arXiv subjects
Publications and source records attributed to V. R. Zoller.
We show that a growth of the proton-proton total cross section with energy can be entirely attributed to the purely perturbative mechanism. The infrared regularization at rather short distances, $R_c\simeq 0.3$ fm, allows to extend the BFKL technique from deep inelastic to hadron-hadron scattering. With the account of the absorption corrections our results are in agreement with the LHC data on $σ_{tot}^{pp}$.
A model of diffractive neutrino scattering is formulated in terms of the chiral hadronic current which is conserved in the limit of vanishing pion mass. This current has the correct singularity structure and, naturally, does not lead to contradictions with a partial conservation of the axial current (PCAC). In that respect we differ from earlier work in the literature, where a breakdown of PCAC had been reported. We show that such a breakdown of PCAC is an artifact of the hadronic current non-conservation in the model developed there.
A feasible mechanism of unitarization of amplitudes of deep inelastic scattering at small values of Bjorken $x$ is the gluon fusion. However, its efficiency depends crucially on the vacuum color screening effect which accompanies the multiplication and the diffusion of BFKL gluons from small to large distances. From the fits to lattice data on field strength correlators the propagation length of perturbative gluons is $R_c\simeq 0.2-0.3$ fermi. The probability to find a perturbative gluon with short propagation length at large distances is suppressed exponentially. It changes the pattern of (dif)fusion dramatically. The magnitude of the fusion effect appears to be controlled by the new dimensionless parameter $\sim R_c^2/8B$, with the diffraction cone slope $B$ standing for the characteristic size of the interaction region. It should slowly $\propto 1/\ln Q^2$ decrease at large $Q^2$. Smallness of the ratio $R_c^2/8B$ makes the non-linear effects rather weak even at lowest Bjorken $x$ available at HERA. We report the results of our studies of the non-linear BFKL equation which has been generalized to incorporate the running coupling and the screening radius $R_c$ as the infrared regulator.
The perturbative non-linear (NL) effects in the small-$x$ evolution of the gluon densities depend crucially on the infrared (IR) regularization. The IR regulator, $R_c$, is determined by the scale of the non-perturbative fluctuations of QCD vacuum. From the instanton models and from the lattice $R_c\sim 0.3$ fm. For perturbative gluons with the propagation length $R_c= 0.26$ fm the linear BFKL gives a good description of the proton structure function $F_2(x,Q^2)$ in a wide range of $x$ and $Q^2$. The NL effects turn out to be rather weak and amount to the 10% correction to $F_2(x,Q^2)$ for $x\lsim 10^{-5}$. Much more pronounced NL effects were found in the non-linear model, described in the literature, with a very soft IR regularization corresponding to the IR cutoff at $\simeq Λ^{-1}_{QCD}$. The latter issue is also commented below.
We discuss heavy quark contributions to the neutrino-nucleon total cross section at very high energies, well above the real top production threshold. The top-bottom weak current is found to generate strong left-right asymmetry of neutrino-nucleon interactions. We separate contributions of different helicity states and make use of the $\bkappa$-factorization to derive simple and practically useful formulas for the left-handed ($F_L$) and right-handed ($F_R$) components of the conventional structure function $2xF_3=F_L-F_R$ in terms of the integrated gluon density. We show that $F_L\gg F_R$ and, consequently, $xF_3\approx F_T$, where $F_T$ is the transverse structure function. The conventional structure function $F_2=F_S+F_T$ at $Q^2\ll m_t^2$ appears to be dominated by its scalar (also known as longitudinal) component $F_S$ and the hierarchy $F_S\gg F_L\gg F_R$ arises naturally. We evaluate the total neutrino-nucleon cross section at ultra-high energies within the color dipole BFKL formalism.
