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Dieter Schildknecht

Publications and source records attributed to Dieter Schildknecht.

At least 19 recordsLinked to original sources
arXiv2026

Photoabsorption cross section in the low-$x$ and low-$Q^2$ domain, and DGLAP evolution

The behavior of the gluon distribution of the proton in the low-$x$, low-$Q^2$ domain of deep inelastic electron-proton scattering (DIS) is being investigated. By considering two-gluon exchange as the dominant interaction in the low-$x$, low-$Q^2$ domain, we imply the well-known result of scaling of the photoabsorption cross section in terms of the scaling variable $η(W^2,Q^2)$. From this, we derive a reliable result for the gluon distribution at the leading order of the perturbative QCD improved parton model, based on evolution from a starting scale of $Q_0^2\cong 2$ GeV$^2$. The validity of evolution, when considering its quantitative modification at low-$Q^2$ without any alteration at larger values of $Q^2$, leads to a quantitative improvement in the extraction of the gluon distribution based on evolution from a starting scale of $Q^2$ conventionally chosen as $Q^2= Q_0^2\cong 2$ GeV$^2$.

hep-ph↗
arXiv2023

The Proton Gluon Distribution from the Color Dipole Picture

Employing the representation of the experimental data on deep inelastic electron-proton scattering (DIS) in the color-dipole picture (CDP), we determine the gluon distribution of the proton at small Bjorken $x$. At sufficiently large momentum transfer, $Q^2$, the extracted gluon distribution fulfills the standard evolution equation for the proton structure function. For low values of $Q^2$, e.g. for $Q^2 = 1.9 {\rm GeV}^2$, the evolution equation for the proton structure function is violated. The standard procedure of adopting a low-$Q^2$ starting scale for the extraction of the gluon density is questionable and requires further investigations.

hep-ph↗
arXiv2021

Color-Dipole Picture versus Hard Pomeron in Deep Inelastic Scattering

For photon virtualities of $Q^2 \gsim 20 {\rm GeV}^2$, the results of the (hard Pomeron) fit in the tensor-Pomeron model in terms of the variables $Q^2$ and the virtual-photon-proton energy squared, $W^2$, provide empirical evidence for the validity of the Color Dipole Picture (CDP). Consistency of the CDP with the perturbative QCD (pQCD) improved parton model implies the prediction of $C_2 = ε_0 \cong 0.30$ for the exponent $C_2$ of the energy-squared dependence in agreement with the results of the fits. For $Q^2 \lsim 20 GeV^2$, the CDP yields a parameter-free smooth transition from $Q^2 \gsim 20 {\rm GeV}^2$ to $Q^2 = 0$ photoproduction, in distinction from the tensor-Pomeron model that relies on the additional parameter quantifying the intercept of the soft-Pomeron trajectory.

hep-ph↗
arXiv2020

Saturation of the Infrared Absorption by Carbon Dioxide in the Atmosphere

Based on new radiative transfer numerical evaluations, we reconsider an argument presented by Schack in 1972 that says that saturation of the absorption of infrared radiation by carbon dioxide in the atmosphere sets in as soon as the relative concentration of carbon dioxide exceeds a lower limit of approximately 300 ppm. We provide a concise brief and explicit representation of the greenhouse effect of the earth's atmosphere. We find an equilibrium climate sensitivity (temperature increase $ΔT$ due to doubling of atmospheric $CO_2$ concentration) of $ΔT \simeq 0.5 ^0C$. We elaborate on the consistency of these results on $ΔT$ with results observationally obtained by satellite-based measurements of short-time radiation-flux versus surface-temperature changes.

physics.ao-ph↗
arXiv2016

On the Color Dipole Picture

We give a brief representation of the theoretical results from the color dipole picture, covering the total photoabsorption cross section, high-energy $J/ψ$ photoproduction with respect to recent experimental data from the LHCb Collaboration at CERN, and ultra-high energy neutrino scattering, relevant for the ICE-CUBE experiment.

hep-ph↗
arXiv2016

Color Dipole Picture of Deep Inelastic Scattering, Revisited

Based upon the color-dipole picture, we provide closed analytic expressions for the longitudinal and the transverse photoabsorption cross sections at low values of the Bjorken variable of x<0.1. We compare with the experimental data for the longitudinal-to-transverse ratio of the (virtual) photoabsorption cross section and with our previous fit to the experimental data for the total photoabsorption cross section. Scaling in terms of the low-x scaling variable eta(W^2,Q^2) is analyzed in terms of the reduced cross section of deep inelastic scattering.

