arXiv subjects

Tuomas Lappi

Publications and source records attributed to Tuomas Lappi.

At least 19 recordsLinked to original sources

arXiv2026

Diffractive structure functions from JIMWLK evolution

We compute diffractive structure functions from Wilson line configurations whose energy evolution is given by the JIMWLK equation. We use a JIMWLK evolution setup that has already been constrained with exclusive vector meson production data from HERA. We compare our results to HERA measurements and also extended to heavy nuclei. In particular we can calculate predictions for the nuclear modification factor and diffractive-to-total cross section ratios at the EIC.

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arXiv2026

TMD factorization in diffractive heavy-quark production in photon-nucleus collisions

Using the Colour Glass Condensate effective theory, we study the diffractive production of a massive quark-antiquark pair accompanied by a gluon in coherent photon-nucleus collisions at high energy. This partonic configuration provides the leading twist contribution to the cross section in the correlation limit where two of the partons are hard and nearly back to back in the transverse plane, while the third one is semi-hard, with a transverse momentum of the order of the nuclear saturation momentum. We consider two scenarios: (i) a hard quark-antiquark pair together with a semi-hard gluon; in this case we demonstrate transverse momentum dependent (TMD) factorization with a mass-dependent ''hard'' factor and the standard expression for the gluon diffractive TMD, and (ii) a hard antiquark-gluon pair and a semi-hard quark; in this case we find TMD factorization with a mass-independent ''hard'' factor and a mass-dependent quark diffractive TMD, which represents a new result. We show that increasing the quark mass reduces (or even washes out) the effects of gluon saturation on the quark diffractive TMD. In particular, it leads to the suppression of the Cronin peak that we observe in the massless limit. Our results are the basis for future phenomenological studies of quarkonium and open charm production in the saturation regime in ultraperipheral collisions at the Large Hadron Collider, and in deep inelastic scattering at the Electron-Ion Collider.

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arXiv2026

Light-front Hamiltonian jet evolution in the Glasma

We develop a light-front Hamiltonian formalism to study the real-time quantum evolution of a high-energy quark propagating through the Glasma phase of a heavy-ion collision. In this work, the quark Fock space is truncated to the $\ket{q}$ sector and the wavefunction is expanded in a discrete basis representation, following the time-dependent Basis Light-Front Quantization (tBLFQ) framework. The classical Glasma background fields enter as a time-dependent external potential, and physical observables are extracted as expectation values of quantum operators over the time-evolved state. We compute the transverse momentum broadening and the jet quenching parameter, finding results consistent with classical estimates, including the expected scaling with respect to the saturation momentum, and use them to perform phenomenological estimations for different collision systems. We also study the color rotation of the quark state induced by the Glasma fields, and examine its dependence on the saturation scale and the gauge choice. This formalism allows systematic improvements to include, in particular, non-eikonal propagation and parton splittings that will be considered in forthcoming publications.

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arXiv2026

Kinetic and canonical momentum broadening in the Glasma

We lay the foundations for a quantum formalism describing the real-time evolution of particles in the Glasma phase of a heavy-ion collision, focusing on the implications of gauge invariance in the definition of the momentum of a particle in a classical background field. We first establish the correspondence between the classical Wong's equations and the Heisenberg equations of motion for a particle in a classical non-Abelian background field. Using this correspondence, we obtain equations of motion for both the kinetic momentum -- the gauge invariant, physically measurable quantity -- and the canonical momentum, which is conjugate to the coordinates in the Hamiltonian. In particular, the kinetic momentum broadening receives non-trivial contributions from the transverse field components, even in the eikonal limit. Finally, we demonstrate that imposing a transverse Coulomb gauge condition at the initial time significantly reduces the accumulation of numerical errors, thereby providing an optimized framework for the forthcoming quantum implementation.

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arXiv2026

The leading Lyapunov exponent in the glasma

We show that small perturbations in the boost-invariant color fields of the glasma exhibit an exponential growth with the square root of time. We interpret this growth rate as a Lyapunov exponent, related to entropy production and the thermalization timescale in the earliest stage of heavy-ion collisions. Working in a regime that is linear in this perturbation, we extract the time dependence of this mode as $\sim \exp(0.4\sqrt{g^2\mu\tau})$ for SU($2$), where $g^2\mu$ is proportional to the saturation scale and the square-root dependence is caused by the boost-invariant expansion of the system. We show that the growth rate of this mode is, unlike its amplitude, remarkably insensitive to the details of how the perturbations are initialized. In particular, we show that the unstable mode couples to all momentum scales present in the initial perturbation.

