arXiv subjects

Claudelle Capasia Madjuogang Sandeu

Publications and source records attributed to Claudelle Capasia Madjuogang Sandeu.

5 recordsLinked to original sources

arXiv2026

Lévy structure of the forward fixed-coupling BFKL kernel and a fixed-order obstruction to positivity in the symmetric scheme

We establish a Levy interpretation of normalized forward BFKL small-$x$ evolution at leading order and fixed coupling, and exclude a probability law at fixed-order next-to-leading accuracy in the symmetric scheme. After the Marchesini-Onofri conjugation and growth subtraction, one positive step measure in closed form covers all conformal spins, on the cylinder of logarithmic transverse momentum and azimuth. The process is pure jump, and the Pomeron intercept is the relaxation rate of its first azimuthal harmonic. With $s_0=q_1q_2$ and the coupling at that argument, the negative cubic collinear pole of the truncated eigenvalue excludes a probability law at every positive coupling and rapidity. Its leading coefficient is independent of $N_c$ and $n_f$. The pole dominates the leading-order simple pole within $\sqrt{\barα/2}$ of the edge in the leading collinear approximation. Translation-preserving multiplicative conjugations cannot restore positivity. No non-negative step measure generates that truncated evolution, while a positive radial completion at zero conformal spin matches the computed order, so the obstruction is a property of the fixed-order truncation. The tested symmetric-scheme resummations also fail positivity, as shown in closed form for the pure and matched all-poles forms, except for a degenerate zero process, and by computation at the examined couplings for the full prescription. The improved finite-rapidity Green function fails at the displayed parameters under the contour assumption. A resummed kernel in another rapidity scheme has a non-negative step measure at tested couplings. An unweighted transverse walk describes the leading-order evolution with no approximation, but a probabilistic resummation of the symmetric next-to-leading kernel must establish positivity beyond perturbative matching, and whether one exists is left open.

hep-ph↗

arXiv2026

The next-to-next-to-leading order BFKL eigenvalue at odd conformal spin in planar N=4 super Yang-Mills

We give the next-to-next-to-leading order color-singlet BFKL eigenvalue of planar N=4 super Yang-Mills at odd conformal spin n in closed form. At the two lower orders the known expressions contain nested harmonic sums only at the two conjugate points z=(|n|-1)/2+i nu and zbar. At three loops the sums are evaluated on a ladder of integer-shifted arguments from the reflected point -zbar up to z, with one point past it, the coefficient at a rung fixed by its two distances to the ends. Seven families are the exception, their coefficients written through ladder sums whose summand shifts with the summation index. For one of the seven the coefficient lies outside the fixed-coefficient algebra of nested harmonic sums of the two distances, an arithmetic obstruction in the denominators. That exclusion reaches the eigenvalue coefficient only through an agreement of rule and coefficient verified and not proved. Rules uniform in the conformal spin produce all forty-seven families at every odd n>=3; no per-spin coefficient is tabulated in the closed form, and the n=1 boundary block is supplied separately. Those rules are a reconstruction from the computed spins, exact at every one of them, verified over the range n<=99 and at the holdout spin n=101, and not proved at arbitrary odd n. Each atom-table coefficient is a rational combination of 1, pi^2 and zeta_3, coefficient and atom together carrying transcendental weight five. Along nu=0 the intercepts match the Quantum Spectral Curve values at each computed odd spin through n=91, the extent of those values. The comparison tests the integrand and the reduction together at one point of each spin, for most of them for the first time. Away from that line the closed form gives the collinear behavior of the block uniformly in the spin, which the intercepts alone do not fix.

hep-th↗

arXiv2026

The next-to-next-to-leading order BFKL eigenvalue at odd conformal spin in planar N=4 super Yang-Mills: a reconstructed closed form, coefficient structure, and arithmetic

We give the colour-singlet eigenvalue of the three-loop BFKL kernel of planar N=4 super Yang-Mills in closed form at odd conformal spin n. It splits into a holomorphic block and its conjugate, chi_2(n,nu)=(1/4)[F_n(z)+F_n(zbar)] with z=(|n|-1)/2+i nu, and the block is a finite combination of nested harmonic sums of one variable, rational functions and transcendental constants, of uniform transcendental weight five. At the two lower orders the sums are evaluated at the two conjugate points only. At three loops they are evaluated at every point of the integer ladder running from the reflected endpoint -zbar up to z, and one step beyond it, and for all but seven of the slots the coefficient at each rung is fixed by the two distances to the ends. Summing over the one-variable functions before summing along the ladder replaces the rules of those slots by one function of one variable under each ladder weight. The remaining seven are carried by a sum along the ladder whose summand moves with the summation index. All forty-seven coefficient slots follow from rules uniform in the conformal spin at every odd n>=3, with no per-spin coefficient tabulated in the definition; the n=1 boundary block is supplied separately. Those rules are a reconstruction from the computed spins, exact at every one of them, verified over the range n<=99 and at the holdout spin n=101, and not proved at arbitrary odd n. Along nu=0 the intercepts agree with the Quantum Spectral Curve values at every computed odd spin through n=91. That comparison tests the three-loop integrand and the reduction performed here together, at one point of each spin, and for most of those spins it is the first comparison of its kind.

hep-th↗

arXiv2026

Higher-order local constraints from reciprocal symmetry and entanglement entropy of charged-particle multiplicity distributions in $pp$ collisions

The KNO-violating term $f_s$ of the charged-particle multiplicity distribution in $pp$ collisions measures the relative deviation of $\langle n\rangle P_n$ from $e^{-z}$, with $z=n/\langle n\rangle$, and is reported to obey the reciprocal symmetry $f_s(z)=f_s(1/z)$, taken here as input. Being an evenness condition in $\ln z$, it generates a tower of local constraints on the derivatives of $P_n$ at the mean. The lowest member holds for the ATLAS data at $7$, $8$ and $13$~TeV at the few-per-cent level, while the third-derivative residual testing the next member is not determined with a controlled uncertainty by the present binning and stays inconclusive. The global test is consistent at $7$ and $8$~TeV, while at $13$~TeV a residual deviation remains, which a closure test shows is not a binning artefact. Multiplicative noise in the Mueller colour-dipole cascade, the negative binomial and the dipole cascades with recombination each give an $f_s$ that is not invariant under $z\to1/z$, so none of them carries the symmetry. We further obtain a dynamics-independent entropy in the KNO continuum, $S=\ln\langle n\rangle+I_0-\tfrac12\int e^{-z}f_s^2\,dz$, with $I_0$ a support factor tending to unity in the continuum limit. The linear term cancels by normalisation and unit mean, independently of the symmetry, and the remaining correction is quadratic and negative. It reproduces the Shannon entropy of the ATLAS data at the $10^{-3}$ level.

hep-ph↗

arXiv2023

Pole decomposition of BFKL eigenvalue at zero conformal spin and the real part of digamma function

We consider the powers of leading order eigenvalue of the Balitsky-Fadin-Kuraev-Lipatov~(BFKL) equation at zero conformal spin. Using reflection identities of harmonic sums we demonstrate how involved generalized polygamma functions are introduced by pole separation of a rather simple digamma function. This generates higher weight generalized polygamma functions at any given order of perturbative expansion. As a byproduct of our analysis we develop a general technique for calculating powers of the real part of digamma function in a pole separated form.

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