sign in sign up
<<
Home , Bottomness, Charm (quantum number), Strangeness, Topness

Nuclear and Junior Honours: Lecture 5: and Leptons February 22nd 2007

Leptons • Quantum Numbers

Quarks • • • 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 : 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 : − 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 . − 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: • Number, B - total number of quarks • B=+1/3 for quarks, B=!1/3 for anti-quarks • Strangness: S, : C, : B, : 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 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 • Lepton Number and 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 we define a new quantum number: isospin, I • In , 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 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 . Decay via .

• 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

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"$3' quarks to explain isospin symmetry and strangeness. F I .A0,E*�$,%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*�$,%E,",&0J,)"$.*: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/"+

• 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 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 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 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. at the decadesTevatron. before the top was fi- evidence for the top matter and the February 6, 2002. !!! • Production:nally pp found.!"tt! quark from both CDF forces that gov- !!! “ If the people in the treasurer’s of- Produced in conjunction with and D0. In simulta- ern the physical The top is so heavy it decays via weak force “Water is one of the strangest sub- fice, and their consultants,• had been its antiparticle the t-bar, the top neous publications in world. Chief stances on earth. It has a myriad of doing the kind of thorough invbeforeestigat- it formsquark q hadrons.uickly decays into a vari- April 1995, both teams among these is properties that make it unique for life ing that they claimed to do Decaybefore t"Wbety of daughter particles. The reported a probability the Higgs boson, and unique for how a ski slides on investing in anything, then t•hey should best way2 to search for the top was of less than one in which is proving snow. It’s often impossible to predict.” have uncovered that there •wasM(t) some(-170 GeV/cto look for its decay into a W 500,000 that their top even more elu- —David Lind, University of Colo- thing wrong in Enron’s books, which boson and the next lightest quark candidates could sive than the top rado, on the physics of skiing, we now all know.” quark, the b quark. A chief prob- be explained by background alone. quark. It is the last undiscovered ABCnews.com, February 8, 2002. —Charles Schwartz, University of lem is the fact that the energetic The extremely large mass of the top particle in the Standard Model’s !!! California, Berkeley, News Hour with b’s and W’s are also unstable and — the current value is 175.6 GeV, bestiary. A precise mass for the “The mission proposal is com- Jim Lehrer, February 19, 2002. quickly decay into particle jets similar to the mass of a gold top quark will help theorists con- pletely new. The idea extends an !!! that typically emanate from less- nucleus, which contains 197 pro- strain the Higgs mass, improving existing mission concept — the La- “We know how to make metals interesting background tons and neutrons — suggests that its chances of detection at ser Interferometer Space Antenna or that have strength. But we have never collisions. Identifying the top it may be fundamentally different Fermilab or the LHC in the next LISA — to much higher sensitivity been able before to predict whether quark required distinguishing a from the other quarks. The sheer decade. and into a different frequency range.” an alloy, for example, would get real top signature from those of enormousness of the