DOCSLIB.ORG

Supersymmetry and How It Helps Us Understand Our World

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Supersymmetry and How It Helps Us Understand Our World Supersymmetry and how it helps us understand our world Spitalfields Day Gauge Theory, String Theory and Unification, 8 October 2007 M. Shifman Theoretical Physics Institute, University of Minnesota M. Shifman What is supersymmetry? Supersymmetry, if it holds in nature, is part of the quantum structure of space and time. In everyday life, we measure space and time by numbers, “The linear dimension of this building is 40 meters, its area is 1600 square meters.” Numbers are classical concepts. Our basic way of thinking about space and time has not been affected by physics revolutions of the 20th century: quantum mechanics and Einstein’s relativity. x t,x,y,z t,x,y,z; θi { } −→ { α} In 1+3 dimensions “fermion” direction of the superspace y θ2 = 0 θ −→ Supersymmetry introduces, apart from the three obvious dimensions plus time, new “quantum” dimensions, not measurable by ordinary numbers. They are “quantum” (or “fermionic” dimensions, like the spin of the electron. M. Shifman M. Shifman ✵ Particles vibrating in the new dimesnions look in detectors like new elementary particles. Thus, quantum dimensions would be manifested in the existence of new elementary particles, which would be produced in accelerators and whose behavior would be governed by supersymmetric laws. Supersymmetry entails that for every particle that has been found there are mirror particles that are identical in all respects except for their spin. Bosons of spin 1 — the photon, W, Z, and gluon — have spin 1/2 partners called the photino, wino, and gluino. Fermions of spin 1/2 — leptons and quarks — have spin 0 partners called the sleptons and squarks. ∼∼∼∼ Fermion Boson Fermions Bosons e γ Spin 1/2, 3/2, ... Building blocks of matter ... Spin 0, 1, ... Force mediators/helpers in Absolute individualists: delicate issues... Love to congregate and Pauli’s Exclusion Principle mimic each other: Huge ensembles -> Classical M. Shifman Can there be any symmetry between bosons and fermions? Golfand & Likhtman, 71 Wess & Zumino, 73 1970’s: YES! M. Shifman E = mc2 Cultural icon of the 20th century µ st Q¯ ˙ , Q = 2σ P Of the 21 ? { α β} αβ˙ µ Defying the Coleman-Mandula theorem! M. Shifman M. Shifman ✵ ✵ ✵✵ ✵ ✵ ✵ ✵ ✵ ✵ ✵ LHC ... ✵ ✵ SUSY or NOT? M. Shifman ✷✷✷ Why do we need SUSY ? ✷✷✷ Supersymmetric model-building A tool for solving otherwise unsolvable problems of Hierarchy problem: Mpart 1-100 GeV strong coupling dynamics while M 1019 GeV Planck ≈ Costs nothing; E ≈ 0 vac Cold Dark Matter Enormous progress since mid-1990’s! More efficient decoupling of high ▲▲▲▲▲▲▲▲▲ energies: Comes at a price ▲▲▲▲▲▲▲▲▲ Lots of problems + SUSY partners to be discovered M. Shifman Spontaneous symmetry breaking magnon =gapless excitation Goldstone boson Goldstino Fermion gravitino goldstino gravitino goldstino = massive gravitino ∼∼∼∼ M. Shifman ? 1 a µν a i b L = G G + λ¯D/ λ −4g2 µν 2 f gluon gluino ∼∼∼∼∼∼ SUSY Yang-Mills supersymmetric gluodynamics ∼ ∼ ∼ M. Shifman A success of SUSY: gauge coupling unification ● We are here MPlanck M. Shifman ✷✷✷ SUSY as a tool in strongly coupled gauged theories: QCD and the like ✷✷✷ Quantum Chromodynamics (QCD): • Quantum Field Theory of Strong Interactions of quarks and gluons, • Interaction mediated by exchange of gluons • Gluons carry color charges; Special Properties of QCD: • "Asymptotic Freedom," • Color Confinement: Hadrons are always "white," • Linear potential between quarks. M. Shifman QED 2 force 1/r QCD distance ▲▲▲▲▲▲▲▲▲ Nature keeps surprising us !!! ☞ Are we aware of precedents? ☞ Yes, the Meissner effect! 