A Generalization of the One-Dimensional Boson-Fermion Duality Through the Path-Integral Formalsim
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Supersymmetric Dark Matter
Supersymmetric dark matter G. Bélanger LAPTH- Annecy Plan | Dark matter : motivation | Introduction to supersymmetry | MSSM | Properties of neutralino | Status of LSP in various SUSY models | Other DM candidates z SUSY z Non-SUSY | DM : signals, direct detection, LHC Dark matter: a WIMP? | Strong evidence that DM dominates over visible matter. Data from rotation curves, clusters, supernovae, CMB all point to large DM component | DM a new particle? | SM is incomplete : arbitrary parameters, hierarchy problem z DM likely to be related to physics at weak scale, new physics at the weak scale can also solve EWSB z Stable particle protect by symmetry z Many solutions – supersymmetry is one best motivated alternative to SM | NP at electroweak scale could also explain baryonic asymetry in the universe Relic density of wimps | In early universe WIMPs are present in large number and they are in thermal equilibrium | As the universe expanded and cooled their density is reduced Freeze-out through pair annihilation | Eventually density is too low for annihilation process to keep up with expansion rate z Freeze-out temperature | LSP decouples from standard model particles, density depends only on expansion rate of the universe | Relic density | A relic density in agreement with present measurements (Ωh2 ~0.1) requires typical weak interactions cross-section Coannihilation | If M(NLSP)~M(LSP) then maintains thermal equilibrium between NLSP-LSP even after SUSY particles decouple from standard ones | Relic density then depends on rate for all processes -
Quantum Statistics: Is There an Effective Fermion Repulsion Or Boson Attraction? W
Quantum statistics: Is there an effective fermion repulsion or boson attraction? W. J. Mullin and G. Blaylock Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003 ͑Received 13 February 2003; accepted 16 May 2003͒ Physicists often claim that there is an effective repulsion between fermions, implied by the Pauli principle, and a corresponding effective attraction between bosons. We examine the origins and validity of such exchange force ideas and the areas where they are highly misleading. We propose that explanations of quantum statistics should avoid the idea of an effective force completely, and replace it with more appropriate physical insights, some of which are suggested here. © 2003 American Association of Physics Teachers. ͓DOI: 10.1119/1.1590658͔ ͒ϭ ͒ Ϫ␣ Ϫ ϩ ͒2 I. INTRODUCTION ͑x1 ,x2 ,t C͕f ͑x1 ,x2 exp͓ ͑x1 vt a Ϫ͑x ϩvtϪa͒2͔Ϫ f ͑x ,x ͒ The Pauli principle states that no two fermions can have 2 2 1 ϫ Ϫ␣ Ϫ ϩ ͒2Ϫ ϩ Ϫ ͒2 the same quantum numbers. The origin of this law is the exp͓ ͑x2 vt a ͑x1 vt a ͔͖, required antisymmetry of the multi-fermion wavefunction. ͑1͒ Most physicists have heard or read a shorthand way of ex- pressing the Pauli principle, which says something analogous where x1 and x2 are the particle coordinates, f (x1 ,x2) ϭ ͓ Ϫ ប͔ to fermions being ‘‘antisocial’’ and bosons ‘‘gregarious.’’ Of- exp imv(x1 x2)/ , C is a time-dependent factor, and the ten this intuitive approach involves the statement that there is packet width parameters ␣ and  are unequal. -
1 Standard Model: Successes and Problems
Searching for new particles at the Large Hadron Collider James Hirschauer (Fermi National Accelerator Laboratory) Sambamurti Memorial Lecture : August 7, 2017 Our current theory of the most fundamental laws of physics, known as the standard model (SM), works very well to explain many aspects of nature. Most recently, the Higgs boson, predicted to exist in the late 1960s, was discovered by the CMS and ATLAS collaborations at the Large Hadron Collider at CERN in 2012 [1] marking the first observation of the full spectrum of predicted SM particles. Despite the great success of this theory, there are several aspects of nature for which the SM description is completely lacking or unsatisfactory, including the identity of the astronomically observed dark matter and the mass of newly discovered Higgs boson. These and other apparent limitations of the SM motivate the search for new phenomena beyond the SM either directly at the LHC or indirectly with lower energy, high precision experiments. In these proceedings, the successes and some of the shortcomings of the SM are described, followed by a description of the methods and status of the search for new phenomena at the LHC, with some focus on supersymmetry (SUSY) [2], a specific theory of physics beyond the standard model (BSM). 