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Daniël Boer

Publications and source records attributed to Daniël Boer.

At least 19 recordsLinked to original sources
arXiv2026

Gluon GTMDs in the exclusive electroproduction of heavy-quark pairs

We study exclusive electroproduction of heavy quark-antiquark pairs off nucleons in the framework of generalized transverse momentum dependent parton distributions (GTMDs) for gluons. The short-distance part of the process is treated at leading order in perturbative Quantum Chromodynamics and in first order in a collinear expansion, which allows identification with the description in terms of Generalized Parton Distributions (GPDs). For the results for the structure functions in terms of GTMDs and GPDs we consider only unpolarized (spin-averaged) nucleons, but include all possible azimuthal modulations that can arise. The presented results extend known expressions in the literature and are relevant for experimental studies of this exclusive process at the future Electron Ion Collider. Furthermore, we introduce a convenient decomposition of the gluon-gluon correlation matrix in terms of GTMDs, expanded in a Lorentz basis of symmetric traceless tensors obtained from the partonic momentum $k_T$ and the momentum transfer $Δ_T$. The adopted notation for the GTMDs relates to the nucleon helicity states at the amplitude level, rather than to polarization states of the incoming nucleon or of the gluons, which makes it more transparent which contributions from helicity difference and helicity flip matrix elements can be accessed with unpolarized nucleon beams.

hep-ph↗
arXiv2025

The impact of the TMD shape function on matching the transverse momentum spectrum in $J/ψ$ production at the EIC

The impact of the inclusion of TMD shape functions on the transverse momentum spectrum in $J/ψ$ production at the EIC is investigated by considering the matching of the TMD factorization description at low transverse momentum with the collinear factorization description at high transverse momentum by means of the inverse-error weighting method. Despite large uncertainties from scale variations and the $J/ψ$ long-distance matrix elements, predictions for the differential cross section and its $\cos(2ϕ_ψ)$ modulation are obtained. We find that physical constraints are satisfied in case a process-dependent term is included for color octet production, but not in all cases when it is excluded. These numerical results support the analytic calculations in \cite{Boer:2023zit}. Future experimental data can thus test the validity of TMD factorization in $J/ψ$ production and explore the presence of nontrivial process-dependent effects in the soft-gluon resummation. This will be crucial in the extraction of gluon unpolarized and linearly polarized TMD distributions of the proton. In addition, we suggest how the sign of the latter can be determined by investigating the presence of a node in the $\cos(2ϕ_ψ)$ modulation as a function of transverse momentum.

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arXiv2025

Azimuthal asymmetries in lepton and heavy-quark pair production in UPCs

Azimuthal modulations in lepton and heavy-quark pair production in ultraperipheral collisions (UPCs) of highly charged ions are investigated. The modulations in the azimuthal angles of the sum and difference of the transverse momenta of the pair of particles in the final state, as well as of the transverse impact parameter, arise from the collisions of unpolarized and polarized photons. A full description of the cross section in terms of Generalized Transverse Momentum Dependent parton distributions (GTMDs) for photons is given including a careful consideration of the Fourier transform to impact parameter space. In particular, this leads to a feed-in mechanism among harmonics of different orders, which in principle generates harmonics of all (even) orders. Wherever comparable, our analytical results for the azimuthal modulations agree with those presented in other papers on this topic. Compared to these other works, we separate effects that arise from the anisotropies of the GTMDs from those that do not and retain terms proportional to the mass of the produced particles, as they are relevant for muon, charm and bottom quark production. We show that the normalized differential cross section changes considerably with the produced particle mass, which should be discernible in UPCs at RHIC and LHC. For the numerical results we adopt several models for the photon GTMD correlator, and find that all of them are in fairly good agreement with each other and with UPC data from STAR. We also present results for various azimuthal modulations for RHIC kinematics, where we compare $e^+ e^-$ production with the production of heavier particles, and for LHC kinematics, focusing on $μ^+ μ^-$ production. These results exhibit interesting mass-dependent features in the asymmetries that may help study the anisotropies arising from the underlying photon GTMD description.

