Notes 4: Experimental evidence for electroweak

Size: px

Start display at page:

Download "Notes 4: Experimental evidence for electroweak"

Jesse Jonas Grant
5 years ago
Views:

1 Nots 4: Exprimntal vidnc for lctrowak hav sn how th EM and wak forcs can b arrangd in a unifid way, i.. all dscribd undr a singl combind st of mathmatics. To summaris, th main stps wr (1) Rbundl th 1 2 (1 γ 5) from th intraction to b part of th spinors instad and trat th lft and right chiral parts of a particl as sparat ntitis (vn though in rality thy always stay togthr). (2) Introduc a 0 using symmtry, guidd by th wak thory of th + and. (3) Cook up an additional fild B 0 which is rally th bits of th EM intraction which w didn t lt in whn w addd th 0. (4) Allow th 0 and B 0 to mix so that on componnt rproducs th known EM forc. Th part lft ovr (which is compltly constraind) is th nutral currnt. now look ovr som points concrning th lctrowak thory. 1. Elctrowak thory givs us th unification condition linking th coupling constants for th wak intraction g and g to th lctromagntic coupling. = 4πα = g sin θ = g cosθ can liminat θ btwn ths two qualitis to gt = gg g 2 + g 2 (49) 2. Comparing th wak chargd currnt at low nrgy (q 2 << M 2 ) [s Burcham+Jobs p501] w gt a rlation btwn g and G F from th old thory G F / 2 = g 2 /(8M 2 ). Doing a similar comparison for nutral currnt procsss (.g. µ µ ) w obtain G F / 2 = g 2 /(8M 2 cos 2 θ ). Putting ths two rlations togthr, w obtain M M = cosθ (50) 3. Th original Frmi 4-point thory had a problm, th cross sction σ G F E 2 whr E is th cntr of mass nrgy. This is fin at low nrgy, but at 300 GV th scattring probability bcoms biggr than on. This is known as unitarity violation and is bad nws for a thory. By introducing th boson and moving away from a four point intraction, a propagator trm 1/(M 2 q2 ) is introducd and th cross sction stops incrasing Anothr similar problm occurs vn with -bosons in th thory. Th procss + in th thory bfor lctrowak unification (diagram on lft) is divrgnt (i.. bcoms vry larg at high nrgy). Elctrowak thory prdicts nutral currnts and in particular th diagram on th right involving which cancls th divrgnc. 19

2 5. Also th two diagrams blow on th right nd cancllation from th lft diagram which coms from th combind lctrowak thory. γ 6. Rnormalisation hav not gon into full dtail about calculating Fynman diagrams. Highr ordr diagrams contain intrnal loops. Th Fynman ruls rquir that w intgrat ovr th particl momntum in ach loop. Th diagram + γ + γ + _ is a problm in that th intgral (which w want to valuat with an uppr limit of infinity) is 1 q 4q3 dq = ln q (51) i.. it divrgs. Th solution to this took a long tim to dvlop and prov that it works. Th rsult is rnormalisation thory. t Hooft provd that all local gaug invariant thoris ar rnormalisabl. 7. Our thory of th EM intraction (QED) is locally gaug invariant and w can us t Hooft s thorm to b assurd that it is rnormalisabl. Good. Sam for QCD. 8. For th wak intraction howvr w hav a problm. Th bosons ar massiv and ntr in a diffrnt (non locally gaug invariant) way to th EM intraction in th Dirac quation. So w can t apply t Hooft s thorm and don t know whthr our thory is rnormalisabl. Th solution to this is th Higgs. now turn to xprimntal vidnc for th lctrowak thory, th nutral currnts wr first discovrd in nutrino intractions and subsquntly studid thr. dfr our discussion of th discovry of th and bosons to Trinity trm, and mov straight to th most accurat masurmnts mad on th, which wr at LEP. Discovry of nutral currnts Th nutral currnt was first discovrd in th Gargamll bubbl chambr at CERN in th raction µ µ i.. lastic scattring off atomic lctrons. Th scattring raction of ithr µ or µ off lctrons is an unambiguous signal for nutral currnts. Scattring of ithr or is ambiguous as thr is a chargd currnt diagram for ach of ths ractions. About 100 vnts wr obsrvd in total and by masuring th cross sction, a valu of sin 2 θ = 0.24 ± 0.04 was obtaind. Th amplitud for th procss from th lctrowak lctur is M = g 2 [ u(µ )γ 8M 2 cos 2 µ (c () V c () A γ 5 )u( µ ) ] [ u()γ µ (c () V c () A γ 5 )u() ] (52) θ can look up th couplings from th lctur: c () V = c () A = 1, 2 c() V = 1 and c() 2 A = sin2 θ. Th calculation of th cross sction involvs avraging ovr spins, sinc 20

