Ch 43. Elementary Particles Fundamental forces in Nature

Transcription

1 Ch 43 Elemenary Paricles Fundamenal forces in Naure

2 Finer Srucure observed As he momenum of a paricle increases, is wavelengh decreases, providing deails of smaller and smaller srucures: Cf: he Heisenberg microscope l (0 GeV) ~ m 1) Deep Inelasic Scaering (similar o Ruherford scaering); seeing smaller deails ) Wih addiional kineic energy more massive paricles can be produced: paricle physics = high energy physics The Nobel Prize in Physics 1961 Rober Hofsader "for his pioneering sudies of elecron scaering in aomic nuclei and for his hereby achieved discoveries concerning he srucure of he nucleons"

3 High-Energy Paricles and Acceleraors Cycloron/Synchroron Charged paricles are mainained in near-circular pahs by magnes, while an elecric field acceleraes hem repeaedly. The volage is alernaed so ha he paricles are acceleraed each ime hey raverse he gap. The Nobel Prize in Physics 1939 The Nobel Prize in Chemisry 1951 Ernes Lawrence "for he invenion and developmen of he cycloron and for resuls obained wih i" Edwin McMillan "for he chemisry of ransuranium elemens" Invenor of he synchroron

4 Cycloron Frequency Alernaing elecric field acceleraes he paricles Lorenz force keep he paricles in orbi (via magneic Field) F c mv r qvb v qbr m Period of revoluion: T r r m v qbr / m qb Small cycloron: R=5 cm, B=1.7 T f=6 MHz (RF) K=8.7 MeV (non-relaivisic) (Noe: Volage does no appear) Required field acceleraion frequency f Kineic energy 1 T K qb m 1 mv q B R m Synchroron: relaivisic speeds (Noe: Radiaion problem/ energy loss

5 The principle of paricle creaion Based on: E mc LHC CERN M proon ~ 1 GeV Collision energy = x 7 TeV Sufficien for proons

6 Paricle Exchange The elecromagneic force acs over a disance direc conac is no necessary. How does ha work? Because of he wave paricle dualiy, we can regard he elecromagneic force beween charged paricles as due o: 1. an elecromagneic field, or. an exchange of phoons. Visualizaion of ineracions using Feynman diagrams

7 Paricle Exchange The phoon is emied by one elecron and absorbed by he oher; i is never visible and is called a virual phoon. The phoon carries he elecromagneic force. Originally, he srong force was hough o be carried by mesons. The mesons have nonzero mass, which is wha limis he range of he force, as conservaion of energy can only be violaed for a shor ime. Virual paricle limied energy Limied lifeime ~ mc E Maximum disance ravelled (Range) x c ~ mc Elecromagneism Graviaion Infinie range m = 0 Srong force Weak force Finie range m 0

8 Paricle Exchange The mass of he meson can be calculaed, assuming he range, d, is limied by he uncerainy principle: For d = 1.5 x m, his gives 130 MeV. (NOT he muon wih 106 MeV/c ) Yukawa prediced a paricle ha would mediae he srong forces in he bonding of a nucleus: M ~ 100 MeV (Yukawa assumed: d = fm) Laer is was found: m( + )=m( - )=140 MeV/c m( 0 )=135 MeV/c Hideki Yukawa The Nobel Prize in Physics 1949 "for his predicion of he exisence of mesons on he basis of heoreical work on nuclear forces"

9 Inermezzo Wave equaions, quanum fields Schrödinger equaion free paricle non-relaivisic ime-dependen x i x x m,, x i p ˆ i E ˆ x E x m p,, ˆ Operaors Relaivisic analog for he energy x E x c m x p c, ˆ,, ˆ 4 x x c m x x c,,, 4 Or (use operaors): Klein-Gordon equaion: valid for spinless massive paricles Similar relaivisic wave equaion for paricles wih spin x i x mc x x c i i i,,, for spinor wave funcions Dirac equaion: valid for massive paricles wih spin

10 Inermezzo Ineracions via virual paricles Klein-Gordon equaion (rewrie and 3-dimensional) 1 m c c 1 Massless m 0 0 c This is he classical wave equaion for elecromagneism: Phoons are he (virual) parciles mediaing he force Mass 1 d d dr Saic problem: r 0 Soluion: m m e 4 r Soluion: 0 r dr r e g r / r' wih: r' m c Concep of he Yukawa poenial -mesons mediae he nuclear force ( residual srong force )

11 Paricle Exchange Srong force: The meson was soon discovered, and is called he pi meson, or pion, wih he symbol π. Pions are creaed in ineracions in paricle acceleraors. Here are wo examples: (Noe, mesons no he rue carriers gluons) The weak nuclear force is also carried by paricles; hey are called he W +, W -, and Z 0. They have been direcly observed in ineracions. A carrier for he graviaional force, called he gravion, has been proposed, bu here is as ye no heory ha will accommodae i.