Currently available estimates of the gluon-fusion effect in ultra-high energy neutrino-nucleon interactions as well as in DIS on protons suffer from uncertainty in defining the scattering profile function $Γ(b)$. Indeed, the area, $S$, in the impact parameter space populated with interacting gluons varies by a factor of $4 - 5$ from one analysis to another. To get rid of uncertainties we specify the dipole-nucleon partial-wave amplitude $Γ(b)$ which meets the restrictions imposed by both the total dipole-nucleon cross section and the small angle elastic scattering amplitude. The area $S$ becomes a well defined quantity proportional to the diffraction cone slope. We solve numerically the non-linear color dipole BFKL equation and evaluate the UHE neutrino-nucleon total cross section. Our finding is that the saturation is a rather weak effect, $\lsim 25%$, up to $E_ν\sim 10^{12}$ GeV.
It is shown that in the ultra-high energy neutrino interactions the higher twist corrections brought about by the non-conservation of the top-bottom current dramatically change the longitudinal structure function, $F_L$. To the Double Leading Log Approximation simple and numerically accurate formulas for $F_L$ and $σ^{νN}$ are derived.
The overall hardness scale of the ultra-high energy neutrino-nucleon interactions is usually estimated as $Q^2\sim m_W^2$. The effect of non-conservation of weak currents pushes this scale up to the top quark mass squared and changes dynamics of the scattering process. The Double Leading Log Approximation provides simple and numerically accurate formula for the top-bottom contribution to the total cross section $σ^{νN}$. Corresponding correction to $σ^{νN}$ appears to be numerically large. It is comparable with the leading contribution evaluated in the massless quark approximation.
The non-conservation of charmed-strange current in the neutrino deep inelastic scattering ($ν$DIS) strongly affects the longitudinal structure function, $F_L$, at small values of Bjorken $x$. The corresponding correction to $F_L$ is a higher twist effect enhanced at small-$x$ by the rapidly growing gluon density factor. As a result, the component of $F_L$ induced by the charmed-strange current prevails over the light-quark component and dominates $F_L=F_L^{cs}+F_L^{ud}$ at $x\lsim 0.01$ and $Q^2\sim m_c^2$. The color dipole analysis clarifies the physics behind the phenomenon and provides a quantitative estimate of the effect.
The asymptotic freedom is known to split the leading-$\log$ BFKL pomeron into a series of isolated poles in the complex angular momentum plane. One of our earlier findings was that the subleading hard BFKL exchanges decouple from such experimentally important observables as small-$x$ charm, $F_2^c$, and the longitudinal, $F_L$, structure functions of the proton at moderately large $Q^2$. For instance, we predicted precocious BFKL asymptotics of $F_2^c(x,Q^2)$ with intercept of the rightmost BFKL pole $α_{\Pom}(0)-1=Δ_{\Pom}\approx 0.4$. On the other hand, the small-$x$ open beauty photo- and electro-production probes the vacuum exchange for much smaller color dipoles which entails significant subleading vacuum pole corrections to the small-$x$ behavior. In view of the accumulation of the experimental data on small-$x$ $F_{2}^{c}$, $F_{2}^{b}$ and $F_{L}$ we extend our early predictions to the kinematical domain covered by new HERA measurements. Our parameter-free results agree well with the determination of $F_2^c$, $F_L$ and published H1 results on $F_2^b$ but slightly overshoot the very recent (2008, preliminary) H1 results on $F_2^b$.
One of the well known effects of the asymptotic freedom is splitting of the leading-$\log$ BFKL pomeron into a series of isolated poles in complex angular momentum plane. Following our earlier works we explore the phenomenological consequences of the emerging BFKL-Regge factorized expansion for the small-$x$ charm ($F_2^c$) and beauty ($F_{2}^{b}$) structure functions of the proton. As we found earlier,the color dipole approach to the BFKL dynamics predicts uniquely decoupling of subleading hard BFKL exchanges from $F_2^c$ at moderately large $Q^{2}$. We predicted precocious BFKL asymptotics of $F_2^c(x,Q^2)$ with intercept of the rightmost BFKL pole $α_{\Pom}(0)-1=Δ_{\Pom}\approx 0.4$. High-energy open beauty photo- and electro-production probes the vacuum exchange at much smaller distances and detects significant corrections to the BFKL asymptotics coming from the subleading vacuum poles. In view of the accumulation of the experimental data on small-$x$ $F_{2}^{c}$ and $F_{2}^{b}$ we extended our early predictions to the kinematical domain covered by new HERA measurements.Our structure functions obtained in 1999 agree well with the determination of both $F_2^c$ and $F_2^b$ by the H1 published in 2006 but contradict to very recent (2008, preliminary) H1 results on $F_2^b$. We present also comparison of our early predictions for the longitudinal structure function $F_L$ with recent H1 data (2008) taken at very low Bjorken $x$. We comment on the electromagnetic corrections to the Okun-Pomeranchuk theorem.
