of Physics, University of California, Santa Barbara, CA 93106 No warranty expressed or implied. This will eventually grow into a more polished public document, so please don't disseminate beyond the PiTP community, but please do enjoy. Suggestions, clarifications, and comments are welcome. Contents 1 Introduction 2 1.0.1 The proton mass . .3 1.0.2 Flavor hierarchies . .4 2 The Electroweak Hierarchy Problem 5 2.1 A toy model . .8 2.2 The naturalness strategy . 13 3 Old Hierarchy Solutions 16 3.1 Lowered cutoff . 16 3.2 Symmetries . 17 3.2.1 Supersymmetry . 17 3.2.2 Global symmetry . 22 3.3 Vacuum selection . 26 4 New Hierarchy Solutions 28 4.1 Twin Higgs / Neutral naturalness . 28 4.2 Relaxion . 31 4.2.1 QCD/QCD0 Relaxion . 31 4.2.2 Interactive Relaxion . 37 4.3 NNaturalness . 39 5 Rampant Speculation 42 5.1 UV/IR mixing . 42 6 Conclusion 45 1 1 Introduction What are the natural sizes of parameters in a quantum field theory? The original notion is the result of an aggregation of different ideas, starting with Dirac's Large Numbers Hypothesis (\Any two of the very large dimensionless numbers occurring in Nature are connected by a simple mathematical relation, in which the coefficients are of the order of magnitude unity" [1]), which was not quantum in nature, to Gell- Mann's Totalitarian Principle (\Anything that is not compulsory is forbidden." [2]), to refinements by Wilson and 't Hooft in more modern language. -
UC Berkeley UC Berkeley Electronic Theses and Dissertations
UC Berkeley UC Berkeley Electronic Theses and Dissertations Title Discoverable Matter: an Optimist’s View of Dark Matter and How to Find It Permalink https://escholarship.org/uc/item/2sv8b4x5 Author Mcgehee Jr., Robert Stephen Publication Date 2020 Peer reviewed|Thesis/dissertation eScholarship.org Powered by the California Digital Library University of California Discoverable Matter: an Optimist’s View of Dark Matter and How to Find It by Robert Stephen Mcgehee Jr. A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Physics in the Graduate Division of the University of California, Berkeley Committee in charge: Professor Hitoshi Murayama, Chair Professor Alexander Givental Professor Yasunori Nomura Summer 2020 Discoverable Matter: an Optimist’s View of Dark Matter and How to Find It Copyright 2020 by Robert Stephen Mcgehee Jr. 1 Abstract Discoverable Matter: an Optimist’s View of Dark Matter and How to Find It by Robert Stephen Mcgehee Jr. Doctor of Philosophy in Physics University of California, Berkeley Professor Hitoshi Murayama, Chair An abundance of evidence from diverse cosmological times and scales demonstrates that 85% of the matter in the Universe is comprised of nonluminous, non-baryonic dark matter. Discovering its fundamental nature has become one of the greatest outstanding problems in modern science. Other persistent problems in physics have lingered for decades, among them the electroweak hierarchy and origin of the baryon asymmetry. Little is known about the solutions to these problems except that they must lie beyond the Standard Model. The first half of this dissertation explores dark matter models motivated by their solution to not only the dark matter conundrum but other issues such as electroweak naturalness and baryon asymmetry. -
Arxiv:0902.0628V3 [Hep-Ph] 20 Aug 2009 Nhne If Unchanged Suethat Assume Xeso Ftes Ya Xr Clrsnltwsas Icse N[2], in Problem
IFT-09-01 UCRHEP-T463 Pragmatic approach to the little hierarchy problem - the case for Dark Matter and neutrino physics - Bohdan GRZADKOWSKI∗ Institute of Theoretical Physics, University of Warsaw, Ho˙za 69, PL-00-681 Warsaw, Poland Jos´e WUDKA† Department of Physics and Astronomy, University of California, Riverside CA 92521-0413, USA We show that the addition of real scalars (gauge singlets) to the Standard Model can both ame- liorate the little hierarchy problem and provide realistic Dark Matter candidates. To this end, the coupling of the new scalars to the standard Higgs boson must be relatively strong and their mass should be in the 1 − 3 TeV range, while the lowest cutoff of the (unspecified) UV completion must be >∼5 TeV, depending on the Higgs boson mass and the number of singlets present. The existence of the singlets also leads to realistic and surprisingly reach neutrino physics. The resulting light neutrino mass spectrum and mixing angles are consistent with the constraints from the neutrino oscillations. PACS numbers: 12.60.Fr, 13.15.+g, 95.30.Cq, 95.35.