12 Paricle Exchange four known forces relaive srenghs for wo proons in a nucleus, and heir field paricles

13 Inermezzo Klein-Gordon equaion: Relaivisic quanum fields and aniparicles c, x i N exp For every soluion (E, p) x, ~ * 4 x, m c x, x p x ie * There is also a soluion: x, x, N p i exp p x ie Corresponding o negaive energy and momenum -p 4 E Ep p c m c mc p Inerpreaion by Dirac Ani-paricle Noe: Dirac equaion more elegan: four soluions found : wo wih posiive energy, wo wih negaive energy For each spin= ½ and spin = -½ The Nobel Prize in Physics 1933 "for he discovery of new producive forms of aomic heory"

14 Inermezzo Quesion; Wha are hose negaive energy saes? Vacuum: All he negaive energy saes are normally filled The vacuum is a sea of elecrons Pauli principle Fermi-energy level Choice of zero-level for energy The Dirac Sea Pair creaion A phoon excies an elecrom from he vacuum A posiron is a hole in he elecron sea cf: semi-conducors

15 Paricles and Aniparicles The posiron is he same as he elecron, excep for having he opposie charge (and lepon number). Every ype of paricle has is own aniparicle, wih he same mass and mos wih he opposie quanum number. A few paricles, such as he phoon and he π 0, are heir own aniparicles, as all he relevan quanum numbers are zero for hem. bubble chamber phoograph incoming aniproon and a proon (no seen) ha resuls in he creaion of several differen paricles and aniparicles.

16 Paricle Ineracions and Conservaion Laws In he sudy of paricle ineracions, i was found ha cerain ineracions did no occur, even hough hey conserve energy and charge, such as: A new conservaion law was proposed: he conservaion of baryon number. Baryon number is a generalizaion of nucleon number o include more exoic paricles. + Conservaion of Energy, Momenum, Angular momenum, Charge

17 Inermezzo Concep of Paricle Physics: Isospin - Proons and neurons undergo he same nuclear force - No need o make a disincion beween he wo - There is jus a wo-valuedness of he same paricle Define proons and neurons as idenical paricles Bu wih differen quanum numbers Isospin I = ½, M I = + ½ for proon M I = - ½ for neuron Imporance of symmery in paricle physics

18 Paricle Ineracions and Conservaion Laws Baryon Number: B = +1; proons, neurons, B = -1; ani-proons, ani-neurons B = 0 : elecrons, phoons, neurino s (all lepons and mesons) Conservaion of Baryon number: principle of physics Lepons : - Elecron - Muon (abou 00 imes more massive) - Tau (abou 3000 elecron masses) Conservaion of Lepon numbers; L e, L m, L Conservaion of energy, momenum, and angular momenum Noeher heorems: Emmy Noeher Conservaion laws Fundamenal symmeries in naure

19 Paricle Ineracions and Conservaion Laws This accouns for he following decays (weak ineracion): B=1, L e =0 B=0, L m =0 Decays ha have an unequal mix of e-ype and μ-ype lepons are no allowed. (Neurino-oscillaions seem o sugges ha his is no always rue; Tha is an unsolved quesion of conemporary physics)

20 Paricle Ineracions and Conservaion Laws Which of he following decay schemes is possible for muon decay? (a) (b) (c) Lef: L m =1; L e =0 All of hese paricles have L τ = 0.

21 Paricle Classificaion BE-FD saisics Bosons Fermions Bosons Fermions Noe: Fermions obey Pauli principle!

22 Paricle Classificaion Gauge bosons are he paricles ha mediae he forces. Lepons inerac weakly and (if charged) elecromagneically, bu no srongly. Hadrons inerac srongly; here are wo ypes of hadrons, baryons (B = 1) and mesons (B = 0). Hadron decay Weak force Srong force Weak force

23 A Peculiariy of he weak force: Pariy nonconservaion Discuss : Real vecors vs. Axial vecors

24 Paricle Sabiliy and Resonances Almos all of he paricles ha have been discovered are unsable. Weak decay: lifeimes ~ s Elecromagneic: ~ s Srong decay: ~ 10-3 s. The lifeime of srongly decaying paricles is calculaed from he variaion in heir effecive mass using he uncerainy principle. These resonances are ofen called paricles.