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arXiv2023

Transverse momentum dependent shape function for $J/ψ$ production in SIDIS

It has been shown previously that the transverse momentum dependent (TMD) factorization of heavy quarkonium production requires a TMD shape function. Its perturbative tail can be extracted by matching the cross sections valid at low and high transverse momenta. In this article we compare the order-$α_s$ TMD expressions with the order-$α_s^2$ collinear ones for $J/ψ$ production in semi-inclusive deep inelastic scattering (SIDIS), employing nonrelativistic QCD in both cases. In contrast to previous studies, we find that the small transverse momentum limit of the collinear expressions contain discontinuities. We demonstrate how to properly deal with them and include their finite contributions to the TMD shape functions. Moreover, we show that soft gluon emission from the low transverse momentum Born diagrams provide the same leading order TMD shape functions as required for the matching. Their revised perturbative tails have a less divergent behaviour as compared to the TMD fragmentation functions of light hadrons. Finally, we investigate the universality of TMD shape functions in heavy quarkonium production, identify the need for process dependent factorization and discuss the phenomenological implications.

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arXiv2023

The case for an EIC Theory Alliance: Theoretical Challenges of the EIC

We outline the physics opportunities provided by the Electron Ion Collider (EIC). These include the study of the parton structure of the nucleon and nuclei, the onset of gluon saturation, the production of jets and heavy flavor, hadron spectroscopy and tests of fundamental symmetries. We review the present status and future challenges in EIC theory that have to be addressed in order to realize this ambitious and impactful physics program, including how to engage a diverse and inclusive workforce. In order to address these many-fold challenges, we propose a coordinated effort involving theory groups with differing expertise is needed. We discuss the scientific goals and scope of such an EIC Theory Alliance.

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arXiv2023

Probing gluon GTMDs through exclusive coherent diffractive processes

We extend a previous GTMD model to improve the description of the HERA data on diffractive dijet production, and include exclusive coherent diffractive $J/ψ$ production data. We find that within our gluon GTMD model context and assumptions, there is considerable tension between the data for these two types of processes concerning the $t$ dependence. Photo- and electroproduction data for protons and nuclei from EIC and UPC data from LHC and RHIC can help to establish whether a common GTMD description is possible, as one would expect, and to facilitate studies of such data we provide predictions for the various experiments. We point out explicitly in which sense this goes beyond the description in terms of GPDs.

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arXiv2022

TMD Evolution Study of the $\cos 2 ϕ$ Azimuthal Asymmetry in Unpolarized $J/ψ$ Production at EIC

Semi-inclusive $J/ψ$ production in electron-proton collisions is a promising process to study gluon transverse momentum distributions (TMDs) at the future Electron-Ion Collider. In this article, we improve on previous studies of the $\cos 2 ϕ$ azimuthal asymmetry that arises from the linear polarization of gluons inside unpolarized protons by including TMD evolution. We find that in the TMD regime the asymmetry grows monotonically with increasing transverse momentum of the outgoing $J/ψ$, in contrast to tree level calculations with Gaussian TMDs. Our predictions for the asymmetry at EIC can become very large at larger $x$, $Q$, and transverse momenta, even larger than the positivity bound. This problem stems from the very small $b$ region and implies a range of validity of TMD factorization that is more restricted than usually expected. We also include an estimate of the nonperturbative uncertainty from the large $b$ region and we conclude that it is smaller than the largest source of uncertainty, which stems from the choice of Color Octet Long-Distance Matrix Elements.

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arXiv2022

Energy evolution of T-odd gluon TMDs at small $x$

We study the energy or TMD evolution of the three leading twist dipole type T-odd gluon TMDs inside a transversely polarized nucleon, all of which at small $x$ dynamically originate from the spin dependent odderon. Their energy dependence presents a unique opportunity to study the polarization dependent TMD evolution in the small-$x$ region, where the distributions are identical up to a normalization constant at tree level. We further propose to study their evolution via azimuthal asymmetries in virtual photon-jet production in polarized proton-proton collisions at RHIC. We present model predictions for the asymmetries as functions of the large jet or photon transverse momentum and $Q^2$ which set the hard scales in this process.

