Solving the Hierarchy Problem
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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. -
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. -
A Modified Naturalness Principle and Its Experimental Tests
A modified naturalness principle and its experimental tests Marco Farinaa, Duccio Pappadopulob;c and Alessandro Strumiad;e (a) Department of Physics, LEPP, Cornell University, Ithaca, NY 14853, USA (b) Department of Physics, University of California, Berkeley, CA 94720, USA (c) Theoretical Physics Group, Lawrence Berkeley National Laboratory, Berkeley, USA (d) Dipartimento di Fisica dell’Universita` di Pisa and INFN, Italia (e) National Institute of Chemical Physics and Biophysics, Tallinn, Estonia Abstract Motivated by LHC results, we modify the usual criterion for naturalness by ig- noring the uncomputable power divergences. The Standard Model satisfies the modified criterion (‘finite naturalness’) for the measured values of its parameters. Extensions of the SM motivated by observations (Dark Matter, neutrino masses, the strong CP problem, vacuum instability, inflation) satisfy finite naturalness in special ranges of their parameter spaces which often imply new particles below a few TeV. Finite naturalness bounds are weaker than usual naturalness bounds because any new particle with SM gauge interactions gives a finite contribution to the Higgs mass at two loop order. Contents 1 Introduction2 2 The Standard Model3 3 Finite naturalness, neutrino masses and leptogenesis4 3.1 Type-I see saw . .5 3.2 Type-III see saw . .6 3.3 Type-II see saw . .6 arXiv:1303.7244v3 [hep-ph] 29 Apr 2014 4 Finite naturalness and Dark Matter7 4.1 Minimal Dark Matter . .7 4.2 The scalar singlet DM model . 10 4.3 The fermion singlet model . 10 5 Finite naturalness and axions 13 5.1 KSVZ axions . 13 5.2 DFSZ axions . 14 6 Finite naturalness, vacuum decay and inflation 14 7 Conclusions 15 1 1 Introduction The naturalness principle strongly influenced high-energy physics in the past decades [1], leading to the belief that physics beyond the Standard Model (SM) must exist at a scale ΛNP such that quadratically divergent quantum corrections to the Higgs squared mass are made finite (presumably up to a log divergence) and not much larger than the Higgs mass Mh itself. -
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. -
Hep-Ph] 19 Nov 2018
The discreet charm of higgsino dark matter { a pocket review Kamila Kowalska∗ and Enrico Maria Sessoloy National Centre for Nuclear Research, Ho_za69, 00-681 Warsaw, Poland Abstract We give a brief review of the current constraints and prospects for detection of higgsino dark matter in low-scale supersymmetry. In the first part we argue, after per- forming a survey of all potential dark matter particles in the MSSM, that the (nearly) pure higgsino is the only candidate emerging virtually unscathed from the wealth of observational data of recent years. In doing so by virtue of its gauge quantum numbers and electroweak symmetry breaking only, it maintains at the same time a relatively high degree of model-independence. In the second part we properly review the prospects for detection of a higgsino-like neutralino in direct underground dark matter searches, col- lider searches, and indirect astrophysical signals. We provide estimates for the typical scale of the superpartners and fine tuning in the context of traditional scenarios where the breaking of supersymmetry is mediated at about the scale of Grand Unification and where strong expectations for a timely detection of higgsinos in underground detectors are closely related to the measured 125 GeV mass of the Higgs boson at the LHC. arXiv:1802.04097v3 [hep-ph] 19 Nov 2018 ∗[email protected] [email protected] 1 Contents 1 Introduction2 2 Dark matter in the MSSM4 2.1 SU(2) singlets . .5 2.2 SU(2) doublets . .7 2.3 SU(2) adjoint triplet . .9 2.4 Mixed cases . .9 3 Phenomenology of higgsino dark matter 12 3.1 Prospects for detection in direct and indirect searches . -
A Natural Introduction to Fine-Tuning
