Resummation of Large Logs in DIS at x->1. Xiangdong Ji University of Maryland. SCET workshop, University of Arizona, March 2-4, 2006. Outline. Introduction to DIS at large x and resummation of large logarithms Resummation to N 3 LL in the standard and EFT approaches
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Large Logs in DIS at x->1
University of Maryland
SCET workshop, University of Arizona, March 2-4, 2006
f is the parton distribution function, nonperturbative
C is the coefficient function, a power series in coupling αs
A resummation is needed to get reliable predictions
The expansion parameter is αsln2N!
The expansion parameter is now αslnN!
where =0αslnN. The expansion is now in αs
A is the anomalous dimension of a Wilson-line cusp A= αsn An
B is a perturbation series B= αsn Bn which can be extracted
from fixed order calculation
LL: A1 NLL: A1,A2,B1
N2LL: A1-A3,B1,B2 N3LL: A1-A4,B1-B3
Up to N3LL, all are known except A4
Q2 (1-x) by RG running of the effective current
Where B is the related to the coefficient of the delta
function in the anomalous dimension
where the logarithms of type lnQ/N has been set to zero
some additional manipulation shows the full equivalence with the traditional approach.
In principle, this is not a problem because there is no proof that the DIS in this region is factorizable.
Soft contribution is at scale Q(1-x) and is non-perturbative.
A different factorization and hence the resumed perturbative part is different from the usual coefficient function.
Chay & Kim
There is no room for the soft contribution
New factorization beyond the usual pQCD factorization?
Explicit calculation shows that the soft factor has no infrared divergence and lives in the scale Q(1-x) which is on the order of ΛQCD Only in that sense the soft factor is non-perturbative!
Large double logs
Large double logs