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H. Navelet

Publications and source records attributed to H. Navelet.

At least 19 recordsLinked to original sources
arXiv2002

Conformal invariant saturation

We show that, in onium-onium scattering at (very) high energy, a transition to saturation happens due to quantum fluctuations of QCD dipoles. This transition starts when the order $α^2$ correction of the dipole loop is compensated by its faster energy evolution, leading to a negative interference with the tree level amplitude. After a derivation of the the one-loop dipole contribution using conformal invariance of the elastic 4-gluon amplitude in high energy QCD, we obtain an exact expression of the saturation line in the plane (Y,L) where Y is the total rapidity and L, the logarithm of the onium scale ratio. It shows universal features implying the Balitskyi - Fadin - Kuraev - Lipatov (BFKL) evolution kernel and the square of the QCD triple Pomeron vertex. For large L, only the higher BFKL Eigenvalue contributes, leading to a saturation depending on leading log perturbative QCD characteristics. For initial onium scales of same order, however, it involves an unlimited summation over all conformal BFKL Eigenstates. In all cases, conformal invariance is preserved for the saturation mechanism based on dipole loops.

hep-ph↗
arXiv2001

Unifying approach to hard diffraction

We find a consistency between two different approaches of hard diffraction, namely the QCD dipole model and the Soft Colour Interaction approach. A theoretical interpretation in terms of S-Matrix and perturbative QCD properties in the small $x_{Bj}$ regime is proposed.

hep-ph↗
arXiv2001

Unified QCD picture of hard diffraction

Using a combination of S-Matrix and perturbative QCD properties in the small x_{Bjorken} regime, we propose a formulation of hard diffraction unifying the partonic (Ingelman-Schlein) Pomeron, Soft Colour Interaction and QCD dipole descriptions. In particular, we show that all three approaches give an unique and mutually compatible formula for the proton diffractive structure functions incorporating perturbative and non perturbative QCD features.

hep-ph↗
arXiv2001

Virtual photon impact factors with exact gluon kinematic

An explicit analytic formula for the transverse and longitudinal impact factors S_{T,L}(N,γ) of the photon using k_T factorization with exact gluon kinematics is given. Applications to the QCD dipole model and the extraction of the unintegrated gluon structure function from data are proposed.

hep-ph↗
arXiv2000

QCD dipole model and k_T factorization

It is shown that the colour dipole approach to hard scattering at high energy is fully compatible with k_T factorization at the leading logarithm approximation (in -log x_Bj). The relations between the dipole amplitudes and unintegrated diagonal and non-diagonal gluon distributions are given. It is also shown that including the exact gluon kinematics in the k_T factorization formula destroys the conservation of transverse position vectors and thus is incompatible with the dipole model for both elastic and diffractive amplitudes.

hep-ph↗
arXiv2000

On Certain Two Dimensional Integrals that Appear In Conformal Field Theory

In a first part, we generalize a theorem for an holomorphic $\times $ anti-holomorphic integrand, in the case of 2 dimensional Fourier transform. In the second part, we derive p-uple conformal integrals the integrand of which are linear combination of holomorphic times holomorphic generalized hypergeometric functions. The specific case $p=3$ is relevant to determine the triple Pomeron vertex in QCD.

math-ph↗
arXiv1999

The (BFKL) Pomeron-virtual photon-photon vertex for any conformal spin

To study diffractive photon production at HERA, we compute the projection of the virtual photon-photon impact-factor on the BFKL leading-order eigenfunctions E(n,nu) for non-zero transfer. This calculation supplements former ones performed for n=0. We provide an expression for n=+/-2 and check that all the other components are zero.

hep-ph↗
arXiv1998

Non-forward double Pomeron exchange in QCD

We derive the analytic expression of the two one-loop dipole contributions to the elastic 4-gluon amplitude in QCD for arbitrary transverse momentum. The first one corresponds to the double QCD pomeron exchange, the other to an order $α^2$ correction to one-pomeron exchange.

hep-ph↗
arXiv1998

The elastic QCD dipole amplitude at one-loop

We derive the analytic expression of the two one-loop dipole contributions to the elastic 4-gluon amplitude in QCD. The first one corresponds to the double QCD pomeron exchange, the other to an order alpha^2 correction to one-pomeron exchange. Both are expressed in terms of the square of the recently derived triple QCD pomeron vertex and involve a summation over all conformal Eigenvectors of the BFKL kernel.

hep-ph↗
arXiv1997

The QCD triple Pomeron coupling from string amplitudes

Using the recent solution of the triple Pomeron coupling in the QCD dipole picture as a closed string amplitude with six legs, its analytical form in terms of hypergeometric functions and numerical value are derived.

