Abstract
We discuss unpolarized neutrino- and anti-neutrino-nucleon deep inelastic scattering using a chiral doublet of baryonic sources with explicit symmetry breaking, in a slice of ${\mathrm{AdS}}_{5}$ with both a hard and soft wall. We explicitly derive the direct and transition form factors for the vector and axial-vector currents for the holographic dual of a proton and neutron. We use them to derive the $s$-channel structure functions for neutrino and antineutrino scattering on a proton and neutron in bulk. The $t$-channel contributions stemming from the Pomeron and Reggeon exchanges are also evaluated explicitly. The pertinent even and odd structure functions in the limit of large and small parton momentum fraction $x$ are given. The results allow for the extraction of the nonperturbative parton distribution functions carried by the sea and valence quarks both at large-$x$ and small-$x$ regimes. Our holographic parton distribution function (PDF) sets compare well with the Les Houches accord PDF (LHAPDF) and the coordinated theoretical-experiment project on QCD (CTEQ) PDF sets in the large-$x$ and small-$x$ regimes in the intermediate range of ${Q}^{2}<10\text{ }\text{ }{\mathrm{GeV}}^{2}$.
Highlights
At extremely low x, the measured nucleon structure functions on unpolarized nucleon targets, show a rapid growth of sea quarks and gluons at low x [1,2]
A central question is this: what is the primary mechanism for the growth of the sea quarks at low x?
II we briefly review the setting for the model with bulk chiral gauge fields and a doublet of Dirac fermions in a slice of AdS5, for both the soft and hard wall
Summary
The measured nucleon structure functions on unpolarized nucleon targets, show a rapid growth of sea quarks and gluons at low x [1,2]. A central question is this: what is the primary mechanism for the growth of the sea quarks at low x?. Deep inelastic scattering (DIS) in holography at moderate x is different from weak coupling as it involves hadronic and not partonic constituents [5]. The large gauge coupling at the low renormalization point, causes the color charges to rapidly deplete their energy and momentum, making them visible to hard probes only through double trace operators.
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