Nuclear and Particle Physics Junior Honours: Particle Physics Lecture 5: Quarks and Leptons February 22nd 2007 Leptons • Quantum Numbers Quarks • Isospin • Strangeness • Quark Model • J/" • Heavy Quarks: bottom and top 1 Leptons ! ! ! • Six leptons: e µ " #e #µ #" + + + • Six anti-leptons: e µ " #e! #µ! #"! • Three quantum numbers used to characterise leptons: • Electron number, Le, muon number, Lµ, tau number L" • Total Lepton number: L= Le + Lµ + L" • Le, Lµ, L" & L are conserved in all interactions Lepton Le Lµ Lτ Q(e) electron e− +1 0 0 1 Think of Le, Lµ and L" like electric − muon µ− 0 +1 0 1 charge: − tau τ − 0 0 +1 1 They have to be conserved at − • electron neutrino νe +1 0 0 0 every vertex. muon neutrino νµ 0 +1 0 0 • They are conserved in every tau neutrino ντ 0 0 +1 0 decay and scattering process anti-electron e+ 1 0 0 +1 anti-muon µ+ −0 1 0 +1 anti-tau τ + 0 −0 1 +1 Parity: intrinsic quantum number. − electron anti-neutrino ν¯e 1 0 0 0 !=+1 for lepton − muon anti-neutrino ν¯µ 0 1 0 0 !=!1 for anti-leptons tau anti-neutrino ν¯ 0 −0 1 0 τ − 2 Introduction to Quarks • Six quarks: d u s c t b Parity: intrinsic quantum number. Six anti-quarks: d ! u ! s ! c ! t ! b! !=+1 for quarks • !=!1 for anti-quarks • Lots of quantum numbers used to describe quarks: • Baryon Number, B - total number of quarks • B=+1/3 for quarks, B=!1/3 for anti-quarks • Strangness: S, Charm: C, Bottomness: B, Topness: T - number of s, c, b, t • S=N(s)! !N(s) C=N(c)!N(c)! B=N(b)! !N(b) T=N(t)!N(t)! • Isospin: I, IZ - describe the up and down quarks • B conserved in all Quark I IZ S C B T Q(e) interactions down d 1/2 1/2 0 0 0 0 1/3 up u 1/2 −1/2 0 0 0 0 +2− /3 • S, C, B, T conserved in strange s 0 0 1 0 0 0 1/3 strong and charm c 0 0 −0 +1 0 0 +2− /3 electromagnetic bottom b 0 0 0 0 1 0 1/3 • I, IZ conserved in strong top t 0 0 0 0 −0 +1 +2− /3 interactions only 3 Conservation Laws Noether’s Theorem: Every symmetry of nature has a conservation law associated with it, and vice-versa. • Energy & Momentum; Angular Momentum conserved in all interactions Symmetry: translations in space and time; rotations in space • Charge conservation conserved in all interactions Symmetry: gauge transformation - underlying symmetry in QM description of electromagnetism • Lepton Number and Baryon Number symmetry L , L , L baryon number, e µ τ B symmetry: mystery! • Quark Flavour, Isospin, Parity conserved in strong and electromagnetic interactions violated in weak interactions Symmetry: unknown 4 Isospin • Protons uud and neutrons udd have almost equal mass: 2 2 • mp = 938.3 MeV/c mn = 939.6 MeV/c • #± (ud,! ud)! and #0 (uu,! dd)! have almost the same mass • To describe this symmetry between sets of hadrons we define a new quantum number: isospin, I • In baryons, we combine isospin in the same way as spin • total isospin I and third component of isospin, IZ: I!IZ!"I • p and n form an ‘isospin doublet’ with I=$ 1 ¯ • proton has IZ=+$ neutron has IZ=!$ IZ = N(u) N(d) + N(d) N(u¯) 2 − − + 0 ! • # , # and # form an ‘isospin triplet’ with I=1 ! " + 0 ! • # has IZ=+1, # has IZ=0, # has IZ=!1 η = 0, 0 Isospin sets for the | ! lightest baryons p = 1 , 1 n = 1 , 1 | 2 2 ! | 2 2 ! π+ = 1, 1 π0 = 0, 0 π+ = 1, 1 | ! | ! | − ! ++ 3 3 + 3 1 0 3 1 3 3 ∆ = , ∆ = , ∆ = , ∆− = , | 2 2 ! | 2 2 ! | 2 − 2 ! | 2 − 2 ! 5 Strangeness • Strange particles found 1947 in cosmic rays: “V” and “K” K0 % V 0 0 23 π−p K Λ τ(K ) = (10− s) → O 0 + 0 10 K π π− τ(K ) = 0.9 10− s → × 10 Λ π−p τ(λ) = 2.6 10− s • Entirely unexpected! → × • Particles are produced in pairs via strong interaction. Decay via weak interaction. • Introduce a new quantum number to describe these K± K(ink) particles: Strangeness. • conserved in strong interactions and electromagnetic interactions. • violated in weak interactions. 6 Quark Model S2.5*&0S2.5*&0 !"#$%&' !"#$%&',3&%J&,*&,NQTO ('%')*&+,-.$"&/0&0'' 12"$3,4%#05 6,75"8%2$',2+,#+,' Quark Model40'%&' 9'02#%':"5"$ Quark Model • By the mid-1960’"&#,80:.%$,;s 0so'% &many' particles were being found Murray Gell-Man, 1969 S2.5*&0S2.5*&0 no one<"$=%&' knew what was going on... Nobel Prize in Physics >0:2)50.+,%:.0. !"#$%&' • These!"#$% &could',3&%J& ,not*&,NQ TallO be fundamental particles... ('%')*&+,-.$"&/0&0'' !"#$%& 4"''0' 12"$3,4%#05 -)*&?')*&,:%2)5*&/ 6,75"8%2$',2+,#+,' !0"8=,12"$3' 40'%&' @A"$;+,B%..%;+, 9'02#%':"5"$ !0"8=,C2"$3, "&#,80:.%$,;0'%&' 40'%&' <"$=%&' D%),C2"$3 >0:2)50.