DOCSLIB.ORG

Applications of Effective Field Theory Techniques to Jet Physics by Simon

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Applications of Effective Field Theory Techniques to Jet Physics by Simon Applications of Effective Field Theory Techniques to Jet Physics by Simon M. Freedman A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy Graduate Department of Physics University of Toronto c Copyright 2015 by Simon M. Freedman Abstract Applications of Effective Field Theory Techniques to Jet Physics Simon M. Freedman Doctor of Philosophy Graduate Department of Physics University of Toronto 2015 In this thesis we study jet production at large energies from leptonic collisions. We use the framework of effective theories of Quantum Chromodynamics (QCD) to examine the properties of jets and systematically improve calculations. We first develop a new formulation of soft-collinear effective theory (SCET), the appropriate effective theory for jets. In this formulation, soft and collinear degrees of freedom are described using QCD fields that interact with each other through light-like Wilson lines in external cur- rents. This formulation gives a more intuitive picture of jet processes than the traditional formulation of SCET. In particular, we show how the decoupling of soft and collinear degrees of freedom that occurs at leading order in power counting is explicit to next-to-leading order and likely beyond. We then use this formulation to write the thrust rate in a factorized form at next-to-leading order in the thrust parameter. The rate involves an incomplete sum over final states due to phase space cuts that is enforced by a measurement operator. Subleading corrections require matching onto not only the next-to-next-to leading order SCET operators, but also matching onto subleading measurement operators. We derive the appropriate hard, jet, and soft functions and show they reproduce the expected subleading thrust rate. Next, we renormalize the next-to-leading order dijet operators used for the subleading thrust rate. Constraints on matching coefficients from current conservation and reparametrization in- variance are shown. We also discuss the subtleties involved in regulating the infrared divergences of the individual loop diagrams in order to extract the ultraviolet divergences. The results can be used to increase the theoretical precision of the thrust rate. Finally, we study the (exclusive) k? and C/A jet algorithms in SCET. Regularizing the virtualites and rapidities of the individual graphs, we are able to write the O(αs) dijet cross ii section as the product of separate hard, jet, and soft contributions. We show how to reproduce the Sudakov form factor to next-to-leading logarithmic accuracy previously calculated by the coherent branching formalism. Our result only depends on the running of the hard function, and we comment that regularizing rapidities is not necessary in this case. iii Dedication To my patient parents and wife iv Acknowledgements I would like to start by giving my sincere thanks to my supervisor Michael Luke, for advising and encouraging me throughout my degree. The work in this thesis would not have been possible without my collaborators: William Man-Yin Cheung and Ray Georke. I would also like to thank Saba Zuberi and Andrew Blechman for teaching me a lot about EFTs during my first few years. As well, I would like to thank my committee members, Bob Holdom and Pierre Savard for keeping me on track, and non-committee member Erich Poppitz for teaching me about the Standard Model. I must also thank my fellow and former graduate students/zombies Catalina Gomez and Santiago Amigo, for many useful discussions and terrible jokes. I would also like to thank my families, both new and old. I owe my new family, the Chiu's, for all their support and great meals throughout the years. My parents, I would like to thank for bearing with me through the long years of wondering when I would finally graduate and my seemingly insane babbling about my research. My sister, I would like to thank for being my best- \man" and for fighting the good fight while I do less practical things. And my grandparents, despite the weekly questions about when I would graduate, I would like to thank them for their strength and passion that I hope I inherited. Finally, I reserve an unimaginable amount of gratitude to my wife Melissa, for her unwa- vering support and encouragment, and an endless energy to keep my spirits high. This work was supported by NSERC and the University of Toronto (and viewers like you). v Contents 1 Introduction 1 1.1 Hadronic Jet Physics . 3 1.2 Factorization From Effective Field Theory . 5 1.3 Organization of the Thesis . 7 2 Effective Theories of QCD 8 2.1 Review of Quantum Chromodynamics . 11 2.2 Heavy Quark Effective Theory . 12 2.3 Soft-Collinear Effective Theory . 14 2.3.1 Examples of SCET Currents . 19 2.4 Conclusion . 21 3 SCET, QCD, and Wilson Lines 22 3.1 Introduction . 