1930s, 1960s Cooper pair condensate Abrikosov vortex (flux tube) →B → S N → →→ S N magnet magnetic flux magnet Superconductor of Abelian ☚ the 2nd kind Dual Meissner effect for confinement conjectured 1970s Mandelstam Nambu ‘t Hooft ✵ ✵ ✵ ✵ ✵ ✵ ✷✷✷ First demonstration of the dual Meissner effect: Seiberg & Witten, 1994 ✷✷✷ N=2 (extended) SUSY ➔ SU(2) →U(1), monopoles ➔ Monopoles become light ➔ N=1 deform. forces M condensatition ➔ U(1) broken, electric flux tube formed ➔ ☺☹ ☺☹ Abelian ... (Abrikosov) Meissner effect does take place: condensation of color charges (squarks) gives rise to non-Abelian flux tubes and confined monopoles. The very fact of their existence in = 1 supersymmetric QCD without adjoint scalars was not known previously. The N Meissner effect does take place: condensation of color charges (squarks) gives rise to analysis presented in Ref. [13] is naonna-lAybtiecliaannflduxistubbaessedanodncotnhfienefdacmtotnhoaptoletsh.eThe v=ery1 fact of their existence in N theory under consideration can be ob=ta1insuepdersstyamrtminetgrifcroQmCD wi=tho2uSt QadCjoDintinscawlahriscwhatshneot known previously. The N N ’t Hooft–Polyakov monopoles do eaxnisatly,stishrporeusgenhteadcienrtRaeifn. [l1im3]iitsinagnaplyrtoicceadnudries ablalsoewdionng the fact that the = 1 theory under consideration can be obtained starting from = 2 SQCD in whNich the one to track the status of these monopoles at various stages (analogous to the onNe ’t Hooft–Polyakov monopoles do exist, through a certain limiting procedure allowing deMscerisisbneedr eaffbecotvdeoeasntdakseupmlacme:acroizneddensiantiFonigo.f c1o)l.or charges (squarks) gives rise to non-Abelian flux tubes and confined moonneoptoletsr.acTkhtehveersytaftaucst of tthheeisreemxisotneonpceoliens at various stages (analogous to the one T=h1e sMupemrsyomdmelestrhicarQeCsDmwainthyofuetaatdduejorsicenrstibwsecdaitlaharbstohwveaesIanSnoSdt skmunmaowgmnaeprtirziecevditohuinesloyF.riygT.h1Ie).will return to N thaisnaflayscits lparteseern.teNdoinwRIefw. o[1u3l]dislaiknealyttoicnTaonhtde iMsthbamatsoedndeoolnnsh-tBahrPeesSfamcfltaunthxyafteuatthbueersesiwn=itt1hhethme IeStSamstaagbnleetic theory. I will return to theory under consideration can be obtatinheisd fsatcatrtliantgerfr.oNmow I=w2oSuQldClDikeintwo hnNiochtetthheat non-BPS flux tubes in the metastable vacua of the SO(Nc) ISS theory with Nc +N 4 flNavors were found by Eto et al. [14]. ’t Hooft–Polyakov monopoles do exist, tvharcouuagohfathceer−StaOin(Nlim)itIiSnSgtphreoocreyduwriethallNow+inNg 4 flavors were found by Eto et al. [14]. In a parallel consideration, they made one extra cstep on the way cfrom the SU(Nc) one to track the status of these monopoles at various stages (analogous to the one − ISS magnetic theory towards theInMa pmaroadllell.coTnshideeyragtiaoun,gtehdeythmeadbeaornyeonextUra(1s)t.ep Tonhethe way from the SU(Nc) described above and summarized in FiIgS. S1)m. agnetic theory towards the M model. They gauged the baryon U(1). The U(N)Thme aMgnmeotdiecl sthhaeroesrymaonbytfaeaintuerdesiUwni(tNthh)tihsme waISgaSnyemtisacugtnphepetiocrrtythseoobflrtuya.xinIewtduilblinreestthuiirnsnwttoahye smupeptoarsttsaflbulxe tubes in the metastable vatchuisafa[c1t4l]a.ter. Now I would like to notveatchuaat [n1o4n].-BPS flux tubes in the metastable vacua of the SO(N ) ISS theory with N +N 4 flavors were found by Eto et al. [14]. The M modelc can be regardedc asTt−hheeMfirmstodcoelucsainn boef rQegCarDdesdinascethtehfiersatdcjoouisnint fiofeQldCsD since the adjoint fields tyIpnicaaplaorafllel co=nsid2eratrieone, ltihmeyinmaatdeedtoyinpneiceatxhltirosaf stthepe=oorny2.thaerEewveaelyinmfritnohmatoetudhgehinSUstu(hNipsce)trhseyomrym. eEtvreyn itshough supersymmetry is ISS magnetic theory towards the M model. TheNy gauged the baryon U(1). The considerablNy weakened, the overaclolnsqiudearlaitbalytivweeapkeincteud,rethseuorvveirvaells.quTalhitiastivise ppircotubraebsluyrvives. This