DOCSLIB.ORG

Particle Physics Handout 7 the Strong Force: Quantum Chromodynamics

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Particle Physics Handout 7 the Strong Force: Quantum Chromodynamics Subatomic Physics: Particle Physics Handout 7 The Strong Force: Quantum Chromodynamics QCD Colour quantum number Gluons The parton model Colour confinement, hadronisation & jets 1 2 QCD 2 Quantum ChromodynamicsQCD (QCD) QUANTUM ELECTRODYNAMICS: is the quantum •QUQCDANTUM isELECTR thetheor quantumODyYNAMICS:of the descriptionelectris theomaquantumgnetic ofinteraction. the strong force. theory of the electr!omamediatedgnetic interaction.by massless photons ! mediatedQEDby massless! photonphotonscouples to electric charge,QCD ! photon couples! toStrengthelectricofcharinteractionge, : . quantum! Strength theoryof interaction of the : quantum. theory of the strong electromagnetic interactions interactions QUANTUM CHROMO-DYNAMICS: is the quantum QUANTUM CHROMO-DYNAMICS: is the quantum mediated by the exchangetheory of the ofstr ong interaction.mediated by the exchange of theory of the strong interaction. virtual photons! mediated by massless gluons, i.egluons. ! mediated by massless gluons, i.e. propagator propagator acts on all charged! particles acts on quarks only ! gluon couples togluon“strong”coupleschargtoe “strong” charge ! Only quarks ha!veOnlnon-zy quarksero “strhaong”ve non-zchargereo, “strong” charge, couplestheref to electricalore only quarkstheref chargeforeeel stronlongy quarksinteractioncouplesfeel strong tointeraction colour charge Basic QCD interactionBasic QCDlooksinteractionlike a stronglookser like a stronger coupling strength ! e ! !! coupling strength gS !!S version of QED, version of QED, ! ! QED QEDq QCD q QCDq q √α Q √α Qq√α √αS S q q q q q 2 α = e /4π ~ 1/137 2 α = g 2/4π ~ 1 2 α = e /4γ π ~ S1/137S γ αS = gS /4π ~ 1 g ( subscript em is sometimes( subscriptusedemtoisdistinguishsometimestheused to distinguish the 2 of electromagnetismoffrelectrom oma). gnetism from ). Dr M.A. Thomson Lent 2004 Dr M.A. Thomson Lent 2004 Colour • Colour charge is the charge associated with QCD interactions. • Three colours: red, blue, green. • Like electric charge, it is a conserved quantum number. • Quarks always have a colour charge: r , g or b • Anti-quarks always have an anti-colour charge: r ̅ , b ̅ or g̅ • Leptons and bosons for other forces (", W, Z) don’t carry colour charge. • Mesons are colour neutral; colour charges are: (r r)̅ , (b b)̅ or (g g)̅ • Baryons are colour neutral; colour charges are: ( r g b ) • Anti-baryons have: ( r ̅ g ̅ b ̅ ) Formally different colours of quarks are different fundamental particles.G luons # 1st generation is: e $e ur ub ug dr db dg !"#$%&'($)*(+,*- 4 4 3 F F !"#$%&* '()** +'&&")&& &,-%./*0$&$%& * * E E D D 8 Glu!o% 1n2s3*% ,($,'4'5$( /67 $=5)5D $=5)5D $ $ 5 5 4())%* 4())%* =$%&)(?)@ =$%&)(?)