Advanced Particle Physics & Introduction to Standard Model: II. Prerequisites

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1 vace Pacle Phyc & Iouco o Saa oel: II. Peeque J. Pawlowk / U. Uwe II. Peeque. Relavc keac. Wave eco o ee acle. o elavc eubao heoy. Scaeg a a ao alue 5. o eco a hae ace 6. ecay wh lee a alz lo Leaue: F. Halze.. a Quak a Leo O. acha leeaelchehyk. Relavc keac. oao -veco coa-vaa o covaa o ν ν g g ν ν ν ν g g b a b a b a g b a ab ν ν ec eo evave oeao Scala ouc

2 vace Pacle Phyc & Iouco o Saa oel: II. Peeque J. Pawlowk / U. Uwe. Loez a Pocaé aoao oal Leave he cala ouc o ace-e eece vaa: y y y y y ν ν a Pocaé aoao obe aoao a a a a o σ σ ± e Loez gou e > ohocho eachable o uy ν ω ν γ βγ βγ γ K e Ray ω: ω acaβ K Wh geeao [ ] k jk j K K K ε Reebe oao: [ ] k jk j J J J ε [ ] k jk j K K J ε Roao & Loez- P cee Pocae aoao: Pay P: e eveal:

3 vace Pacle Phyc & Iouco o Saa oel: II. Peeque J. Pawlowk / U. Uwe 5. Loez vaa Loez aoao: l l γ βγ βγ γ acle wh ovg Scala ouc ae vaa ue Loez aoao: ab b a ale : vaa a ale : S eegy o acle collo calculae ay ae β / β γ c v β γ w/ o e ae: Reak: Loez vaa e.g. co eco ca oly ee o cala 6. aela vaable uolaze acle Wha ae he Loez cala he co eco ca ee o? k k wh coa -o. coevao: coa eee ouc c u u Iea o k ue ou o he aela vaable cobao

4 vace Pacle Phyc & Iouco o Saa oel: II. Peeque ale: -boy ecay o le acle lab θ β Ω co γ γβ lab γβ coθ lab coθ lab lab wh co γβ coθ coθ lab lab la γ ± γβ lab a I cae o he ecay o a acle wh J agula oeu coevao lea o a evao o he ooc ecay. 7.5 og u c u og: u u 8 J. Pawlowk / U. Uwe

5 vace Pacle Phyc & Iouco o Saa oel: II. Peeque. Wave eco o ee acle. Schöge quao o o-elavc ee acle ψ ψ Soluo o eegy ψ e [ ] Schöge q ue clacal - elao / a he elacee ouy equao: ρ ψ j ψ ψ ψ ψ ρ j a 9. Kle-Goo quao Sa o elavc eegy elao : ecbe elavc S acle φ φ φ Soluo o eegy value: > ± ± < v [ k ] φ e ω ± egave value cao be goe a ohewe oluo ae colee oalzao lae o geeal oluo ueoo: k k e α k e α k k φ wh k ω k J. Pawlowk / U. Uwe 5

6 vace Pacle Phyc & Iouco o Saa oel: II. Peeque wh ρ φ φ φ φ a j φ φ φ φ ρ ouy equao: j j Fo he oluo: φ φ φ φ ρ φ φ φ φ φ e [ ] ± j ρ Wha ae egave obable o he < oluo? oalzao chee: / acle e u volue / acle e u volue. -acle Hocal elue ac eeao o eo: acuu ea o occue eg. level Fo eo he egave eegy level ae w/o luece a log a hey ae ully occue e g e w/ egave eegy coeo o o a oo w/ > e e ahlao: Fee eegy level he ea. e o o he hole a eleae eegy by hoo eo: γ > e Phoo coveo o γ > e cao o e o eg. eegy level o o. level: γe e oel ec a-acle covey o oo by eo 9 J. Pawlowk / U. Uwe 6

7 vace Pacle Phyc & Iouco o Saa oel: II. Peeque covey o he oo eo 9 el og cuvaue bobe: egy lo all cuvaue F L qv q e Feya Sückelbeg eeao : φ e Soluo wh eg. eegy oagae backwa e: : φ e Soluo ecbe a-acle oagag owa e: < > eg. obably ey ρ j q J q J q hage ey / cue J. Pawlowk / U. Uwe 7

8 vace Pacle Phyc & Iouco o Saa oel: II. Peeque ale Pacle wh q e a eegy < J e J e e e J J wh > eco o ceao a ahlao: o o a-acle wh aboo o acle wh - - boo o a-acle wh eo o wh - - he cuo o eg./o. eegy oluo ca be avoe whe ug QF he coec elavc quau heoy 5 Ieeao Quau Fel heoy I quau echac obevable becoe oeao wh a eecao value. he oeao wok o ae veco o a Hlbe ace. obevable clacal el e.g. o becoe a el oeao wh a eecao value. he clacal obevable o a eo wave a cala el uco φ. oeogly hee a aocae quaeechacal el oeao Φ wh φ < Φ >: k k e a k e a k k Φ ω ga oble ae ae veco o a Hlbe ace. he le ae he vacuu >. Oe ha a ahlae a acle wh oeu k whle b k ceae a acle wh oeu k: I h way a k k a k k a k o eg. 6 J. Pawlowk / U. Uwe 8