3 th lctrons ar unpolarizd. It is a long calculation with svral tim saving tricks. Th rsult for dσ( µ µ )/de is dσ = G2 F m [ ( (c () V c () A ) 2 + (c () V c () A ) 1 E ) 2 m ] E ((c () V ) 2 (c () A ) 2 ) (53) de 2π E This can b intgratd to gt th cross sction σ = dσ de de = E m 2 whr E is in GV. i.. it is tiny. Nutral currnts in hadronic nutrino intractions Th nutral currnt is also obsrvabl in nutrino-nuclon collisions. Th cross sctions ar still small, but somwhat largr than for scattring off lctrons. Nutrino dtctors ar thrfor mad as massiv and as chap pr kg as possibl. MINOS for xampl is mad from a sandwich of stl shts with scintillator. SuprKamiokand is a larg tank of watr and has phototubs surrounding to dtct Crnkov light. SNO is similar, but uss havy watr (andis consquntly smallr). Bothchargd currnt andnutral currnt intractions ar sn. Chargd currnt (CC) intractions appar as a lpton (corrsponding to th nutrino flavour) and a clump of hadronic particls. Nutral currnts (NC) appar as just th clump of hadronic particls as th outgoing nutrino is not dtctd. can us th ratio of cross sctions σ NC /σ CC to obtain th masurmnt sinθ = ± Th cross sction calculation procds as for th lctron scattring with a fw xtra dtails: Th quarks ar insid nuclons so w nd form factors; Cabibbo rotation must b applid in th chargd currnt cas; for nutral currnts, it is quivalnt to us ithr Cabibbo rotatd or unrotatd stats th rsult is th sam. Tsts of Elctrowak thory at LEP + machins As a prlud to studying phtsics at collidrs in mor dtail in Trinity trm, w now tak a dtailld look at th LEP acclrator and xprimnts. This will lad on to th mor xprimntally challnging hadron collidrs (short rason thy ar mor difficult: mor backgrounds). All th dtails on LEP ar collctd hr, but dpnding on how much tim is availabl in th lcturs, som of it may b discussd in th trinity trm lcturs. + machins ar th plac of choic to study 0 s th + and ar point lik so, unlik what w will s in a hadron collidr, thr is no undrlying vnt (from th othr quarks in th particls which collid) and w can assum that th cntr of mass of th collision is fixd. Th antiparticl + is also much asir to produc than antiprotons. Th big disadvantag of + collisions, howvr, is that at high nrgy, Brmsstrahlung is much wors for lctrons th ring circumfrnc of th SPS (usd to discovr th and is 5 km) whil for LEP it is 27 km! It is also possibl to mak a linar collidr (at SLAC) all in a straight lin whr th bams collid only onc. Sinc th luminosity L = fn 1N 2 (54) A it is important focus th bams down to th smallst possibl ara A at th points whr thy collid. Dtaild look at th dtctors Th dtctors ar almost 4π (stradians) i.. thy ar snsitiv to particls going in any dirction from th intraction point (no cracks xcpt for th two bam hols), This is vry important for som of th analysis tchniqus w ar going to discuss latr. 21 E 2

4 Figur 1: Th Opal dtctor Th dtctors ar layrd lik rings on an onion with tracking dtctors in th middl, thn particl ID dtctors (.g. Crnkov dtction), thn lctromagntic calorimtrs, thn hadronic calorimtrs and finally muon chambrs on th outsid. Thr is usually a magntic fild so th momntum of th particls is masurd as thy travrs th tracking rgion. Thr wr 4 LEP dtctors all diffrnt (diffrnt ways of dtcting and idntifying particls). An important part is th silicon vrtx dtctors which wr usd at all four LEP xprimnts - tracking dtctors with high position rsolution clos to th vrtx usd to distinguish b-jts. now go through th diffrnt typs of vnts sn at LEP whn running at th 0 rsonanc as a rviw of what particls do as thy pass through matrial and on what th dtctors s (s vnt displays in lctur). + µ + µ τ + τ 2-jts b-jts 3-jts 2 back-to-back showrs in EM calorimtr with tracks lading towards thm. Nothing in hadron calorimtr or muon dtctors. 2 back-to-back tracks lading all th way out to th muon dtctors. A varity of topologis which hav low multiplicitis and missing momntum (from th nutrino). Nothing qq th quarks form jts a sris of msons and baryons which appar along th sam dirction as th initial quark dirction. Gnrally it is not possibl to tll what flavour th original quark had, howvr... with b (and c) quarks, using th silicon vrtx dtctors, it is possibl to dtct whthr th particls all xtrapolat back to th primary vrtx or whthr thr is a scondary vrtx whr th b-quark dcayd. qq with a gluon Brmsstrahlung mittd from on of th quarks. 22

