Download presentation

Presentation is loading. Please wait.

Published byAylin Fairbrother Modified over 2 years ago

1
Confronting NLO BFKL Kernels with proton structure function data L. Schoeffel (CEA/SPP) Work done in collaboration with R. Peschanski (CEA/SPhT) and C. Royon (CEA/SPP) hep-ph/0411338 1.Introduction to BFKL equation 2.LO BFKL fit to F2(x,Q²) [H1 data 96/97] 3.NLO case (Kernels + fits) 4.Direct study of the resummation schemes needed in the expression of BFKL Kernels 40th Rencontres de Moriond

2
F2 well described by DGLAP fits What happens if S Ln(Q²/Q 0 ²) << S Ln(1/x) ? => Needs a resummation of S Ln(1/x) to all orders (by keeping the full Q² dependence) => Relax the strong ordering of k T ² => We need an integration over the full k T space xG(x,Q²) = dk T ²/k T ² f(x,k T ²) BFKL equation relates f n and f n-1 (f n = K f n-1 ) => f(x, k T ²) ~ x - k T diffusion term => increase of F2(x,Q²) at low x… ** p Introduction to BFKL equation (in DIS)

3
After a Mellin transform in x and Q², F2 can be written as F2(x,Q²) = d d /(2i )² (Q²/Q 0 ²) x - F2( , ) At LO F2( , ) = H( , ) / [ - LO ( )] with = S 3/ LO ( ) is the BFKL Kernel ~ 1/ + 1/(1- ) For example DGLAP at LO would give ( )~1/ H( , ) is a regular function and the pole contribution = LO ( ) leads to a unique Mellin transform in . Then, a saddle point approx. at low x => L = Ln(Q 2 /Q 0 2 ) et Y = Ln(1/x) F 2 (x,Q 2 ) = N exp{ ½ L+Y LO (½)-½L 2 /(’’ LO (½)Y)} ~ Q/Q 0 x -= (½) F2 expression from the BFKL Kernel at LO Note : c = ½ is the saddle point

4
F 2 (x,Q 2 ) = N exp{ ½ L+Y LO (½)-½L 2 /(’’ LO (½)Y)} ~ Q/Q 0 x -= (½) L = Ln(Q 2 /Q 0 2 ) et Y = Ln(1/x) Very good description of F2 at low x<0.01 with a 3 parameters fit // global QCD fit of H1… We get : Q 0 ² = 0.40 +/- 0.01 GeV² and = 0.09 +/- 0.01 [ = S 3/ ] => Much lower than the typical value expected here ~ 0.25 => Higher orders (NLO) corr. needed with S running (RGE)… Results at LO F2 (measured by H1 96-97 data)

5
Consistency condition at NLO NLO ( , , RGE ) verifies the relation : = p = RGE NLO ( , p, RGE ) // LO condition = LO ( ) Numerically => p ( , RGE ) Then we get : NLO ( , p, RGE ) eff ( , RGE ) BFKL Kernel(s) at NLO Calculations at NLO => singularities => resummation required by consistency with the RGE (different schemes aviable) NLO BFKL Kernels ( , , ) = LO case

6
F 2 (x,Q 2 ) = N exp{ c L+ RGE Y eff ( c, RGE )- ½L 2 /( RGE ’’ eff ( c, RGE )Y)} L = Ln(Q 2 /Q 0 2 ) et Y = Ln(1/x) Saddle point approximation in (// LO case) : with c = saddle such that ’ eff ( c,…) = 0 NLO and LO values of the intercept are compatible For a reasonnable value of RGE Deriving F2(x,Q²) from BFKL at NLO

7
Results at NLO F2 compared with LO predictions and 2 schemes at NLO… Sizeable differences are visible between the two resummation schemes at NLO The LO fit (with 3 param.) gives a much better description than NLO fit (2 param.) for Q²<8.5 GeV² => Pb with the saddle pt approx? => Pb with the NLO Kernels?

8
From F2( ,Q²) = d /(2i ) (Q²/Q0²) f( , ) => ∂lnF 2 (,Q 2 )/∂lnQ 2 = *(,Q 2 ) Then we can determine *(,Q 2 )~ saddle from parametrisations of F2 data(x,Q²) -> F 2 (,Q 2 ) -> saddle Then, we will study the consistency relation = RGE (Q 2 ) NLO ( *(), , RGE ) (reminiscent from the similar relation at LO) Study of the consistency relation at NLO Determination of saddle ( ,Q²)

9
From *(, ) => we determine NLO (*,, RGE ) Consistency relation and verify the relation NLO ( *, , RGE )= / RGE ( ) ? In black : NLO ( *, ,Q²) In Red : / RGE ( ) The consistency relation does not hold exactly BUT NLO ( *, ,Q²) is linear in and does not diverge => spurious singularities properly resummed! (it is not the case for all schemes…) In practice we have : NLO ( *, , RGE ) ~ / OUT Note : Recalculating eff with this relation does not change the results on the F2(x,Q²) fits…

10
Effective approximation of the BFKL Kernels at NLO => 2 parameters formula for F2(x,Q²) at low x<0.01 => Reasonnable description of the F2 data => Sensitivity to the resum. schemes + pb with the 2 lowest Q² bins… Direct studies of the resum. schemes in Mellin space => The consistency relation holds approximately => Discrimination of the different schemes / existence of spurious singularities Further studies : * Beyond the saddle point approximation : unknown aspects of prefactors could play a role (NLO impact factors…) * New resum. schemes… Summary

Similar presentations

OK

Measurement of FL at HERA Have we seen anything beyond (N)NLO DGLAP? AM Cooper-Sarkar for the ZEUS and H1 Collaborations Why measure FL? How to measure.

Measurement of FL at HERA Have we seen anything beyond (N)NLO DGLAP? AM Cooper-Sarkar for the ZEUS and H1 Collaborations Why measure FL? How to measure.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on different occupations in nursing Ppt on save tigers in india download music Ppt on conservation of wildlife and natural vegetation regions Science ppt on crop production and management Ppt on power grid failure in india 2012 full Ppt on intelligent manufacturing ppt Led based message display ppt online Ppt on magnetism and matter class 12 Ppt on ip address classes and special ip Ppt on kpo and bpo