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D. N. Triantafyllopoulos

Publications and source records attributed to D. N. Triantafyllopoulos.

At least 19 recordsLinked to original sources
arXiv2026

When JIMWLK evolution really matters: the example of incoherent diffraction

We consider high energy scattering in the effective theory of the Color Glass Condensate. The most convenient degrees of freedom are Wilson lines encoding multiple gluon exchanges, whose evolution with energy follows the JIMWLK equation. Instead of using the latter, very often one resorts to a Gaussian Approximation (GA), which is known to be remarkably accurate in describing a wide class of multi-gluon correlators whose expansion in the weak scattering limit starts with an exchange of only two gluons. Here we demonstrate, both analytically and numerically, that such an approximation is not valid for correlators which start with an exchange of four gluons. As a main example, we focus on incoherent diffraction in photon-nucleus collisions and we show that the discrepancy between the JIMWLK and the GA results is driven by weak scattering and further persists in the regime where unitarity corrections begin to become important. The JIMWLK calculation leads to cross sections which are systematically larger in all kinematic regimes of interest.

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arXiv2025

The quantum evolutions of the diffractive transverse-momentum dependent gluon distribution

Using the Colour Glass Condensate description of electron-nucleus collisions at high energy, we study the diffractive production of a pair of jets with transverse momenta much larger than the nuclear saturation momentum $Q_s$. At leading order in the QCD coupling, the di-jet cross-section exhibits transverse-momentum dependent (TMD) factorisation, with a gluon diffractive TMD distribution (DTMD) which is controlled by gluon saturation and describes the transverse-momentum imbalance between the produced jets. The next-to-leading corrections generate the various quantum evolutions of the diffractive gluon distribution. We focus on the Collins-Soper-Sterman (CSS) evolution which describes the change in the gluon DTMD when increasing the ''hard scale'' (the typical transverse momentum of the di-jets). We consider two different representations for this equation, one in transverse-momentum space, the other one in transverse-coordinate space. They are not fully equivalent with each other (despite being related by a Fourier transform) because of the respective boundary conditions. These conditions encode the essential physics of gluon saturation together with the effects of two other types of quantum evolution: the BK/JIMWLK evolution over the rapidity gap (''inside the Pomeron'') and the DGLAP evolution outside the rapidity gap (''within the diffractive system''). We demonstrate that, due to gluon saturation, one can compute both the boundary conditions and the CSS solutions fully from first principles, without reference to non-perturbative physics. We numerically find a good agreement between the CSS solutions in the two aforementioned representations.

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arXiv2024

Incoherent diffractive production of jets in electron DIS off nuclei at high energy

We study incoherent diffractive production of two and three jets in electron-nucleus deep inelastic scattering (DIS) at small $x_{\scriptscriptstyle \rm Bj}$ using the color dipole picture and the effective theory of the Color Glass Condensate (CGC). We consider color fluctuations in the CGC weight-function as the source of the nuclear break-up and the associated momentum transfer $\sqrt{|t|}$. We focus on the regime in which the two jets are almost back-to-back in transverse space and have transverse momenta $P_{\perp}$ much larger than both the momentum transfer and the saturation scale $Q_s$. The cross section for producing such a hard dijet is parametrically dominated by large size fluctuations in the projectile wave-function that scatter strongly and for which a third, semi-hard, jet appears in the final state. The 2 + 1 jets cross section can be written in a factorized form in terms of incoherent quark and gluon diffractive transverse momentum distributions (DTMDs) when the third jet is explicit, or incoherent diffractive parton distribution functions (DPDFs) when the third jet is integrated over. We find that the DPDFs and the corresponding cross section saturate logarithmically when $|t| \ll Q_s^2$, while they fall like $1/|t|^2$ in the regime $Q_s^2 \ll |t| \ll P_{\perp}^2$. We further show that there is no angular correlation between the hard jet momentum and the momentum transfer. For typical EIC kinematics the 2 jets and 2 + 1 jets cross sections are of the same order.

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arXiv2024

TMD factorisation for diffractive jets in photon-nucleus interactions

Using the colour dipole picture and the colour glass condensate effective theory, we study the diffractive production of two or three jets via coherent photon-nucleus interactions at high energy. We consider the hard regime where the photon virtuality and/or the transverse momenta of the produced jets are much larger than the saturation momentum $Q_s$ of the nuclear target. We show that, despite this hardness, the leading-twist contributions are controlled by relatively large parton configurations, with transverse sizes $R\sim 1/Q_s$, which undergo strong scattering and probe gluon saturation. For exclusive dijets, this implies that both final jets have semi-hard transverse momenta ($P_\perp\sim Q_s$) and that one of them is aligned with the photon. The dominant contributions to the diffractive production of hard dijets ($P_\perp\gg Q_s$) rather come from three-jet final states, which are very asymmetric and will be referred to as 2+1 jets: two of the jets are hard, while the third one is semi-hard. We demonstrate that the leading-twist contributions to both exclusive dijets and the diffractive production of 2+1 jets admit transverse-momentum dependent (TMD) factorisation, in terms of quark and gluon diffractive TMD distribution functions, for which we obtain explicit expressions from first principles. We show that the contribution of 2+1 jets to diffractive SIDIS (semi-inclusive deep inelastic scattering) takes the form of one step in the DGLAP evolution of the quark diffractive PDF.