+,%:.0. !"#$%& 4"''0' 4%.*8".*%&,E%$,12"$3,4%#05 -)*&?')*&,:%2)5*&/ In 1964 Gell-Mann and Zweig proposed the idea of • 9"$.*:50,FG%%H )$%5*E0$".0' !0"8=,12"$3' quarks to explain isospin symmetry and strangeness. F I .A0,E*&#0$,%E,",&0J,)"$.*:50,2'0#,.%,B0,$0J"$#0#, @A"$;+,B%..%;+, Three quarks:B=,",K up,%B0 5down,)$*L0+ ,Band2.,' 2strange.:A,",#*':%80$=,%2/A.,.%,B0, !0"8=,C2"$3, • )2&*'A0#,B=,",MNOOOO,E*&0H P";B+,NQRR 40'%&' Charge, Isospin Strange- D%),C2"$3 Quark Nuclear and Particle Physicse |I,Fra nIzZ >Muheim ness, S 1 4%.*8".*%&,E%$,12"$3,4%#05 Up +2/3 |$, +$> 0 9"$.*:50,FG%%H )$%5*E0$".0' Down !1/3 |$, !$> 0 F I .A0,E*&#0$,%E,",&0J,)"$.*:50,2'0#,.%,B0,$0J"$#0#, B=,",K%B05,)$*L0+,B2.,'2:A,",#*':%Strange80$=,%2/A.,.%,B!01/3, |0, 0> !1 George Zweig )2&*'A0#,B=,",MNOOOO,E*&0H P";B+,NQRR 7 Nuclear and Particle Physics Franz Muheim 1 Discovery of the J/" • In 1974 a new resonance state found in strong interactions: p+Be"J/"+X • Decay: J/""e+e!, J/""µ+µ! • Lifetime &(J/") = 7.6'10!21 s - decays by electroweak force. • Mass M(J/") = 3.1 GeV/c2. • The discovery caused a revolution in particle physics. Lead to acceptation of Gell-Mann and Zweig’s idea that hadrons were composed of quarks. • J/" is composed of c and c.! Richter and Ting independently discovered the J/". 1976 Noble prize in physics 8 Bottom Quark • Bottom quark was discovered in 1977. New resonance state #. • M(#) = 9640 MeV/c2 • Decays: #"e+e!, #"$+$! • Lifetime %(#)=1.3'10!20 s • # = bb! 2 April 2002 NEWS This Month in Physics History “If one were hunting for gold, this !!! !"#$%&'(()*&+$,-./0#1&.2&340&3."&567#8&73&90#:$%7; would be the map of where not to dig.” “A number of very clever people —Maria Spiropulu, on results of a have been chipping away at the The Standard Model of par- to 91 GeV. Over the course of a improved the efficiency of iden- search for supersymmetric particles problem and I think now we can ticle physics holds that all matter decade, both the CDF and D0 col- tifying top quarks, allowing at Fermilab, New York Times, Feb- answer: yes, it would be very diffi- is made from a small alphabet of laborations constructed scientists a more detailed look at ruary 5, 2002. cult but it should be possible without elementary particles consisting enormous, complicated instru- the top’s characteristics. The !!! breaking the laws of physics to send of six quarks and six leptons. ments in order to isolate the top’s groundwork has been laid for the “We literally spray the liquid probes to the nearest stars.” The heaviest of these, the top (or signature. To do so, the two col- Large Hadron Collider at CERN, lithium on the walls and then it —Geoffrey Landis, NASA, The Inde- t) quark, is unstable and can laborations sifted through the which will be9gin operation in flows through a bottom drain.” pendent (London), February 16, only be detected when it is cre- debris from collisions of protons 2006, producing two proton —Robert Kaita, Princeton Univer- 2002. ated artificially, for example in and antiprotons at energies of beams colliding at 14 TeV — sity, on building a fusion reactor !!! the collisions between the high- 1800 GeV. seven times the energy at with liquid metal walls, “It is based on the idea that for a energy proton and antiproton After intensive analysis and Fermilab — generating almost ABCnews.com, February 5, 2002. short period of time, energy and value beams at Fermilab in Batavia, Il- scrutiny, the final results, made one t-t bar pair per second. !!! of money is conserved. The value of linois. Physicists have been public nearly a year af- P h y s i c i s t s “The change in friction you get money is conserved when there are convinced that the top quark ter researchers can now use the is equivalent to going from being transitions between currencies.” must exist since 1977,T whenop its Quarkannounced evidence top quark to on ice to dry pavement.” —Amador Muriel, Data Transport partner, the bottom (or b) quark, for the quark’s detec- help answer the —Victor Petrenko, Dartmouth Col- Systems, on predicting the short term was discovered. Little did they tion in April 1994, many remaining The top quark was discovered in 1995 at CDF and lege, on electronic brakes built into behavior of currencies, Busi•ness World know it would be nearly two showed overwhelming questions about skis and snowboards, New Scientist, (Philippines), February 14, 200DØ2.