lhc実験での2光子生成の イベントジェネレータを...
TRANSCRIPT
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
イベントジェネレータは必須Gr@ppa arXiv:1201.5702
GRACE
Userinput
TheorymodelfileDiagram generator
amplitude generator
LibraryCHANEL, loop
Kinematics library
kinematics code
generated code
diagram description
convergence information
Make file etc.
symbolic codeREDUCE, Form etc.
PS file
Drawer
BASES(MC integral)
SPRING (EG manager)
parameter file
Diagrams
(figure)
EventsCross sections
distributions
TREELOOP
FORTRAN code
.fin .mdl .rin
Overview of GRACE system
Userinput
TheorymodelfileDiagram generator
amplitude generator
LibraryCHANEL, loop
Kinematics library
kinematics code
generated code
diagram description
convergence information
Make file etc.
symbolic codeREDUCE, Form etc.
PS file
Drawer
BASES(MC integral)
SPRING (EG manager)
parameter file
Diagrams
(figure)
EventsCross sections
distributions
TREELOOP
FORTRAN code
.fin .mdl .rin
Overview of GRACE system%%%%%%%%%%%%%
Model="sm.mdl"Process;
ELWK={2,2}; QCD ={0,2};
Kinem="2201";-----------------------------
Initial={u, u-bar};------------------------------------- Final ={photon,photon};
Userinput
TheorymodelfileDiagram generator
amplitude generator
LibraryCHANEL, loop
Kinematics library
kinematics code
generated code
diagram description
convergence information
Make file etc.
symbolic codeREDUCE, Form etc.
PS file
Drawer
BASES(MC integral)
SPRING (EG manager)
parameter file
Diagrams
(figure)
EventsCross sections
distributions
TREELOOP
FORTRAN code
.fin .mdl .rin
Overview of GRACE system
Overview of event generator
p
p
i
j
fi(x1)
fj(x2)�ij
parton shower
hadronization
Overview of event generator
p
p
i
j
fi(x1)
fj(x2)�ij
parton shower
hadronizationGrace
Gr@ppaInterface Interface(PYTHIA)
d�(pp� X) =�
ij
�dx1dx2fi(x1, µF )fj(x2, µF )d�(ij � X, x1, x2, µF )
i,j ->quark or gluon f : Parton Distribution Functions(PDF)
(x : fraction of momentum carried by parton )
:partonic cross section
: factorization scale.
�ij
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
Fully exclusive 実験屋さんの好きなcut
SHERPADiphoxResbos
(exclusiveだけどloopなし)(loopありだけどinclusive)
Loop補正も入れたい
arXiv:0811.4622
arXiv:9911.340
arXiv:0704.0001
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
非摂動まで含めた効果
たくさんのdiagramLoop ライブラリ
Soft/Collinear singularity
FragmentationParton shower
GRACE1-loop ◯ 2-loop ×
collinear approximation
尾高さんの話
Double counting LL-subtraction
NLO Cross section
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
�s �s
�NLO =��Tree + �virtual
Matrix element:Tree
�(1, 2� 1, 2, · · · , n, n + 1)
�(1, 2� 1, 2, · · · , n)
Tree cross section:Born:Real radiation
�Born =
�Real =
�Real = �soft + �collinear + �hard(If massless particle)
21
Soft/Collinear correction (final color)
Two types of div.● Collinear div.● Soft div.
Lorentz inv./Process indep. ● Phase space slicing● Subtraction● Slicing/LLL-Subtraction
hybridsoft region
Q2c :hard scattering scale
, はGRACE�Born �hard
Phase spaceを分解
Soft/Collinear corrections2pi · pg = 2EiEg(1� � cos �ig)
:Soft singularities :Collinear singularities(massless-> )Eg � 0
� = 1cos �ig = 1
Soft Part
dPS2+g � dPS2dPSg
|Areal1 (ij � 2 + g)|2 � Feik|A0|2
the eikonal factor contains the soft pole
d�soft = dPS2
�
softdPSgFelk|A0|2
Feik = ��sCF
�
�Q2c
µ2F
���Q2c
s
��� 1�2� �2
4
�Feik
Soft/Collinear correctionsCollinear Part
p zp
(1-z)p
dPS2+g � dPS2(1� z)dPSg
|Areal1 (ij � 2 + g)|2 � Pii�(z)
(1� z)pi · pg|A0|2
DGLAP equation
d�Collinear = dPS2
�
colldPSg
Pii�
pi · pg|A0|2
A0(s)� A0(z · s)
logの近似では不十分non-logの効果まで入れる k2
�s
Matrix element:LoopLoop cross section
�virtual = �(1, 2� 1, 2, · · · , n) :Virtual corrections
Effective vertex(3点関数まで)
=5�
i
ii� 1
Box,Pentagon
+ �D = 6� 2�
Bern-Dixon-Kosower(94)
Infrared safety
発散はBornで分けられる
=�(�soft + �collinear)�Born + �hard + �virtual
=��soft + �collinear + �hard + �virtual
��NLO =��Real + �virtual
1�
�s
2�Pii�
1�,
1�2
are caneled
Q2cHardとSoft/Collinearを切り分ける 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)
赤外発散やQc,factorization scaleScheme dependenceはない
HARD SOF/COL/Vir sum
10^-4*√s’
10^-3*√s’
10^-2*√s’
10^-1*√s’
10^0*√s’
1200.1 -1145.2 54.9
788.9 -733.9 55.0
463.1 -408.0 55.1
223.5 -168.4 55.1
77.1 -22.2 54.9-1500
-1125
-750
-375
0
375
750
1125
1500
10^-4 10^-3 10^-2 10^-1 10^0
HARD(GRC) SOF/COL/Vir sum
E�min = 10GeV
10� < cos �� < 170��
s = 14TeV
Negative weight eventが少なくなるようなpointを探る
Next step
N2LO,N3LOの効果を追加していくUnder development
Future
寄与が大きいかも？(qgが一番大きい)
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
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
TreeのBornやradiativeプロセス ◯