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arXiv2023

Incoherent diffractive dijet production in electron DIS off nuclei at high energy

We study incoherent diffractive dijet production in electron-nucleus deep inelastic scattering at small $x_{\rm \scriptscriptstyle Bj}$ within the Color Glass Condensate. We follow the general approach of [1] but we focus on the correlation limit, that is, when the momentum transfer $Δ_{\perp}$ and the gluon saturation momentum $Q_s$ of the nucleus are much smaller than the individual jet momentum $P_{\perp}$. We arrive at analytic expressions for the dijet cross section, which can be written as a sum of four terms which exhibit factorization: each such term is a product between a hard factor, which includes the decay of the virtual photon to the $q\bar{q}$ pair, and a semi-hard one which involves the dipole-nucleus scattering amplitude. We further calculate the azimuthal anisotropies $\langle \cos 2 ϕ\rangle$ and $\langle \cos 4 ϕ\rangle$. They are of the same order in the hard momentum $P_{\perp}$, but the $\langle \cos 4 ϕ\rangle$ is logarithmically suppressed due to its dependence on the semi-hard factor. Finally, in order to extend the validity of our result towards the perturbative domain, we calculate the first higher kinematic twist, i.e. the correction of relative order $Δ_{\perp}^2/P_{\perp}^2$.

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arXiv2023

Probing gluon saturation via diffractive jets in ultra-peripheral nucleus-nucleus collisions

We argue that semi-inclusive photo-production of a pair of hard jets via coherent diffraction in nucleus-nucleus ultra-peripheral collisions at high energy is a golden channel to study gluon saturation. The dominant contribution is the diffractive production of three jets in an asymmetric configuration. Two of the jets are hard and propagate at nearly central pseudo-rapidities. The third jet is semi-hard, with transverse momentum comparable to the nuclear saturation momentum, and is well separated in pseudo-rapidity from the hard dijets. The emission of the semi-hard jet allows for strong scattering, thus avoiding the "higher-twist" suppression of the exclusive dijet production due to colour transparency. We compute the trijet cross-section using the diffractive TMD factorisation which emerges from the CGC effective theory at high energy. The cross-section is controlled by gluon saturation, which leaves its imprints on the structure of the final state, notably on the rapidity distribution.

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arXiv2022

Gluon dipole factorisation for diffractive dijets

Within the colour dipole picture for deep inelastic scattering at small Bjorken $x$, we study the production of a pair of relatively hard jets via coherent diffraction. By "relatively hard" we mean that the transverse momenta of the two jets -- the quark ($q$) and the antiquark ($\bar{q}$) generated by the decay of the virtual photon -- are much larger than the target saturation momentum $Q_s(Y_{\mathbb{P}})$ evaluated at the rapidity gap $Y_{\mathbb{P}}$. We argue that the typical final-state configurations are such that the hard $q\bar q$ dijets are accompanied by a semi-hard gluon jet, with a transverse momentum of the order of $Q_s(Y_{\mathbb{P}})$. The presence of this third jet ensures that the scattering is strong and thus avoids the strong suppression of exclusive (hard) dijet production due to colour transparency. For such "2+1" jet configurations, we demonstrate that both the emission of the semi-hard gluon and its scattering with the hadronic target can be factorised in terms of an effective gluon-gluon dipole. This effective description, originally proposed in [1-4], builds a bridge between the colour dipole picture and collinear factorisation: the cross-section for diffractive 2+1 jets can be written as the product between a hard factor describing the $q\bar{q}$ dijets and a semi-hard factor expressing the unintegrated gluon distribution of the Pomeron. The latter is controlled by gluon dipole scattering in the black disk limit and hence is strongly sensitive to gluon saturation. By integrating out the kinematics of the 3 jets, we obtain the $q\bar{q}g$ contribution to the diffractive structure function in collinearly-factorised form.