is probably U(N) magnetic theory obtained in thiosnweaoyfstuhpepmorotstfliumxptourbtaesntinfinthdeinmgsetaatsttahbelecurrent stage. onveacoufa t[1h4e].most important findings at the current stage. Can a dual of the M model be identified? If yes, this would be equivalent to the The M model can be regarded as the first cousin of QCD since the adjoint fields Can a dual of the M model bediedmeonntsitfiraetdio?nIoffytehse,ntohni-sAwbeoluialnddbuealeMqueisvsanleernetffteocttihne = 1. detmypoicnasltorfation= o2f atrheeelnimonin-aAtebdeliniatnhids utaheloMry.eisEsvneenrtehffouegcht siunpersy=mm1e.try is N considerablNy weakened, the overall qualitative pic1994ture -psurveisenves.t: TInhNi sseais rpcrohb aofb lynon-Abelian dual one of the most important findings at t3he cuDrrenutaMeissnstlaigze.inegr e(ffaelcmt (noosn-At)belMian mfluxo dtubeel s) ▲ Can a dual of the M model be identified?MIf yes, this would be equivalent to the 3demoDnsturataiolniozf ithne gnon-(Aabellmian odusaltM)eissner effmectoinde=l 1. I started my talk frNom ISS who slightly mass-deformed SQCD. This small deforma- tion led to drastic consequences in the infrared-free magnetic dual theory: emergence I started my talk from ISS who slightly mass-deformed SQCD. This small defInotremrnaa-l d.o.f 3 Dualizing (almost) MoAfuzzia mn oetno -asdlu, peelrsymmetric metastable vacuum. tion led to drastic consequences inShthifmaneItintu f&rna Ysrueondug-tfrtNhoen-Aaetmbelfuiaanrgt shntreeinrtgqicuidteuamliltdhdeoefroyr:meamtioenrsgoefntcheis “electric” theory result Hanany & Tong ofIastnarotned-smuypetarlskyfmrommeItSrSicwhmoestliagshttalyibnmleaasvdsau-dacelufo“urmmmae.gdneStQicC”Dt.hTeohriys swmhaicllhdiesfovremrya-close to the M model discussed above. It tioInt lteudrtnosdroausttictchoantseqfuuernthceesrinqtuhieteinpfmrreasirleedrdv-edfrseeaefolmlrsmaaglanieetntiiotcnfdesuaatoulfrthetsehooirsfy:t“heemleMecrtgrmeincoc”deetlh. eory result of a non-supersymmetric metastable vacuuSmh.ifman and Yung considered [15] = 1 SQCD with the gauge group U(Nc) in a dual “magnetic” theory which is very close to the M model disNcussed above. It ☛an SU(2)d N di+ag Nbrokqenua
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]
  • Zero-Point Energy in Bag Models
    Ooa/ea/oHsnif- ^*7 ( 4*0 0 1 5 4 3 - m . Zero-Point Energy in Bag Models by Kimball A. Milton* Department of Physics The Ohio State University Columbus, Ohio 43210 A b s t r a c t The zero-point (Casimir) energy of free vector (gluon) fields confined to a spherical cavity (bag) is computed. With a suitable renormalization the result for eight gluons is This result is substantially larger than that for a spher­ ical shell (where both interior and exterior modes are pre­ sent), and so affects Johnson's model of the QCD vacuum. It is also smaller than, and of opposite sign to the value used in bag model phenomenology, so it will have important implications there. * On leave ifrom Department of Physics, University of California, Los Angeles, CA 90024. I. Introduction Quantum chromodynamics (QCD) may we 1.1 be the appropriate theory of hadronic matter. However, the theory is not at all well understood. It may turn out that color confinement is roughly approximated by the phenomenologically suc­ cessful bag model [1,2]. In this model, the normal vacuum is a perfect color magnetic conductor, that iis, the color magnetic permeability n is infinite, while the vacuum.in the interior of the bag is characterized by n=l. This implies that the color electric and magnetic fields are confined to the interior of the bag, and that they satisfy the following boundary conditions on its surface S: n.&jg= 0, nxBlg= 0, (1) where n is normal to S. Now, even in an "empty" bag (i.e., one containing no quarks) there will be non-zero fields present because of quantum fluctua­ tions.