+d Keywords: little hierarchy problem, gauge singlet, dark matter, neutrinos Introduction The goal of this project is to provide the most economic extension of the Standard Model (SM) for which the little hierarchy problem is ameliorated while retaining all the successes of the SM. We focus here on leading corrections to the SM, so we will consider only those extensions that interact with the SM through renormalizable interactions (below we will comment on the effects of higher-dimensional interactions). Since we concentrate on taming the quadratic divergence of the Higgs boson mass, it is natural to consider extensions of the scalar sector: when adding a new field ϕ, the gauge-invariant coupling ϕ 2H†H (where H denotes the SM scalar doublet) will generate additional radiative corrections to the Higgs boson mass| | that can serve to soften the little hierarchy problem. -
Solving the Hierarchy Problem
solving the hierarchy problem Joseph Lykken Fermilab/U. Chicago puzzle of the day: why is gravity so weak? answer: because there are large or warped extra dimensions about to be discovered at colliders puzzle of the day: why is gravity so weak? real answer: don’t know many possibilities may not even be a well-posed question outline of this lecture • what is the hierarchy problem of the Standard Model • is it really a problem? • what are the ways to solve it? • how is this related to gravity? what is the hierarchy problem of the Standard Model? • discuss concepts of naturalness and UV sensitivity in field theory • discuss Higgs naturalness problem in SM • discuss extra assumptions that lead to the hierarchy problem of SM UV sensitivity • Ken Wilson taught us how to think about field theory: “UV completion” = high energy effective field theory matching scale, Λ low energy effective field theory, e.g. SM energy UV sensitivity • how much do physical parameters of the low energy theory depend on details of the UV matching (i.e. short distance physics)? • if you know both the low and high energy theories, can answer this question precisely • if you don’t know the high energy theory, use a crude estimate: how much do the low energy observables change if, e.g. you let Λ → 2 Λ ? degrees of UV sensitivity parameter UV sensitivity “finite” quantities none -- UV insensitive dimensionless couplings logarithmic -- UV insensitive e.g. gauge or Yukawa couplings dimension-full coefs of higher dimension inverse power of cutoff -- “irrelevant” operators e.g. -
Mass Hierarchy and Physics Beyond the Standard Theory
Mass hierarchy and physics beyond the Standard Theory I. Antoniadis HEP 2014 - Conference on Recent Developments in High Energy Physics and Cosmology Naxos, Greece, 8-10 May 2014 Low energy SUSY and 126 GeV Higgs Live with the hierarchy Low scale strings and extra dimensions I. Antoniadis (CERN) 1 / 35 Entrance of a Higgs Boson in the Particle Data Group 2013 particle listing I. Antoniadis (CERN) 2 / 35 Couplings of the new boson vs SM Higgs Agreement with Standard Model Higgs expectation at 1.5 σ Most compatible with scalar 0+ hypothesis Measurement of its properties and decay rates currently under way I. Antoniadis (CERN) 3 / 35 Fran¸cois Englert Peter Higgs Nobel Prize of Physics 2013 ↓ ↓ I. Antoniadis (CERN) 4 / 35 Remarks on the value of the Higgs mass ∼ 126 GeV consistent with expectation from precision tests of the SM 2 2 favors perturbative physics quartic coupling λ = mH /v ≃ 1/8 1st elementary scalar in nature signaling perhaps more to come triumph of QFT and renormalized perturbation theory! Standard Theory has been tested with radiative corrections Window to new physics ? very important to measure precisely its properties and couplings several new and old questions wait for answers Dark matter, neutrino masses, baryon asymmetry, flavor physics, axions, electroweak scale hierarchy, early cosmology, . I. Antoniadis (CERN) 5 / 35 6 incertitude théorique ∆α 5 ∆α(5) ± had = 0.02761 0.00036 4 2 3 ∆χ 2 95% CL 1 région exclue 0 20100 400 260 [ ] mH GeV I. Antoniadis (CERN) 6 / 35 Beyond the Standard Theory of Particle Physics: driven by the mass hierarchy problem Standard picture: low energy supersymmetry Natural framework: Heterotic string (or high-scale M/F) theory Advantages: natural elementary scalars gauge coupling unification LSP: natural dark matter candidate radiative EWSB Problems: too many parameters: soft breaking terms MSSM : already a % - %0 fine-tuning ‘little’ hierarchy problem I. -
What Is Not the Hierarchy Problem (Of the SM Higgs)