9 vace Pacle Phyc & Iouco o Saa oel: II. Peeque. o-elavc eubao heoy Fee acle Schöge equao wh oluo φ : H φ φ wh φ φ Fo lcy: oalzao δ acle / olve Schöge equao eece o aoal eaco oeal H ψ ψ Oe o he coece a : ψ a φ e a a e φ φ e O ay oluo y ug al coo: a O a o 7 a e Fo eal ee a & Halze. 79 ee ao alue: Fo : a e φ φ a he ao alue be eee a ao obably o? ue ha e eee: ao obably e e l w... l δ δ Fe ck 8 J. Pawlowk / U. Uwe 9

10 vace Pacle Phyc & Iouco o Saa oel: II. Peeque h equao ca oly be gve a hycal eag ae egag ove he e o oble al ae: ρ he ey o al ae a ρ he ube o ae wh a eegy [ ; ]. ao ae: Γ ρ ρ δ Fe gole ule oe coeco ake a e Hghe oe a Fe ule a a e φ φ Poagao o eeae ae 9 e ε. Scaeg a a ao alue Scaeg oce: c ecbe hough quau ube o al a al ae: Scaeg oeao S a: S eauee elec a ecc ae. Pobably o : S S hee he obably ha ueul o ouce he ao oeao S wh J. Pawlowk / U. Uwe

11 vace Pacle Phyc & Iouco o Saa oel: II. Peeque J. Pawlowk / U. Uwe Iea o coveoally oe ue he ao o caeg alue δ oalzao: k / acle/ -oeu coevao Feya ule o calculao ao obably: I h coveo he ao obably gve o a gle oble al ae. I u ou ha he al ae acle a ca be oe ha oe ae. he ube o oble al ae ecbe by he hae ace aco a wll be coee whe calculag obevable quae. 8 ] [ w δ ao ae e u volue: 8 ] [ W δ ] [ δ δ δ Fe ck: ] [ e δ δ δ

12 vace Pacle Phyc & Iouco o Saa oel: II. Peeque 5. o eco a hae ace c ao ae: W δ o eco W ube o al ae al lu W F o eco: σ ρ ρ ube o al ae o gve coguao F ce acle lu o a 5. ube o al ae hae ace h Quau echac ec he ube o al ae ρ o a gle acle a volue wh oeu [ ] ρ h h Faco he eul o oalzao o he wave uco: acle / Fo acle a caee o oeu elee a ρ J. Pawlowk / U. Uwe

13 vace Pacle Phyc & Iouco o Saa oel: II. Peeque J. Pawlowk / U. Uwe 5 5. Ice acle lu F hooe e ae o acle o calculae F le F lu ey ey v F v v wh F S ae: Geeal o : ay ae w F w wh ee acha Loez vaa hae ace aco δ δ σ c c v v Loez vaa -acle hae ace aco Φ Pacle lu F Reak: volue o ou! F W ρ σ Pug eveyhg ogehe S

14 vace Pacle Phyc & Iouco o Saa oel: II. Peeque J. Pawlowk / U. Uwe 7 Φ al P P δ K K Fal ae See alo PG h://g.lbl.gov/8/evew/8-ev-keac. Phae ace aco o acle he al ae: 8 Phae ace egao o wo-acle al-ae S Φ Φ δ δ Sye : Ω Φ 6 θ ϕ co Ω o eo he egao ee e.g. alo. ege.

15 vace Pacle Phyc & Iouco o Saa oel: II. Peeque J. Pawlowk / U. Uwe eeal co eco ug eveyhg ogehe F Ω Φ 6 σ 6 Ω σ c S he yac o he caeg oce coae he a elee whch ca be calculae ug Feya ule / eeece o he co eco becaue o al/al ae keac 6. ecay wh lee a alz lo 5. ecay wh Γ Γ Γ τ eeal ecay wh ae: δ ρ W Γ Γ wo-boy ecay: Ω Φ Γ 6 S: Ω Γ Ω 6

16 vace Pacle Phyc & Iouco o Saa oel: II. Peeque hee-boy ecay: o cala o aveage ove la a Φ α co β γ 5 8 Γ 6 Reak: Iea o vaable a oe ca ue vaable a vaa a o a j j j Γ 56 I hae ace la he alo la j o beg a cala o aveage ove all ae eeal eho o eloe behavo o : alz aly 6. alz Plo eho: Pu evey eaue ecay o a -. o buo. la buo ove he allowe ego coeo o a la a elee. Sucue he buo o o a vayg a elee J. Pawlowk / U. Uwe 6

17 vace Pacle Phyc & Iouco o Saa oel: II. Peeque alz-plo a Wok: K. Sac HP 7 achee K K K K Rece covey o a ew eoc acle Z K ± ψ ψ Ge K* K eo Keo * K? axv:78.79 ub. o PRL 6.5σ ± ± e Γ 5 7 e K Ge ± ψ Ge K*89 K* J. Pawlowk / U. Uwe 7