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arXiv2022

A Unified View on Geometric Phases and Exceptional Points in Adiabatic Quantum Mechanics

We present a formal geometric framework for the study of adiabatic quantum mechanics for arbitrary finite-dimensional non-degenerate Hamiltonians. This framework generalizes earlier holonomy interpretations of the geometric phase to non-cyclic states appearing for non-Hermitian Hamiltonians. We start with an investigation of the space of non-degenerate operators on a finite-dimensional state space. We then show how the energy bands of a Hamiltonian family form a covering space. Likewise, we show that the eigenrays form a bundle, a generalization of a principal bundle, which admits a natural connection yielding the (generalized) geometric phase. This bundle provides in addition a natural generalization of the quantum geometric tensor and derived tensors, and we show how it can incorporate the non-geometric dynamical phase as well. We finish by demonstrating how the bundle can be recast as a principal bundle, so that both the geometric phases and the permutations of eigenstates can be expressed simultaneously by means of standard holonomy theory.

quant-ph↗
arXiv2021

GTMD model predictions for diffractive dijet production at EIC

In this paper we consider a small-$x$ model for gluon GTMDs that we fit to data on diffractive dijet production in electron-proton collisions obtained by HERA's H1 Collaboration. Assuming a small number of free parameters, each with a physical motivation, we are able to describe those data fairly well and with this model we obtain predictions for the EIC for both electroproduction and photoproduction which may allow to further test the underlying GTMD description. In the general discussion of the impact parameter dependence we recall some subtle issues related to localization of states, choice of frames, and discuss what these aspects imply for the range of applicability of the model.

hep-ph↗
arXiv2021

The hierarchy problem and fine-tuning in a decoupling approach to multi-scale effective potentials

In many realizations of beyond the Standard Model theories, new massive particles are introduced, leading to a multi-scale system with widely separated energy scales. In this setting the Coleman-Weinberg effective potential, which describes the vacuum of the theory at the quantum level, has to be supplemented with a prescription to handle the hierarchy in mass scales. In any quantum field theory involving scalar fields and multiple, highly differing mass scales, it is in general not possible to choose a single renormalization scale that will remove all the large logarithms in the effective potential. In this paper, we focus on the so-called decoupling method, which freezes the effects of heavy particles on the renormalization group running of the light degrees of freedom at low energies. We study this for a simple two-scalar theory and find that, while the decoupling method leads to an acceptable and convergent effective potential, the method does not solve the fine-tuning problem that is inherent to the hierarchy problem of multi-scale theories. We also consider an alternative implementation of the decoupling approach, which gives different results for the shape of the potential, but still leads to similar conclusions on the amount of fine-tuning in the model. We suggest a way to avoid running into this fine-tuning problem by adopting a prescription on how to fix parameters in such decoupling approaches.

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arXiv2021

Extracting color octet NRQCD matrix elements from $J/ψ$ production at the EIC

Recently unpolarized and polarized $J/ψ\,(Υ)$ production at the Electron-Ion Collider (EIC) has been proposed as a new way to extract two poorly known color-octet NRQCD long-distance matrix elements: $\langle0\vert{\cal O}_{8}^{J/ψ}(^{1}S_{0})\vert0\rangle$ and $\langle0\vert{\cal O}_{8}^{J/ψ}(^{3}P_{0})\vert0\rangle$. The proposed method is based on a comparison to open heavy-quark pair production ideally performed at the same kinematics. In this paper we analyze this proposal in more detail and provide predictions for the EIC based on the available determinations of the color-octet matrix elements. We also propose two additional methods that do not require comparison to open heavy-quark pair production.