25 Srange Paricles? Charm? Toward a New Model When he K, Λ, and Σ paricles were firs discovered in he early 1950s, here were myseries associaed wih hem: They are always produced in pairs. p K Never alone: p K n They are creaed in a srong ineracion, decay o srongly ineracing paricles, bu have lifeimes characerisic of he weak ineracion. To explain his, a new quanum number, called srangeness, S, was inroduced. Srangeness is no conserved in weak ineracions Parially conserved quaniy

26 Srange Paricles? Charm? Toward a New Model Paricles such as he K, Λ, and Σ have S = 1 (and heir aniparicles have S = -1); oher paricles have S = 0. The srangeness number is conserved in srong ineracions bu no in weak ones; herefore, hese paricles are produced in paricle aniparicle pairs, and decay weakly. More recenly, anoher new quanum number called charm was discovered o behave in he same way. (Laer: Boomness, Topness)

27 Paricle classificaions; symmery schemes Quanum numbers, symmeries, and mehods of Group heory : SU(3), SU(), ec. Meson oce Baryon decuple Predicion of he W - paricle; observaion afer wo years The Nobel Prize in Physics 1969 "for his conribuions and discoveries concerning he classificaion of elemenary paricles and heir ineracions" So hese symmery models work! Murray Gell-Mann

28 Quarks quark composiions for some baryons and mesons: Due o he regulariies seen in he paricle ables, as well as elecron scaering resuls ha showed inernal srucure in he proon and neuron, a heory of quarks was developed. There are six differen flavors of quarks; each has baryon number B = ⅓. Hadrons are made of hree quarks; mesons are a quark aniquark pair.

29 Quarks Table : properies of he six known quarks. Flavor Mass of he proon?

30 Quarks hadrons ha have been discovered conaining c,, or b quarks.

31 Quarks Truly elemenary paricles (having no inernal srucure): quarks, he gauge bosons, and he lepons. Three generaions ; each has he same paern of elecric charge, bu he masses increase from generaion o generaion.

32 Three generaions Three families Only hree? Have we missed he fourh because of high mass?

33 Noe: weak decay beween families Heavier families are unsable

34 Cross secion Only hree families, i seems Z 0 decays in quark pairs (no op quarks!) lepon pairs e e, m m, neurino pairs Lifeime 1/ G wih G S G i Sum over all decay channels energy (GeV) 4 h family enirely forbidden?

35 Color Soon afer he quark heory was proposed, i was suggesed ha quarks have anoher propery, called color, or color charge. Unlike oher quanum numbers, color akes on hree values. Real paricles mus be colorless; his explains why only 3-quark and quark aniquark configuraions are seen. Color also ensures ha he exclusion principle is sill valid. The need for an addiional quanum number (saisfy Pauli principle) Oherwise uuu or ddd canno exis... Baryons and mesons do no have color (whie)

36 Quanum Chromodynamics (QCD) Quark Confinemen The color force becomes much larger as quarks separae; quarks are herefore never seen as individual paricles, as he energy needed o separae hem is less han he energy needed o creae a new quark aniquark pair. Conversely, when he quarks are very close ogeher, he force is very small. U color 4 sc 3 r T 0 r T GeV/fm confinemen shor disance large disance

37 The Sandard Model : Quanum Chromodynamics (QCD) and gluons These Feynman diagrams show a quark quark ineracion mediaed by a gluon; a baryon baryon ineracion mediaed by a meson; and he baryon baryon ineracion as mediaed on a quark level by gluons. ime

38 The Elecroweak Theory Range of weak force. The weak nuclear force is of very shor range, meaning i acs over only a very shor disance. Esimae is range using he masses of he W ± and Z: m 80 or 90 GeV/c 10 GeV/c. Compare o Yukawa s heory and analysis

39 Consider he following decay reacions Argue wheher hey are allowed or no Based on he conservaion laws 0 n No allowed; Charge conservaion is violaed; also srangeness. 0 p K No allowed; Energy conservaion is violaed; E()=1115 MeV; E(p)=938 MeV; E(K)=493 MeV 0 No allowed: Baryon number is violaed Spin is violaed Srangeness is violaed p e n e Baryon number is no conserved m e n m Elecron lepion number L e is no conserved 0 S Srangeness is no conserved (sill a possibiliy under weak decay) Energy is no conserved; E()=1315 MeV; E(S)=1189 MeV; E()=140 MeV W S 0 n Lepon number is no conserved S 0 0 Decay is possible; Charge, Baryon number, Lepon number, Srangeness are all conserved. Energy conservaion

40 The D S+ meson Wha is he quark srucure of such a paricle. Look up in Table and find: Charge Q=+1; Baryon number B=0; Charm C=1; Mass M= 1968 MeV/c. In view of mass No boomness, no opness. For he charm here mus be a c-quark, wih charge +/3e To ge a charge of +1 here mus be anoher quark wih +1/3 e To have B=0 he second quark mus be an ani-quark. To have srangeness s=+1, he second quark mus be an ani-srange. D s cs