22 3.2 Label SCET Formulation . 23 3.3 SCET as QCD Fields Coupled to Wilson Lines . 26 3.3.1 Dijet Production at Leading Order . 27 3.3.2 Subleading Corrections to Dijet Production . 31 3.4 Heavy-to-Light Current . 36 3.5 Conclusions . 39 4 Subleading Corrections To Thrust Using Effective Field Theory 41 4.1 Introduction . 41 4.2 Review of SCET . 43 4.3 Leading Order Calculation . 45 4.4 Next-to-Leading Order Calculation . 50 4.4.1 Measurement Operator . 50 4.4.2 Factorization . 53 4.5 Conclusion . 58 4.6 Appendix: Dijet Operators . 59 4.7 Appendix: Jet and Soft Operators . 61 vi 5 Renormalization of Subleading Dijet Operators in Soft-Collinear Effective Theory 70 5.1 Introduction . 70 5.2 SCET and NLO Operators . 73 5.2.1 Constraining the NLO Operators . 77 5.3 Infrared Regulator . 80 5.3.1 The Delta Regulator . 80 5.3.2 Gluon mass . 82 5.4 Anomalous Dimensions . 83 5.5 Conclusion . 88 6 The Exclusive kT and C/A Dijet Rates in SCET with a Rapidity Regulator 89 6.1 Introduction . 89 6.2 Review of Previous Work . 92 6.3 Next-to-Leading-Order calculation . 95 6.4 Next-to-leading logarithm summation . 97 6.5 Discussion . 102 6.6 Conclusion . 103 6.7 Appendix: General Rapidity Anomalous Dimension . 103 7 Conclusion 105 7.1 Future Directions . 106 vii Chapter 1 Introduction The Standard Model describes the strong and electroweak interactions at low energies. Elec- troweak symmetry is spontaneously broken at low energies by the Higgs mechanism resulting in four particles, three of which are Nambu-Goldstone bosons that become the longitudinal modes of the massive weak bosons. The fourth particle is a fundamental scalar called the Higgs boson that couples to massive Standard Model particles with a strength proportional to their mass. Only recently was a scalar particle with the Higgs boson's quantum numbers observed at the Large Hadron Collider (LHC) with a mass of 125:36 ± 0:37(stat.) ± 0:18(syst) GeV [1] and +0:26 +0:26 125:02 −0:27 (stat.) −0:15 (syst.) GeV [2] as measured by the ATLAS and CMS collaborations respectively. The discovery of the Higgs boson gives a portal to explore the electroweak sym- metry breaking mechanism. In order to explore this mechanism further, the LHC is increasing the luminosity, and increasing the collision energy from the current 8 TeV to 13 TeV energy. While the increased luminosity and collision energy allows for larger statistics and smaller dis- tance scales to be probed, the large hadronic background in the form of jets will still make precision measurements at the LHC difficult. Improvements in the understanding of jets from the theory side will become more important in order to search for new physics and test the Standard Model. In this thesis, we will study jets in simpler leptonic colliders using effective theory techniques with the future goal of applying this understanding to the LHC environment. The majority of hadron production and interactions occur due to Quantum Chromody- namics (QCD). The Lagrangian of QCD is gauged under SU(3) and describes the interac- tions between coloured quarks and gluons. However, the final states observed at detectors are hadrons, which are colour singlet bound states of the quarks and gluons held together by long distance non-perturbative effects. The discrepancy between the degrees of freedom of the QCD Lagrangian and the observed final states is due to the property of asymptotic freedom. The QCD coupling as a function of energy αs(Q), which describes the strength of the interactions between quarks and gluons, increases at low energy to the point where it is no longer a suitable expansion parameter. The energy scale where the coupling is large enough that the theory becomes non-perturbative is above ΛQCD ≈ 250 MeV in the MS regularization scheme. These non-perturbative effects make theoretical predictions involving QCD interactions challenging. 1 Chapter 1. Introduction 2 Studying large energy quark and gluon production requires understanding the large energy sprays of hadrons called jets. In order to simplify the analysis we will concentrate on high energy lepton collisions, which share many key similarities with hadron collisions for jet production at small distance scales. Leptonic collisions provide a cleaner environment for calculations because effects from parton distribution functions, initial state radiation, and beam remnants are either non-existent or suppressed by the electroweak coupling and can be mostly ignored. The only processes that need be considered at leading order in the electroweak coupling are the large energy collision and the hadronization of the final states. The strategy for calculating jet production is to factorize the different scales in the process. Factorization helps to restore predictive power by separating the long distance non-perturbative physics of the hadronization process, from the various short distance dynamics of the large energy particle collision.