1 Standard model: successes and problems The standard model of particle physics describes the interactions of fundamental matter particles (quarks and leptons) via the fundamental forces (mediated by the force carrying particles: the photon, gluon, and weak bosons). The Higgs boson, also a fundamental SM particle, plays a central role in the mechanism that determines the masses of the photon and weak bosons, as well as the rest of the standard model particles. -
A Young Physicist's Guide to the Higgs Boson
A Young Physicist’s Guide to the Higgs Boson Tel Aviv University Future Scientists – CERN Tour Presented by Stephen Sekula Associate Professor of Experimental Particle Physics SMU, Dallas, TX Programme ● You have a problem in your theory: (why do you need the Higgs Particle?) ● How to Make a Higgs Particle (One-at-a-Time) ● How to See a Higgs Particle (Without fooling yourself too much) ● A View from the Shadows: What are the New Questions? (An Epilogue) Stephen J. Sekula - SMU 2/44 You Have a Problem in Your Theory Credit for the ideas/example in this section goes to Prof. Daniel Stolarski (Carleton University) The Usual Explanation Usual Statement: “You need the Higgs Particle to explain mass.” 2 F=ma F=G m1 m2 /r Most of the mass of matter lies in the nucleus of the atom, and most of the mass of the nucleus arises from “binding energy” - the strength of the force that holds particles together to form nuclei imparts mass-energy to the nucleus (ala E = mc2). Corrected Statement: “You need the Higgs Particle to explain fundamental mass.” (e.g. the electron’s mass) E2=m2 c4+ p2 c2→( p=0)→ E=mc2 Stephen J. Sekula - SMU 4/44 Yes, the Higgs is important for mass, but let’s try this... ● No doubt, the Higgs particle plays a role in fundamental mass (I will come back to this point) ● But, as students who’ve been exposed to introductory physics (mechanics, electricity and magnetism) and some modern physics topics (quantum mechanics and special relativity) you are more familiar with.. -
Higgsino DM Is Dead
Cornering Higgsino at the LHC Satoshi Shirai (Kavli IPMU) Based on H. Fukuda, N. Nagata, H. Oide, H. Otono, and SS, “Higgsino Dark Matter in High-Scale Supersymmetry,” JHEP 1501 (2015) 029, “Higgsino Dark Matter or Not,” Phys.Lett. B781 (2018) 306 “Cornering Higgsino: Use of Soft Displaced Track ”, arXiv:1910.08065 1. Higgsino Dark Matter 2. Current Status of Higgsino @LHC mono-jet, dilepton, disappearing track 3. Prospect of Higgsino Use of soft track 4. Summary 2 DM Candidates • Axion • (Primordial) Black hole • WIMP • Others… 3 WIMP Dark Matter Weakly Interacting Massive Particle DM abundance DM Standard Model (SM) particle 500 GeV DM DM SM Time 4 WIMP Miracle 5 What is Higgsino? Higgsino is (pseudo)Dirac fermion Hypercharge |Y|=1/2 SU(2)doublet <1 TeV 6 Pure Higgsino Spectrum two Dirac Fermions ~ 300 MeV Radiative correction 7 Pure Higgsino DM is Dead DM is neutral Dirac Fermion HUGE spin-independent cross section 8 Pure Higgsino DM is Dead DM is neutral Dirac Fermion Purepure Higgsino Higgsino HUGE spin-independent cross section 9 Higgsino Spectrum (with gaugino) With Gauginos, fermion number is violated Dirac fermion into two Majorana fermions 10 Higgsino Spectrum (with gaugino) 11 Higgsino Spectrum (with gaugino) No SI elastic cross section via Z-boson 12 [N. Nagata & SS 2015] Gaugino induced Observables Mass splitting DM direct detection SM fermion EDM 13 Correlation These observables are controlled by gaugino mass Strong correlation among these observables for large tanb 14 Correlation These observables are controlled by gaugino mass Strong correlation among these observables for large tanb XENON1T constraint 15 Viable Higgsino Spectrum 16 Current Status of Higgsino @LHC 17 Collider Signals of DM p, e- DM DM is invisible p, e+ DM 18 Collider Signals of DM p, e- DM DM is invisible p, e+ DM Additional objects are needed to see DM. -
