Predictions for nuclear PDFs Predictions for impact parameter dependent nuclear PDFs Nuclear diffractive PDFs
Back to V.Guzey at JLab
Overview of the formalism
The leading twist theory of nuclear shadowing enables one to predict the x, Q2, and impact parameter b dependence of sea quark and gluon parton distributions in nuclei [both at the next-to-leading (NLO) and leading orders (LO)].Fortran codes and required data files with grids for nuclear PDFs, impact parameter dependent nuclear PDFs, and diffractive nuclear PDFs can be found following the corresponding links on the left. To summarize our approach, using the formalism outlined below, we predict the sea quark and gluon parton distributions (PDFs) in nuclei in the shadowing region, 10-5 < x < 0.1, at the initial scale Q02=4 GeV2. In this region of small Bjorken x, nuclear PDFs fj/A(x,Q2) (j is the parton flavor) are suppressed compared to the corresponding sum of the PDFs of the free nucleons, fj/N(x,Q2), i.e., fj/A(x,Q2) < A fj/N(x,Q2). This suppression is called nuclear shadowing.
In the interval 0.1 < x < 0.2, nuclear PDFs are enhanced compared to the sum of the free nucleon PDFs -- this is called antishadowing. We assume no antishadowing for the sea quarks; antishadowing for the gluons is modeled on the interval 0.03 < x < 0.1 by requiring the conservation of the momentum sum rule for nuclear PDFs. We do not apply our approach to valence quark nuclear PDFs since nuclear shadowing in the valence channel comes mainly from the interference between the exchanges with the Pomeron and Reggeon quantum numbers and the latter is essentially unknown. Hence, for the valence quark nuclear PDFs, we use the results of the QCD fits from K.J. Eskola, V.J. Kolhinen and P.V. Ruuskanen, "Scale evolution of nuclear parton distributions", Nucl. Phys. B 535 (1998) 351. All this specifies nuclear PDFs at some input scale, Q02 (Q02=4 GeV2 in our case). Predictions for nuclear PDFs for an arbitrary scale Q2 > Q02 are obtained using the usual DGLAP QCD evolution. The leading twist theory of nuclear shadowing is based on the following three ingredients:
- The generalization of the Gribov-Glauber multiple scattering formalism for soft hadron-deuteron scattering to deep inelastic scattering (DIS) with arbitrary nuclei
- QCD factorization theorems (the leading twist approximation) for inclusive DIS and hard diffraction in DIS
- QCD analyses of hard diffraction in ep DIS at HERA.
- the experimental uncertainty (at the level of 15%) in the slope of the t dependence of the ep diffractive structure function, Bdiff
- the uncertainty in the rescattering cross section σsoftj which is needed to model the interaction with N ≥ 3 nucleons of the nucleus.
The corresponding master equation for nuclear PDFs reads:
where Bdiff=6 GeV-2 is the slope of the t dependence of the ep diffractive cross section;
η=0.17 is the ratio of the real to imaginary parts of the ep diffractive amplitude;
fj/ND(3)(β,Q2,xP) is the diffractive parton
distribution function of the proton;
ρA(b,z) is the nuclear density;
b and z are the transverse and longitudinal coordinates of the involved nucleons (b is also the impact parameter);
σsoftj is the effective cross section needed to model
the interaction with N ≥ 3 nucleons of the nucleus.
The impact parameter dependent nuclear PDFs, fj/A(x,Q2,b), can be obtained "for free" from the above master
equation
by not-integrating over the impact parameter b:
where TA(b) is the nuclear optical density.
Fortran codes and required data files with grids for nuclear PDFs, impact parameter dependent nuclear PDFs, and diffractive nuclear PDFs can be found following the corresponding links on the left.