5 DELPHI Intractiv Analysis Bam: 45.6 GV Run: Evt: 4754 Proc: 4-May-1994 DAS : 5-Jul :21:08 Scan: 2-Jun-1994 TD TE TS TK TV ST PA Act ( 41) ( 22) ( 0) ( 3) ( 0) ( 0) ( 0) Dact ( 0) ( 2) ( 0) ( 4) ( 0) ( 0) ( 0) DELPHI Intractiv Analysis Bam: 45.6 GV Run: Evt: 1417 Proc: 1-Oct-1991 DAS : 25-Aug :36:22 Scan: 19-Fb-1992 TD TE TS TK TV ST PA Act ( 28) ( 29) ( 0) ( 2) ( 3) ( 0) ( 0) Dact ( 0) ( 2) ( 0) ( 2) ( 0) ( 0) ( 0) Y Y X X DELPHI Intractiv Analysis Bam: 45.6 GV Run: Evt: 581 Proc: 8-Mar-1992 DAS : 18-Jun :22:19 Scan: 29-Apr-1992 TD TE TS TK TV ST PA Act ( 44) ( 48) ( 0) ( 9) ( 9) ( 0) ( 0) Dact ( 0) ( 4) ( 0) ( 6) ( 5) ( 0) ( 0) DELPHI Intractiv Analysis Bam: 45.6 GV Run: Evt: 3018 Proc: 1-Oct-1991 DAS : 25-Aug :47:02 Scan: 19-Fb-1992 TD TE TS TK TV ST PA Act ( 93) (133) ( 0) ( 23) ( 18) ( 0) ( 0) Dact ( 0) ( 13) ( 0) ( 23) ( 12) ( 0) ( 0) Y Y X X Figur 2: Four vnt typs (a) +, (b) µ + µ, (c) τ + τ, (d) quark antiquark pair. Aspcts of a physics analysis hat is said hr is tru for any analysis of data but I dscrib it in th contxt of a LEP xprimnt. An analysis gnrally gos along th following lins: th xprimntrs first choos slction critria (cuts) which slct th vnts which ar ndd forstudying such as rquiring n tracks which look lik muons, or tracks abov a crtain nrgy tc. This may involv rconstructing th mass of a combination of particls from th masurd fourmomnta of th tracks and showrs. Quit oftn thr is background in th sampl which is slctd whr a diffrnt physical procss producs vnts which pass th sam cuts (and is thrfor indistinguishabl from th signal). Triggring is an important concpt in a high nrgy physics xprimnt th lctronics is monitoring th signals on all th lctronics channls all th tim, but just lik with a digital camra, somon has to choos at what momnt to stor th information which is going on in th dtctor. This involvs som fast-thinking lctronics computing various quantitis (numbr of tracks, nrgy tc.) onlin and choosing th momnts in tim whn somthing intrsting is happning for th data acquisition to thn rcord vrything as an vnt. 23