In the neutrino DIS diffraction the charged current non-conservation gives rise to sizable corrections to the longitudinal structure function, $F_L$. These corrections is a higher twist effect enhanced at small-$x$ by the rapidly growing gluon density. The phenomenon manifests itself in abundant production of charm and strangeness by longitudinally polarized W bosons of moderate virtualities $Q^2\lsim m_c^2$.
Due to the weak current non-conservation the diffractive excitation of charm and strangeness dominates the longitudinal structure function $F_L(x,Q^2)$ of neutrino DIS at small Bjorken $x$. Based on the color dipole BFKL approach we report quantitative predictions for this effect in the kinematical range of the CCFR/NuTeV experiment. We comment on the relevance of our findings to experimental tests of PCAC.
The color dipole analysis of small-$(x, Q^2)$ neutrino DIS induced by the charmed-strange ($cs$) current reveals ordering of dipole sizes $m_c^{-2}<r^2<m_s^{-2}$ typical of the Double Leading Log Approximation (DLLA). The DLLA resummation leads to the $cs$ component of the longitudinal structure function $F_L$ rising to small $x$ much faster than its light quark component. Based on the color dipole BFKL approach we report quantitative predictions for this effect in the kinematical range of the CCFR/NuTeV experiment.
Being reformulated in the color dipole basis of small-x QCD Adler's theorem establishes a connection between perturbative and non-perturbative descriptions of DIS and quantifies the effect of non-perturbative dynamics on would-be-perturbative observables. In particular, it provides a quantitative measure of the non-perturbative influence on the longitudinal structure function in charged current DIS and imposes stringent constraints on non-perturbative parameters of color dipole models. Our analysis calls for new experimental tests of Adler's theorem in diffractive neutrino scattering.
The color dipole analysis of nuclear effects in charge current DIS is presented. The emphasis is put on the pronounced effect of left-right asymmetry of shadowing in neutrino-nucleus DIS at small values of Bjorken $x$. Strikingly different scaling behavior of nuclear shadowing for the left-handed andright-handed $W^+$ is predicted. Large, about 25%, shadowing in the $Fe$ structure functions is predicted, which is important for a precise determination of the P-odd nucleon structure functions $xF^{ν(\barν)}_3$ and $Δx F_3=xF_3^ν-xF_3^{\bar ν}$.
Future electron-ion colliders (eIC) will focus on the unitarity properties of deep inelastic scattering (DIS) in the limit of strong nuclear absorption. Strong nuclear shadowing and a large abundance of coherent diffraction are the most striking consequences of unitarity, and here we report quantitative predictions for these effects in the kinematical range of the planned eIC.
The parity non-conservation effect in diffractive charged current DIS is quantified in terms of color dipole sizes of left-handed and right-handed electroweak bosons. We identify the origin and estimate the strength of the left-right asymmetry effect and present comparison with experimental data on the parity-odd structure function $ΔxF_3 =xF_3^{νN}-xF_3^{\barνN}$. We study the shadowing effect in absorption of left-handed and right-handed $W$-bosons by atomic nuclei. The target nucleus is found to be quite transparent for the charmed-strange Fock component of the light-cone $W^+$ in the helicity state $λ=+1$ and rather opaque for the $c\bar s$ dipole with $λ=-1$.