Load more

Recommended publications
  • Quantum Field Theory*
    Quantum Field Theory y Frank Wilczek Institute for Advanced Study, School of Natural Science, Olden Lane, Princeton, NJ 08540 I discuss the general principles underlying quantum eld theory, and attempt to identify its most profound consequences. The deep est of these consequences result from the in nite number of degrees of freedom invoked to implement lo cality.Imention a few of its most striking successes, b oth achieved and prosp ective. Possible limitation s of quantum eld theory are viewed in the light of its history. I. SURVEY Quantum eld theory is the framework in which the regnant theories of the electroweak and strong interactions, which together form the Standard Mo del, are formulated. Quantum electro dynamics (QED), b esides providing a com- plete foundation for atomic physics and chemistry, has supp orted calculations of physical quantities with unparalleled precision. The exp erimentally measured value of the magnetic dip ole moment of the muon, 11 (g 2) = 233 184 600 (1680) 10 ; (1) exp: for example, should b e compared with the theoretical prediction 11 (g 2) = 233 183 478 (308) 10 : (2) theor: In quantum chromo dynamics (QCD) we cannot, for the forseeable future, aspire to to comparable accuracy.Yet QCD provides di erent, and at least equally impressive, evidence for the validity of the basic principles of quantum eld theory. Indeed, b ecause in QCD the interactions are stronger, QCD manifests a wider variety of phenomena characteristic of quantum eld theory. These include esp ecially running of the e ective coupling with distance or energy scale and the phenomenon of con nement.
    [Show full text]
  • Effective Field Theories, Reductionism and Scientific Explanation Stephan
    To appear in: Studies in History and Philosophy of Modern Physics Effective Field Theories, Reductionism and Scientific Explanation Stephan Hartmann∗ Abstract Effective field theories have been a very popular tool in quantum physics for almost two decades. And there are good reasons for this. I will argue that effec- tive field theories share many of the advantages of both fundamental theories and phenomenological models, while avoiding their respective shortcomings. They are, for example, flexible enough to cover a wide range of phenomena, and concrete enough to provide a detailed story of the specific mechanisms at work at a given energy scale. So will all of physics eventually converge on effective field theories? This paper argues that good scientific research can be characterised by a fruitful interaction between fundamental theories, phenomenological models and effective field theories. All of them have their appropriate functions in the research process, and all of them are indispens- able. They complement each other and hang together in a coherent way which I shall characterise in some detail. To illustrate all this I will present a case study from nuclear and particle physics. The resulting view about scientific theorising is inherently pluralistic, and has implications for the debates about reductionism and scientific explanation. Keywords: Effective Field Theory; Quantum Field Theory; Renormalisation; Reductionism; Explanation; Pluralism. ∗Center for Philosophy of Science, University of Pittsburgh, 817 Cathedral of Learning, Pitts- burgh, PA 15260, USA (e-mail: [email protected]) (correspondence address); and Sektion Physik, Universit¨at M¨unchen, Theresienstr. 37, 80333 M¨unchen, Germany. 1 1 Introduction There is little doubt that effective field theories are nowadays a very popular tool in quantum physics.
