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Field Theory I Aug 7 , 20 20 Lecture 1 4 cross Section Is the Scattering Process 2 m k A tkB-tpnt.it pm k A * -_- 7 P 2 Pn differential Gross Section d P do -_- T 4 = 1 NA - YB 1 - 1lux d P = Kf 1 8 1 i > 1 2 weed ない d d 3 pj lp : 1 - Particle State LPI q ) = 1 2 ) 3 2 Ep ftp.GD ID - 1 2 2 Ep 810 ) [ -8( 0 ) 2 Ep T

Aito/qft1-2020_14.pdfField Theory I Aug 7 2020 Lecture 14 cross Section Is the Scattering Process 2 → m k A tkB-tpnt.it pm k A-_-* 7 P 2 が Pn differential Gross Section dP do-_-

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Page 1: Aito/qft1-2020_14.pdfField Theory I Aug 7 2020 Lecture 14 cross Section Is the Scattering Process 2 → m k A tkB-tpnt.it pm k A-_-* 7 P 2 が Pn differential Gross Section dP do-_-

Field Theory I Aug 7 ,2020

Lecture 14

cross Section Is the Scattering Process 2 → m

kA tkB-tpnt.it pmkA*-_-7 P2

がPn

differential Gross Section

dPdo -_-

T 4

中 = 1 NA - YB 1

で一- 1lux

d P =Kf 1 8 1 i > 1

2

weedない礐dた な点。 d

3

pj

• lp : 1 - Particle State LPI q ) = 12万 )32 Ep ftp.GD

ID - 12が 2 Ep 810) [黒が -8( 0)→ 2 Ep T

Page 2: Aito/qft1-2020_14.pdfField Theory I Aug 7 2020 Lecture 14 cross Section Is the Scattering Process 2 → m k A tkB-tpnt.it pm k A-_-* 7 P 2 が Pn differential Gross Section dP do-_-

li 〉 = IKA , RB7

H) = 1mi , pn >

< i II ) = 2 EA V 2 EB V{ AID = ま (2 Ej V)S : Time Evolution operator fromEt o

t= to

I軾- o) > → IIIt)に Uェ ( tDIEtoD11

琳蟖城II (o)に UI (かの 1 も北の )

は 1 で 、 1の〉 = CHTexp fifdt HA)/ 1 で 〉に は1 SI i )

S = 1 + iTも T- operator invariant matrix

element

( 1- 1 5 1 i > → Ali T 1 i > f= 12 万 ) 4 8

4( KA tk B 一喜 Pi) ib.no

Page 3: Aito/qft1-2020_14.pdfField Theory I Aug 7 2020 Lecture 14 cross Section Is the Scattering Process 2 → m k A tkB-tpnt.it pm k A-_-* 7 P 2 が Pn differential Gross Section dP do-_-

14151が 12= (2た )40410) 12 万 ) 4 0

4 ( Jp)

1MTdP-_@T1aI4E_l1EDlM12C2EAD12.EBv) だ (2 号 な器心が

二 三重坦が 12 な璺唁は甁ははがき別-d 「LIPS'

s

have

Lorentz in is Phase Space

_$の 貯金 。爾1MRdTip.eedifferential Gross Section

YA = 器 、NB = 器

Page 4: Aito/qft1-2020_14.pdfField Theory I Aug 7 2020 Lecture 14 cross Section Is the Scattering Process 2 → m k A tkB-tpnt.it pm k A-_-* 7 P 2 が Pn differential Gross Section dP do-_-

2→ 2 Scatteringstress

Mass m,

KA + RB -」 p、tpzo-massmz.CM( Center of Mass Iframe

IKA + KB = Q = Im + P2

EA + EB - E cm = E、 t Ez

Sd た lps = S !器。言っ!寄った。

x 1翃484( Rat RB - Pi - P2 )Integration is

Pz - = p。 → - py'

L、 興

に邳 店、主になり SCEcm- E 、一旦)

は「2

⇒前でFiIm = dが がた= an /器。 I 8( Ecm-Et -ED

4E 、 Ez

い、嚴亹っい

咠 +然Ez

Page 5: Aito/qft1-2020_14.pdfField Theory I Aug 7 2020 Lecture 14 cross Section Is the Scattering Process 2 → m k A tkB-tpnt.it pm k A-_-* 7 P 2 が Pn differential Gross Section dP do-_-

