Factorization of soft j's
Transcript of Factorization of soft j's
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Soft Collinear EffectiveTheory Scot
Bauer Fleming Pirjol Stewart Zoo o
Outline
Lecture b
Introduction
Soft EffectiveTheory
Factorization of soft j's in QED
lecture 2
Momentum regions in the
Sudekou form factor
Soft Collinear EffectiveTheory
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Lecture 3
vector current in SCET
Factorization of Sudoku FF
PDF factorization in Dhs
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Soft Collinear Effective Theory
On Monday we obtained the factorization
theorem4 Es
T H Ime Efts4
in meggine QED In QCD and messless
QED often also the collinear region is
relevant Factorization then takes the
schematic form Q2 pj 77 5et e
r HCQ Tfp Tfp 545
with A s P5pE p I see later
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An important complication is that
we encounter aw interplay of two
low energy regionsAs in the QED case
we'll construct the EFT by expanding
full theory diagrams The appropriate
tool is the method of regions Beneke
Smirnov 97 for loop phasespaceintegrals
a Expand integrand in relevant
momentum regions
b Integrate over the full momentum
space fddle
c Add up the different contributions
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Will illustrate this for Sudakou form
factor and then construct Leff
with field for the different regions
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Method of regions for the Sudakou
form factor
A
Q2 Ip e5
P2 P2 L e e
v P2 Cs Q2
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uh It o o 1 a PIpo
him 1 o O 1 Effo
ht O IZ e O Tr h 2
Mh h
gm h 9 Iz t n g g t of
check h g EX t h g1
TO
yds V
m a9 t g I t 9 s
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g 29 9 t 95
h g ii gZhi 2
4t 94
LnL
Expansion parametera n Pyon Toi
O 1
p2 R2 Q ni p n p t PI
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Seahingighn g
ti g 91
pn f X 1 d Q
e n l s d d Q
Loop momentum
herd 1h K f I I 1 Q
coli K k f it 1 d Qto pre
coli re kn f 1 A X Q
folk
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soft r s Kh f it d d Q
alewter kn n f N N R Q
fddk n
gAd fork u
o
k Ak
I f da k1
15 Ktp Lte2
Expand in eed region
hard I k t p 5 k t p I toldtete f k te I t 01117
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courcy Ik tp j I Ktp 5 weep
late 2K et t old
coli E Ktp 2 Ktp told
k e2
ho exp
soft is Ktp p t 2p letd p
T d
oras
k e 2 e t 2kt k
1 o dB
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The expanded loop integrals are
Kt et T k Il l
mQ2
T coli Seele
ai Er EpQ2
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I
sit
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Effective Lagrangian
4 Ye t Ye t 4s
An A t AE t Ai
Saling of fieldse b
L ol T thx Ar o to 7
ik x
f DI e f g t34UT
in Aa Krh As I As A J n M A M
n Ac in Ae AE r f d I d
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Lol ex Is 1 x o i
sa ei
i
TA4
at RG
4g A 3
Collinear quarks
k e k w I t k I f t kiar to d
Ye e t ye Pt http 4
Pt 4 p 4
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I
Pf Pf I
P t P I
T 4 KYI23
1,1 2yL
Lo I T Six 370 I 07K I
Sg ei
4 X EfT
K ft t kiar a A
X 4 I d
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B 3 a R
tf e 12
Insert into QCD action
Jaa Ss t Se t Se
t Se st
Ss fd4x Ig IDs 4g testT p T T
5 as a as
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So fd4X I 3 a tile
in Do t i ri De4g ti J
3 e t ya
fd9x Ic in Dc 23 e t I ii De 4
JaiDls yet ifi 3
Shift
he yo HIaDk e
R Q
Le 3 Elin Dot IDs zi0D3
icE in
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Tdet