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arXiv2026

Two-Loop DGLAP Splitting Functions from Light Cone Perturbation Theory

We perform a two-loop calculation in Light Cone Perturbation Theory (LCPT) to evaluate the next-to-leading order nonsinglet splitting function. Our calculation demonstrates the methodology and feasibility of performing higher order calculations in LCPT. Since in Hamiltonian perturbation theory the longitudinal $k^+$ momentum is always positive, poles in $1/k^+$ can be regularized by a simple cutoff which cancels in physical results, without any associated ambiguities. For transverse momentum integrals we use dimensional regularization. Developing methods for loop calculations in LCPT paves the way for a systematical, automatizable procedure for precision calculations in this framework with a transparent physical partonic interpretation. This can provide a standard framework in higher order calculations in the gluon saturation regime of QCD.

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arXiv2026

The DIS dipole picture cross section in exact kinematics

We implement a finite energy constraint in the dipole picture of deep inelastic scattering by restricting the invariant mass of the produced partonic system by the virtual photon-target center of mass energy. We show that, for $Q^2=1$GeV$^2$, the effect of this constraint can reach up to $\sim$35% for charm quarks and $\sim$7% for light quarks at $x=0.01$, but then rapidly decreases at smaller $x$ or larger $Q^2$.

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arXiv2025

Heavy flavor angular correlations as probes of the glasma

We study the effect of the glasma fields, formed in the early stage of heavy-ion collisions, on the transport of $Q\bar{Q}$ pairs produced back-to-back. We find that for pairs with moderate initial transverse momentum $p_T$ evolving in glasma fields with sufficiently large saturation momentum $Q_s$, the azimuthal correlation $C({\Delta\phi})$ is quickly affected. The decorrelation widths $\sigma_{\Delta\phi}$ during the glasma and Quark Gluon Plasma (QGP) phases are comparable.

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arXiv2025

Initial stage jet momentum broadening in tBLFQ formalism

We study the momentum broadening of a high-energy quark jet in the large density gluon medium created right after the collision of two ultrarelativistic heavy nuclei, the Glasma. Previous Glasma studies modeled the jet as a classical probe particle, for which position and momentum are simultaneously determined. In this work, we use the light-front QCD Hamiltonian formalism to treat the jet as a fully quantum state. We compute its real-time evolution while propagating through the Glasma classical background fields, which act as an interaction potential in the quantum evolution of the jet. We present results for the momentum broadening and jet quenching parameter of a jet at mid-rapidity, with special emphasis on the anisotropies between the longitudinal and transverse directions relative to the collision axis. In addition, we compare our results to classical calculations, and initiate a study of the distinction between kinetic and canonic momentum in the context of jet momentum broadening.

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arXiv2025

Scattering and gluon emission of physical quarks in a SU(3) colored field

We study the scattering of the gluon-dressed physical quarks, defined as the eigenstates of the vacuum QCD Hamiltonian, off a colored medium. We solve the wavefunction of the physical quark state by diagonalizing the QCD Hamiltonian in vacuum in a $\ket{q}+\ket{qg}$ Fock space, with implementing the sector-dependent mass renormalization scheme. We then perform numerical simulations of the real-time quantum state evolution of the initially dressed quark state at various medium densities. The results are compared with those of an initially bare or off-shell quark states. With the obtained light-front wavefunction of the evolved state, we extract the quark jet transverse momentum broadening, the quenching parameter, the cross section, the gluon emission rate, and the evolution of the invariant mass. The scenario considered is relevant for high energy scattering processes, where the quark originates from far outside the color field describing the scattering target. This investigation on dressed quarks complements our earlier studies of the single quark scattering in the $\ket{q}$ Fock space, and of the bare quark scattering in the $\ket{q}+\ket{qg}$ Fock space, providing a novel systematic description of quark scattering process using a non-perturbative formalism.

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arXiv2025

The impact of glasma on heavy quark spectra and correlations

We investigate the effect of the glasma classical color fields, produced in the very early stage of heavy-ion collisions, on the transport of heavy quarks. The glasma fields evolve according to the classical Yang-Mills equations, while the dynamics of heavy quarks is described by Wong's equations. We numerically solve these equations and compute the transport coefficient $\kappa$, which is anisotropic and initially very large. Further, we extract observables sensitive to the initial glasma stage. The heavy quark nuclear modification factor $R_{AA}$ is affected by the glasma but the effect is moderate compared to the nPDF contribution. Our main finding is that the glasma has a large impact on the azimuthal correlation between $Q\overline{Q}$ pairs, initially produced back-to-back.

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arXiv2025

Inclusive $\mathrm{D}^0$ photoproduction in ultraperipheral collisions

We compute the differential cross section for inclusive $\mathrm{D}^0$ production in ultraperipheral collisions within the Color Glass Condensate framework. Our predictions are found to be in relatively good agreement with the CMS data at small transverse momentum, which is the region of validity of our approach. Furthermore, we quantify saturation effects by a nuclear modification ratio $R_{pA}$ for $\mathrm{D}^0$ photoproduction and examine both analytically and numerically the collinear factorization limit of the $\mathrm{D}^0$ differential photoproduction cross section.

