- Email: [email protected]
Photon structure functions with heavy particle mass effects
Available online at www.sciencedirect.com
Nuclear Physics B (Proc. Suppl.) 234 (2013) 70–73 www.elsevier.com/locate/npbps
«
! " # $ %$% &
!"# $ % & ' &
−
$
( ) * + ) + ( ( ! , & - -& - - .!!"#/ & - - .!"#/ %
&
0 - ., 1/ $
. /
. / $ & - .!"#/
- '% (
+
e (e )
0920-5632/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysbps.2012.11.017
‘Probe Photon’ q2=-Q2<0
+ − e (e )
2
2
p =-P <0 ‘Target Photon’
·
. / . 2/ % 31 45 ."#/ & .#67/ 385 & - - . / #67 *
9 .*9/ : : 3;5 - 9< * 3=5 , 6 3>5 $ 3?5 , . / . / "# 3@5 !"# 3A5 - !"#
71
T. Uematsu / Nuclear Physics B (Proc. Suppl.) 234 (2013) 70–73
-$ $ % ' & D 4 1 1 D 4 . 1/. 4/ ; 4 1
; . 1/ . 4/ . 1/. 4/
1 . / ; 4 / ;. / 1 . . / . / 1 . / / 1 . . / . /
.1/
- Æ B - . / -
. / - . /
.8/ , 4 $ 6" #E & 3115 . / . /.84/ . /
. / $ . /
& B . / 3145
«
nf=4, Q2=5 GeV2, P2=0.35 GeV2, Λ=0.2 GeV, mc =1.3 GeV
. /
0.6
0.4
. /
0.2
. 2/ . / .4/ . /
. /
1
. /
1 ; 4 . /
. /
. / 1
. /
4 . / $ C
Æ 14 . /.D / 14
2
.D
/
14 .D /
Massless NLO HQE Resum-HQE Resum-HQE-Exp PLUTO Data
0.8
Feffγ(x,Q2,P2)/α
$ & -4 $ % !"# 3125
1
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
x
« ! " # $% " & '( ) *'( ) *( ) +,
! " " % $
, . 2/ : : + 1 . / . / 3185C
. / 2
.;/
! $ 1 : . /
72
T. Uematsu / Nuclear Physics B (Proc. Suppl.) 234 (2013) 70–73
. / .1/ 1
% - $ ' . / .=/
" % $
% . / % 1 ./ .@/ . / ; 4 , 14 & . / 4; & .A/ & & ! $ - ' C
4; &
.12/
0.5
2
2
Q =20 GeV 2 2 P =0.35GeV nf=4
2
! + F 31;5
% & !"# & - -& - - .!!"#/ . / 8- 4- Æ
31=5 $ # - Æ & ! 1 1 1 1 D 4
. 1/ 1 1
; . 1/ . 1/ .?/
2
0
4
massless
−0.5
with mass effect of charm quark
2
2
. / . / 8
& 1 4 . / . /
. /
. / .>/
γ
g1 (x,Q ,P )/3nf −α ln(Q /P ) π
$ & . / $ .>/ 1 $
:G 31>5 , 8
. / 429F
2 8=9F ; $ $ $ 4 4=9F
2
mc =2.25 GeV
0
2
−1 0.2
0.4
- . *
!
0.5
2
x
0.6
1
0.8
- .
&
Q =120 GeV 2 2 P =3.7GeV nf=5
2
. / 3?5C
2
( )
" *'( )
2
0
4
&
massless
−0.5
with mass effect of bottom quark
2
8
2
. /
1 ; 4 8 & . / .11/
. /
γ
g1 (x,Q ,P )/3nf −α ln(Q /P ) π
0 % $
2
mb =20.25 GeV −1 0
2
0.2
0.4
- . *
!
x
0.6
0.8
- .
'
( )
1
"
*/( )
73
T. Uematsu / Nuclear Physics B (Proc. Suppl.) 234 (2013) 70–73
! . / . / $ F $ $
, ; 1429F 8 ?9F = $
$ $ 42 4=9F & .11>/& .+/ & $ $ $ 31?5 , + .6,E/ 9"B6 $ $ 6, . $ $ / :
6, : H % , =
. / 2 1.1 ; / 3.5
Q2=(1000)2 GeV2, P2=(10)2 GeV2, msquark=300 GeV, mgluino=700 GeV
2.5
#
.+/ 0 % $ I
% &
. /
$ 7&
$ % 6 + !