6 ALEPH E ch (GV) N ch 10 0 Figur 3: Main cuts usd to sparat th diffrnt classs of + vnts. Calibration concrns subtracting pdstals and masuring th gains and linaritis of ach channl (important particularly in th calorimtrs). If th calibration is not don thn th nrgy rsolution of th calorimtrs suffrs. Th accptanc for th procss w ar studying has to b masurd. Accptanc concrns what is th probability of th particls in an vnt to hit a crtain part of th dtctor. Usually in a 4π LEP dtctor it is almost 100% howvr it may b rducd if cuts ar mad around any dad channls. Accidntals or pil-up concrns th problm that two vnts occur at th sam tim (within dtctabl rsolution) and th rsulting combination gts into th data sampl accidntals can also b a problm if a prcding vnt causs lctronics to momntarily bcom dad bfor rady to masur a nw puls or if th prcding vnt causs a movmnt in th pdstals which causs th nrgy to b masurd slightly wrongly. Accidntal problms ar not big in LEP xprimnts whr th rat of vnts is low. A big tool for this analysis is a Mont Carlo 10 simulation computr program. Th ida is to produc simulatd vnts, using a random numbr gnrator at ach point whr a choic in what happns must b mad. So for xampl in gnrating a simulatd + 0 τ + τ, th choics bgin with (1) pick th dirction along which th τ + dcays along and us momntum consrvation to work out th dirction of th τ. (2) choos th lngth of tim ach τ livs by picking from an xponntial probability distribution t/ττ whr τ τ is th man dcay tim of th τ-lpton and work out whr it dcays. (3) choos from a tabl of masurd branching ratios what daughtr particls ach τ will dcay into.... and so on. Th random numbrs can also b usd to choos how ach particl procds as it passs through various bits of matrial in th dtctor and can produc ralistic looking lctromagntic and hadronic showrs. Th tchniqu works wll and by gnrating lots of ths simulatd vnts w ar ffctivly prforming an intgral ovr all th possibl outcoms of what might happn by randomly sampling th intgrand. Th Mont Carlo tchniqu is a widly usd on and can b usd to comput triggr fficincis, accptancs and accidntal ffcts in an analysis. 10 Namd aftr th city in Monaco (tax-havn adjacnt to Franc) whr thr is a big casino. 24

7 Physics at LEP LEP producd a hug numbr of 0 s, pr dtctor. 0 s dcay into almost vry typ of particl w know, so many things can b studid. Thr wr also a numbr of individual masurmnts of high importanc which w will now discuss, th mass of th 0 boson, th masurmnts of th numbr of nutrinos, and production cross sction and dcay paramtrs of th 0 which ar usd to obtain th couplings c (f) V and c (f) A to compar with th lctrowak thory prdiction. will discuss masurmnts mad whn LEP was run abov M in a latr lctur. So th list of what to do (i.. what was don) is: Tak runs at diffrnt valus of th bam nrgy around th 0 pak. Rcord vrything whnvr thr is a triggr ( an vnt). Rconstruct vnts offlin. Classify as, µµ, ττ, qq, Luminosity Bhabha. Masur cross sction as a function of nrgy s and sub cross sctions. Th cross sction as a function of s (i.. bam nrgy) displays a nic pak at th -rsonanc. Th cross sctions as a function of s for + 0 ff (whr f is on of, µ, τ or quarks) is givn by: sγ 2 σ f (s) = σf 0 (s) (QEDcorr.) (QCDcorr.) (55) (s m 2 ) 2 + m 2 Γ 2 whr σf 0 12π Γ Γ f (s) = (56) M 2 Γ 2 and th lctrowak thory from last tim can b usd to comput Γ f to giv Γ f = G F 2M 3 [ (f) (c V ) 2 + (c (f) A ) 2] N colours (QCDcorr.) (57) 12π Equations (55) and (56) whn put togthr mak th usual Brit-ignr formula. In th lctur, thr will b a quick rviw of th lctrowak thory. Hr w just not th formula for th final stps: whn w inspct th lctromagntic part of th xprssion for th E intraction, w gt th unification conditions = g sin θ = g cosθ ; also G F 2 = g2 8M 2 and whn w look at th nutral currnt part of th E intraction w gt g z J µ = (58) g 1 [ (f) uγ µ c V cos θ 2 c(f) A γ 5] u (59) whr c (f) V quark). = I 3 (f) 2Q(f) sin 2 θ and c (f) A = I 3 (f) for ach frmion typ f (, µ, τ or LEP Masurmnt 1: Mass of th This is don by simply taking th curv of th cross sction as a function of bam nrgy and fitting th xprssion givn in quations (55) to (57) to find th bst valu for M. In practic thr ar various complications to tak car of including th QED and QCD corrctions indicatd in th formula. Anothr important point is to know xactly what th bam nrgy is. 25

