THE WEAK INTERACTION. e - MISN by J. Christman. 1. Overview Assigned Readings... 1

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1 MISN0281 THE WEAK INTERACTION by J. Christma THE WEAK INTERACTION 1. Ovrviw Assigd Radigs s d d _ u d s d u _ 3. Charactristics of th Wak Itractio a. Th Wak Forc: Uivrsal b. Hug Fluxs For Dirct Nutrio Obsrvatio c. Chag i S if O Wak Vrtx d. Rag of th Wak Itractio A FourFrmio Itractio Catgoris of Wak Itractio a. Catgoris Basd o Particls Ivolvd b. Examls of Wak Ltoic Procsss c. Examls of Wak SmiLtoic Procsss d. Examls of Wak Hadroic Procsss Strog Dcays Occur Bfor Wak Dcays Th Itrmdiat Vctor Boso a. Th W Particl as th WakForc Mso b. Th Mass of th W Particl c. Th Si of th W Particl d. Th Nutral Wak Boso A Problm with Nutral K Dcay Ackowldgmts Projct PHYSNETPhysics Bldg. Michiga Stat UivrsityEast Lasig, MI 1

2 ID Sht: MISN0281 Titl: Th Wak Itractio Author: J. R. Christma, Dt. of Physical Scic, U.S. Coast Guard Acadmy, Nw Lodo, CT Vrsio: 11/8/2001 Lgth: 2 hr; 16 ags Iut Skills: Evaluatio: Stag B1 1. Itrrt Particl Diagrams ad giv th associatd coulig costats (MISN0279). Outut Skills (Kowldg): K1. List th thr catgoris of wak itractios ad giv xamls ad ossibl Particl Diagrams for ach. K2. Giv argumts that lad to rdictios of th mass ad si of th W articls. Outut Skills (Problm Solvig): S1. Giv a wak dcay, dvis a lausibl Particl Diagram for it, showig th wak itractio as a fourfrmio itractio. S2. Giv a wak dcay, dvis a lausibl Particl Diagram for it, showig th wak itractio as th xchag of a (chargd) W or a (utral) Z 0. Extral Rsourcs (Rquird): 1. M. J. Logo, Fudamtals of Elmtary Particl Physics, PrticHall (1973). 2. Scitific Amrica, March, PostOtios: 1. SU(3) ad th Quark Modl (MISN0282). 2. Currt Work i Elmtary Particls (MISN0284). THIS IS A DEVELOPMENTALSTAGE PUBLICATION OF PROJECT PHYSNET Th goal of our rojct is to assist a twork of ducators ad scitists i trasfrrig hysics from o rso to aothr. W suort mauscrit rocssig ad distributio, aloith commuicatio ad iformatio systms. W also work with mloyrs to idtify basic scitific skills as wll as hysics toics that ar dd i scic ad tchology. A umbr of our ublicatios ar aimd at assistig usrs i acquiriuch skills. Our ublicatios ar dsigd: (i) to b udatd quickly i rsos to fild tsts ad w scitific dvlomts; (ii) to b usd i both classroom ad rofssioal sttigs; (iii) to show th rrquisit ddcis xistig amog th various chuks of hysics kowldg ad skill, as a guid both to mtal orgaizatio ad to us of th matrials; ad (iv) to b adatd quickly to scific usr ds ragig from siglskill istructio to comlt custom txtbooks. Nw authors, rviwrs ad fild tstrs ar wlcom. PROJECT STAFF Adrw Sch Eug Kals Ptr Sigll Wbmastr Grahics Projct Dirctor ADVISORY COMMITTEE D. Ala Bromly Yal Uivrsity E. Loard Jossm Th Ohio Stat Uivrsity A. A. Strassburg S. U. N. Y., Stoy Brook Viws xrssd i a modul ar thos of th modul author(s) ad ar ot cssarily thos of othr rojct articiats. c 2001, Ptr Sigll for Projct PHYSNET, PhysicsAstroomy Bldg., Mich. Stat Uiv., E. Lasig, MI 48824; (517) For our libral us olicis s: htt:// 3 4