@ 7#'(<&* 7#'(<&* 9+-&&-$%*$(*&5'5)&* '0&$(,5-$%*&5'5)&* $:*4"#$%&*0;*7#'(<&* 5 5 -&* -&* 0;* 0;* ) ) " " 7C,>$ 7C,>$ Gluons -%5$ -%5$ C=$"$#(* C=$"$#(* =>'%4)&*=$"$#(*4 $:*4 7#'(<& . 2$"$#(*-&*=$%&)(?)@ !"#$%&'($)*(+,*- m m i i % % 5>)+&)"?)& 5>)+&)"?)& e e - - 0 0 h h & & u u 0 0 Gluons are massless, spin-1ℏ bosons. * * • M M 2$"$#(* 2$"$#(* 0$&$%& 0$&$%& / / B B !"#$%& '()*+'&&")&& &,-%./*0$&$%& 193B* 193B* 4"#$%&* 4"#$%&* z z 7#'(<* 7#'(<* 4 4 . n n * * a a 4 4 r r @ @ s s 8 s s G'5#() G'5#() F F $:* $:* B B 8 8 They propagate the strong force: !exchange momentum ) ) • 123*,($,'4'5$( /67 '%@* '%@* ( ( 7 7 n n n n (( (( 6 6 :($+* :($+* &,-%./* &,-%./* between quarks. 0;* 0;* B B / / & & o o o o 9+-&&-$%*$(*'0&$(,5-$%*$:*4"#$%&*4 4 0;*7#'(<&* ) ) 7#'(<& 7#'(<& 0 0 4"#$%&* 4"#$%&* u u 4 4 u u $=5)5 $=5)5 B B l l l l % % I* I* $:* $:* ( ( ' ' =>'%4)&*=$"$#(*$:*7#'(<& . 2$"$#(*L* -&*L* =$%&)(?)@ 0 0 * * &&")&& &&")&& G G > > G G B B s s We draw gluons as curly-wurly lines: = = c c • '0&$(,5-$%* '0&$(,5-$%* * * i i ( ( ()'"-&)@* ()'"-&)@* .K* .K* s s +' +' % % 4 4 @-::)()%5* @-::)()%5* y y $,'4'5$( $,'4'5$( - - $ $ h h B B ( ( $(* $(* 2"#$%- 2"#$%- % % P P =$"$#(* =$"$#(* # # 0 0 , , )H,)=5* )H,)=5* " " ! $ $ !"#$%&*='((;*=$"$#(*=>'(4)e 5>)+&)"?)&e * * l l '()* '()* 4 4 4 4 # # c c i i " " 3 3 t t B B $1& $1& ?)(;* ?)(;* Gluons also carry colour charge. r r • 4 4 2 2 4 4 a a ( ( &2 &2 P P )A4A*(4 4"#( $%*=>'( %4)& ()@*7#'(<*-%5$ 4())%** '($)*(+,*- '($)*(+,*- 1 1 3 3 !"#$%&*='((;*=$"$#(*=>'(4) !"#$%&*='((;*=$"$#(*=>'(4) d d B B Colour charged is always conserved. n n 0 0 • a a ! ! J;++)5(; J;++)5(; ! ! ! )A4A* ! )A4A* !"#$%& 9+-&&-$%* !"#$%& =>'%4)&* 9+-&&-$%* =>'%4)&* G'-?)"; ( G'-?)"; ( 123* 123* 123*?)(;*@-::)()%5*:($+*193B*r 7C,>$r 5$%D E*F a a e e l l c c u u !"#$%& !"#$%& .#/0*(&.#/0*(& $1&2"#$%-.#/0*(& N N • Number of gluons: there are eight different gluons. G'-?)"; )H,)=5*I*4"#$%&* • Symmetry of the strong interaction! tell!"#$%&*='((;*=$"$#(*=>'(4) us these are: 5>)+&)"?)& (0B (4B 40B 4(B 0(B 04B ((B 44B 00 rb ̅ rg ̅ bg ̅ br ̅ gr ̅ gb ̅ (rr ̅ − gg)A4A*)/̅ !2 ((rr4 ̅4+" gg#$% ̅ −*= 2>bb'%)/̅ 4!)6& ()@*7#'(<*-%5$ 4())%** J;++)5(; .K**L*$=5)5 '%@*/*&-%4")5 &5'5)&* 123*?)(;*@-::)()%5*:($+*193B*7C,>$5$%D E*F One big difference between QED and QCD .#/0*(&$1&2"#$%- ! QED propagated by photons: photons no electric charge ! QCD propagated by gluons: gluonsG'-?)"; have colour)H,)=5* chargeI*4"#$%&* (0B (4B 40B 4(B 0(B 0!4B 3((&2B "4#4$B%-00()'"-&)@*0;*G'5#() C=$"$#(*$=5)5D 4 J;++)5(; .K**L*$=5)5 '%@*/*&-%4")5 &5'5)&* Nuclear and Particle Physics Franz Muheim 4 ! 