hep-ph↗
arXiv2014

Problems with Ultrahigh-energy Neutrino Interactions

The IceCube collaboration has recently identified events due to ultrahigh-energy neutrino interactions. Predictions of the neutrino-nucleon cross section at ultrahigh energies require a huge extrapolation of the cross sections experimentally measured at laboratory energies. Upon relating neutrino scattering to deep inelastic electron scattering, we show that the empirically verified color dipole picture is well suited for such an extrapolation. The dominant contribution to the total neutrino-nucleon cross section, even at ultrahigh energies, is due to the kinematic range where color transparency is valid for the color dipole interaction. We deviate from various claims in the literature on the presence of screening effects due to non-linear evolution at ultrahigh neutrino energies.

hep-ph↗
arXiv2013

On Ultrahigh-energy Neutrino Scattering

We predict the neutrino-nucleon cross section at ultrahigh energies relevant in connection with the search for high-energy cosmic neutrinos. Our investigation, employing the color-dipole picture, among other things allows us to quantitatively determine which fraction of the ultrahigh-energy neutrino-nucleon cross section stems from the saturation versus the color-transparency region. We disagree with various results in the literature that predict a strong suppression of the neutrino-nucleon cross section at neutrino energies above $E \cong 10^9 GeV$. Suppression in the sense of a diminished increase of the neutrino-nucleon cross section with energy only starts to occur at neutrino energies beyond $E \cong 10^{14} GeV$.

hep-ph↗
arXiv2012

Color Transparency and Saturation in QCD

We review the theoretical interpretation of deep-inelastic electron-proton scattering at low values of the Bjorken variable $x \simeq Q^2/W^2 \lsim 0.1$. The process proceeds via the interaction of quark-antiquark $(q \bar q)$ color-dipole fluctuations of the (virtual) photon with the proton. In terms of the forward Compton scattering amplitude, two reaction channels contribute to the interaction of the $q \bar q$ color dipole with the gluon field in the proton. Dependent on the kinematics, there is either {\it color transparency}, corresponding to a cancellation of the amplitudes for the two reaction channels, or {\it saturation}, occuring when the process is dominated by a single interaction channel. The connection between the color-dipole picture and the pQCD improved parton model is elaborated upon.

hep-ph↗
arXiv2012

Comment on "The New F_L Measurement from HERA and the Dipole Model"

The upper bound on the ratio of the proton structure functions $F_L/F_2$ tested in the recent paper "The New $F_L$ Measurement from HERA and the Dipole Model", contrary to what is said therein, does not provide a model-independent "rigorous" experimental test of the color-dipole picture. The validity of the theoretical upper bound depends on an ad hoc assumption on the dipole cross section. -- The analysis in the paper "The New $F_L$ Measurement from HERA and the Dipole Model" can be reinterpreted as an additional confirmation of the absolute model-independent prediction from the color-dipole picture of $F_L = 0.27 F_2$.

hep-ph↗
arXiv2011

The color dipole picture of low-x DIS

Deep inelastic electron scattering (DIS) from nucleons at low values of the Bjorken variable $x \cong Q^2/W^2 \lsim ~ 0.1$ proceeds via fluctuations of the photon into quark-antiquark dipole states that subsequently interact with the gluon field in the nucleon. Dependent on the interaction energy, $W$, the color-gauge-invariant dipole interaction with the gluon field in the nucleon, for any fixed dipole size, contains the limits of i) color transparency and ii) saturation, where "saturation" stands for the approach to a hadronlike dipole-proton interaction cross section. All essential features of the experimental results on low-x DIS, as a consequence of the color-gauge-invariant dipole interaction follow model independently i.e. without specific ansatz for the dipole cross section. The model-independent results in particular include the low-x scaling behavior of the photoabsorption cross section, $σ_{γ^*p} (W^2,Q^2) = σ_{γ^*p} (η(W^2,Q^2))$, with definite functional dependence on the low-x scaling variable $η(W^2,Q^2) \cong Q^2/Λ^2_{sat} (W^2)$ in the limits of $η(W^2,Q^2) \gg 1$ and $η(W^2,Q^2) \ll 1$, respectively. Consistency with the pQCD-improved parton model implies the definite value of $C_2 \cong 0.29$ for the exponent in the "saturation scale", $Λ^2_{sat} (W^2) \approx (W^2)^{C_2}$. The longitudinal-to-transverse ratio of the photoabsorption cross section at large $Q^2$ has the definite value of $R = 1/2 ρ$ with $ρ= 4/3$. For $W^2 \to \infty$ at any fixed $Q^2$, the photoabsorption cross section converges towards a $Q^2$-independent saturation limit that coincides with the cross section for $Q^2 = 0$ photoproduction.