hep-ph↗
arXiv1997

High-mass diffraction in the QCD dipole picture

Using the QCD dipole picture of the BFKL pomeron, the cross-section of single diffractive dissociation of virtual photons at high energy and large diffractively excited masses is calculated. The calculation takes into account the full impact-parameter phase-space and thus allows to obtain an exact value of the triple BFKL Pomeron vertex. It appears large enough to compensate the perturbative 6-gluon coupling factor (alpha/pi)^3 thus suggesting a rather appreciable diffractive cross-section.

hep-ph↗
arXiv1997

Selection rules at the quark-antiquark vertex of the QCD Pomeron

We derive the full analytic expression for the QCD eikonal coupling of a quark-antiquark state to the exchanged gluon-gluon state in the BFKL formalism. The formula is valid for all conformal spin configurations of the quark-antiquark and gluon-gluon states. In particular, a new selection rule on conformal spins characterizes the non-dominant BFKL components with intercept below the Pomeron in the conformal-invariant framework.

hep-ph↗
arXiv1997

Onium-Onium scattering at fixed impact parameter: exact equivalence between the color dipole model and the BFKL Pomeron

We compute the onium-onium scattering amplitude at fixed impact parameter in the framework of the perturbative QCD dipole model. Relying on conformal properties of the dipole cascade and of the elementary dipole-dipole scattering amplitude, we obtain an exact result for this onium-onium scattering amplitude, which is proven to be identical to the BFKL result, and which exhibits the frame invariance of the calculation. The asymptotic expression for this amplitude and for the dipole distribution in an onium at fixed impact parameter agree with previous numerical simulations. We show how it is possible to describe onium-$e^{\pm}$ deep inelastic scattering in the dipole model, relying on k_T-factorization properties. The elementary scattering amplitudes involved in the various processes are computed using eikonal techniques.

hep-ph↗
arXiv1997

Conformal Invariance and the exact solution of BFKL equations

The conformal invariance properties of the QCD Pomeron in the transverse plane allow us to give an explicit analytical expression for the solution of the BFKL equations both in the transverse coordinate and momentum spaces. This result is obtained from the solution of the conformal eigenvectors in the mixed representation in terms of two conformal blocks, each block being the product of an holomorphic times an antiholomorphic function. This property is used to give an exact expression for the QCD dipole multiplicities and dipole-dipole cross-sections in the whole parameter space, proving the equivalence between the BFKL and dipole representations of the QCD Pomeron.

hep-ph↗
arXiv1996

Conformal blocks in the QCD Pomeron formalism

The conformal invariance properties of the QCD Pomeron in the transverse plane allow us to give an explicit analytical expression for the conformal eigenvectors in the mixed representation in terms of two conformal blocks, each block being the product of an holomorphic times an antiholomorphic function. This property is used to give an exact expression for various functions of interest, the Pomeron amplitude in both momentum and impact-parameter variables, the QCD dipole multiplicities and dipole-dipole cross-sections in the whole parameter space, and we recover the expression of the four-point gluon Green function given recently by Lipatov

hep-ph↗
arXiv1996

On the origin of the rise of $F_2$ at small $x$

We show that, provided that the non-perturbative input is regular at the right of the $ω=0$ singularity of the dominant DGLAP anomalous dimension, the rise of $F_2$ at small $x,$ experimentally measured by the averaged observable $λ= <(\partial ln F_2)/(\partial ln 1/x)>,$ is input-independent in the perturbative $Q^2$ regime at small $x$. $(\partial ln xF)/(\partial ln Q^2)$ appears to be more input-dependent in the same range. The GRV-type parametrisations verify these properties. Other models, namely the BFKL kernel(QCD dipoles), DGLAP(hard pomeron singularity) give different predictions for $λ$. At moderate $Q^2,$ there is a possibility of distinguishing these different perturbative QCD predictions in the near future.

hep-ph↗
arXiv1996

Proton structure functions in the dipole picture of BFKL dynamics

The $F_2$, $F_G$, $R = F_L/F_T$ proton structure functions are derived in the QCD dipole picture. Assuming $k_T$ and renormalization-group factorization, we relate deep-inelastic proton scattering to deep-inelastic onium scattering. We get a three-parameter fit of the 1994 H1 data in the low-$x,$ moderate $Q^2$ range. The ratios $F_G/F_2$ and $R$ are predicted without further adjustment. The dipole picture of BFKL dynamics is shown to provide a relevant model for quantitatively describing the proton structure functions at HERA. The predictions for $F_2$ and $F_G$ are compatible with the next-to-leading order DGLAP analysis, while $R$ is expected to be significantly lower at very small $x$.

hep-ph↗