hep-ph↗
arXiv2020

$J/ψ$ meson production in SIDIS: matching high and low transverse momentum

We consider the transverse momentum spectrum and the $\cos 2ϕ$ azimuthal distribution of $J/ψ$ mesons produced in semi-inclusive, deep-inelastic electron-proton scattering, where the electron and the proton are unpolarized. At low transverse momentum, we propose factorized expressions in terms of transverse momentum dependent gluon distributions and shape functions. We show that our formulae, at the order $α_s,$ correctly match with the collinear factorization results at high transverse momentum. The latter are computed at the order $α_s^2$ in the framework of nonrelativistic QCD (NRQCD), with the inclusion of the intermediate $^3S_1^{[1]}$ color-singlet Fock state, as well as the subleading color-octet ones that are relatively suppressed by a factor $v^4$ in the NRQCD velocity parameter $v$. We show that the $^1\!S_0^{[8]}$ and $^3\!P_J^{[8]}$ ($J = 0,1,2$) contributions diverge in the small transverse momentum region and allow us to determine the perturbative tails of the shape functions, which carry the same quantum numbers. These turn out to be identical, except for the overall magnitude given by the appropriate NRQCD long distance matrix element.

hep-ph↗
arXiv2020

Fine-tuning and the doublet-triplet splitting problem in the minimal $SU(5)$ GUT

In this paper we analyse the doublet-triplet splitting problem in the minimal non-super-symmetric $SU(5)$ GUT. We take into account the full symmetry breaking pattern with both high scale $SU(5)$ breaking and electroweak symmetry breaking. Our analysis shows that the only phenomenologically acceptable model has three vevs, with a strong hierarchy determined by the minimization conditions. The amount of fine-tuning in the model is then numerically evaluated by looking at the effect of variation of input parameters on both the minimization conditions and the bosonic masses. Regarding the vevs as output parameters, a large amount of fine-tuning is required in this scenario, which is an expression of the doublet-triplet splitting problem. We show that this problem is more general, since a model with coupled scalar sectors will in general never realise a hierarchy in vevs. To avoid these problems we advocate imposing the desired hierarchy in vevs as part of the theory. We argue for this viewpoint because the $SU(5)$ breaking and electroweak symmetry breaking need to be adjusted to each other anyway and cannot be regarded as independent mechanisms. We suggest that not only the symmetry breaking pattern needs to be imposed, but also the scales at which the breakings happen. We show quantitatively that the generic theory with hierarchy imposed does not require any fine-tuning of the free parameters which can all be natural and perturbative as desired.

hep-ph↗
arXiv2019

Gluon TMDs and NRQCD matrix elements in $J/ψ$ production at an EIC

In this paper we analyze azimuthal asymmetries in the processes of unpolarized and polarized $J/ψ\,(Υ)$ production at an Electron-Ion Collider. Apart from giving access to various unknown gluon transverse momentum distributions, we suggest to use them as a new method to extract specific color-octet NRQCD long-distance matrix elements, i.e.\ $\langle0|{\cal O}_{8}^{J/ψ}(^{1}S_{0})|0\rangle$ and $\langle0|{\cal O}_{8}^{J/ψ}(^{3}P_{0})|0\rangle$, whose values are still quite uncertain and for which lattice calculations are unavailable. The new method is based on combining measurements of analogous asymmetries in open heavy-quark pair production which can be performed at the same energy. To enhance the gluon contribution one can consider smaller values of $x$ and, in order to assess the impact of small-$x$ evolution, we perform a numerical study using the MV model as a starting input and evolve it with the JIMWLK equations.

hep-ph↗
arXiv2019

Studies of gluon TMDs and their evolution using quarkonium-pair production at the LHC

$J/ψ$- or $Υ$-pair production at the LHC are promising processes to study the gluon transverse momentum distributions (TMDs) which remain very poorly known. In this article, we improve on previous results by including the TMD evolution in the computation of the observables such as the pair-transverse-momentum spectrum and asymmetries arising from the linear polarization of gluons inside unpolarized protons. We show that the azimuthal asymmetries generated by the gluon polarization are reduced compared to the tree level case but are still of measurable size (in the 5%-10% range). Such asymmetries should be measurable in the available data sets of $J/ψ$ pairs and in the future data sets of the high-luminosity LHC for $Υ$ pairs.

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