3 MISN THE WEAK INTERACTION by J. Christma 1. Ovrviw This modul fills i som dtails of th wak itractio. I articular, it dals with th basic couligs of th itractio ad with th W articls which ar xchagd i it. Chatr 6, Logo 2. Assigd Radigs S. B.,Trima, Th Wak Itractios, Scitific Amrica, March, Charactristics of th Wak Itractio 3a. Th Wak Forc: Uivrsal. All articls articiat i th wak itractio i th ss that all kow articls (xct th rsoacs) hav b obsrvd to articiat i a itractio or dcay that ivolvs th wak forc (at o or mor vrtics i th associatd Particl Diagram). Study of th wak forc, howvr, is comlicatd by th strog itractio: som itractios may rocd i mor tha o st, th first st big a strog dcay to othr articls, som of which th itract wakly. Th strog rocss taks lac i such a short tim ad ovr such a small distac that it is imossibl to obsrv ad hc it is imossibl (xct by idirct vidc) to ascrtai whthr or ot th strog itractio actually took lac. This maks dductio of th wak art of th itractio ucrtai. 3b. Hug Fluxs For Dirct Nutrio Obsrvatio. Nutrios ar th oly articls that itract via th wak forc alo so thy mak idal bullts to study th wak itractio. Th wak itractio is so wak, howvr, that oly about 1 utrio i vry udrgos a itractio with th uclos i fluids usd to dtct utrios. So th xrimtal study of th wak itractio rquirs ormous utrio fluxs ad also dtctio chambrs th siz of larg rooms. MISN Th articiatio of a utrio guarats that th itractio is wak. Howvr, it is xtrmly difficult, i most cass, to show that a utrio is, i fact, v rst. 3c. Chag i S if O Wak Vrtx. All first ordr wak itractios (i.., dcays with o wak vrtx), ithr do ot chag stragss or ls chag stragss by ±1. That is, S = 0, ±1 for first ordr wak dcays. Scod ordr wak itractios, dcays with two wak vrtics, ar xtrmly rar ad will ot b cosidrd hr. 3d. Rag of th Wak Itractio. Thoris suggst that th rag of th wak itractio is o th ordr of m, which is shortr tha th rag of th strog itractio. 3. A FourFrmio Itractio. A wak itractio vrtx i a Particl Diagram must hav xactly four articl lis ad th articls must all b frmios. Th itractio strgth at th vrtx is dotd. 4. Catgoris of Wak Itractio 4a. Catgoris Basd o Particls Ivolvd. Wak itractios ar classifid i thr catgoris: ltoic, i which oly ltos ar ivolvd; smiltoic, i which both ltos ad hadros ar ivolvd; ad hadroic, i which oly hadros ar ivolvd. 4b. Examls of Wak Ltoic Procsss. Hr ar two scattrig ractios ad a dcay ivolvig oly ltos i th iitial ad fial stats (ot that th utrio is charglss so th scattrig caot b lctromagtic): ν + ν + ν µ + µ ν µ + µ µ ν µ + ν (scattrig) (scattrig) 4c. Examls of Wak SmiLtoic Procsss. Hr ar som diagrams for Wak SmiLtoic Procsss: 5 6

4 MISN MISN ν (uclar β dcay): K + π + +π + +π : _ π + π ν : Σ Λ ν : Λ 0 + π : 0 4. Strog Dcays Occur Bfor Wak Dcays. Th hadros that tr th wak vrtx of th abov diagrams ar th lowst mass baryos with S = 0 ad S = 1. All hadros coul strogly to at last o of ths baryos, ad sic th strog itractio is so fast o xcts a iitial hadro to first itract strogly util o of ths low mass baryos is roducd. 4d. Examls of Wak Hadroic Procsss. Hr ar som diagrams for Wak Hadroic Procsss: K + π + +π 0 : _ Th Itrmdiat Vctor Boso 5a. Th W Particl as th WakForc Mso. Th lctromagtic itractio is carrid by th hoto ad th strog itractio is carrid by hadros, i th ss that th itractios ar causd by xchag of such itrmdiary articls. Similarly, th wak itractio is carrid by th itrmdiat vctor boso ad its symbol is W. Thr is a ositivly chargd W +, a gativly chargd W, ad a utral W 0. Ths articls ca b roducd by aroriat airs of wakly itractig articls ad thy dcay ito aroriat airs: + W + + W + Λ 0 W + + Λ 0 W µ + + ν µ W + µ + ν µ W For xaml, β dcay rocds accordig to: 7 8