Glueball Searches Using Electron-Positron Annihilations with BESIII
FAIRNESS2019 IOP Publishing Journal of Physics: Conference Series 1667 (2020) 012019 doi:10.1088/1742-6596/1667/1/012019 Glueball searches using electron-positron annihilations with BESIII R Kappert and J G Messchendorp, for the BESIII collaboration KVI-CART, University of Groningen, Groningen, The Netherlands E-mail: [email protected] Abstract. Using a BESIII-data sample of 1:31 × 109 J= events collected in 2009 and 2012, the glueball-sensitive decay J= ! γpp¯ is analyzed. In the past, an exciting near-threshold enhancement X(pp¯) showed up. Furthermore, the poorly-understood properties of the ηc resonance, its radiative production, and many other interesting dynamics can be studied via this decay. The high statistics provided by BESIII enables to perform a partial-wave analysis (PWA) of the reaction channel. With a PWA, the spin-parity of the possible intermediate glueball state can be determined unambiguously and more information can be gained about the dynamics of other resonances, such as the ηc. The main background contributions are from final-state radiation and from the J= ! π0(γγ)pp¯ channel. In a follow-up study, we will investigate the possibilities to further suppress the background and to use data-driven methods to control them. 1. Introduction The discovery of the Higgs boson has been a breakthrough in the understanding of the origin of mass. However, this boson only explains 1% of the total mass of baryons. The remaining 99% originates, according to quantum chromodynamics (QCD), from the self-interaction of the gluons. The nature of gluons gives rise to the formation of exotic hadronic matter. -
BCS Thermal Vacuum of Fermionic Superfluids and Its Perturbation Theory
www.nature.com/scientificreports OPEN BCS thermal vacuum of fermionic superfuids and its perturbation theory Received: 14 June 2018 Xu-Yang Hou1, Ziwen Huang1,4, Hao Guo1, Yan He2 & Chih-Chun Chien 3 Accepted: 30 July 2018 The thermal feld theory is applied to fermionic superfuids by doubling the degrees of freedom of the Published: xx xx xxxx BCS theory. We construct the two-mode states and the corresponding Bogoliubov transformation to obtain the BCS thermal vacuum. The expectation values with respect to the BCS thermal vacuum produce the statistical average of the thermodynamic quantities. The BCS thermal vacuum allows a quantum-mechanical perturbation theory with the BCS theory serving as the unperturbed state. We evaluate the leading-order corrections to the order parameter and other physical quantities from the perturbation theory. A direct evaluation of the pairing correlation as a function of temperature shows the pseudogap phenomenon, where the pairing persists when the order parameter vanishes, emerges from the perturbation theory. The correspondence between the thermal vacuum and purifcation of the density matrix allows a unitary transformation, and we found the geometric phase associated with the transformation in the parameter space. Quantum many-body systems can be described by quantum feld theories1–4. Some available frameworks for sys- tems at fnite temperatures include the Matsubara formalism using the imaginary time for equilibrium systems1,5 and the Keldysh formalism of time-contour path integrals3,6 for non-equilibrium systems. Tere are also alterna- tive formalisms. For instance, the thermal feld theory7–9 is built on the concept of thermal vacuum. -
Introduction to Supersymmetry