What is not the hierarchy problem (of the SM Higgs) Matěj Hudec Výjezdní seminář ÚČJF Malá Skála, 12 Apr 2019, lunchtime Our ecological footprint he FuFnu wni twhit th the ggs AbAebliealina nH iHiggs mmodoedlel ký MM. M. Maalinlinsský 5 (2013) EEPPJJCC 7 733, ,2 244115 (2013) 660 aarrXXiivv::11221122..44660 12 pgs. 2 Our ecological footprint the Aspects of FuFnu wni twhith the Aspects of ggs renormalization AbAebliealina nH iHiggs renormalization of spontaneously mmodoedlel of spontaneously broken gauge broken gauge theories theories ký MM. M. Maalinlinsský MASTER THESIS MASTER THESIS M. H. M. H. 5 (2013) supervised by M.M. EEPPJJCC 7 733, ,2 244115 (2013) supervised by M.M. iv:1212.4660 2016 aarrXXiv:1212.4660 2016 12 pgs. 56 pgs. 3 Our ecological footprint Aspects of Fun with the H Fun with the Aspects of ierarchy and n Higgs renormalization AbAebliealian Higgs renormalization dHecoup of spontaneously ierarclhing mmodoedlel of spontaneously y and broken gauge decoup broken gauge ling theories theories M. Hudec, M. Malinský M M. Malinský MASTER THESIS .M M. alinský MASTER THESIS Hudec, M. M M. H. alinský M. H. (hopeful 5 (2013) supervised by M.M. ly EPJC) EEPPJJCC 7 733, ,2 244115 (2013) supervised by M.M. arX (hopef iv:190u2lly. 0EPJ 12.4660 2016 4C4) 70 aarrXXiivv::112212.4660 a 2016 rXiv:190 2.04470 12 pgs. 56 pgs. 17 pgs. 4 Hierarchy problem – first thoughts 5 Hierarchy problem – first thoughts In particle physics, the hierarchy problem is the large discrepancy between aspects of the weak force and gravity. 6 Hierarchy problem – first thoughts In particle physics, the hierarchy problem is the large discrepancy between aspects of the weak force and gravity. -
Atomic Electric Dipole Moments and Cp Violation
261 ATOMIC ELECTRIC DIPOLE MOMENTS AND CP VIOLATION S.M.Barr Bartol Research Institute University of Delaware Newark, DE 19716 USA Abstract The subject of atomic electric dipole moments, the rapid recent progress in searching for them, and their significance for fundamental issues in particle theory is surveyed. particular it is shown how the edms of different kinds of atoms and molecules, as well Inas of the neutron, give vital information on the nature and origin of CP violation. Special stress is laid on supersymmetric theories and their consequences. 262 I. INTRODUCTION In this talk I am going to discuss atomic and molecular electric dipole moments (edms) from a particle theorist's point of view. The first and fundamental point is that permanent electric dipole moments violate both P and T. If we assume, as we are entitled to do, that OPT is conserved then we may speak equivalently of T-violation and OP-violation. I will mostly use the latter designation. That a permanent edm violates T is easily shown. Consider a proton. It has a magnetic dipole moment oriented along its spin axis. Suppose it also has an electric edm oriented, say, parallel to the magnetic dipole. Under T the electric dipole is not changed, as the spatial charge distribution is unaffected. But the magnetic dipole changes sign because current flows are reversed by T. Thus T takes a proton with parallel electric and magnetic dipoles into one with antiparallel moments. Now, if T is assumed to be an exact symmetry these two experimentally distinguishable kinds of proton will have the same mass. -
Pos(ICHEP 2010)536 [email protected] an Overview of Models Oflittle Electroweak Hierarchy Problem Symmetry and Breaking Show Isof How Presented
A (Critical) Review of Electroweak Symmetry Breaking PoS(ICHEP 2010)536 Csaba Csáki Institute of High Energy Phenomenology Laboratory of Elementary Particle Physics Cornell University Ithaca, NY 14853, USA E-mail: [email protected] An overview of models of electroweak symmetry breaking is presented. First we explain the little hierarchy problem and show how it is manifested in supersymmetric theories. Then ways of avoiding the little hierarchy in SUSY models is shown, which fall into two classes: hiding the higgs at LEP or increasing the quartic self coupling of the higgs, both of which call for extensions of the MSSM. In the second half strongly interacting theories of electroweak symmetry breaking are reviewed, including technicolor and monopole condensation models. Particular attention is paid to warped extra dimensional theories and its cousins (higgsless, little higgs and composite higgs models. 35th International Conference of High Energy Physics - ICHEP2010, July 22-28, 2010 Paris France c Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. http://pos.sissa.it/ A (Critical) Review of Electroweak Symmetry Breaking 1. The SM, big vs. little hierarchy The standard Higgs mechanism is an eminently successful description of electroweak sym- metry breaking. The analysis of electroweak precision data suggest that there is a light weakly coupled higgs boson, below about 200 GeV. However, it is very hard to understand how such an el- ementary higgs would remain light. Examining quantum corrections one finds that the higgs mass is quadratically sensitive to any new physics: 2 2 g 2 Dm ∼ L (1.1) PoS(ICHEP 2010)536 H 16p2 where L is the scale of new physics. -