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arXiv2024

Next-to-leading order evolution of structure functions without PDFs

We formulate and numerically solve the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi~(DGLAP) evolution equations at next-to-leading order in perturbation theory directly for a basis of 6 physical, observable structure functions in deeply inelastic scattering. By expressing the evolution in the physical basis one evades the factorization scale and scheme dependence. Working in terms of observable quantities, rather than parametrizing and fitting unobservable parton distribution functions (PDFs), provides an unambiguous way to confront predictions of perturbative Quantum Chromodynamics with experimental measurements. We compare numerical results for the DGLAP evolution for structure functions in the physical basis to the conventional evolution with PDFs.

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arXiv2024

The impact of glasma on heavy flavor azimuthal correlations and spectra

We study the phenomenological impact of the pre-equilibrium glasma initial stage of heavy-ion collisions on heavy quark azimuthal correlations and spectra. Using our numerical solver, we simulate the transport of heavy quark test particles in an SU(3) glasma background field. The glasma field equations are formulated using classical real-time lattice gauge theory, and the heavy quark dynamics are described by classical transport equations numerically solved using the colored particle-in-cell method. For the first time, the effect of the glasma stage on the azimuthal correlations of $c\overline{c}$ and $b\overline{b}$ pairs is studied. The resulting azimuthal width $\sigma_{\Delta\phi}$ exhibits a large and quick decorrelation due to the strong glasma fields. Further, we evaluate how the $p_T$-broadening in the glasma affects heavy quark $p_T$-spectra, which are initialized according to the Fixed-Order Next-to-Leading Logarithm (FONLL) heavy quark production calculation. The nuclear modification factor $R_{AA}$ is extracted for $c$ and $b$ quarks in the glasma and additional nuclear PDF effects accounting for gluon shadowing are included.

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arXiv2024

Heavy flavor angular correlations as a direct probe of the glasma

We use classical equations of motion for heavy quarks to show that the pre-equilibrium glasma phase of a heavy ion collision has an extremely strong effect on heavy quark angular correlations. At the same time, the effect on the single inclusive spectrum is much more moderate. This suggests that $D\overline{D}$ meson angular correlations in future LHC measurements could provide direct experimental access to the physics of the pre-equilibrium stage.

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arXiv2024

Inclusive $\mathrm{J}/\psi$ production in forward proton-proton and proton-lead collisions at high energy

We calculate the cross section for forward $\mathrm{J}/\psi$ production in proton-proton and minimum bias proton-lead collisions using the Color Glass Condensate (CGC) and Non-Relativistic QCD (NRQCD) formalism consistently with Deep Inelastic Scattering data. The cross section for color singlet states is sensitive to a 4-point correlator of Wilson lines for which we describe in the Gaussian approximation in the large-$N_c$ limit. Furthermore, we quantify the importance of finite-$N_c$ corrections to have a small $\sim 12\%$ effect. In contrast with the generic NRQCD expectation, we show that the color singlet contribution is only $15\%$ to the total cross section. We also compare our predictions for $\mathrm{J}/\psi$ production as well as for the nuclear modification ratio $R_{pPb}$ to LHCb and ALICE data. We find a good agreement at forward rapidities, except at low transverse momenta where the cross sections are overestimated.

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arXiv2024

Evolution of structure functions at NLO without PDFs

We formulate the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution of the Deep Inelastic Scattering (DIS) structure functions $F_2$ and $F_{\rm L}$ at next to leading order in $\alpha_s$ (NLO) directly in terms of the structure functions rather than parton distributions (PDFs). We call this the physical basis approach. In practice, we first express the NLO quark singlet and gluon PDFs in terms of the structure functions $F_2$ and $F_{\rm L}$ in momentum space. Employing these expressions in the DGLAP evolution, we arrive at the evolution equations for $F_2$ and $F_{\rm L}$ in the physical basis. We demonstrate how one is free from defining a factorization scale and scheme when using the physical basis evolution equations. We also discuss the process of applying the NLO physical basis to global analysis of LHC cross sections.

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arXiv2024

Diffractive deep inelastic scattering at NLO in the dipole picture

We compute the transverse and longitudinal diffractive structure functions to full next-to-leading order accuracy in the dipole picture of deep inelastic scattering. Our calculation uses the standard light-cone perturbation theory method for the partonic content of the virtual photon, together with the Color Glass Condensate description of the target color field. Our result includes as a subset the $q\bar{q}g$ contribution calculated earlier. We show that there is a rapidity divergence that can be factorized into the BK/JIMWLK evolution of the target Wilson lines, and that all other divergences cancel.

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