3&2"#$%- ()'"-&)@*0;*G'5#() C=$"$#(*$=5)5D Nuclear and Particle Physics Franz Muheim 4 Quark & Gluon Interactions Quark-anti-quark scattering q2 q1 α VQED(r) = = −4π0r − r 6 6 Short distance potential: SELF-INTERASELF-INTERACTIONSCTIONS 4 αs VQCD(r) = %" = duhhhljkhsdlkh̅ describes a meson: e.g. hhhljkhsdlkh −3 r AtAtthisthispoint,point,QCDQCDlookslookslikelikea stra strongongererverversionsionofofQEDQED. strong force is responsible for holding meson together. ThisThisis istruetrueupuptotoa point.a point.HoHoweweverver, in, ipracticen practiceQCDQCD behabehavesvesververy diffy differentlerently tyotQEDo QED. The. Thesimilaritiessimilaritiesarisearisefromfrom • Gluons carrythe thecolourfactfactthat charge.thatbothbothin vinolvevolvethetheexecxhangchange oefoMASSLESSf MASSLESS spin-1 bosons. The big difference is that GLUONS carry • They also feelspin-1 the strongbosons. forceThe big ! diffgluonserence canis thatinteractGLUONS withcarr othery gluons! colourcolour“char“charge”.ge”. 12 GLUONSGLUONS3-gluonCANCAN vertexINTERAINTERACTCTWITHWITH4-gluonOTHEROTHER vertexGLUONS:GLUONS: g g Running of g g g g ! g g specifies the strength of the strong interaction g g g g g g 3 GLUON VERTEX 4 GLUON VERTEX ! BUT just as in QED, isn’t a constant, it 3 GLUON VERTEX34 4 GLUON VERTEX “runs” 5 EXAMPLE: Gluon-Gluon Scattering EXAMPLE: Gluon-Gluon Scattering ! In QED the bare electron charge is screened by a cloud of virtual electron-positron pairs. In the limit the propagator for a DECAYING+ + state becomes: The Parton+ Model+ ! In QCD a similar effect occurs. • The parton model proposes that, in high energy interactions,In QCD hadronsquantum interactfluctuations lead to a ‘cloud’ of EXAMPLE: ( NON-EXAMINABLE)as if they were made of their constituentEle parts.ctro ne.g.-Proton: vir tualScatteringpairs q • (Problem sheet 2, Q3) J/'&µ+µ# decay • (Handout 4, p11) ep&ep scattering. - - !"#$%&'()*+*Proton interacts,# as if it were !" #$! !" # e one of many (an infinite set) J/ψ e.g. rµ g+gb→r r%&'()*+*,($+r b -.#/*+01! q q γ c γ e.g. r g+gb→threer r+ independentr b quarks. q 0)!$2!3(.'( &0/!) such diagrams analogous to + + Electron scatters off one quark e c µ )*.#/!$*4$(!5/!6+*(5$)#*() q those for QED. q In centre-of-mass system ( ) would expect cross 1 e 2 4!" M $ e e # # q Dr M.A. Thomson 2 2 2 Lent 2004 section to be of form: Dr M.A. Thomson q q q Lent 2004 • At higher energies, proton consist of more-$.//' than/*0#%., three quarks:In QCD the gluon self-interactions ALSO lead to a quarks are- constantly+ exchanging gluons. Gluons7&,8'8 */can*+3$4 ,convert&$)6'++!&* (5$ 4 2 2‘cloud’ of virtual gluons d3 2 e 16! " First, note partialintowidth quarkfor !anti-quark :pairs. $ M $ # d2 q4 q4 g one of many (an infinite set) • Proton consists of three “valance quarks9”" .plus,.! (gluons+0.$+&'( )and4!& such diagrams. Here there is no 2 g “sea quarks”. q2 # q 1 q # p1 - p1 # p2 / p2 - 2 p . p g 1 % f i & f i f i 1 q ! analogy in QED, photons don’t giving p f # %E f , p f & - + 2 ! ! The sea quarks are exactly balanced between# 2me quarks- 2%E f Ei - andp f pi cos0 & 1 • p # %E , p! & have self-interactions since they anti-quarks. g i i i Partial width for : 2 , 0 ) q don’t carry the charge of the in- # -4E f Ei sin * ' :;!($(!5/!6+*(5$. + 2 ( q ! • Net quark content of proton is u, u, d. teraction. 