Sd T.ms = dr 高2 貴の

NA - NB 1 - 1器 ・ 劇T.im (新高 )

-1割が誌。器が-

• Computation of invariant matrix element M

で の藿 )〈 p、 一 pn li T 1 km KB >

の o 卬が 、 pnl Texp { ij Hitsdtllkn.tn"

T( 1 - で Idt Hilti )-

Page 6: Aito/qft1-2020_14.pdfField Theory I Aug 7 2020 Lecture 14 cross Section Is the Scattering Process 2 → m k A tkB-tpnt.it pm k A-_-* 7 P 2 が Pn differential Gross Section dP do-_-

. 0 4 - theoryL = 主 が 4 2µ 4- Im2 _た 4 4

2→ 2 Scattering

PA + PB -) Pttp 。

S = 1 ti Tmn

OGR, 1Pz 1 PA , pDo =

EEREzteo-p.co/a,azafajllD=2EA2EB12lTf(STPA-lPD8( PB - P2)

t ( PA - 肌) 83( PB - PD )

Reino PA Player PA/

Pz- PB pz PB

no interaction

Hut) = ft (な いっ)

Page 7: Aito/qft1-2020_14.pdfField Theory I Aug 7 2020 Lecture 14 cross Section Is the Scattering Process 2 → m k A tkB-tpnt.it pm k A-_-* 7 P 2 が Pn differential Gross Section dP do-_-

•o くかに 1 -等で4×4でしかIIPA.ppo.tl/DlPo=f器。高.am で

""FE.ph

= 1器3動が"嘨峪では脇

= e- iは 1

- .9 1の IP = e

- i P で 1 0> feet

GTEy = Cole は北 ←(p

• discourse cted diagram

aan Et Film .が -8※=たきか• Self - interaction in external Linesor mosso -0_cpi.IR144041 IPA 、 PB > en -tert た がredef initionot Ware functions

or Mass

Page 8: Aito/qft1-2020_14.pdfField Theory I Aug 7 2020 Lecture 14 cross Section Is the Scattering Process 2 → m k A tkB-tpnt.it pm k A-_-* 7 P 2 が Pn differential Gross Section dP do-_-

Connected diagramo.name rtti ※2

cm 、 pz 1 4444 IIDA i PB) 通金。

ITETてていた fd4の Cm、 肌 14444 TPA 、 PB7

= 岩 に裟 ) fd4xetimxtipza-ipnx.ip.scns

= i 12た)4841 PHP2 - PA - PB) の

imtitp

(劉i 齒.int

=惶m = 器嵪

Page 9: Aito/qft1-2020_14.pdfField Theory I Aug 7 2020 Lecture 14 cross Section Is the Scattering Process 2 → m k A tkB-tpnt.it pm k A-_-* 7 P 2 が Pn differential Gross Section dP do-_-

• 4 3 - theory

の 一言 が42µg _ しか 一言 43

2 一つ 2 Scattering k 、 tkz-skftk.dk、

鸝機で讝に鍵を なkz だ だ

た、 -

ein- i [ ,

2話なt嵓だが㝡翃

Mandel stands variables

S = 1 hitkz )2

= 1 2 E)2

← totalwy

t = は、一 ki )

2= 2 m

2- 2ET 21には1

)Scatteringand

U = は、一 kd)

2= 2 m

2- 2E

2-2

k.lk/oeStttu=4m29hom・ In CM frume M = 1E.lk?kz=lE,-k)k/=1E!lN),kd=1E

、-1たり

Page 10: Aito/qft1-2020_14.pdfField Theory I Aug 7 2020 Lecture 14 cross Section Is the Scattering Process 2 → m k A tkB-tpnt.it pm k A-_-* 7 P 2 が Pn differential Gross Section dP do-_-

im = g2 [言いたい高2 ]

笹谷 窹 1MI2

%器。[ 高い高い高 ]

2

2

讝洗点が した恭尼磯

のは = 一 [ Srednicki is text ]