8 N=2 N=3 N=4 DELPHI Enrgy, GV Figur 4: N and mass pak plot LEP bam nrgy masurmnt (dtail is not on syllabus) hn w talk about th LEP prcision masurmnt of M in a momnt, w will nd to know th actual nrgy of th bam as prcisly as possibl. This was a vry carful study. How do you masur th bam nrgy? A tchniqu calld rsonant dpolarisation involving th anomalous magntic momnt of th lctron (g-2) was mployd (rcall th xprimnt to masur accuratly th anomalous magntic momnt of th muon as on of th most stringnt tsts of QED). Approximat LEP by a circl immrsd in a uniform vrtical B fild (providing th bnding). p B R L (circumfrnc) F = dp = v B; p = BR = BL (60) dt 2π Also th orbit angular frquncy is ω c = B/γm. Elctrons naturally bcom polarisd ovr about 5 hours by going around in LEP. Th polarisation can b masurd with 26

9 backscattrd light. Th spin prcssion angular frquncy is givn by ω s = B [ 1 + γ γm ( )] g 2 and so w can comput th numbr of prcssions pr turn in LEP s s = ω s ω c ω c ( ) g 2 = γ 2 2 = E bam m ( ) g 2 2 (61) (62) (g 2)/2 is known to an accuracy of and th lctron mass m to a prcision of so if w can masur s w gt th nrgy of th bam. Th tchniqu for masuring s (rsonant dpolarisation) procds by adding a small magnt with fild in th x dirction (horizontal, transvrs to th bam) with a fild which varis as sin t. hn = s th contribution will accumulat ach turn and caus th bam to dpolaris (as masurd in th backscattrd light). Th prcision obtaind in th bam nrgy was 2 MV (out of 45 GV). It involvd undrstanding various ffcts including th tidal pull of th moon (which changs L slightly), movmnts in th watr tabl and vn ground currnts causd whn th fast TGV trains to Paris passd by (discovrd on a day whn thr was a rail strik!). Paramtrs of th lctrowak thory Rcalling again formula from th lctrowak thory: = g sin θ = g cosθ ; M γ = 0; M = M cos θ (63) w s that thr ar thr paramtrs lft, g, sin θ and M. In practic, ths thr paramtrs ar xprssd in trms of th bst masurd quantitis: α QED (0) = 2 4π = 1 (64) (61) (µ dcay) G F = (2) 10 5 GV 2 (65) (LEP) M = ± GV (66) thn w can chck th othr paramtrs by masuring thm and chcking with sin 2 θ cos 2 θ = πα QED 2GF M 2 (67) M = M cos θ (68) LEP Masurmnt 2: Th width; Numbr of nutrinos g 2 = 4πα QED sin 2 θ (69) Th 0 can dcay into a pair of nutrinos 0. How many gnrations of lptons ar thr? know of thr (, µ and τ). Providd th mass of th associatd nutrino is lss than half th 0 mass, thr is a way to dtct if thr ar any mor. Th total width of th 0, Γ is mad up of th sum of th partial width of all it s dcay mods, i.. Γ = Γ HAD + Γ + Γ µµ + Γ ττ + N Γ (70) = Γ HAD + 3Γ ll + N Γ (71) 27

10 whr lpton univrsality has bn assumd for th scond stp. Th partial widths can b prdictd from th lctrowak modl (quation 57) and th branching ratios can b usd to chck. Thrfor, by masuring th total width Γ (again by fitting th shap of th cross sction as a function of bam nrgy using quations 55 to 57, th numbr of nutrinos N can b masurd. Howvr, sinc σ 0 1 Γ 2 (quation 56) it is most snsitiv to simply masur th cross sction at th vry top of th pak. find th rsult is (72) N = ± (73) LEP Masurmnt 3: σ, A FB ar now going to show how th couplings c V and c A for ach frmion typ can b xtractd from masurmnts of th cross sction and th forward-backward asymmtry A FB (to b dfind shortly). Starting with quation (59), w can show (complicatd) dσ dω = G2 FM 4 [( () (c 32π 2 Γ 2 V )2 + (c () ( A )2) (c (f) V )2 + (c (f) A )2) (1 + cos 2 θ) + 8c () V c() A c(f) V c(f) A cos θ] (74) whr θ is th angl btwn th incoming lctron dirction and th outgoing lpton or quark (or btwn th incoming positron and outgoing anti-lpton or anti-quark). Intgrating this xprssion, w find σ( + ff) [ (c () V )2 + (c () A )2] [ (c (f) V )2 + (c (f) A )2] (75) Dfining th forward backward asymmtry A FB as A f FB = N F N B N F + N B (76) whr N F is th numbr of vnts in which θ < 90 (forward) and N B is th numbr of vnts in which θ > 90 (backward). Intgrating again from quation (74) (f) V )2 (c (f) A )2 A FB = 3 2(c () V )2 (c () A )2 2(c (77) 4 (c () V ) 2 + (c () A ) 2 (c (f) V ) 2 + (c (f) A ) 2 = 3 4 A A f whr A = 2(c() V ) 2 (c () A ) 2 and A (c () V ) 2 + (c () f = 2(c (f) V ) 2 (c (f) A ) 2 A ) 2 (c (f) V ) 2 + (c (f) A ) 2(78) So by masuring σ and A FB for a particular final stat f, w gt two quations involving c (f) V and c (f) A which can b solvd to gt c(f) V and c (f) A sparatly. Masuring σ corrctly rquirs accurat knowldg of th luminosity which is dscribd in th sction blow. Manwhil, lts look at th lctrowak information w can obtain by making ths masurmnts. On a plot of c V vs c A, σ c 2 V + c2 A is a circl and A FB is a lin. [S finals qustion )]. This can b don for ach final stat f. On subtlty is that σ and A FB still nd th lctron constants c () V and c () A to b compltly unravld. This can b don with a sparat masurmnt on th τ dcay products. hav drivd th A FB formula assuming all th intractions ar mdiatd by th only, but sinc th photon is involvd as wll, A FB varis as a function of bam nrgy as shown in th plots. So in summary, from th masurd quantitis σ, σ µµ, σ ττ, A FB, A µ FB, A τ FB and som information from τ dcay, w obtain c () V, c (µ) V, c (τ) V, c () A, c (µ) A and c (τ) A. From data, w s: 28