12#3*$4.$5'60"##*$%,712#3*$4.$5'12#3*$4.$5'60"##*$%,7'60"##*$%,7'Dr M.A. Thomson Lent 2004 with </')+*6$<4 =$<* =$<>$$$$(!5/!6+$#&,+,($&!6,*/ d3 " 2 Dr M.A. Thomson Lent 2004 # d2 2 4 , 0 ) Lab 4E sin * ' 6 + 2 ( 2 2 d3 " E f , , 0 ) q , 0 )) # *cos2 * ' - sin2 * '' * 2 ' d2 Lab 2 4 , 0 ) E + 2 ( 2M + 2 ( 4E sin * ' i + p ( + 2 ( Nuclear and Particle Physics Franz Muheim 8 Parton Distributions in the Proton • Positron-proton scattering measurements (at HERA accelerator) have measured the valance and sea quarks and gluon in the proton. pparton • Key parameter is “Feynman x”: x = | | p | proton| • Graph shows measured fraction, f, of each parton (u-, d-, s-, c-quarks & gluons) as a function of x. • f also depends on momentum, Q 2 = ( q ) 2 transferred by the boson ("). − ! The higher the Q2, the more energetic 7 the partons. ! At LHC energies,CONFINEMENT proton contain lots of gluons! NEVER OBSERVE: single FREE quarks/gluons • LHC collisions will be a mixture of: quark-quark,! quarks quark-gluon,are always gluon-gluon,confined within hadrons anti-quark! This!quark,is a consequence anti-quark!gluonof the etc.strong • One challenge:self-interactions for each individualof gluons.
Load more

Recommended publications
  • The Five Common Particles
    The Five Common Particles The world around you consists of only three particles: protons, neutrons, and electrons. Protons and neutrons form the nuclei of atoms, and electrons glue everything together and create chemicals and materials. Along with the photon and the neutrino, these particles are essentially the only ones that exist in our solar system, because all the other subatomic particles have half-lives of typically 10-9 second or less, and vanish almost the instant they are created by nuclear reactions in the Sun, etc. Particles interact via the four fundamental forces of nature. Some basic properties of these forces are summarized below. (Other aspects of the fundamental forces are also discussed in the Summary of Particle Physics document on this web site.) Force Range Common Particles It Affects Conserved Quantity gravity infinite neutron, proton, electron, neutrino, photon mass-energy electromagnetic infinite proton, electron, photon charge -14 strong nuclear force ≈ 10 m neutron, proton baryon number -15 weak nuclear force ≈ 10 m neutron, proton, electron, neutrino lepton number Every particle in nature has specific values of all four of the conserved quantities associated with each force. The values for the five common particles are: Particle Rest Mass1 Charge2 Baryon # Lepton # proton 938.3 MeV/c2 +1 e +1 0 neutron 939.6 MeV/c2 0 +1 0 electron 0.511 MeV/c2 -1 e 0 +1 neutrino ≈ 1 eV/c2 0 0 +1 photon 0 eV/c2 0 0 0 1) MeV = mega-electron-volt = 106 eV. It is customary in particle physics to measure the mass of a particle in terms of how much energy it would represent if it were converted via E = mc2.