hep-ph↗
arXiv2011

The Color Dipole Picture of low-x DIS: Model-Independent and Model-Dependent Results

We present a detailed examination of the color-dipole picture (CDP) of low-$x$ deep inelastic scattering. We discriminate model-independent results, not depending on a specific parameterization of the dipole cross section, from model-dependent ones. The model-independent results include the ratio of the longitudinal to the transverse photoabsorption cross section at large $Q^2$, or equivalently the ratio of the longitudinal to the unpolarized proton structure function, $F_L (x,Q^2)=0.27 F_2 (x, Q^2)$, as well as the low-$x$ scaling behavior of the total photoabsorption cross section $σ_{γ^*p} (W^2, Q^2)=σ_{γ^*p} (η(W^2, Q^2))$ as $\log (1 / η(W^2, Q^2))$ for $η(W^2, Q^2) <1$, and as $1/η(W^2, Q^2)$ for $η(W^2, Q^2) \gg 1$. Here, $η(W^2, Q^2)$ denotes the low-$x$ scaling variable, $η(W^2, Q^2)=(Q^2 + m^2_0) / Λ^2_{sat} (W^2)$ with $Λ^2_{sat} (W^2)$ being the saturation scale. The model-independent analysis also implies $\lim\limits_{W^2\rightarrow\infty, Q^2 {\rm fixed}} σ_{γ^*p} (W^2, Q^2) / σ_{γp} (W^2) \rightarrow 1$ at any $Q^2$ for asymptotically large energy, $W$. Consistency with pQCD evolution determines the underlying gluon distribution and the numerical value of $C_2 = 0.29$ in the expression for the saturation scale, $Λ^2 (W^2) \sim (W^2)^{C_2}$. In the model-dependent analysis, by restricting the mass of the actively contributing $q \bar q$ fluctuations by an energy-dependent upper bound, we extend the validity of the color-dipole picture to $x \cong Q^2 / W^2 \le 0.1$. The theoretical results agree with the world data on DIS for $0.036 {\rm GeV}^2 \le Q^2 \le 316 {\rm GeV}^2$.

hep-ph↗
arXiv2011

Perturbative QCD Evolution and Color Dipole Picture

The proton structure function in the diffraction region of small Bjorken-$x$ and $10 {\rm GeV}^2 \le Q^2 \le 100 {\rm GeV}^2$ behaves as $F_2 (x, Q^2) = F_2 (W^2) = f_0 \cdot (W^2)^{C_2}$, where $x = Q^2 / W^2$. The exponent $C_2$ of the $γ^* p$ center-of-mass energy squared, $W^2$, is predicted from evolution of the flavor-singlet quark distribution, $C_2 = 0.29$, and the only free parameter, the normalization $f_0 = 0.063$, is fitted. The evolution of the gluon density multiplied by $α_s (Q^2)$ is dentical to the evolution of the flavor-singlet quark density. This simple picture is at variance with the standard approach to evolution based on the coupled equations of flavor-singlet and gluon density.

hep-ph↗
arXiv2009

The Color-dipole Picture and FL

The prediction of FL(x,Q2)=0.27F2(x,Q2) in the color-dipole picture based on color-transparency and transverse-size reduction, is consistent with the experimental results from HERA.

hep-ph↗
arXiv2008

The Color Dipole Picture and the Ratio of the Longitudinal to the Transverse Photoabsorption Cross Section

The transverse size of q q-bar fluctuations of a longitudinally polarized photon is reduced relative to the transerve size of q q-bar fluctuation of a transversely polarized photon. This implies a model-independent prediction of the ratio R(W2,Q2)=sigma_L/sigma_T=0.375, or, equivalently, F_L/F_2=0.27, for x=Q2/W2<<1 and Q2 sufficiently large, while R(W2,Q2)=0.50, if this effect is ignored. Experimental data from HERA confirm the transverse-size reduction.

hep-ph↗