wga theory
DESCRIPTION
WGA Theory. Low x BFKL and DGLAP BK Structure functions Diffraction. BFKL and DGLAP. L.N. Lipatov presented the talk “ DGLAP and BFKL equations in supersymmetric gauge theories ”. - PowerPoint PPT PresentationTRANSCRIPT
DIS’03 St.PetersburgApril 23-27, 2003
V. FadinInstitute of Nuclear Physics, Novosibirsk
WGA TheoryWGA Theory
• Low x BFKL and DGLAP BK • Structure functions • Diffraction
DIS’03 St.PetersburgApril 23-27, 2003
V. FadinInstitute of Nuclear Physics, Novosibirsk
L.N. Lipatov presented the talk
“DGLAP and BFKL equations in supersymmetric gauge theories”.
Next-to-leading corrections to the BFKL kernel and to anomalous dimension matrix in N=4 SUSY are calculated.
The DGLAP equation
The BFKL equation for the gluon distributions at small x
BFKL and DGLAP
DIS’03 St.PetersburgApril 23-27, 2003
V. FadinInstitute of Nuclear Physics, Novosibirsk
The eigenvalues of the kernel
DIS’03 St.PetersburgApril 23-27, 2003
V. FadinInstitute of Nuclear Physics, Novosibirsk
DIS’03 St.PetersburgApril 23-27, 2003
V. FadinInstitute of Nuclear Physics, Novosibirsk
DIS’03 St.PetersburgApril 23-27, 2003
V. FadinInstitute of Nuclear Physics, Novosibirsk
DIS’03 St.PetersburgApril 23-27, 2003
V. FadinInstitute of Nuclear Physics, Novosibirsk
DIS’03 St.PetersburgApril 23-27, 2003
V. FadinInstitute of Nuclear Physics, Novosibirsk
21QQ
2121 ,, kkQQs 2211 QkkQs sQkkQ 2211
’ ’ ’’ ’ ’
0n
),( ),( ),( i 2
ddd
dd
d2221112
2
22
21
12
21
21
kQhkkGkQhs
k
k
k
k
0s
Dmitry Colfefrai
Gluon Evolution at small-x:Gluon Evolution at small-x:Extending the PT Domain of QCDExtending the PT Domain of QCD
DIS’03 St.PetersburgApril 23-27, 2003
V. FadinInstitute of Nuclear Physics, Novosibirsk
)(1
0 )(
AN ggf )(),( fixed 2
2
k
k
s kkK;
210 QQs
reg)0(
2
11 )()()(
123
010
A
K ss
kk
ss
210 Qs
)( 1
1
)()(As
ggs
Scale change: 21
210 QQQs
2
2
1
2
1
1
212
1 k
Q
k
k
Q
k
s
Q
s
22
)( 1 )()( ),(),(
2
2
2
Akk
k
kkk s
LLA
ss
n
n
sG
11
)(1
0
0
)(1
)()0(
2
1
1 2
2
KOAs
h’ h G’ G h’ h
DIS’03 St.PetersburgApril 23-27, 2003
V. FadinInstitute of Nuclear Physics, Novosibirsk
Resummed splitting Resummed splitting functionfunction
is independent of : important check of RG factorization
Evolution eqn.