    [Show full text]
  • Fundamentals of Particle Physics
    Fundamentals of Par0cle Physics Particle Physics Masterclass Emmanuel Olaiya 1 The Universe u The universe is 15 billion years old u Around 150 billion galaxies (150,000,000,000) u Each galaxy has around 300 billion stars (300,000,000,000) u 150 billion x 300 billion stars (that is a lot of stars!) u That is a huge amount of material u That is an unimaginable amount of particles u How do we even begin to understand all of matter? 2 How many elementary particles does it take to describe the matter around us? 3 We can describe the material around us using just 3 particles . 3 Matter Particles +2/3 U Point like elementary particles that protons and neutrons are made from. Quarks Hence we can construct all nuclei using these two particles -1/3 d -1 Electrons orbit the nuclei and are help to e form molecules. These are also point like elementary particles Leptons We can build the world around us with these 3 particles. But how do they interact. To understand their interactions we have to introduce forces! Force carriers g1 g2 g3 g4 g5 g6 g7 g8 The gluon, of which there are 8 is the force carrier for nuclear forces Consider 2 forces: nuclear forces, and electromagnetism The photon, ie light is the force carrier when experiencing forces such and electricity and magnetism γ SOME FAMILAR THE ATOM PARTICLES ≈10-10m electron (-) 0.511 MeV A Fundamental (“pointlike”) Particle THE NUCLEUS proton (+) 938.3 MeV neutron (0) 939.6 MeV E=mc2. Einstein’s equation tells us mass and energy are equivalent Wave/Particle Duality (Quantum Mechanics) Einstein E
    [Show full text]
  • Introduction to Particle Physics
    SFB 676 – Projekt B2 Introduction to Particle Physics Christian Sander (Universität Hamburg) DESY Summer Student Lectures – Hamburg – 20th July '11 Outline ● Introduction ● History: From Democrit to Thomson ● The Standard Model ● Gauge Invariance ● The Higgs Mechanism ● Symmetries … Break ● Shortcomings of the Standard Model ● Physics Beyond the Standard Model ● Recent Results from the LHC ● Outlook Disclaimer: Very personal selection of topics and for sure many important things are left out! 20th July '11 Introduction to Particle Physics 2 20th July '11 Introduction to Particle PhysicsX Files: Season 2, Episode 233 … für Chester war das nur ein Weg das Geld für das eigentlich theoretische Zeugs aufzubringen, was ihn interessierte … die Erforschung Dunkler Materie, …ähm… Quantenpartikel, Neutrinos, Gluonen, Mesonen und Quarks. Subatomare Teilchen Die Geheimnisse des Universums! Theoretisch gesehen sind sie sogar die Bausteine der Wirklichkeit ! Aber niemand weiß, ob sie wirklich existieren !? 20th July '11 Introduction to Particle PhysicsX Files: Season 2, Episode 234 The First Particle Physicist? By convention ['nomos'] sweet is sweet, bitter is bitter, hot is hot, cold is cold, color is color; but in truth there are only atoms and the void. Democrit, * ~460 BC, †~360 BC in Abdera Hypothesis: ● Atoms have same constituents ● Atoms different in shape (assumption: geometrical shapes) ● Iron atoms are solid and strong with hooks that lock them into a solid ● Water atoms are smooth and slippery ● Salt atoms, because of their taste, are sharp and pointed ● Air atoms are light and whirling, pervading all other materials 20th July '11 Introduction to Particle Physics 5 Corpuscular Theory of Light Light consist out of particles (Newton et al.) ↕ Light is a wave (Huygens et al.) ● Mainly because of Newtons prestige, the corpuscle theory was widely accepted (more than 100 years) Sir Isaac Newton ● Failing to describe interference, diffraction, and *1643, †1727 polarization (e.g.
    [Show full text]
  • 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]
  • 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..
    [Show full text]
  • On Particle Physics
    On Particle Physics Searching for the Fundamental US ATLAS The continuing search for the basic building blocks of matter is the US ATLAS subject of Particle Physics (also called High Energy Physics). The idea of fundamental building blocks has evolved from the concept of four elements (earth, air, fire and water) of the Ancient Greeks to the nineteenth century picture of atoms as tiny “billiard balls.” The key word here is FUNDAMENTAL — objects which are simple and have no structure — they are not made of anything smaller! Our current understanding of these fundamental constituents began to fall into place around 100 years ago, when experimenters first discovered that the atom was not fundamental at all, but was itself made of smaller building blocks. Using particle probes as “microscopes,” scientists deter- mined that an atom has a dense center, or NUCLEUS, of positive charge surrounded by a dilute “cloud” of light, negatively- charged electrons. In between the nucleus and electrons, most of the atom is empty space! As the particle “microscopes” became more and more powerful, scientists found that the nucleus was composed of two types of yet smaller constituents called protons and neutrons, and that even pro- tons and neutrons are made up of smaller particles called quarks. The quarks inside the nucleus come in two varieties, called “up” or u-quark and “down” or d-quark. As far as we know, quarks and electrons really are fundamental (although experimenters continue to look for evidence to the con- trary). We know that these fundamental building blocks are small, but just how small are they? Using probes that can “see” down to very small distances inside the atom, physicists know that quarks and electrons are smaller than 10-18 (that’s 0.000 000 000 000 000 001! ) meters across.