top’s mass The discovery of the top —Neil Cornish, Montana State stronger and better. This technique background processes that can makes its decays fertile ground for quark was not a “Eureka” event . University, on plans to measure will allow us to tailor the strength of mimic one. new particle searches. “We discovered the top quark gravitational shock waves from the materials and take years off the de- In 1985, when the Fermilab The top also has the shortest not in one lightning stroke, but big bang, UPI, February 12, 2002. velopment process because we won’t collider was first acti- lifetime among quarks — less than over a long pe1r0iod of time, event !!! have to rely on trial-and-error.” vated, the search for the top 10-24 seconds — and decays as a by event,” D0 physicist Nick “You should aim to flip the pan- —Bennett Larson, Oak Ridge Na- quark was well underway, but free particle, the only quark to do Hadley (University of Maryland) cake into the air at a speed of 10 tional Laboratory, on a new technique early efforts at SLAC and at DESY so. All other quarks created in such said at the time of the discovery. miles an hour, which will mean it for making 3-D images of small in Germany proved fruitless. As a collision live long enough to pull “No single piece of evidence, no will take less than .5 of a second to samples, UPI, February 20, 2002. the 1980s drew to a close, CERN, more quarks from the vacuum and matter how strong, was enough reach the top of its trajectory. If you !!! at that time the most powerful make complicated “jets” com- to let us claim a discovery. We are lucky, the pancake should now “I believe we have made cold anti-mat- accelerator with energies up to posed of many particles. The top’s couldn’t be sure we had found have rotated 90 degrees, at a rate ter atoms... but I can’t really prove it.” 315 GeV, had failed to find the independence has enabled the the top quark until we had seen of .55 revs per second. If not, you —Gerald Gabrielse, Harvard Univer- top quark. Experiments had de- Fermilab teams to determine its so many events with the right could be in trouble and have a sity, on experiments at CERN to create termined that the mass of the top mass to far greater precision than characteristics that there was al- sticky mass of flying batter spinning anti-hydrogen, Sydney Morning Herald, could be no lower than 77 GeV the mass of any other quark. most no chance the statistics through the air.” February 22, 2002. — beyond the limits of CERN’s Since then, Fermilab’s Tevatron were fooling us into making a —Garry Tungate, Birmingham !!! energy beams. has been revamped and both the false claim.” University, Belfast News Letter, “I still cannot recover, right In the 1990s, the focus CDF and D0 collaborations have February 12, 2002. now even. Sometimes I think it’s shifted to Fermilab and its two dramatically improved their detec- Particular Pastimes: !!! a kind of nightmare.” main experiments: the CDF and tors, resuming collection of data The Top Quark Game: http:/ “At the end, you realize most of —Yoji Totsuka, University of Tokyo, on D0 detector collaborations. By in 1999. The accelerator upgrades e d u c a t i o n . j l a b . o r g / what you’ve got in your hand is 75 per- the disastrous implosion of phototubes the time researchers had begun have allowed top quarks to be pro- topquarkgame/ cent air. This tiny sheet of paper, which at the Superkamiokande facility, Daily taking data in 1992, the top duced at 20 times the previous The Particle Adventure: http:/ has not much strength at all, is able to Yomiuri, February 26, 2002. mass limit had been pushed up rate, while detector upgrades have /www.particleadventure.org resist your squeezing very, very well. !!! Why is it as strong as it is?” “Recognizing the limitations in —Sidney R. Nagel, University of Chi- the budget the department faces, cago, on the physics of crumpling, New I’ll work with the scientific commu- York Times, February 19, 2002. See IN THE MEDIA on page 4