    [Show full text]
  • 18. Lattice Quantum Chromodynamics
    18. Lattice QCD 1 18. Lattice Quantum Chromodynamics Updated September 2017 by S. Hashimoto (KEK), J. Laiho (Syracuse University) and S.R. Sharpe (University of Washington). Many physical processes considered in the Review of Particle Properties (RPP) involve hadrons. The properties of hadrons—which are composed of quarks and gluons—are governed primarily by Quantum Chromodynamics (QCD) (with small corrections from Quantum Electrodynamics [QED]). Theoretical calculations of these properties require non-perturbative methods, and Lattice Quantum Chromodynamics (LQCD) is a tool to carry out such calculations. It has been successfully applied to many properties of hadrons. Most important for the RPP are the calculation of electroweak form factors, which are needed to extract Cabbibo-Kobayashi-Maskawa (CKM) matrix elements when combined with the corresponding experimental measurements. LQCD has also been used to determine other fundamental parameters of the standard model, in particular the strong coupling constant and quark masses, as well as to predict hadronic contributions to the anomalous magnetic moment of the muon, gµ 2. − This review describes the theoretical foundations of LQCD and sketches the methods used to calculate the quantities relevant for the RPP. It also describes the various sources of error that must be controlled in a LQCD calculation. Results for hadronic quantities are given in the corresponding dedicated reviews. 18.1. Lattice regularization of QCD Gauge theories form the building blocks of the Standard Model. While the SU(2) and U(1) parts have weak couplings and can be studied accurately with perturbative methods, the SU(3) component—QCD—is only amenable to a perturbative treatment at high energies.
    [Show full text]
  • Quantum Mechanics Quantum Chromodynamics (QCD)
    Quantum Mechanics_quantum chromodynamics (QCD) In theoretical physics, quantum chromodynamics (QCD) is a theory ofstrong interactions, a fundamental forcedescribing the interactions between quarksand gluons which make up hadrons such as the proton, neutron and pion. QCD is a type of Quantum field theory called a non- abelian gauge theory with symmetry group SU(3). The QCD analog of electric charge is a property called 'color'. Gluons are the force carrier of the theory, like photons are for the electromagnetic force in quantum electrodynamics. The theory is an important part of the Standard Model of Particle physics. A huge body of experimental evidence for QCD has been gathered over the years. QCD enjoys two peculiar properties: Confinement, which means that the force between quarks does not diminish as they are separated. Because of this, when you do split the quark the energy is enough to create another quark thus creating another quark pair; they are forever bound into hadrons such as theproton and the neutron or the pion and kaon. Although analytically unproven, confinement is widely believed to be true because it explains the consistent failure of free quark searches, and it is easy to demonstrate in lattice QCD. Asymptotic freedom, which means that in very high-energy reactions, quarks and gluons interact very weakly creating a quark–gluon plasma. This prediction of QCD was first discovered in the early 1970s by David Politzer and by Frank Wilczek and David Gross. For this work they were awarded the 2004 Nobel Prize in Physics. There is no known phase-transition line separating these two properties; confinement is dominant in low-energy scales but, as energy increases, asymptotic freedom becomes dominant.