    [Show full text]
  • Particle Physics Dr Victoria Martin, Spring Semester 2012 Lecture 11: Mesons and Baryons
    Particle Physics Dr Victoria Martin, Spring Semester 2012 Lecture 11: Mesons and Baryons !Measuring Jets !Fragmentation !Mesons and Baryons !Isospin and hypercharge !SU(3) flavour symmetry !Heavy Quark states 1 From Tuesday: Summary • In QCD, the coupling strength "S decreases at high momentum transfer (q2) increases at low momentum transfer. • Perturbation theory is only useful at high momentum transfer. • Non-perturbative techniques required at low momentum transfer. • At colliders, hard scatter produces quark, anti-quarks and gluons. • Fragmentation (hadronisation) describes how partons produced in hard scatter become final state hadrons. Need non-perturbative techniques. • Final state hadrons observed in experiments as jets. Measure jet pT, !, ! • Key measurement at lepton collider, evidence for NC=3 colours of quarks. + 2 σ(e e− hadrons) e R = → = N q σ(e+e µ+µ ) c e2 − → − • Next lecture: mesons and baryons! Griffiths chapter 5. 2 6 41. Plots of cross sections and related quantities + σ and R in e e− Collisions -2 10 ω φ J/ψ -3 10 ψ(2S) ρ Υ -4 ρ ! 10 Z -5 10 [mb] σ -6 R 10 -7 10 -8 10 2 1 10 10 Υ 3 10 J/ψ ψ(2S) Z 10 2 φ ω to theR Fermilab accelerator complex. In addition, both the CDF [11] and DØ detectors [12] 10 were upgraded. The resultsρ reported! here utilize an order of magnitude higher integrated luminosity1 than reported previously [5]. ρ -1 10 2 II. PERTURBATIVE1 QCD 10 10 √s [GeV] + + + + Figure 41.6: World data on the total cross section of e e− hadrons and the ratio R(s)=σ(e e− hadrons, s)/σ(e e− µ µ−,s).
    [Show full text]
  • MIT at the Large Hadron Collider—Illuminating the High-Energy Frontier
    Mit at the large hadron collider—Illuminating the high-energy frontier 40 ) roland | klute mit physics annual 2010 gunther roland and Markus Klute ver the last few decades, teams of physicists and engineers O all over the globe have worked on the components for one of the most complex machines ever built: the Large Hadron Collider (LHC) at the CERN laboratory in Geneva, Switzerland. Collaborations of thousands of scientists have assembled the giant particle detectors used to examine collisions of protons and nuclei at energies never before achieved in a labo- ratory. After initial tests proved successful in late 2009, the LHC physics program was launched in March 2010. Now the race is on to fulfill the LHC’s paradoxical mission: to complete the Stan- dard Model of particle physics by detecting its last missing piece, the Higgs boson, and to discover the building blocks of a more complete theory of nature to finally replace the Standard Model. The MIT team working on the Compact Muon Solenoid (CMS) experiment at the LHC stands at the forefront of this new era of particle and nuclear physics. The High Energy Frontier Our current understanding of the fundamental interactions of nature is encap- sulated in the Standard Model of particle physics. In this theory, the multitude of subatomic particles is explained in terms of just two kinds of basic building blocks: quarks, which form protons and neutrons, and leptons, including the electron and its heavier cousins. From the three basic interactions described by the Standard Model—the strong, electroweak and gravitational forces—arise much of our understanding of the world around us, from the formation of matter in the early universe, to the energy production in the Sun, and the stability of atoms and mit physics annual 2010 roland | klute ( 41 figure 1 A photograph of the interior, central molecules.
    [Show full text]
  • 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].
    [Show full text]
  • Supersymmetry: What? Why? When?