    [Show full text]
  • On the Limits of Effective Quantum Field Theory
    RUNHETC-2019-15 On the Limits of Effective Quantum Field Theory: Eternal Inflation, Landscapes, and Other Mythical Beasts Tom Banks Department of Physics and NHETC Rutgers University, Piscataway, NJ 08854 E-mail: [email protected] Abstract We recapitulate multiple arguments that Eternal Inflation and the String Landscape are actually part of the Swampland: ideas in Effective Quantum Field Theory that do not have a counterpart in genuine models of Quantum Gravity. 1 Introduction Most of the arguments and results in this paper are old, dating back a decade, and very little of what is written here has not been published previously, or presented in talks. I was motivated to write this note after spending two weeks at the Vacuum Energy and Electroweak Scale workshop at KITP in Santa Barbara. There I found a whole new generation of effective field theorists recycling tired ideas from the 1980s about the use of effective field theory in gravitational contexts. These were ideas that I once believed in, but since the beginning of the 21st century my work in string theory and the dynamics of black holes, convinced me that they arXiv:1910.12817v2 [hep-th] 6 Nov 2019 were wrong. I wrote and lectured about this extensively in the first decade of the century, but apparently those arguments have not been accepted, and effective field theorists have concluded that the main lesson from string theory is that there is a vast landscape of meta-stable states in the theory of quantum gravity, connected by tunneling transitions in the manner envisioned by effective field theorists in the 1980s.
    [Show full text]
  • Renormalization and Effective Field Theory
    Mathematical Surveys and Monographs Volume 170 Renormalization and Effective Field Theory Kevin Costello American Mathematical Society surv-170-costello-cov.indd 1 1/28/11 8:15 AM http://dx.doi.org/10.1090/surv/170 Renormalization and Effective Field Theory Mathematical Surveys and Monographs Volume 170 Renormalization and Effective Field Theory Kevin Costello American Mathematical Society Providence, Rhode Island EDITORIAL COMMITTEE Ralph L. Cohen, Chair MichaelA.Singer Eric M. Friedlander Benjamin Sudakov MichaelI.Weinstein 2010 Mathematics Subject Classification. Primary 81T13, 81T15, 81T17, 81T18, 81T20, 81T70. The author was partially supported by NSF grant 0706954 and an Alfred P. Sloan Fellowship. For additional information and updates on this book, visit www.ams.org/bookpages/surv-170 Library of Congress Cataloging-in-Publication Data Costello, Kevin. Renormalization and effective fieldtheory/KevinCostello. p. cm. — (Mathematical surveys and monographs ; v. 170) Includes bibliographical references. ISBN 978-0-8218-5288-0 (alk. paper) 1. Renormalization (Physics) 2. Quantum field theory. I. Title. QC174.17.R46C67 2011 530.143—dc22 2010047463 Copying and reprinting. Individual readers of this publication, and nonprofit libraries acting for them, are permitted to make fair use of the material, such as to copy a chapter for use in teaching or research. Permission is granted to quote brief passages from this publication in reviews, provided the customary acknowledgment of the source is given. Republication, systematic copying, or multiple reproduction of any material in this publication is permitted only under license from the American Mathematical Society. Requests for such permission should be addressed to the Acquisitions Department, American Mathematical Society, 201 Charles Street, Providence, Rhode Island 02904-2294 USA.
    [Show full text]
  • Lectures on Effective Field Theories
    Adam Falkowski Lectures on Effective Field Theories Version of September 21, 2020 Abstract Effective field theories (EFTs) are widely used in particle physics and well beyond. The basic idea is to approximate a physical system by integrating out the degrees of freedom that are not relevant in a given experimental setting. These are traded for a set of effective interactions between the remaining degrees of freedom. In these lectures I review the concept, techniques, and applications of the EFT framework. The 1st lecture gives an overview of the EFT landscape. I will review the philosophy, basic techniques, and applications of EFTs. A few prominent examples, such as the Fermi theory, the Euler-Heisenberg Lagrangian, and the SMEFT, are presented to illustrate some salient features of the EFT. In the 2nd lecture I discuss quantitatively the procedure of integrating out heavy particles in a quantum field theory. An explicit example of the tree- and one-loop level matching between an EFT and its UV completion will be discussed in all gory details. The 3rd lecture is devoted to path integral methods of calculating effective Lagrangians. Finally, in the 4th lecture I discuss the EFT approach to constraining new physics beyond the Standard Model (SM). To this end, the so- called SM EFT is introduced, where the SM Lagrangian is extended by a set of non- renormalizable interactions representing the effects of new heavy particles. 1 Contents 1 Illustrated philosophy of EFT3 1.1 Introduction..................................3 1.2 Scaling and power counting.........................6 1.3 Illustration #1: Fermi theory........................8 1.4 Illustration #2: Euler-Heisenberg Lagrangian..............