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arXiv2022

Fresh look at experimental evidence for odderon exchange

Theory suggests that in high-energy elastic hadron+hadron scattering, $t$-channel exchange of a family of colourless crossing-odd states -- the odderon -- may generate differences between $p\bar p$ and $pp$ cross-sections in the neighbourhood of the diffractive minimum. Using a mathematical approach based on interpolation via continued fractions enhanced by statistical sampling, we develop robust comparisons between $p\bar p$ elastic differential cross-sections measured at $\surd s=1.96\,$TeV by the D0 Collaboration at the Tevatron and function-form-unbiased extrapolations to this energy of kindred $pp$ measurements at $\surd s /{\rm TeV} = 2.76, 7, 8, 13$ by the TOTEM Collaboration at the LHC and a combination of these data with earlier cross-section measurements at $\surd s/{\rm GeV} = 23.5, 30.7, 44.7, 52.8, 62.5$ made at the internal storage rings. Focusing on a domain that straddles the diffractive minimum in the $p\bar p$ and $pp$ cross-sections, we find that these two cross-sections differ at the $(2.2-2.6)σ$ level; hence, supply evidence with this level of significance for the existence of the odderon. If combined with evidence obtained through different experiment-theory comparisons, whose significance is reported to lie in the range $(3.4-4.6)σ$, one arrives at a $(4.0 - 5.2)σ$ signal for the odderon.

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arXiv2022

Saturation effects in SIDIS at very forward rapidities

Using the dipole picture for electron-nucleus deep inelastic scattering at small Bjorken $x$, we study the effects of gluon saturation in the nuclear target on the cross-section for SIDIS (single inclusive hadron, or jet, production). We argue that the sensitivity of this process to gluon saturation can be enhanced by tagging on a hadron (or jet) which carries a large fraction $z \simeq 1$ of the longitudinal momentum of the virtual photon. This opens the possibility to study gluon saturation in relatively hard processes, where the virtuality $Q^2$ is (much) larger than the target saturation momentum $Q_s^2$, but such that $z(1-z)Q^2\lesssim Q_s^2$. Working in the limit $z(1-z)Q^2\ll Q_s^2$, we predict new phenomena which would signal saturation in the SIDIS cross-section. For sufficiently low transverse momenta $k_\perp\ll Q_s$ of the produced particle, the dominant contribution comes from elastic scattering in the black disk limit, which exposes the unintegrated quark distribution in the virtual photon. For larger momenta $k_\perp\gtrsim Q_s$, inelastic collisions take the leading role. They explore gluon saturation via multiple scattering, leading to a Gaussian distribution in $k_\perp$ centred around $Q_s$. When $z(1-z)Q^2\ll Q^2$, this results in a Cronin peak in the nuclear modification factor (the $R_{pA}$ ratio) at moderate values of $x$. With decreasing $x$, this peak is washed out by the high-energy evolution and replaced by nuclear suppression ($R_{pA}<1$) up to large momenta $k_\perp\gg Q_s$. Still for $z(1-z)Q^2\ll Q_s^2$, we also compute SIDIS cross-sections integrated over $k_\perp$. We find that both elastic and inelastic scattering are controlled by the black disk limit, so they yield similar contributions, of zeroth order in the QCD coupling.

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arXiv2022

Probing parton saturation and the gluon dipole via diffractive jet production at the Electron-Ion Collider

We demonstrate that hard dijet production via coherent inelastic diffraction is a promising channel for probing gluon saturation at the Electron-Ion Collider. By $inelastic$ diffraction we mean a process in which the two hard jets - a quark-antiquark pair generated by the decay of the virtual photon - are accompanied by a softer gluon jet, emitted by the quark or the antiquark. This process can be described as the elastic scattering of an effective gluon-gluon dipole. The cross section takes a factorised form, between a hard factor and a unintegrated ("Pomeron") gluon distribution describing the transverse momentum imbalance between the hard dijets. The dominant contribution comes from the black disk limit and leads to a dijet imbalance of the order of the target saturation momentum $Q_s$ evaluated at the rapidity gap. Integrating out the dijet imbalance, we obtain a collinear factorization where the initial condition for the DGLAP evolution is set by gluon saturation.

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arXiv2020

Collinear resummations for the non-linear evolution in QCD at high energy

When computed to next-to-leading order in perturbative QCD, the non-linear Balitsky-Kovchegov (BK) equation for the high-energy evolution of the dipole-hadron scattering appears to be unstable. We show that this instability can be avoided by using the rapidity of the dense hadronic target (instead of that of the dilute dipole projectile) as the evolution time. Using this variable, we construct a collinearly-improved version of the BK equation, where the dominant radiative corrections to the kernel -- those enhanced by double collinear logarithms -- are resummed to all orders.

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arXiv2019

HERA data and collinearly-improved BK dynamics

Within the framework of the dipole factorisation, we use a recent collinearly-improved version of the Balitsky-Kovchegov equation to fit the HERA data for inclusive deep inelastic scattering at small Bjorken $x$. The equation includes an all-order resummation of double and single transverse logarithms and running coupling corrections. Compared to similar equations previously proposed in the literature, this work makes a direct use of Bjorken $x$ as the rapidity scale for the evolution variable. We obtain excellent fits for reasonable values for the four fit parameters. We find that the fit quality improves when including resummation effects and a physically-motivated initial condition. In particular, the resummation of the DGLAP-like single transverse logarithms has a sizeable impact and allows one to extend the fit up to relatively large photon virtuality $Q^2$.

