LHC実験での2光子生成のイベントジェネレータを用いての解析 - kek

LHC実験での２光子生成の
イベントジェネレータを用いての解析
渡辺則之、栗原良将、尾高茂(KEK)
日本物理学会秋季大会@京都産業大学, 2012.9.13
Motivation
コライダー実験では新粒子/現象を発見したい
LOからの予測だけでは不十分
NLO,NNLOからのより精度の高い予測が必要
GRACE
イベントジェネレータは必須
Gr@ppa arXiv:1201.5702
Overview of GRACE system
Diagram generator
User
input
.fin .mdl .rin
model
file
Drawer
diagram description
amplitude generator
Kinematics
library
Theory
LOOP
Make
file
etc.
TREE
symbolic code
Diagrams
(figure)
REDUCE, Form etc.
FORTRAN code
kinematics
code
convergence
information
generated code
BASES(MC integral)
Cross sections
distributions
Library
CHANEL, loop
parameter
file
SPRING (EG manager)
Events
PS file
Overview of GRACE system
%%%%%%%%%%%%%
Model="sm.mdl"
Process;
Diagram generator
ELWK={2,2};
QCDUser
={0,2};
diagram description
.fin .mdl .rin
model
file
Drawer
input
Kinem="2201";
----------------------------- amplitude generator
Kinematics
Initial={u, u-bar};
LOOP
library
------------------------------------TREE
symbolic
code
Final ={photon,photon};
Theory
Make
file
etc.
Diagrams
(figure)
REDUCE, Form etc.
FORTRAN code
kinematics
code
convergence
information
generated code
BASES(MC integral)
Cross sections
distributions
Library
CHANEL, loop
parameter
file
SPRING (EG manager)
Events
PS file
Overview of GRACE system
Diagram generator
User
input
.fin .mdl .rin
model
file
Drawer
diagram description
amplitude generator
Kinematics
library
Theory
LOOP
Make
file
etc.
TREE
symbolic code
Diagrams
(figure)
REDUCE, Form etc.
FORTRAN code
kinematics
code
convergence
information
generated code
BASES(MC integral)
Cross sections
distributions
Library
CHANEL, loop
parameter
file
SPRING (EG manager)
Events
PS file
Overview of event generator
fj (x2 )
i
j
ˆij
hadronization
p
fi (x1 )
parton shower
p
Overview of event generator
i
j
fj (x2 )
ˆij
Grace
Interface
d (pp
X) =
Gr@ppa
dx1 dx2 fi (x1 , µF )fj (x2 , µF )dˆ (ij
ij
i,j ->quark or gluon
f : Parton Distribution Functions(PDF)
(x : fraction of momentum carried by parton )
ˆij :partonic cross section
µF : factorization scale.
hadronization
p
fi (x1 )
parton shower
p
Interface
(PYTHIA)
X, x1 , x2 , µF )
作りたいもの
LHC実験では２光子過程はHiggs探索の
重要なチャンネルの一つである
正確なバックグラウンドの評価は重要
qqbar annilation
Compton scattering
Gluon Fusion
SHERPA (exclusiveだけどloopなし) arXiv:0811.4622
Diphox (loopありだけどinclusive) arXiv:9911.340
Resbos
arXiv:0704.0001
Fully exclusive
実験屋さんの好きなcut
Loop補正も入れたい
Difficulties
精度のよいジェネレータを作るためには
高次摂動のpartonic cross section
たくさんのdiagram
Loop ライブラリ
Soft/Collinear singularity
GRACE
1-loop ⃝ 2-loop ×
collinear approximation
非摂動まで含めた効果
Double counting
LL-subtraction
Fragmentation
Parton shower
尾高さんの話
NLO Cross section
N LO =
Tree + virtual
s
PDF
s
紫外発散はMS-barで繰り込み
赤外発散はPDFとの畳み込みで消える
dimensional regularization d=4+2ε
Matrix element:Tree
Tree cross section
Born
=
(1, 2
Real
=
(1, 2
Real
=
soft
Soft/Collinear correct
:Born
1, 2, · · · , n)
1, 2, · · · , n, n + 1)
+
collinear
+
(If massless particle)
:RealTwo
radiation
types of div.
Collinear div.
●
Soft div.
●
hard
Lore
●
Pha
●
Sub
●
Slic
h
Q2c :hard scattering scale
Phase spaceを分解
Born , hard はGRACE
soft region
Soft/Collinear corrections
2pi · pg = 2Ei Eg (1
Eg
cos
cos
ig )
0 :Soft singularities
ig
= 1 :Collinear singularities(massless->
Soft Part
dP S2 dP Sg
dP S2+g
2
2
|Areal
(ij
2
+
g)|
F
|A
|
eik
0
1
the eikonal factor contains the soft pole
d
sof t
= dP S2
sof t
Feik =
s CF
dP Sg Felk |A0 |2
Q2c
µ2F
Q2c
s
1
2
2
4
Feik
=1)
Soft/Collinear corrections
Collinear Part
dP S2+g
|Areal
(ij
1
dP S2 (1
2 + g)|2
z)dP Sg
Pii (z)
|A0 |2
(1 z)pi · pg
DGLAP equation
d
Collinear
= dP S2
p
Pii
dP Sg
|A0 |2
pi · pg
coll
A0 (s)
zp
(1-z)p
logの近似では不十分
non-logの効果まで入れる
k2
sˆ
A0 (z · s)
Matrix element:Loop
Loop cross section
virtual
= (1, 2
1, 2, · · · , n) :Virtual corrections
Effective vertex(3点関数まで)
Box,Pentagon
i
5
=
i
i
1
+
D=6
2
Bern-Dixon-Kosower(94)
Infrared safety
N LO
=
Real
=
soft
= (
+
+
soft
+
PDF
virtual
collinear
+
hard
collinear ) Born
+
+
virtual
hard
+
PDF
virtual
PDF
発散はBornで分けられる
1 1
, 2 are caneled
1
s
2
Pii
2
Q
HardとSoft/Collinearを切り分ける c 依存性
も消えている
Results
今回はqq-bar->γγ+XのNLO(すぐにgr@ppaに実装)
HARD
SOF/COL/Vir
sum
10^-4*√s’
1200.1
-1145.2
54.9
10^-3*√s’
788.9
-733.9
55.0
10^-2*√s’
463.1
-408.0
55.1
10^-1*√s’
223.5
-168.4
55.1
10^0*√s’
77.1
-22.2
54.9
1500
1125
750
375
0
-375
-750
-1125
-1500
10^-4
s = 14TeV
10 < cos < 170
Emin = 10GeV
10^-3
HARD(GRC)
10^-2
SOF/COL/Vir
10^-1
sum
Scheme dependenceはない
赤外発散やQc,factorization scale
Negative weight eventが少なくなるようなpointを探る
10^0
Next step
N2LO,N3LOの効果を追加していく
Under development
寄与が大きいかも？(qgが一番大きい)
Future
最終的にはここまで
Summary
精度のよいイベントを生成するためには
Loopを含む計算は必要
TreeのBornやradiativeプロセス ⃝
精度の良い Soft/Collinear近似 ⃝
qq-barプロセスは1-loopまで含めた(まもなく実装)
qg/ggプロセスなどのloopも入れる必要あり
2-loopライブラリの構築

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