    [Show full text]
  • Quantum Chromodynamics 1 9
    9. Quantum chromodynamics 1 9. QUANTUM CHROMODYNAMICS Revised October 2013 by S. Bethke (Max-Planck-Institute of Physics, Munich), G. Dissertori (ETH Zurich), and G.P. Salam (CERN and LPTHE, Paris). 9.1. Basics Quantum Chromodynamics (QCD), the gauge field theory that describes the strong interactions of colored quarks and gluons, is the SU(3) component of the SU(3) SU(2) U(1) Standard Model of Particle Physics. × × The Lagrangian of QCD is given by 1 = ψ¯ (iγµ∂ δ g γµtC C m δ )ψ F A F A µν , (9.1) q,a µ ab s ab µ q ab q,b 4 µν L q − A − − X µ where repeated indices are summed over. The γ are the Dirac γ-matrices. The ψq,a are quark-field spinors for a quark of flavor q and mass mq, with a color-index a that runs from a =1 to Nc = 3, i.e. quarks come in three “colors.” Quarks are said to be in the fundamental representation of the SU(3) color group. C 2 The µ correspond to the gluon fields, with C running from 1 to Nc 1 = 8, i.e. there areA eight kinds of gluon. Gluons transform under the adjoint representation− of the C SU(3) color group. The tab correspond to eight 3 3 matrices and are the generators of the SU(3) group (cf. the section on “SU(3) isoscalar× factors and representation matrices” in this Review with tC λC /2). They encode the fact that a gluon’s interaction with ab ≡ ab a quark rotates the quark’s color in SU(3) space.
    [Show full text]
  • Supersymmetry Min Raj Lamsal Department of Physics, Prithvi Narayan Campus, Pokhara Min [email protected]
    Supersymmetry Min Raj Lamsal Department of Physics, Prithvi Narayan Campus, Pokhara [email protected] Abstract : This article deals with the introduction of supersymmetry as the latest and most emerging burning issue for the explanation of nature including elementary particles as well as the universe. Supersymmetry is a conjectured symmetry of space and time. It has been a very popular idea among theoretical physicists. It is nearly an article of faith among elementary-particle physicists that the four fundamental physical forces in nature ultimately derive from a single force. For years scientists have tried to construct a Grand Unified Theory showing this basic unity. Physicists have already unified the electron-magnetic and weak forces in an 'electroweak' theory, and recent work has focused on trying to include the strong force. Gravity is much harder to handle, but work continues on that, as well. In the world of everyday experience, the strengths of the forces are very different, leading physicists to conclude that their convergence could occur only at very high energies, such as those existing in the earliest moments of the universe, just after the Big Bang. Keywords: standard model, grand unified theories, theory of everything, superpartner, higgs boson, neutrino oscillation. 1. INTRODUCTION unifies the weak and electromagnetic forces. The What is the world made of? What are the most basic idea is that the mass difference between photons fundamental constituents of matter? We still do not having zero mass and the weak bosons makes the have anything that could be a final answer, but we electromagnetic and weak interactions behave quite have come a long way.
    [Show full text]
  • The Minkowski Quantum Vacuum Does Not Gravitate
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by KITopen Available online at www.sciencedirect.com ScienceDirect Nuclear Physics B 946 (2019) 114694 www.elsevier.com/locate/nuclphysb The Minkowski quantum vacuum does not gravitate Viacheslav A. Emelyanov Institute for Theoretical Physics, Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany Received 9 April 2019; received in revised form 24 June 2019; accepted 8 July 2019 Available online 12 July 2019 Editor: Stephan Stieberger Abstract We show that a non-zero renormalised value of the zero-point energy in λφ4-theory over Minkowski spacetime is in tension with the scalar-field equation at two-loop order in perturbation theory. © 2019 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3. 1. Introduction Quantum fields give rise to an infinite vacuum energy density [1–4], which arises from quantum-field fluctuations taking place even in the absence of matter. Yet, assuming that semi- classical quantum field theory is reliable only up to the Planck-energy scale, the cut-off estimate yields zero-point-energy density which is finite, though, but in a notorious tension with astro- physical observations. In the presence of matter, however, there are quantum effects occurring in nature, which can- not be understood without quantum-field fluctuations. These are the spontaneous emission of a photon by excited atoms, the Lamb shift, the anomalous magnetic moment of the electron, and so forth [5]. This means quantum-field fluctuations do manifest themselves in nature and, hence, the zero-point energy poses a serious problem.