Introduction to Supersymmetry Pre-SUSY Summer School Corpus Christi, Texas May 15-18, 2019 Stephen P. Martin Northern Illinois University [email protected] 1 Topics: Why: Motivation for supersymmetry (SUSY) • What: SUSY Lagrangians, SUSY breaking and the Minimal • Supersymmetric Standard Model, superpartner decays Who: Sorry, not covered. • For some more details and a slightly better attempt at proper referencing: A supersymmetry primer, hep-ph/9709356, version 7, January 2016 • TASI 2011 lectures notes: two-component fermion notation and • supersymmetry, arXiv:1205.4076. If you find corrections, please do let me know! 2 Lecture 1: Motivation and Introduction to Supersymmetry Motivation: The Hierarchy Problem • Supermultiplets • Particle content of the Minimal Supersymmetric Standard Model • (MSSM) Need for “soft” breaking of supersymmetry • The Wess-Zumino Model • 3 People have cited many reasons why extensions of the Standard Model might involve supersymmetry (SUSY). Some of them are: A possible cold dark matter particle • A light Higgs boson, M = 125 GeV • h Unification of gauge couplings • Mathematical elegance, beauty • ⋆ “What does that even mean? No such thing!” – Some modern pundits ⋆ “We beg to differ.” – Einstein, Dirac, . However, for me, the single compelling reason is: The Hierarchy Problem • 4 An analogy: Coulomb self-energy correction to the electron’s mass A point-like electron would have an infinite classical electrostatic energy. Instead, suppose the electron is a solid sphere of uniform charge density and radius R. An undergraduate problem gives: 3e2 ∆ECoulomb = 20πǫ0R 2 Interpreting this as a correction ∆me = ∆ECoulomb/c to the electron mass: 15 0.86 10− meters m = m + (1 MeV/c2) × . -
Lectures on BSM and Dark Matter Theory (2Nd Class)
Lectures on BSM and Dark Matter theory (2nd class) Stefania Gori UC Santa Cruz 15th annual Fermilab - CERN Hadron Collider Physics Summer School August 10-21, 2020 Twin Higgs models & the hierarchy problem SMA x SMB x Z2 Global symmetry of the scalar potential (e.g. SU(4)) The SM Higgs is a (massless) Nambu-Goldstone boson ~SM Higgs doublet Twin Higgs doublet S.Gori 23 Twin Higgs models & the hierarchy problem SMA x SMB x Z2 Global symmetry of the scalar potential (e.g. SU(4)) The SM Higgs is a (massless) Nambu-Goldstone boson ~SM Higgs doublet Twin Higgs doublet Loop corrections to the Higgs mass: HA HA HB HB yA yA yB yB top twin-top Loop corrections to mass are SU(4) symmetric no quadratically divergent corrections! S.Gori 23 Twin Higgs models & the hierarchy problem SMA x SMB x Z2 Global symmetry of the scalar potential (e.g. SU(4)) The SM Higgs is a (massless) Nambu-Goldstone boson ~SM Higgs doublet Twin Higgs doublet Loop corrections to the Higgs mass: HA HA HB HB SU(4) and Z2 are (softly) broken: yA yA yB yB top twin-top Loop corrections to mass are SU(4) symmetric no quadratically divergent corrections! S.Gori 23 Phenomenology of the twin Higgs A typical spectrum: Htwin Twin tops Twin W, Z SM Higgs Twin bottoms Twin taus Glueballs S.Gori 24 Phenomenology of the twin Higgs 1. Production of the twin Higgs The twin Higgs will mix with the 125 GeV Higgs with a mixing angle ~ v2 / f2 Because of this mixing, it can be produced as a SM Higgs boson (reduced rates!) A typical spectrum: Htwin Twin tops Twin W, Z SM Higgs Twin bottoms Twin taus Glueballs S.Gori 24 Phenomenology of the twin Higgs 1. -
Search for a Higgs Boson Decaying Into a Z and a Photon in Pp
EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN) CERN-PH-EP/2013-037 2015/09/07 CMS-HIG-13-006 Search for a Higgs boson decayingp into a Z and a photon in pp collisions at s = 7 and 8 TeV The CMS Collaboration∗ Abstract A search for a Higgs boson decaying into a Z boson and a photon is described. The analysis is performed using proton-proton collision datasets recorded by the CMS de- tector at the LHC. Events were collected at center-of-mass energies of 7 TeV and 8 TeV, corresponding to integrated luminosities of 5.0 fb−1 and 19.6 fb−1, respectively. The selected events are required to have opposite-sign electron or muon pairs. No excess above standard model predictions has been found in the 120–160 GeV mass range and the first limits on the Higgs boson production cross section times the H ! Zg branch- ing fraction at the LHC have been derived. The observed limits are between about 4 and 25 times the standard model cross section times the branching fraction. The ob- served and expected limits for m``g at 125 GeV are within one order of magnitude of the standard model prediction. Models predicting the Higgs boson production cross section times the H ! Zg branching fraction to be larger than one order of magni- tude of the standard model prediction are excluded for most of the 125–157 GeV mass range. arXiv:1307.5515v3 [hep-ex] 4 Sep 2015 Published in Physics Letters B as doi:10.1016/j.physletb.2013.09.057. -