    Contemporary Physics, 2000, volume41, number6, pages359± 367 Supersymmetry:what? why? when? GORDON L. KANE This article is acolloquium-level review of the idea of supersymmetry and why so many physicists expect it to soon be amajor discovery in particle physics. Supersymmetry is the hypothesis, for which there is indirect evidence, that the underlying laws of nature are symmetric between matter particles (fermions) such as electrons and quarks, and force particles (bosons) such as photons and gluons. 1. Introduction (B) In addition, there are anumber of questions we The Standard Model of particle physics [1] is aremarkably hope will be answered: successful description of the basic constituents of matter (i) Can the forces of nature be uni® ed and (quarks and leptons), and of the interactions (weak, simpli® ed so wedo not have four indepen- electromagnetic, and strong) that lead to the structure dent ones? and complexity of our world (when combined with gravity). (ii) Why is the symmetry group of the Standard It is afull relativistic quantum ®eld theory. It is now very Model SU(3) ´SU(2) ´U(1)? well tested and established. Many experiments con® rmits (iii) Why are there three families of quarks and predictions and none disagree with them. leptons? Nevertheless, weexpect the Standard Model to be (iv) Why do the quarks and leptons have the extendedÐ not wrong, but extended, much as Maxwell’s masses they do? equation are extended to be apart of the Standard Model. (v) Can wehave aquantum theory of gravity? There are two sorts of reasons why weexpect the Standard (vi) Why is the cosmological constant much Model to be extended.
    [Show full text]
  • Spontaneous Symmetry Breaking in the Higgs Mechanism
    Spontaneous symmetry breaking in the Higgs mechanism August 2012 Abstract The Higgs mechanism is very powerful: it furnishes a description of the elec- troweak theory in the Standard Model which has a convincing experimental ver- ification. But although the Higgs mechanism had been applied successfully, the conceptual background is not clear. The Higgs mechanism is often presented as spontaneous breaking of a local gauge symmetry. But a local gauge symmetry is rooted in redundancy of description: gauge transformations connect states that cannot be physically distinguished. A gauge symmetry is therefore not a sym- metry of nature, but of our description of nature. The spontaneous breaking of such a symmetry cannot be expected to have physical e↵ects since asymmetries are not reflected in the physics. If spontaneous gauge symmetry breaking cannot have physical e↵ects, this causes conceptual problems for the Higgs mechanism, if taken to be described as spontaneous gauge symmetry breaking. In a gauge invariant theory, gauge fixing is necessary to retrieve the physics from the theory. This means that also in a theory with spontaneous gauge sym- metry breaking, a gauge should be fixed. But gauge fixing itself breaks the gauge symmetry, and thereby obscures the spontaneous breaking of the symmetry. It suggests that spontaneous gauge symmetry breaking is not part of the physics, but an unphysical artifact of the redundancy in description. However, the Higgs mechanism can be formulated in a gauge independent way, without spontaneous symmetry breaking. The same outcome as in the account with spontaneous symmetry breaking is obtained. It is concluded that even though spontaneous gauge symmetry breaking cannot have physical consequences, the Higgs mechanism is not in conceptual danger.
    [Show full text]
  • Super Symmetry
    MILESTONES DOI: 10.1038/nphys868 M iles Tone 1 3 Super symmetry The way that spin is woven into the in 1015. However, a form of symmetry very fabric of the Universe is writ between fermions and bosons called large in the standard model of supersymmetry offers a much more particle physics. In this model, which elegant solution because the took shape in the 1970s and can quantum fluctuations caused by explain the results of all particle- bosons are naturally cancelled physics experiments to date, matter out by those caused by fermions and (and antimatter) is made of three vice versa. families of quarks and leptons, which Symmetry plays a central role in are all fermions, whereas the physics. The fact that the laws of electromagnetic, strong physics are, for instance, symmetric in and weak forces that act on these time (that is, they do not change with particles are carried by other time) leads to the conservation of particles, such as photons and gluons, energy. These laws are also symmetric The ATLAS experiment under construction at the which are all bosons. with respect to space, rotation and Large Hadron Collider. Image courtesy of CERN. Despite its success, the standard relative motion. Initially explored in model is unsatisfactory for a number the early 1970s, supersymmetry is a of reasons. First, although the less obvious kind of symmetry, which, graviton. Searching for electromagnetic and weak forces if it exists in nature, would mean that supersymmetric particles will be a have been unified into a single force, the laws of physics do not change priority when the Large Hadron a ‘grand unified theory’ that brings when bosons are replaced by Collider comes into operation at the strong interaction into the fold fermions, and fermions are replaced CERN, the European particle-physics remains elusive.
    [Show full text]