1
22res2
2
, ),( d
log
),(
x
Qz
xgQzP
z
z
Q
Qxg
2log
02 ),; /1(log d),(
Q
kkxGtQxgxGluon density
effP 0k
)(2res ),( QsczQzP
High-energy exponent c(s)
DIS’03 St.PetersburgApril 23-27, 2003
V. FadinInstitute of Nuclear Physics, Novosibirsk
ConclusionsConclusions
• 2 main problems of high-energy perturbative QCD:– occurrence of large leading log s contributions and of
subleading ones of comparable size and opposite sign– increasing importance of wee partons, whence a strong
coupling non-perturbative Pomeron regime
• RGI approach tames both problems:– through an understanding and consequent resummation of
the most important subleading contributions– Subleading corrections and running coupling effects lower
high-energy exponents and diffusion/tunneling into NP region
• We expect a large domain of applicability of PT QCD• We have the tools to make reliable physical
predictions: *-*, forward jets, Mueller-Navelet jets, …
DIS’03 St.PetersburgApril 23-27, 2003
V. FadinInstitute of Nuclear Physics, Novosibirsk
DIS’03 St.PetersburgApril 23-27, 2003
V. FadinInstitute of Nuclear Physics, Novosibirsk
DIS’03 St.PetersburgApril 23-27, 2003
V. FadinInstitute of Nuclear Physics, Novosibirsk
DIS’03 St.PetersburgApril 23-27, 2003
V. FadinInstitute of Nuclear Physics, Novosibirsk
Improved Small-xEvolution with
Running Coupling Effects
The talk
was presented by Guido Altarelli .
The talk was devoted to construction of a relatively simple, closed form, improved anomalous dimensions I(,N)
DIS’03 St.PetersburgApril 23-27, 2003
V. FadinInstitute of Nuclear Physics, Novosibirsk
It was shown that BFKL with running coupling is fully compatible with RGE ,
factorisation and duality.
In the Airy approximation the splitting functions are completely free of unphysical oscillations.
An improved anomalous dimension that reduces to the perturbative result at large x and incorporates BFKL with running coupling effects at small x was constructed.
The running coupling effects in the LO softens the asymptoticsmall x behaviour as indicated by the data.
DIS’03 St.PetersburgApril 23-27, 2003
V. FadinInstitute of Nuclear Physics, Novosibirsk
Mellin transf. (MT)
Inverse MT (>0)
DIS’03 St.PetersburgApril 23-27, 2003
V. FadinInstitute of Nuclear Physics, Novosibirsk
M
s=0.2
0+21
0
The minimum value of 0 at M=1/2 is theLipatov intercept:
0=0(1/2)=c0= 4nc/log2~2.65~0.5
It corresponds to (for x->0):
xP(x)~x-0 Too hardnot supported by data
DIS’03 St.PetersburgApril 23-27, 2003
V. FadinInstitute of Nuclear Physics, Novosibirsk
The effect of running on in the Airy modelIs a softer small-x behaviour
xP ~ x- xP ~ x-N0
DIS’03 St.PetersburgApril 23-27, 2003
V. FadinInstitute of Nuclear Physics, Novosibirsk
DIS’03 St.PetersburgApril 23-27, 2003
V. FadinInstitute of Nuclear Physics, Novosibirsk
DIS’03 St.PetersburgApril 23-27, 2003
V. FadinInstitute of Nuclear Physics, Novosibirsk
DIS’03 St.PetersburgApril 23-27, 2003
V. FadinInstitute of Nuclear Physics, Novosibirsk
DIS’03 St.PetersburgApril 23-27, 2003
V. FadinInstitute of Nuclear Physics, Novosibirsk
DIS’03 St.PetersburgApril 23-27, 2003
V. FadinInstitute of Nuclear Physics, Novosibirsk
DIS’03 St.PetersburgApril 23-27, 2003
V. FadinInstitute of Nuclear Physics, Novosibirsk
DIS’03 St.PetersburgApril 23-27, 2003
V. FadinInstitute of Nuclear Physics, Novosibirsk
DIS’03 St.PetersburgApril 23-27, 2003
V. FadinInstitute of Nuclear Physics, Novosibirsk
DIS’03 St.PetersburgApril 23-27, 2003
V. FadinInstitute of Nuclear Physics, Novosibirsk
DIS’03 St.PetersburgApril 23-27, 2003
V. FadinInstitute of Nuclear Physics, Novosibirsk
DIS’03 St.PetersburgApril 23-27, 2003
V. FadinInstitute of Nuclear Physics, Novosibirsk
DIS’03 St.PetersburgApril 23-27, 2003
V. FadinInstitute of Nuclear Physics, Novosibirsk