    [Show full text]
  • Quantum Gravity, Effective Fields and String Theory
    Quantum gravity, effective fields and string theory Niels Emil Jannik Bjerrum-Bohr The Niels Bohr Institute University of Copenhagen arXiv:hep-th/0410097v1 10 Oct 2004 Thesis submitted for the degree of Doctor of Philosophy in Physics at the Niels Bohr Institute, University of Copenhagen. 28th July 2 Abstract In this thesis we will look into some of the various aspects of treating general relativity as a quantum theory. The thesis falls in three parts. First we briefly study how gen- eral relativity can be consistently quantized as an effective field theory, and we focus on the concrete results of such a treatment. As a key achievement of the investigations we present our calculations of the long-range low-energy leading quantum corrections to both the Schwarzschild and Kerr metrics. The leading quantum corrections to the pure gravitational potential between two sources are also calculated, both in the mixed theory of scalar QED and quantum gravity and in the pure gravitational theory. Another part of the thesis deals with the (Kawai-Lewellen-Tye) string theory gauge/gravity relations. Both theories are treated as effective field theories, and we investigate if the KLT oper- ator mapping is extendable to the case of higher derivative operators. The constraints, imposed by the KLT-mapping on the effective coupling constants, are also investigated. The KLT relations are generalized, taking the effective field theory viewpoint, and it is noticed that some remarkable tree-level amplitude relations exist between the field the- ory operators. Finally we look at effective quantum gravity treated from the perspective of taking the limit of infinitely many spatial dimensions.
    [Show full text]
  • Material Matter Effects in Gravitational UV/IR Mixing
    PHYSICAL REVIEW D 101, 084022 (2020) Material matter effects in gravitational UV=IR mixing Joseph Bramante and Elizabeth Gould The McDonald Institute and Department of Physics, Engineering Physics, and Astronomy, Queen’s University, Kingston, Ontario K7L 2S8, Canada and Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada (Received 12 November 2019; accepted 30 March 2020; published 9 April 2020) We propose a matter effect for the gravitational ultraviolet/infrared (UV=IR) mixing solution to the cosmological constant problem. Previously, the gravitational UV=IR mixing model implied a nonstandard equation of state for dark energy, contradicting observation. In contrast, matter effect gravitational UV=IR mixing accommodates a standard ΛCDM cosmology with constant dark energy. Notably, there are new density-dependent predictions for futuristically precise measurements of fundamental parameters, like the magnetic moments of the muon and electron. DOI: 10.1103/PhysRevD.101.084022 I. INTRODUCTION Nelson [2] (CKN) argues to the contrary, that effective field theory breaks down for any UV cutoff Λ ≳ meV in a The cosmological constant problem can be expressed UV region the size of our universe. as follows. Let us compare the observed vacuum energy in The gravitational UV=IR mixing proposal follows from our universe V4 ∼ ð2 meVÞ4 to the zero-point loop obs the observation that there will be inherently nonlocal vacuum energy contribution from a field with mass m gravitational dynamics in sufficiently large and dense and momentum p, systems. If loop-level zero-point field energy densities Z qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Λ 3 1 Λ4 over a space L are so large that a black hole forms inside δρ ≃ UV dp 2 þ 2 ≃ UV ð Þ Λ 3 p m 2 ; 1 L, we have entered a computational regime for which our Λ ð2πÞ 2 16π IR local effective field theory has broken down, unless the theory properly accounts for the presence of virtual black ≪ Λ where the last expression has assumed m UV and for hole states in loop-level field dynamics.