11 1. Univrsality: c () V = c (µ) V = c (τ) V and also c () A = c (µ) A = c (τ) A to high prcision. All thr typs of lpton coupl to th 0 with th sam strngth. 2. sin 2 θ = ± (this is th combination from all LEP tchniqus). L3 + + (γ) 1 pak 2 pak pak+2 d σ / d cos θ [nb] cos θ Figur 5: Cross sction as a function of θ, th angl btwn th incoming lctron and outgoing lpton (th two plots ar th rsults from two diffrnt LEP dtctors, th thr curvs show th thr main bam nrgis at and nar th -pol whr LEP was run. LEP Luminosity Masurmnt (dtail is not on syllabus) It is important to b abl to masur th LEP luminosity to b abl to do th cross sction masurmnts. Rcall that luminosity L is dfind by th following xprssion: N i = Lσ i (79) whr N i is th numbr of vnts from a givn procss i which occur in th dtctor (onc dtctor ffcts lik triggr fficincy and accptanc hav bn corrctd for) and σ i is th cross sction. L is th sam for all procsss - it dpnds on th faturs of th acclrator and how wll it is working (.g. how wll th two bams ar strd into ach othr at a particular intraction rgion). Th way w masur th luminosity is with a procss j for which w know how to calculat th cross sction thortically. count th numbrs of vnts N i and N j, thn using th formula L = N j /σ j and σ i = N i /L w obtain th cross sction w ar intrstd in. For LEP, th channl j usd to masur th luminosity is low angl lctron-positron scattring (Bhabha scattring) for which th QED singl photon xchang diagram dominats. Thr ar only vry small contributions to this from diagrams with 0 or involving annihilation and th thortical uncrtainty is blow 0.1%. Th Bhabha scattrs ar masurd with littl calorimtrs situatd on ach sid of th dtctors (svral tns of mtrs ach sid of th intraction point) and vnts 29

12 A FB (µ) A FB from fit QED corrctd avrag masurmnts ALEPH DELPHI L3 OPAL 0 A FB M E cm [GV] Figur 6: A FB as a function of LEP bam nrgy. From LEP EG. ar countd whn two showrs with th appropriat nrgy ar sn within a radius rgion of (6 cm < R < 15 cm). This cut is mad on on sid only to rduc snsitivity to th location of th intraction point moving around. 30

Standard Model - Electroweak Interactions. Standard Model. Outline. Weak Neutral Interactions. Electroweak Theory. Experimental Tests.

Standard Model - Electroweak Interactions. Standard Model. Outline. Weak Neutral Interactions. Electroweak Theory. Experimental Tests. Standard Modl - Elctrowak Intractions Outlin ak Nutral Intractions Nutral Currnts (NC) Elctrowak Thory ± and Z and γ Discovry of ± Exprimntal Tsts LEP Z Boson Mass and idth Numbr of Nutrinos ± Boson ±