&
+ " )* #
%&& ,%
%& %
%&
2*4 3
+ '# " # '0
%&% 11
%, &%
%% , %%% 7 " # $ %, 1 " )* #
%, %
1 5 + " # '0 & ( 6 4 " # '0 , %
2
7 8 ( " (6 4" " #
γ
F 2/α
! " # $
' $ (#" )* #
- . - / . " # '0
Massless QCD Massless SQCD Massive QCD with Threshold Massive SQCD with Threshold (quark) Massive SQCD with Threshold (squark) Massive SQCD with Threshold (total)
3
& + B % - &
-++( ++( +
1.5
77% 77%9 # '0
: . " # $
77 7&7%
%, %
8 ( " ' 6 " " + # /
1
77 %%%
6 ; . " 6 / . 4# < 6* " # $
0.5
%%, & 6 ) "2 6 2 =5 " )* #
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Bjorken x
- . 0 0 ! +1,
#
% -
%% 1% ( 6 4" " # '0
771
7%7 1 " >> & 8 ( " 8 8 " ' 6 " # '0
7 7&7
, ' 6 " 8 ( " # $ 7 &
Nuclear Physics B (Proc. Suppl.) 234 (2013) 70–73 www.elsevier.com/locate/npbps
«
! " # $ %$% &
!"# $ % & ' &
−
$
( ) * + ) + ( ( ! , & - -& - - .!!"#/ & - - .!"#/ %
&
0 - ., 1/ $
. /
. / $ & - .!"#/
- '% (
+
e (e )
0920-5632/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysbps.2012.11.017
‘Probe Photon’ q2=-Q2<0
+ − e (e )
2
2
p =-P <0 ‘Target Photon’
·
. / . 2/ % 31 45 ."#/ & .#67/ 385 & - - . / #67 *
9 .*9/ : : 3;5 - 9< * 3=5 , 6 3>5 $ 3?5 , . / . / "# 3@5 !"# 3A5 - !"#
71
T. Uematsu / Nuclear Physics B (Proc. Suppl.) 234 (2013) 70–73
-$ $ % ' & D 4 1 1 D 4 . 1/. 4/ ; 4 1
; . 1/ . 4/ . 1/. 4/
1 . / ; 4 / ;. / 1 . . / . / 1 . / / 1 . . / . /
.1/
- Æ B - . / -
. / - . /
.8/ , 4 $ 6" #E & 3115 . / . /.84/ . /
. / $ . /
& B . / 3145
«
nf=4, Q2=5 GeV2, P2=0.35 GeV2, Λ=0.2 GeV, mc =1.3 GeV
. /
0.6
0.4
. /
0.2
. 2/ . / .4/ . /
. /
1
. /
1 ; 4 . /
. /
. / 1
. /
4 . / $ C
Æ 14 . /.D / 14
2
.D
/
14 .D /
Massless NLO HQE Resum-HQE Resum-HQE-Exp PLUTO Data
0.8
Feffγ(x,Q2,P2)/α
$ & -4 $ % !"# 3125
1
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
x
« ! " # $% " & '( ) *'( ) *( ) +,
! " " % $
, . 2/ : : + 1 . / . / 3185C
. / 2
.;/
! $ 1 : . /
72
T. Uematsu / Nuclear Physics B (Proc. Suppl.) 234 (2013) 70–73
. / .1/ 1
% - $ ' . / .=/
" % $
% . / % 1 ./ .@/ . / ; 4 , 14 & . / 4; & .A/ & & ! $ - ' C
4; &
.12/
0.5
2
2
Q =20 GeV 2 2 P =0.35GeV nf=4
2
! + F 31;5
% & !"# & - -& - - .!!"#/ . / 8- 4- Æ
31=5 $ # - Æ & ! 1 1 1 1 D 4
. 1/ 1 1
; . 1/ . 1/ .?/
2
0
4
massless
−0.5
with mass effect of charm quark
2
2
. / . / 8
& 1 4 . / . /
. /
. / .>/
γ
g1 (x,Q ,P )/3nf
$ & . / $ .>/ 1 $
:G 31>5 , 8
. / 429F
2 8=9F ; $ $ $ 4 4=9F
2
mc =2.25 GeV
0
2
−1 0.2
0.4
- . *
!
0.5
2
x
0.6
1
0.8
- .
&
Q =120 GeV 2 2 P =3.7GeV nf=5
2
. / 3?5C
2
( )
" *'( )
2
0
4
&
massless
−0.5
with mass effect of bottom quark
2
8
2
. /
1 ; 4 8 & . / .11/
. /
γ
g1 (x,Q ,P )/3nf
0 % $
2
mb =20.25 GeV −1 0
2
0.2
0.4
- . *
!
x
0.6
0.8
- .
'
( )
1
"
*/( )
73
T. Uematsu / Nuclear Physics B (Proc. Suppl.) 234 (2013) 70–73
! . / . / $ F $ $
, ; 1429F 8 ?9F = $
$ $ 42 4=9F & .11>/& .+/ & $ $ $ 31?5 , + .6,E/ 9"B6 $ $ 6, . $ $ / :
6, : H % , =
. / 2 1.1 ; / 3.5
Q2=(1000)2 GeV2, P2=(10)2 GeV2, msquark=300 GeV, mgluino=700 GeV
2.5
#
.+/ 0 % $ I
% &
. /
$ 7&
$ % 6 + !
&
+ " )* #
%&& ,%
%& %
%&
2*4 3
+ '# " # '0
%&% 11
%, &%
%% , %%% 7 " # $ %, 1 " )* #
%, %
1 5 + " # '0 & ( 6 4 " # '0 , %
2
7 8 ( " (6 4" " #
γ
F 2/α
! " # $
' $ (#" )* #
- . - / . " # '0
Massless QCD Massless SQCD Massive QCD with Threshold Massive SQCD with Threshold (quark) Massive SQCD with Threshold (squark) Massive SQCD with Threshold (total)
3
& + B % - &
-++( ++( +
1.5
77% 77%9 # '0
: . " # $
77 7&7%
%, %
8 ( " ' 6 " " + # /
1
77 %%%
6 ; . " 6 / . 4# < 6* " # $
0.5
%%, & 6 ) "2 6 2 =5 " )* #
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Bjorken x
- . 0 0 ! +1,
#
% -
%% 1% ( 6 4" " # '0
771
7%7 1 " >> & 8 ( " 8 8 " ' 6 " # '0
7 7&7
, ' 6 " 8 ( " # $ 7 &