    [Show full text]
  • Introduction to Effective Field Theory
    IV Introduction to effective field theory The purpose of an effective field theory is to represent in a simple way the dynamical content of a theory in the low energy limit. One uses only those light degrees of freedom that are active at low energy, and treats their interactions in a full field theoretic framework. The effective field theory is often technically non-renormalizable, yet loop diagrams are included and renormalization of the physical parameters is readily accomplished. Effective field theory is used in all aspects of the Standard Model and beyond, from QED to superstrings. Perhaps the best setting for learning about the topic is that of chiral symmetry. Besides being historically important in the development of effective field theory techniques, chiral symmetry is a rather subtle subject which can be used to illustrate all aspects of the method, viz. the low energy expansion, non-leading be- havior, loops, renormalization and symmetry breaking. In addition, the results can be tested directly by experiment since the chiral effective field theory provides a framework for understanding the very low energy limit of QCD. In this chapter we introduce effective field theory by a study of the linear sigma model, and discuss the generalization of these techniques to other settings. IV{1 Effective lagrangians and the sigma model The linear sigma model, introduced in Sects. I{4, I{6, provides a `user friendly' introduction to effective field theory because all the relevant ma- nipulations can be explicitly demonstrated. The Goldstone boson fields, the pions, are present at all stages of the calculation.
    [Show full text]
  • Effective Field Theory with Nambu–Goldstone Modes
    Effective Field Theory with Nambu–Goldstone Modes Antonio Pich Departament de F´ısica Te`orica, IFIC, Universitat de Val`encia - CSIC Apt. Correus 22085, E-46071 Val`encia, Spain Abstract These lectures provide an introduction to the low-energy dynamics of Nambu– Goldstone fields, associated with some spontaneous (or dynamical) symmetry break- ing, using the powerful methods of effective field theory. The generic symmetry proper- ties of these massless modes are described in detail and two very relevant phenomeno- logical applications are worked out: chiral perturbation theory, the low-energy effective theory of QCD, and the (non-linear) electroweak effective theory. The similarities and differences between these two effective theories are emphasized, and their current sta- tus is reviewed. Special attention is given to the short-distance dynamical information encoded in the low-energy couplings of the effective Lagrangians. The successful meth- arXiv:1804.05664v2 [hep-ph] 25 Jan 2020 ods developed in QCD could help us to uncover fingerprints of new physics scales from future measurements of the electroweak effective theory couplings. Contents Effective Field Theory with Nambu–Goldstone Modes 1 1 AtoyLagrangian:thelinearsigmamodel 2 2 Symmetry realizations 4 3 Chiral symmetry in massless QCD 6 4 Nambu–Goldstone effective Lagrangian 7 5 Chiral perturbation theory 14 6 QCD phenomenology at very low energies 21 7 Quantum anomalies 28 8 Massive fields and low-energy constants 31 9 ThelimitofaverylargenumberofQCDcolours 39 10 Electroweak symmetry breaking 45 11 Electroweak effective theory 50 12 Fingerprints of heavy scales 60 13 Summary 67 Exercises 68 References 70 Effective Field Theory with Nambu–Goldstone Modes Field theories with spontaneous symmetry breaking (SSB) provide an ideal envi- ronment to apply the techniques of effective field theory (EFT).