A Natural Introduction to Fine-Tuning Julian De Vuyst ∗ Department of Physics & Astronomy, Ghent University, Krijgslaan, S9, 9000 Ghent, Belgium Abstract A well-known topic within the philosophy of physics is the problem of fine-tuning: the fact that the universal constants seem to take non-arbitrary values in order for live to thrive in our Universe. In this paper we will talk about this problem in general, giving some examples from physics. We will review some solutions like the design argument, logical probability, cosmological natural selection, etc. Moreover, we will also discuss why it's dangerous to uphold the Principle of Naturalness as a scientific principle. After going through this paper, the reader should have a general idea what this problem exactly entails whenever it is mentioned in other sources and we recommend the reader to think critically about these concepts. arXiv:2012.05617v1 [physics.hist-ph] 10 Dec 2020 ∗[email protected] 1 Contents 1 Introduction3 2 A Take on Constants3 2.I The Role of Units . .4 2.II Derived vs Fundamental Constants . .5 3 The Concept of Naturalness6 3.I Technical Naturalness . .6 3.I.a A Wilsonian Perspective . .6 3.I.b A Brief History . .8 3.II Numerical/General Naturalness . .9 4 The Fine-Tuning Problem9 5 Some Examples from Physics 10 5.I The Cosmological Constant Problem . 10 5.II The Flatness Problem . 11 5.III The Higgs Mass . 12 5.IV The Strong CP Problem . 13 6 Resolutions to Fine-Tuning 14 6.I We are here, full stop . 14 6.II Designed like Clockwork . -
Naturalness and Mixed Axion-Higgsino Dark Matter Howard Baer University of Oklahoma UCLA DM Meeting, Feb
Naturalness and mixed axion-higgsino dark matter Howard Baer University of Oklahoma UCLA DM meeting, Feb. 18, 2016 ADMX LZ What is the connection? The naturalness issue: Naturalness= no large unnatural tuning in W, Z, h masses up-Higgs soft term radiative corrections superpotential mu term well-mixed TeV-scale stops suppress Sigma while lifting m(h)~125 GeV What about other measures: 2 @ log mZ ∆EENZ/BG = maxi where pi are parameters EENZ/BG: | @ log pi | * in past, applied to multi-param. effective theories; * in fundamental theory, param’s dependent * e.g. in gravity-mediation, apply to mu,m_3/2 * then agrees with Delta_EW what about large logs and light stops? * overzealous use of ~ symbol * combine dependent terms * cancellations possible * then agrees with Delta_EW SUSY mu problem: mu term is SUSY, not SUSY breaking: expect mu~M(Pl) but phenomenology requires mu~m(Z) • NMSSM: mu~m(3/2); beware singlets! • Giudice-Masiero: mu forbidden by some symmetry: generate via Higgs coupling to hidden sector • Kim-Nilles!: invoke SUSY version of DFSZ axion solution to strong CP: KN: PQ symmetry forbids mu term, but then it is generated via PQ breaking 2 m3/2 mhid/MP Little Hierarchy due to mismatch between ⇠ f m PQ breaking and SUSY breaking scales? a ⌧ hid Higgs mass tells us where 1012 GeV ma 6.2µeV to look for axion! ⇠ f ✓ a ◆ Simple mechanism to suppress up-Higgs soft term: radiative EWSB => radiatively-driven naturalness But what about SUSY mu term? There is a Little Hierarchy, but it is no problem µ m ⌧ 3/2 Mainly higgsino-like WIMPs thermally -
Exploring Supersymmetry and Naturalness in Light of New Experimental Data
Exploring supersymmetry and naturalness in light of new experimental data by Kevin Earl A thesis submitted to the Faculty of Graduate and Postdoctoral Affairs in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Physics Department of Physics Carleton University Ottawa-Carleton Institute for Physics Ottawa, Canada August 27, 2019 Copyright ⃝c 2019 Kevin Earl Abstract This thesis investigates extensions of the Standard Model (SM) that are based on either supersymmetry or the Twin Higgs model. New experimental data, primar- ily collected at the Large Hadron Collider (LHC), play an important role in these investigations. Specifically, we examine the following five cases. We first consider Mini-Split models of supersymmetry. These types ofmod- els can be generated by both anomaly and gauge mediation and we examine both cases. LHC searches are used to constrain the relevant parameter spaces, and future prospects at LHC 14 and a 100 TeV proton proton collider are investigated. Next, we study a scenario where Higgsino neutralinos and charginos are pair produced at the LHC and promptly decay due to the baryonic R-parity violating superpotential operator λ00U cDcDc. More precisely, we examine this phenomenology 00 in the case of a single non-zero λ3jk coupling. By recasting an experimental search, we derive novel constraints on this scenario. We then introduce an R-symmetric model of supersymmetry where the R- symmetry can be identified with baryon number. This allows the operator λ00U cDcDc in the superpotential without breaking baryon number. However, the R-symmetry will be broken by at least anomaly mediation and this reintroduces baryon number violation. -
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.