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Tobias Toll

Publications and source records attributed to Tobias Toll.

15 recordsLinked to original sources
arXiv2026

Precise Determination of the Proton's Gluon Cloud Geometry from HERA data

The transverse shape of the proton's small-$x$ gluon distribution is determined from exclusive $J/ψ$ photoproduction at HERA. We derive analytic expressions for the coherent and incoherent diffractive cross sections in the hotspot model at leading twist, enabling a global fit to all 104 available H1 and ZEUS data points, spanning three decades in $t$, with $χ^2/{\rm ndf}=0.77$. The gluonic hotspots are resolved into a perturbative Gaussian core of size 0.105(2) fm surrounded by a nonperturbative exponential halo of range 0.220(15) fm, in agreement with the gluon-field correlation length of the QCD vacuum and with the core-halo structure of flux tubes recently determined on the lattice. This shape is independent of $x_{I\!\!P}$ and of the assumed number of hotspots or hotspot repulsion. The gluonic geometry evolve only through a slow transverse diffusion of the hotspot centres with $α'_{\rm eff.}=0.046(28)~{\rm GeV}^{-2}$, while the incoherent cross section at small $|t|$ is dominated by shot-noise fluctuations at the order of one gluon per hotspot.

hep-ph↗
arXiv2026

Efficient calculation of exclusive diffractive cross sections at the EIC and LHeC with the Sartre event generator

We present a new version of the Sartre event generator for exclusive diffraction at small xP in the colour dipole model, for $ep$ and $e$A scattering at the EIC and the LHeC as well as ultra-peripheral $pp$, $p$A, and AA collisions at RHIC and the LHC. Sartre stores the first and second moment of the interaction amplitudes in lookup tables which are then used for efficient event generation. There are many possible combinations of processes in Sartre, with different initial state nuclear targets and different final state vector mesons or real photons. We also want to implement different versions of the dipole model: with and without non-linear saturation effects, with and without nucleon hotspot substructure. A long-standing bottleneck for simulating all possible exclusive processes has been the production of lookup tables, which take a few CPU-year for each combination, necessitating the use of computing farms. The calculation also involves integrations of rapidly fluctuating integrands, which may cause numerical glitches which takes much effort to smoothen out. In this paper we present a solution to these issues, by presenting a new numerical calculation which improves the efficiency in the table production by 3-4 orders of magnitudes. This enables us to produce lookup tables for any process that we may be interested in, in a few hours. The new calculation does also not exhibit numerical glitches. We provide novel predictions for the EIC and the LHeC using the new version of Sartre.

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arXiv2025

Describing UPC Data with the Sar$t$re Event Generator

Ultra-peripheral heavy-ion collisions (UPCs) provide a distinct environment for high-energy QCD research, focusing on the production of vector mesons. This proceeding details recent advancements in the Sar$t$re Monte Carlo event generator, a dipole model-based tool, to better describe UPC data. We present the incorporation of the full photon flux, accounting for interference effects and photon transverse momentum ($k_T$), and the integration of an $n_0^0n$ afterburner for neutron-tagged event classification. These extensions significantly improve Sar$t$re's ability to reproduce experimental data from STAR and LHCb, particularly at small $p_T^2$ and for various neutron event classes.

hep-ph↗
arXiv2024

Saturation and fluctuations in the proton wavefunction at large momentum transfers in exclusive diffraction at HERA

We present a model of proton geometry where the number and size of gluon density hotspots in the proton's thickness function evolves with the resolution scale of the event given by the Mandelstam $t$ variable in exclusive diffractive $ep$ collisions. We use the impact-parameter dependent saturation dipole model bSat/IPSat, as well as its linearised (non-saturated) version bNonSat. In the latter the proton thickness has a clear interpretation as a thickness and in the former it is directly related to the saturation scale. The resulting phenomenological model for the splitting of hotspots, making full use of earlier experimental and phenomenological studies, is able to describe the entire incoherent $t$-spectrum for $|t|>1.1~$GeV$^2$ with a single phenomenological parameter. We use the previously suggested hotspot model as an initial condition for our evolution. The resulting model is a resolution scale-evolution in the same vein as a parton shower.The incoherent cross section is directly proportional to geometrical fluctuations in the proton's inital state. The hotspot evolution give rise to several kinds of event-by-event fluctuations such as in the hotspot number, width and normalization, and saturation scale fluctuations is a direct effect of these. A natural consequence of our resolution based evolution is that the hotspots obtain an effective repulsion. We use our hotspot evolution model to investigate saturation scale effects in the $t$-spectrum, and found that HERA data is not sensitive to this physics.