    [Show full text]
  • Introduction to Effective Field Theory BR Holstein [email protected]
    University of Massachusetts Amherst ScholarWorks@UMass Amherst Physics Department Faculty Publication Series Physics 2001 Introduction to effective field theory BR Holstein [email protected] Follow this and additional works at: https://scholarworks.umass.edu/physics_faculty_pubs Part of the Physical Sciences and Mathematics Commons Recommended Citation Holstein, BR, "Introduction to effective field theory" (2001). NUCLEAR PHYSICS A. 307. Retrieved from https://scholarworks.umass.edu/physics_faculty_pubs/307 This Article is brought to you for free and open access by the Physics at ScholarWorks@UMass Amherst. It has been accepted for inclusion in Physics Department Faculty Publication Series by an authorized administrator of ScholarWorks@UMass Amherst. For more information, please contact [email protected]. 1 Introduction to Effective Field Theory Barry R. Holsteina aDepartment of Physics-LGRT University of Massachusetts, Amherst, MA 01003 1. Introduction The basic idea behind effective field theory (EFT) methods is to describe nature in terms of a fully consistent quantum field theory, but one which is valid in a limited energy range. Now strictly speaking this means that almost any theory is an EFT except string theories that try to be a theory of everything (TOE). Indeed even the quintessential quantum field theory—quantum electrodynamics—is an EFT in that it must break down at the very highest energies. In fact we represent the high energy contribution in terms of a conterterm which, together with the divergent component from the loop integration, we fit in terms of the experimental mass and charge. In order to get a better feel for this idea it is useful to consider a simpler example from the regime of ordinary quantum mechanics—that of Rayleigh scattering, or why the sky is blue.
    [Show full text]
  • (2019) Toward Convergence of Effective-Field-Theory Simulations On
    PHYSICAL REVIEW A 100, 062319 (2019) Toward convergence of effective-field-theory simulations on digital quantum computers O. Shehab ,1 K. Landsman,2 Y. Nam,1 D. Zhu,2 N. M. Linke,2 M. Keesan,1 R. C. Pooser,3,4 and C. Monroe2,1 1IonQ, Inc, 4505 Campus Drive, College Park, Maryland 20740, USA 2Joint Quantum Institute, Department of Physics and Joint Center for Quantum Information and Computer Science, University of Maryland, College Park, Maryland 20742, USA 3Computational Sciences and Engineering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA 4Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996, USA (Received 12 April 2019; revised manuscript received 21 November 2019; published 16 December 2019) We report results for simulating an effective field theory to compute the binding energy of the deuteron nucleus using a hybrid algorithm on a trapped-ion quantum computer. Two increasingly complex unitary coupled-cluster ansatze have been used to compute the binding energy to within a few percent for successively more complex Hamiltonians. By increasing the complexity of the Hamiltonian, allowing more terms in the effective field theory expansion, and calculating their expectation values, we present a benchmark for quantum computers based on their ability to scalably calculate the effective field theory with increasing accuracy. Our result of E4 =−2.220 ± 0.179 MeV may be compared with the exact deuteron ground-state energy −2.224 MeV. We also demonstrate an error mitigation technique using Richardson extrapolation on ion traps. The error mitigation circuit represents a record for deepest quantum circuit on a trapped-ion quantum computer.
    [Show full text]
  • Interpreting Effective Field Theories
    Interpreting Effective Field Theories Jonathan Bain Humanities and Social Sciences Polytechnic Institute of New York University Brooklyn, NY 11201 Abstract: An effective field theory (EFT) is a theory of the dynamics of a physical system at energies small compared to a given cut-off. Low-energy states with respect to this cut-off are effectively independent of states at high energies; hence one may study the low-energy dynamics without the need for a detailed description of the high-energy dynamics. Many authors have suggested that, because of the essential role the cut-off plays in the standard (Wilsonian) method of constructing an EFT, an appropriate interpretation of an EFT requires a realistic interpretation of the cut-off. For some, this suggests an ontology of "quasi-autonomous domains" (Cao and Schweber 1993); for others, it suggests an ontology in which space is discrete and finite (Fraser 2009); and for yet others, it suggests that EFTs engage in idealizations and are inherently approximate (Fraser 2009, Castellani 2002). I argue that these interpretations are not forced upon us, in so far as there is an alternative to the Wilsonian method for constructing an EFT that does not explicitly employ a cut-off. Keywords: effective field theory, quantum field theory, ontology, empirical equivalence. Word count: 6534 1. Introduction 2. How to Construct an EFT 3. On Renormalization Schemes and Interpretations of EFTs 3.1. Mass-Dependent Schemes and Wilsonian EFTs 3.2. Mass-Independent Schemes and Continuum EFTs 4. Implications 4.1. Decoupling and Quasi-Autonomous Domains 4.2. Realistic Interpretations of the Cutoff 4.3.
    [Show full text]