5 MISN MISN Z 0 Figur 1. Sis ad momta from W dcay. Figur 2. Th wakitractio xchag of a utral articl (th Z). g _ w W g _ w Th coulig costat at ach vrtx is to mak th ovrall coulig costat. 5b. Th Mass of th W Particl. Sic th rag of th wak itractio is lss tha m, th mass of th W must b gratr tha a amout dtrmid by th ucrtaity ricil : mc 2 > h t = hc R = ( ) ( ) = J = 2.0 GV. (Not: 1 GV = 10 3 MV.) Exrimtally, W articls hav b s. Th obsrvd mass of th W is aroximatly 80 GV. 5c. Th Si of th W Particl. Th si of th W ca b dducd from obsrvatios of th sis of its dcay roducts. Cosidr, for xaml, th β dcay of th utro (s th diagram i Sct. 5a ad Fig. 1, this sctio). I th ctr of mass fram of th lctro ad atiutrio, th si of th atiutrio is h/2 i th dirctio of its momtum (this is tru for th atiutrio i ay fram) ad th si of th lctro is obsrvd to b h/2 i th dirctio oosit to its momtum. Th orbital agular momtum is zro. If th articls rsult from th dcay of a W, th sis ad momta of th dcay roducts look as i Fig. 1. Not that th total si is h, to th lft. Sic agular momtum is cosrvd, th si of th W must hav b h. This is i fact th raso for its am itrmdiat vctor boso. A itgr si articl is a boso ad a si 1 articl has associatd with it a vctor fild (aothr vctor boso, th hoto, is associatd with th vctor lctromagtic fild). It is also asy to dduc that th W articls hav lctro family umbr 0, muo family umbr 0, ad th baryo family umbr 0. 5d. Th Nutral Wak Boso. A utral boso is ot dd for xchag i th usual wak couligs of uclar hysics; all of thm ivolv a trasfr of charg ad so ivolv th xchag of chargd W s. Howvr, th obsrvd wak scattrig of o lto by aothr dos rquir th xchag of a utral boso (s Fig. 2.). Our currt thortical udrstadig is that th W 0 caot itslf b obsrvd, but that it ad aothr uobsrvabl articl combi two diffrt ways to form th obsrvd wakitractio Z 0 ad th wllobsrvd lctromagticitractio γ (th hoto ). Aart from lto scattrig, othr ractios such as ν µ + ν µ + + π 0 ca occur via th xchag of th Z A Problm with Nutral K Dcay. A imortat xaml of wak utral xchag should b th dcay of th utral kao. Th mor usual dcay roducts iclud at last o io. Th dcay to ltos, K 0 µ + + µ, is xtrmly rar. With a Z 0 xistig, K 0 ca dcay that way via a first ordr wak dcay ad for som tim th rarity of that dcay mod was tak as vidc that th utral wako did ot xist. With vidc for th Z 0 i utrio scattrig (s Sct. 5d), a w xlaatio was rquird for th rarity of th utral kao dcay to muos. Th solutio is aothr quatum umbr, calld charm, which w shall discuss lswhr. 1 Ackowldgmts Praratio of this modul was suortd by th Uitd Stats Coast Guard Acadmy for a Dirctd Studis Program. Praratio of this 1 S Color ad Charm (MISN0283). 9 10

6 MISN MISN0281 PS1 modul was suortd i art by th Natioal Scic Foudatio, Divisio of Scic Educatio Dvlomt ad Rsarch, through Grat #SED to Michiga Stat Uivrsity. PROBLEM SUPPLEMENT Not: If you do ot udrstad how a aswr i this sulmt was arrivd at, kidly go back to th txt ad work through it carfully. Mak sur you udrstad all of th txt xamls bfor comig back to this sulmt. Th txt is orgaizd for larig, whras this sulmt is dsigd to hl you tst whthr you lard th subjct from th txt. Problms: Dvis lausibl diagrams for th followiak dcays, both without ad with itrmdiat wakos. 1. Ξ 0 Λ 0 + π 0 (C) 2. K + π ν (B) 3. π + µ + + ν µ (E) 4. Λ ν (A) 5. Σ Λ ν (D) Not: I som cass thr ar a umbr of lgitimat ossibilitis for itrmdiat stats. For xaml, i Aswr (C) th (, ) itrmdiat stat could qually wll b (, ). Aswrs: (A) 0 0 W g _ w g _ w 11 12

7 MISN0281 PS2 (B) (C) (D) + g _ w g _ w + W g _ w g _ w 0 g 0 s g _ g _ w w 0 0 (E) W + Z0 W g _ w g _ w 13 14

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