hep-ph↗
arXiv2023

Predicting the Exclusive Diffractive Electron-Ion Cross Section at small $x$ with Machine Learning in Sar$t$re

The event generator Sar$t$re has been used extensively for simulations of electron-ion collisions in preparation for the Electron-Ion Collider (EIC). Sar$t$re simulates exclusive diffraction in $e$A collisions, in principle for any nuclear species and exclusive final state, usually a vector meson. The coherent and incoherent cross sections for each process are calculated in the colour dipole model for small $x$ from the first and second moments of the respective amplitude, averaged over initial state spatial configurations. Taking these averages is a very CPU demanding task. In order to function as an efficient event generator, these amplitude moments are saved into lookup tables which are used as input for the event generation, making the latter a very fast process. However, there are many recent and ongoing developments of the dipole models underlying the calculations, both in terms of fits of the model parameters to new data as well as new parametrisations of the dipole or proton geometries. Therefore, it is desirable to have a more flexible method for producing the lookup tables. Here, we propose a method using neural networks which can reduce the table production time by 90% while retaining the same precision in the resulting cross sections.

hep-ph↗
arXiv2022

Investigating the structure of gluon fluctuations in the proton with incoherent diffraction at HERA

Impact parameter dependent dipole models are ideal tools for investigating the spatial structure of the proton. We investigate the incoherent $ep$ cross section in exclusive $J/ψ$ photoproduction as measured by HERA, and find that as $|t|$ increases, the models need several levels of the substructure of gluon density fluctuations in order to describe the measured data well. In lieu of a perturbative description, we add this substructure by hand. This substructure is modelled as hotspots within hotspots. This enables us to describe measurements for $|t|> 1$~GeV$^2$, which is necessary for describing any observable which integrates over the $t$-spectrum, such as the rapidity or $W_{γp}$. We find that three levels of proton substructure are adequate for a good description of all available $ep$ data up to $|t|=30~$GeV$^2$. We note that the gluonic density fluctuation structure follows a scaling behaviour, such that the logarithms of the number of hotspots and their size fall on a line, effectively reducing the available parameter space of the model. Our findings systematically constrain and provide a benchmark for the development of a perturbative model of spatial gluon fluctuations in nucleons.

hep-ph↗
arXiv2022

Energy dependence of the proton geometry in exclusive vector meson production

The gluon radius of the proton is expected to increase at small gluon momentum fractions $x$, an effect which has hitherto not been considered in the dipole model framework. We investigate the energy dependence of exclusive $J/ψ$, $ϕ$, and $ρ$ production by introducing three models for $x$ dependence of the gluon thickness function. We allow the transverse width of the proton to increase as $x$ decreases, using novel parametrisations in the spherical proton and the hotspot model. We compare these with a model where the number of hotspots increases as $x$ decreases and confront the models with HERA data. The models exhibit clear differences in the slope of the $t$-spectra and in the cross section ratios between coherent and incoherent events. Comparisons to $t$-slopes and $W_{γp}$ measurements show a preference for models where the proton's size increases as $x$ decreases.

hep-ph↗
arXiv2022

Investigating saturation effects and the virtual pion in leading neutron events at HERA with the dipole model

We investigate events with very forward neutrons in $ep$ collisions at HERA using impact parameter dependent colour dipole models with and without saturation. This is the first study of the leading neutron process deploying these models. The model predictions are compared with the available HERA measurements for $6<Q^2<100$~GeV$^2$, $70<W<245$~GeV. Our analysis shows that the models exhibit Feynman scaling, independent of $Q^2$. Our results demonstrate that the $W$ and $Q^2$ dependence of the cross section is independent of the presence of a forward neutron as predicted by the limiting fragmentation hypothesis, which is a consequence of Feynman scaling itself. We infer that the HERA leading neutron production inclusive data is insensitive to saturation physics and these cross sections may not be able to distinguish gluon saturation effects in future $ep$ colliders. We provide a good description of the leading neutron structure function $F_2^{LN}$ at small $x$ using an assumption that the small-$x$ structure of protons and pions is universal up to a normalisation. We also show that the observables in the exclusive diffractive measurements with a vector meson in the final state are more sensitive to saturation physics at small $x$ than inclusive measurements. At last, we provide a prediction for the $\hat t$ spectrum in exclusive vector meson production in the dipole model using Yukawa theory to model the virtual pion's spatial wave function.

hep-ph↗
arXiv2021

Subnucleon fluctuations in coherent and incoherent ultra-peripheral AA collisions at LHC and RHIC with the Sartre event generator