    [Show full text]
  • 9. Quantum Chromodynamics 1 9
    9. Quantum chromodynamics 1 9. Quantum Chromodynamics Revised September 2017 by S. Bethke (Max-Planck-Institute of Physics, Munich), G. Dissertori (ETH Zurich), and G.P. Salam (CERN).1 This update retains the 2016 summary of αs values, as few new results were available at the deadline for this Review. Those and further new results will be included in the next update. 9.1. Basics Quantum Chromodynamics (QCD), the gauge field theory that describes the strong interactions of colored quarks and gluons, is the SU(3) component of the SU(3) SU(2) U(1) Standard Model of Particle Physics. × × The Lagrangian of QCD is given by 1 = ψ¯ (iγµ∂ δ g γµtC C m δ )ψ F A F A µν , (9.1) q,a µ ab s ab µ q ab q,b 4 µν L q − A − − X µ where repeated indices are summed over. The γ are the Dirac γ-matrices. The ψq,a are quark-field spinors for a quark of flavor q and mass mq, with a color-index a that runs from a =1 to Nc = 3, i.e. quarks come in three “colors.” Quarks are said to be in the fundamental representation of the SU(3) color group. C 2 The µ correspond to the gluon fields, with C running from 1 to Nc 1 = 8, i.e. there areA eight kinds of gluon. Gluons transform under the adjoint representation− of the C SU(3) color group. The tab correspond to eight 3 3 matrices and are the generators of the SU(3) group (cf.
    [Show full text]
  • Basics of Quantum Chromodynamics (Two Lectures)
    Basics of Quantum Chromodynamics (Two lectures) Faisal Akram 5th School on LHC Physics, 15-26 August 2016 NCP Islamabad 2015 Outlines • A brief introduction of QCD Classical QCD Lagrangian Quantization Green functions of QCD and SDE’s • Perturbative QCD Perturbative calculation of QCD Green functions Feynman Rules of QCD Renormalization Running of QCD coupling (Asymptotic freedom) • Non-Perturbative QCD Confinement QCD phase transition Dynamical breaking of chiral symmetry Elementary Particle Physics Today Elementary particles: Quarks Leptons Gauge Bosons Higgs Boson (can interact through (cannot interact through (mediate interactions) (impart mass to the elementary strong interaction) strong interaction) particles) 푢 푐 푡 Meson: 푠 = 0,1,2 … Quarks: Hadrons: 1 3 푑 푠 푏 Baryons: 푠 = , , … 2 2 푣푒 푣휇 푣휏 Meson: Baryon Leptons: 푒 휇 휏 Gauge Bosons: 훾, 푊±, 푍0, and 8 gluons 399 Mesons, 574 Baryons have been discovered Higgs Bosons: 퐻 (God/Mother particle) • Strong interaction (Quantum Chromodynamics) • Electro-weak interaction (Quantum electro-flavor dynamics) The Standard Model Explaining the properties of the Hadrons in terms of QCD’s fundamental degrees of freedom is the Problem laying at the forefront of Hadronic physics. How these elementary particles and the SM is discovered? 1. Scattering Experiments Cross sections, Decay Constants, 2. Decay Processes Masses, Spin , Couplings, Form factors, etc. 3. Study of bound states Models Particle Accelerators Models and detectors Experimental Particle Physics Theoretical Particle Particle Physicist Phenomenologist Physicist Measured values of Calculated values of physical observables ≈ physical observables It doesn’t matter how beautifull your theory is, It is more important to have beauty It doesn’t matter how smart you are.
    [Show full text]
  • Group Theory of Spontaneous Symmetry Breaking
    Group Theory of Spontaneous Symmetry Breaking Christopher de Firmian Physics 251 June 7, 2019 Classical Analogy I Imagine trying to balance a rotationally symmetric pencil on a point. Any tiny perturbation would destabilize the unstable equilibrium and cause it to topple over. I A collision with an air molecule or, even if in vacuum, a stray cosmic ray or quantum fluctuation would cause the pencil to fall over. I In a perfect mathematical world, this rotational symmetry would be realized, but in the real and messy universe we exist in, we say these would-be symmetries are spontaneously broken. Quantum Mechanically I Similar to the classical analogy, one could imagine an electron's magnetic moment anti-aligned with an external magnetic field. This exemplifies another unstable equilibrium. I We, however, want to generalize our search for spontaneously broken symmetries to symmetries beyond what we can intuitively imagine. Hence, for arbitrary potentials, we search for local maxima. Discrete Symmetry Example 1 µ 1 2 2 λ 4 I Consider the Lagrangian L = 2 (@µφ)(@ φ) − 2 m φ − 4! φ 1 2 2 λ 4 I We then have a potential V (φ) = 2 m φ + 4! φ 2 I Consider a scenario in which we have m < 0 and λ > 0. More obvious if we let m2 ! −µ2 < 0 I Then our potential appears quartic with a local maximum and 1 2 2 λ 4 two minima. V (φ) = − 2 µ φ + 4! φ 1 2 2 λ 4 I V (φ) = − 2 µ φ + 4! φ I It is energetically favorable for φ to take the values that minimize the potential V (φ).