Series II, Vol. 11, No. 4 One Physics Ellipse, College Park, MD 20740-3844, Martin Blume*, Brookhaven National Laboratory (emeritus) W. Carl Lineberger (Laser Science), G. Slade Cargill, April 2002 [email protected]. Past-President III (Materials), Bunny C. Clark (Nuclear), Sally NEWS ©2002 The American Physical Society For Nonmembers—Circulation and Fulfillment George H. Trilling*, Lawrence Berkeley National Laboratory Dawson, Peter Meyers (Particles & Fields), Stephen Division, American Institute of Physics, Suite 1NO1, Holmes (Physics of Beams), Richard Hazeltine Coden: ANWSEN ISSN: 1058-8132 2 Huntington Quadrangle, Melville, NY 11747-4502. General Councillors (Plasma), Kannan Jagannathan, (New England), Joe Allow at least 6 weeks advance notice. For address Jonathan A. Bagger, Philip Bucksbaum*, L. Craig Davis, Hamilton (Southeast Section) changes, please send both the old and new addresses, Stuart Freedman*, Frances Houle, Leon Lederman*, Editor ...... Alan Chodos and, if possible, include a mailing label from a recent Gerald Mahan, Margaret Murnane*, Cherry Ann Murray, Associate Editor ...... Jennifer Ouellette issue. Requests from subscribers for missing issues Philip Phillips*, Jin-Joo Song, James Trefil ADVISORS Representatives from Other Societies Special Publications Manager ...... Elizabeth Buchan-Higgins will be honored without charge only if received within Christopher J. Chiaverina, AAPT; Marc Brodsky, AIP Design and Production ...... Stephanie Jankowski 6 months of the issue’s actual date of publication. International Councillor Proofreaders ...... Ken Cole, Edward Lee and Sue Otwell Periodical Postage Paid at College Park, MD and at T. Maurice Rice additional mailing offices. Postmaster: Send address International Advisors changes to APS News, Membership Department, Chair, Nominating Committee Michael Thewalt, Canadian Association of Physicists, APS News (ISSN: 1058-8132) is published 11X regarding APS News should be directed to: Editor, APS American Physical Society, One Physics Ellipse, Susan Nan Coppersmith Gerardo C. Puente, Mexican Physical Society yearly, monthly, except the August/September News, One Physics Ellipse, College Park, MD 20749- College Park, MD 20740-3844. issue, by the American Physical Society, One 3844, E-mail: [email protected]. Chair, Panel on Public Affairs Staff Representatives Physics Ellipse, College Park, MD 20740-3844, APS COUNCIL 2002 James C. H. Tsang Alan Chodos, Associate Executive Officer; Irving (301) 209-3200. It contains news of the Society Subscriptions: APS News is an on-membership President Lerch, Director of International Affairs; Fredrick and of its Divisions, Topical Groups, Sections publication delivered by Periodical Mail. Members William F. Brinkman*, Bell Labs-Lucent Technologies (retired) Division, Forum and Section Councillors Stein, Director of Education and Outreach; Robert and Forums; advance information on meetings residing abroad may receive airfreight delivery for a President-Elect Harold Metcalf (Atomic, Molecular & Optical), Robert L. Park, Director, Public Information; Michael of the Society; and reports to the Society by its fee of $15. Nonmembers: Subscription rates are: Myriam P. Sarachik*, City College of New York - CUNY Eisenberg (Biological), Sylvia Ceyer (Chemical), E. Dan Lubell, Director, Public Affairs; Stanley Brown, committees and task forces, as well as opinions. domestic $105; Canada, Mexico, Central and South Vice-President Dahlberg*, Allen Goldman* (Condensed Matter Physics), Editorial Director; Charles Muller, Director, Journal America, and Caribbean $105; Air Freight Europe, Helen Quinn*, Stanford University (SLAC) Steven White (Computational), Jerry Gollub* (Fluid Operations; Robert Kelly, Director of Journal Letters to the editor are welcomed from the Asia, Africa and Oceania $120. Executive Officer Dynamics), Peter Zimmerman (Forum on Education), Information Systems; Michael Stephens, Controller membership. Letters must be signed and should Judy R. Franz*, University of Alabama, Huntsville (on leave) Gloria Lubkin (Forum on History of Physics), Stuart Wolf and Assistant Treasurer include an address and daytime telephone Subscription orders, renewals and address changes Treasurer (Forum on Industrial and Applied Physics), James Vary Administrator for Governing Committees number. The APS reserves the right to select and should be addressed as follows: For APS Members— Thomas McIlrath*, University of Maryland (emeritus) (Forum on International Physics), Ed Gerjuoy (Forum on Ken Cole to edit for length or clarity. All correspondence Membership Department, American Physical Society, Editor-in-Chief Physics and Society), Timothy P. Lodge, (Polymer Physics), * Members of the APS Executive Board Summary

Leptons are described by three quantum numbers: Le, Lµ, L" • conserved in all interactions. Quarks, , baryons are described by six quantum numbers: • Baryon Number, B - total number of quarks • B=+1/3 for quarks, B=!1/3 for anti-quarks • Conserved in all interactions. • 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)! • Conserved in strong and electromagnetic interactions. 1 I = N(u) N(d) + N(d)¯ N(u¯) • Isospin, I, IZ Z 2 − − • Describes the symmetry! between the up and down" quarks • Conserved in strong interactions. Strange, charm, bottom and top quarks discovered in strong interactions production of a qq ! pair. • Decay by electromagnetic or weak decay indicated that something new had been created!

11