Sartre has been extensively used for describing photon-nuclei processes at the electron-ion collider (EIC) as well as ultra-peripheral collisions (UPC) at LHC and RHIC. Sartre is an event generator which implements the dipole model for DIS, and models the transverse geometry of the target nucleus or proton in coordinate space. It uses the Good-Walker mechanism for simulating fluctuations which contribute to the incoherent cross section for which the target breaks up after the interaction. With improved precision of UPC measurements in the last years, a detailed test of the dipole model has become possible, and Sartre's model was found lacking. In these proceedings we add subnucleon fluctuations to the nucleus and show that this is sufficient for describing the vast majority of the present measurements. We also find that for larger momentum transfers in the nucleus, which probes gluon fluctuations at higher resolution, the current complexity of the model may not suffice. Future measurements at the LHC, RHIC and especially the EIC has the potential to reveal these gluon vacuum fluctuations and glean novel insights into the self-interacting quantum field of QCD.

hep-ph↗
arXiv2020

Investigating saturation effects in ultraperipheral collisions at the LHC with the color dipole model

We investigate saturation effects in $ep$ scattering as well as in ultraperipheral $p$A and AA collisions at small $x$ with four variants of the impact parameter dependent color dipole model: with and without gluon saturation and with and without a novel mechanism that suppresses unphysical dipole radii above the confinement scale, a problem not addressed by most implementations. We show that $ep$ scattering at HERA can be very well described by any of the four variants. When going from $ep$ to $e$A scattering, saturation effects are expected to increase as $\sim$A$^{1/3}$. In lieu of an electron-ion collider, we confront the different versions of the dipole model with data recorded in ultraperipheral collisions at the LHC in order to estimate the sensitivity of the data to gluon saturation in the target nuclei. We find that ultraperipheral PbPb collisions indicate strong saturation effects while $p$Pb collisions turn out to not have any discriminating power to distinguish saturation from non-saturation scenarios.

hep-ph↗
arXiv2019

Exclusive diffractive vector meson production: A comparison between the dipole model and the leading twist shadowing approach

With the imminent construction of an electron-ion collider in the USA, both saturation physics and nuclear shadowing physics will be important for the same processes for the first time. In particular for exclusive production of vector mesons, such as the J/$ψ$. In this paper we investigate the underlying assumptions commonly made when phenomenologically investigating this process from a shadowing and saturation perspective respectively. We use the bSat model which is commonly used to describe saturation physics, and a calculation by M.G. Ryskin which is commonly used when describing nuclear shadowing at leading twist. It is expected that the bSat model is equivalent to Ryskin's result in the hard scattering and non-relativistic limits. By explicitly taking these limits we show that the bSat model does indeed become equivalent to Ryskin's result. However, two more approximations are needed for this result. Firstly, the factorisation and renormalisation scales in the bSat model has to be independent of the dipole radius, and secondly, we need to omit a term in the overlap between the vector meson and virtual photon wave functions. We show that for the typical dipole radius of the J/$ψ$, the different approximations off-set each other and the bSat model agrees very well with Ryskin's calculation in hard-scattering and non-relativistic limits.

hep-ph↗
arXiv2013

Exclusive diffractive processes in electron-ion collisions

We present a new technique to calculate the cross-section for diffractive vector meson production and DVCS in electron-ion collisions based on the dipole model. The measurement of these processes can provide valuable information on non-linear QCD phenomena, such as gluon saturation, and is the the only known way to gain insight into the spatial distribution of gluons in nuclei. We present predictions of differential cross-section distribution $dσ/dQ^2$ and $dσ/dt$ for $J/ψ$ and $ϕ$ meson production for diffractive processes of heavy nuclei and demonstrate the feasibility of extracting the gluon source distribution of heavy nuclei, F(b), from coherent diffraction. We briefly introduce a new event generator based on our method that can be used for studying exclusive diffractive processes at a future electron-ion collider.

hep-ph↗
arXiv2011

Charm and bottom photoproduction at HERA with MC@NLO

We apply the MC@NLO formalism to the production of heavy-quark pairs in pointlike photon-hadron collisions. By combining this result with its analogue relevant to hadron-hadron collisions, we obtain NLO predictions matched to parton showers for the photoproduction of QQ^{-} pairs. We compare MC@NLO results to the measurements of c- and b-flavoured hadron observables performed by the H1 and ZEUS collaborations at HERA.

hep-ph↗
arXiv2008

MC@NLO for Heavy Quarks in Photoproduction

An MC@NLO for heavy quarks in photoproduction is presented. This is the first lepton-hadron process to be included into MC@NLO. To construct an MC@NLO process dependent so called MC-subtraction terms need to be calculated. The resulting calculation is compared to a fixed order NLO calculation and the HERWIG event generator and is shown to perform well.

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