    [Show full text]
  • The Quantum Chromodynamics Theory of Tetraquarks and Mesomesonic Particles Unfinished Draft Version
    The Quantum Chromodynamics Theory Of Tetraquarks And Mesomesonic Particles Unfinished draft version Based on a generalized particle diagram of baryons and anti-baryons which, in turn, is based on symmetry principles, this theory predicts the existence of all the tetraquarks and dimeson molecules (mesomesonic particles) there exist in nature. by R. A. Frino Electronics Engineer - Degree from the University of Mar del Plata. March 4th, 2016 (v1) Keywords: mirror symmetry, parity, P symmetry, charge conjugation, C symmetry, time reversal, T symmetry, CP symmetry, CPT symmetry, PC+ symmetry, Q symmetry, quantum electrodynamics, quantum chromodynamics, quark, antiquark, up quark, down quark, strange quark, charm quark, bottom quark, top quark, anti-up quark, anti-down quark, anti-strange quark, anti-charm quark, anti-bottom quark, anti-top quark, tetraquark, pentaquark, antitetraquark, non-strange tetraquark, colour charge, anticolour, anticolour charge, strangeness, charmness, bottomness, topness, fermion, hadron, baryon, meson, boson, photon, gluon, mesobaryonic particle, meso-baryonic particle, mesobaryonic molecule, meso-mesonic molecule, meso-mesonic particle, dimeson particle, dimeson molecule, Pauli exclusion principle, force carrier, omega- minus particle, matter-antimatter way, quadruply flavoured tetraquark, MAW, MMP, MMM, LHC. (see next page) The Quantum Chromodynamics Theory Of Tetraquarks And Mesomesonic Particles - v1. Copyright © 2016 Rodolfo A. Frino. All rights reserved. 1 1. Introduction Quantum Chromodynamics (QCD) [1, 2, 3, 4] is a quantum mechanical description of the strong nuclear force. The strong force is mediated by gluons [4, 5] which are spin 1ℏ bosons (spin is quoted in units of reduced Plank's constant: ℏ =h/2π ). Gluons act on quarks only (only quarks feel the strong force).
    [Show full text]
  • QCD, Strings and Black Holes
    QCD, Strings and Black holes The large N limit of Field Theories and Gravity Juan Maldacena Field Theory = Gravity theory Gauge Theories Quantum Gravity QCD String theory Plan QCD, Strings, the large N limit Supersymmetric QCD N large Gravitational theory in 10 dimensions Calculations Correlation functions Quark-antiquark potential Black holes Strings and Strong Interactions Before 60s Æ proton, neutron Æ elementary During 60s Æ many new strongly interacting particles Many had higher spins s = 2, 3, 4 …. All these particles Æ different oscillation modes of a string. This model explained “Regge trajectories” Rotating String model 2 From E. Klempt hep-ex/0101031 m~ TJmax + const Strong Interactions from Quantum ChromoDynamics 3 colors (charges) Experiments at higher energies revealed quarks and gluons They interact exchanging gluons Electrodynamics Chromodynamics (QCD) photon g g g g gluon electron Gauge group 3 x 3 matrices Gluons carry U(1) SU(3) color charge, so they interact among themselves Coupling constant decreases at high energy Gross, Politzer, Wilczek g 0 at high energies QCD is easier to study at high energies Hard to study at low energies Indeed, at low energies we expect to see confinement V = T L q q Flux tubes of color field = glue At low energies we have something that looks like a string Can we have an effective theory in terms of strings ? Large N limit t’ Hooft ‘74 Take N colors instead of 3, SU(N) Large N and strings Gluon: color and anti-color Open strings Æ mesons Closed strings Æ glueballs Looks like a string theory, but… 1.
    [Show full text]