Unified Equations of Boson and Fermion at High Energy and Some
Unified Equations of Boson and Fermion at High Energy and Some Unifications in Particle Physics Yi-Fang Chang Department of Physics, Yunnan University, Kunming, 650091, China (e-mail: [email protected]) Abstract: We suggest some possible approaches of the unified equations of boson and fermion, which correspond to the unified statistics at high energy. A. The spin terms of equations can be neglected. B. The mass terms of equations can be neglected. C. The known equations of formal unification change to the same. They can be combined each other. We derive the chaos solution of the nonlinear equation, in which the chaos point should be a unified scale. Moreover, various unifications in particle physics are discussed. It includes the unifications of interactions and the unified collision cross sections, which at high energy trend toward constant and rise as energy increases. Key words: particle, unification, equation, boson, fermion, high energy, collision, interaction PACS: 12.10.-g; 11.10.Lm; 12.90.+b; 12.10.Dm 1. Introduction Various unifications are all very important questions in particle physics. In 1930 Band discussed a new relativity unified field theory and wave mechanics [1,2]. Then Rojansky researched the possibility of a unified interpretation of electrons and protons [3]. By the extended Maxwell-Lorentz equations to five dimensions, Corben showed a simple unified field theory of gravitational and electromagnetic phenomena [4,5]. Hoffmann proposed the projective relativity, which is led to a formal unification of the gravitational and electromagnetic fields of the general relativity, and yields field equations unifying the gravitational and vector meson fields [6]. -
P-Shell Hyperon Binding Energies
fruin&£t& P-Shell Hyperon Binding Energies D. Koetsier and K. Amos School of Physics University of Melbourne Parkville, Victoria 3052 Australia A shell model for lambda hypernuclei has been used to determine the binding energy of the hyperon in nuclei throughout the p shell. Conventional (Cohen and Kurath) potential energies for nucleon-nucleon interactions were used with hyperon-nucieon interactions taken from Nijmegen one boson exchange poten tials. The hyperon binding energies calculated from these potentials compare well with measured values. Although many studies have been made of hypernuclear structure1, most have been concerned with only a small number of hypernuclei. We consider the mass variation of hyperon binding energies in single hyperon hypernuclei throughout the entire p shell. We do so with the assumption that the ground states of p shell hypernuclei art- described by Os shell hypeions coupled to complex nuclear cores; cores which have closed Os shells and partially filled Op shells. Hypernuclear wavefunctions can then be determined by the diagonalisation of an appropriate Hamiltonian using the basis formed by such coupled states. The Hamiltonian to be considered is described in terms of one and two body matrix elements. The one body matrix elements were those of Cohen and Kurath2 for nucle- ons but were taken from data for the hyperon. The Cohen and Kurath (8-16)2BME potential energies were used for the two nucleon matrix elements, while the two body hyperon-nucleon matrix elements were calculated from the Nijmegen one boson ex change potentials3. These hyperon-nucleon potentials include amplitudes associated with several different meson exchanges, but do not allow for medium effects due to the presence of the other particles, for the transfer of more than one boson, or for basis space truncation.