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Register a new userNeutrino-nucleon DIS from Holographic QCD: PDFs of sea and valence quarks, form factors, and structure functions of the proton
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We discuss unpolarized neutrino- and anti-neutrino-nucleon deep inelastic scattering (DIS) using a chiral doublet of baryonic sources with explicit symmetry breaking, in a slice of 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 anti-neutrino 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 nonperterbative parton distribution functions carried by the sea and valence quarks both at large-x and small-x regimes. Our holographic PDF sets compare well with LHAPDF and CTEQ PDF sets in the large-x and small-x regimes in the intermediate range of $Q^2<10~rm{GeV^2}$.
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We present a comprehensive analysis of the spacelike nucleon electromagnetic form factors and their flavor decomposition within the framework of light-front holographic QCD. We show that the inclusion of the higher Fock components $ket {qqqqbar{q}}$ has a significant effect on the spin-flip elastic Pauli form factor and almost zero effect on the spin-conserving Dirac form factor. We present light-front holographic QCD results for the proton and neutron form factors at any momentum transfer range, including asymptotic predictions, and show that our results agree with the available experimental data with high accuracy. In order to correctly describe the Pauli form factor we need an admixture of a five quark state of about 30$%$ in the proton and about 40$%$ in the neutron. We also extract the nucleon charge and magnetic radii and perform a flavor decomposition of the nucleon electromagnetic form factors. The free parameters needed to describe the experimental nucleon form factors are very few: two parameters for the probabilities of higher Fock states for the spin-flip form factor and a phenomenological parameter $r$, required to account for possible SU(6) spin-flavor symmetry breaking effects in the neutron, whereas the Pauli form factors are normalized to the experimental values of the anomalous magnetic moments. The covariant spin structure for the Dirac and Pauli nucleon form factors prescribed by AdS$_5$ semiclassical gravity incorporates the correct twist scaling behavior from hard scattering and also leads to vector dominance at low energy.
We extend the study of lowest moments, $<x>$ and $<x^2>$, of the parton distribution function of the nucleon to include those of the sea quarks; this entails a disconnected insertion calculation in lattice QCD. This is carried out on a $16^3 times 24$ quenched lattice with Wilson fermion. The quark loops are calculated with $Z_2$ noise vectors and unbiased subtractions, and multiple nucleon sources are employed to reduce the statistical errors. We obtain 5$sigma$ signals for $<x>$ for the $u,d,$ and $s$ quarks, but $<x^2>$ is consistent with zero within errors. We provide results for both the connected and disconnected insertions. The perturbatively renormalized $<x>$ for the strange quark at $mu = 2$ GeV is $<x>_{s+bar{s}} = 0.027 pm 0.006$ which is consistent with the experimental result. The ratio of $<x>$ for $s$ vs. $u/d$ in the disconnected insertion with quark loops is calculated to be $0.88 pm 0.07$. This is about twice as large as the phenomenologically fitted $displaystylefrac{< x>_{s+bar{s}}}{< x>_{bar{u}}+< x>_{bar{d}}}$ from experiments where $bar{u}$ and $bar{d}$ include both the connected and disconnected insertion parts. We discuss the source and implication of this difference.
We present the first direct lattice calculation of the isovector sea-quark parton distributions using the formalism developed recently by one of the authors. We use $N_f=2+1+1$ HISQ lattice gauge ensembles (generated by MILC Collaboration) and clover valence fermions with pion mass 310 MeV. We are able to obtain the qualitative features of the nucleon sea flavor structure even at this large pion mass: We observe violation of the Gottfried sum rule, indicating $overline{d}(x) > overline{u}(x)$; the helicity distribution obeys $Delta overline{u}(x) > Delta overline{d}(x)$, which is consistent with the STAR data at large and small leptonic pseudorapidity.
We present a holographic analysis of diffractive photoproducton of charmonium $J/psi$ and upsilonium $Upsilon$ on a proton, considered as a bulk Dirac fermion, for all ranges of $sqrt{s}$, i.e., from near threshold to very high energy. Using the bulk wave functions of the proton and vector mesons, within holographic QCD, and employing Witten diagrams in the bulk, we compute the diffractive photoproduction amplitude of $J/psi$ and $Upsilon$. The holographic amplitude shows elements of the strictures of vector meson dominance (VMD). It is dominated by the exchange of a massive graviton or $2^{++}$ glueball resonances near threshold, and its higher spin-j counterparts that reggeize at higher energies. Both the differential and total cross sections are controlled by the gravitational form factor $A(t)$, and compare well to the recent results reported by the GlueX collaboration near threshold and the world data at large $sqrt{s}$. The holographic gravitational form factors, including the D-term, which is due to the exchange of massive spin-0 glueballs, are in good agreement with lattice simulations. We use it to extract the holographic pressure and shear forces inside the proton. Finally, using a pertinent integral representation of the holographic gravitational form factor $A(t)$ near threshold, and its Pomeron counterpart way above threshold, we extract the generalized parton distribution (GPD) of gluons inside the proton at different resolutions.
We present results for the isovector electromagnetic form factors of the nucleon computed on the CLS ensembles with $N_f=2+1$ flavors of $mathcal{O}(a)$-improved Wilson fermions and an $mathcal{O}(a)$-improved vector current. The analysis includes ensembles with four lattice spacings and pion masses ranging from 130 MeV up to 350 MeV and mainly targets the low-$Q^2$ region. In order to remove any bias from unsuppressed excited-state contributions, we investigate several source-sink separations between 1.0 fm and 1.5 fm and apply the summation method as well as explicit two-state fits. The chiral interpolation is performed by applying covariant chiral perturbation theory including vector mesons directly to our form factor data, thus avoiding an auxiliary parametrization of the $Q^2$ dependence. At the physical point, we obtain $mu=4.71(11)_{mathrm{stat}}(13)_{mathrm{sys}}$ for the nucleon isovector magnetic moment, in good agreement with the experimental value and $langle r_mathrm{M}^2rangle~=~0.661(30)_{mathrm{stat}}(11)_{mathrm{sys}},~mathrm{fm}^2$ for the corresponding square-radius, again in good agreement with the value inferred from the $ep$-scattering determination [Bernauer et~al., Phys. Rev. Lett., 105, 242001 (2010)] of the proton radius. Our estimate for the isovector electric charge radius, $langle r_mathrm{E}^2rangle = 0.800(25)_{mathrm{stat}}(22)_{mathrm{sys}},~mathrm{fm}^2$, however, is in slight tension with the larger value inferred from the aforementioned $ep$-scattering data, while being in agreement with the value derived from the 2018 CODATA average for the proton charge radius.
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