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arXiv2019

Non-linear evolution in QCD at high-energy beyond leading order

The next-to-leading order (NLO) Balitsky-Kovchegov (BK) equation describing the high-energy evolution of the scattering between a dilute projectile and a dense target suffers from instabilities unless it is supplemented by a proper resummation of the radiative corrections enhanced by (anti-)collinear logarithms. Earlier studies have shown that if one expresses the evolution in terms of the rapidity of the dilute projectile, the dominant anti-collinear contributions can be resummed to all orders. However, in applications to physics, the results must be re-expressed in terms of the rapidity of the dense target. We show that although they lead to stable evolution equations, resummations expressed in the rapidity of the dilute projectile show a strong, unwanted, scheme dependence when their results are translated in terms of the target rapidity. Instead, in this paper, we work directly in the rapidity of the dense target where anti-collinear contributions are absent but where new, collinear, instabilities arise. These are milder since disfavoured by the typical BK evolution. We propose several prescriptions for resumming these new double logarithms and find only little scheme dependence. The resummed equations are non-local in rapidity and can be extended to full NLO accuracy.

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arXiv2018

Forward particle production in proton-nucleus collisions at next-to-leading order

We consider the next-to-leading order (NLO) calculation of single inclusive particle production at forward rapidities in proton-nucleus collisions and in the framework of the Color Glass Condensate (CGC). We focus on the quark channel and the corrections associated with the impact factor. In the first step of the evolution the kinematics of the emitted gluon is kept exactly (and not in the eikonal approximation), but such a treatment which includes NLO corrections is not explicitly separated from the high energy evolution. Thus, in this newly established "factorization scheme", there is no "rapidity subtraction". The latter suffers from fine tuning issues and eventually leads to an unphysical (negative) cross section. On the contrary, our reorganization of the perturbation theory leads by definition to a well-defined cross section and the numerical evaluation of the NLO correction is shown to have the correct size.

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arXiv2018

On the use of a running coupling in the calculation of forward hadron production at next-to-leading order

We study a puzzle raised recently regarding the running coupling prescription used in the calculation of forward particle production in proton-nucleus collisions at next-to-leading order: using a coordinate space prescription which is consistent with the one used in the high energy evolution of the target leads to results which can be two orders of magnitude larger than the ones obtained with a momentum space prescription. We show that this is an artefact of the Fourier transform involved when passing between coordinate and momentum space and propose a new coordinate space prescription which avoids this problem.

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arXiv2017

On the use of a running coupling in the NLO calculation of forward hadron production

We address and solve a puzzle raised by a recent calculation [1] of the cross-section for particle production in proton-nucleus collisions to next-to-leading order: the numerical results show an un- reasonably large dependence upon the choice of a prescription for the QCD running coupling, which spoils the predictive power of the calculation. Specifically, the results obtained with a prescription formulated in the transverse coordinate space differ by one to two orders of magnitude from those obtained with a prescription in momentum space. We show that this discrepancy is an artefact of the interplay between the asymptotic freedom of QCD and the Fourier transform from coordinate space to momentum space. When used in coordinate space, the running coupling can act as a fictitious potential which mimics hard scattering and thus introduces a spurious contribution to the cross-section. We identify a new coordinate-space prescription which avoids this problem and leads to results consistent with those obtained with the momentum-space prescription.

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arXiv2017

Resumming double non-global logarithms in the evolution of a jet

We consider the Banfi-Marchesini-Smye (BMS) equation which resums non-global energy logarithms in the QCD evolution of the energy lost by a pair of jets via soft radiation at large angles. We identify a new physical regime where, besides the energy logarithms, one has to also resum (anti)collinear logarithms. Such a regime occurs when the jets are highly collimated (boosted) and the relative angles between successive soft gluon emissions are strongly increasing. These anti-collinear emissions can violate the correct time-ordering for time-like cascades and result in large radiative corrections enhanced by double collinear logs, making the BMS evolution unstable beyond leading order. We isolate the first such a correction in a recent calculation of the BMS equation to next-to-leading order by Caron-Huot. To overcome this difficulty, we construct a collinearly-improved version of the leading-order BMS equation which resums the double collinear logarithms to all orders. Our construction is inspired by a recent treatment of the Balitsky-Kovchegov (BK) equation for the high-energy evolution of a space-like wavefunction, where similar time-ordering issues occur. We show that the conformal mapping relating the leading-order BMS and BK equations correctly predicts the physical time-ordering, but it fails to predict the detailed structure of the collinear improvement.

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