UV/IR Mixing and the Hierarchy Problem
UV/IR Mixing and the Hierarchy Problem David Rittenhouse Lab, UPenn Seth Koren EFI Oehme Fellow University of Chicago Broida Hall, UCSB Based (mainly) on - IR Dynamics from UV Divergences: UV/IR Mixing, NCFT, and the Hierarchy Problem [1909.01365, JHEP] with N. Craig - The Hierarchy Problem: From the Fundamentals to the Frontiers [2009.11870, PhD thesis] Michelson Center for Physics, UChicago UMichigan HEP Seminar, 11/11/20 Fine-tuning problems come from asking big, important questions Space Time It just is Why is there macroscopic structure? The Hierarchy Problem There is no hierarchy problem in the Standard Model Our toy model of the SM – a single scalar whose mass is an input parameter 1 1 푆 = න d4푥 − 휕 휙휕휇휙 − 푚2휙2 − 푉 휙 − 푔휙풪(휓 휓 ) 2 휇 2 0 푖 푖 푔2 1 푚2 = 푚2 + 푀2 phys 0 4휋 2 휖 푖 푖 The Higgs mass is an input so just choose the bare mass to give the right answer Hierarchy problem when Higgs mass is an output Now imagine in the UV there is an SU(2) global symmetry 휓 Φa = Where we’ve measured 휙 to be very light, but 휓 must be heavy 휙 1 † 1 푆 = න d4푥 − 휕 Φ 휕휇Φ − 푀2Φ†Φ − 휆 Φ†ΣΣ†Φ − 푉 Φ 2 휇 2 0 0 2 2 푚2 = 푀2 + 휆 푣2 Tree-level 푚휓 = 푀0 휙 0 0 1 1 Loop-level 푚2 = 푀2 + 푀2 + ⋯ 푚2 = 푀2 + 푀2 + ⋯ + 휆 푣2 휓 0 휖 Σ 휙 0 휖 Σ 0 2 2 푚2 = 푀2 + 휆 푣2 Renormalized 푚휓 = 푀phys 휙 phys phys phys 2 푀푝ℎ푦푠 Fine-tuned unless m휙 ∼ scale of new physics 휆phys = −1.00000000000000000000000000001 × 2 푣푝ℎ푦푠 The Hierarchy Problem: From the Fundamentals to the Frontiers How to get a light scalar: Classic edition Introduce UV structure to forbid large contributions, and IR dynamics to break that structure to the observed SM EFT E.g. -
Arxiv:1812.08975V1 [Physics.Hist-Ph] 21 Dec 2018 LHC, and Many Particle Physicists Expected BSM Physics to Be Detected
Two Notions of Naturalness Porter Williams ∗ Abstract My aim in this paper is twofold: (i) to distinguish two notions of natu- ralness employed in Beyond the Standard Model (BSM) physics and (ii) to argue that recognizing this distinction has methodological consequences. One notion of naturalness is an \autonomy of scales" requirement: it prohibits sensitive dependence of an effective field theory's low-energy ob- servables on precise specification of the theory's description of cutoff-scale physics. I will argue that considerations from the general structure of effective field theory provide justification for the role this notion of natu- ralness has played in BSM model construction. A second, distinct notion construes naturalness as a statistical principle requiring that the values of the parameters in an effective field theory be \likely" given some ap- propriately chosen measure on some appropriately circumscribed space of models. I argue that these two notions are historically and conceptually related but are motivated by distinct theoretical considerations and admit of distinct kinds of solution. 1 Introduction Since the late 1970s, attempting to satisfy a principle of \naturalness" has been an influential guide for particle physicists engaged in constructing speculative models of Beyond the Standard Model (BSM) physics. This principle has both been used as a constraint on the properties that models of BSM physics must possess and shaped expectations about the energy scales at which BSM physics will be detected by experiments. The most pressing problem of naturalness in the Standard Model is the Hierarchy Problem: the problem of maintaining a scale of electroweak symmetry breaking (EWSB) many orders of magnitude lower than the scale at which physics not included in the Standard Model be- comes important.1 Models that provided natural solutions to the Hierarchy Problem predicted BSM physics at energy scales that would be probed by the arXiv:1812.08975v1 [physics.hist-ph] 21 Dec 2018 LHC, and many particle physicists expected BSM physics to be detected.