arXiv subjects

Daniël Boer

Publications and source records attributed to Daniël Boer.

34 records · Page 2Linked to original sources

arXiv2019

Opportunities for spin physics at EIC

This is a brief overview of the spin physics opportunities at a high energy, high luminosity, polarized Electron-Ion Collider (EIC). It covers measurements of electroweak polarized structure functions, quark and gluon PDFs, TMDs, GPDs and GTMDs. Exploiting the many possible final states allows to probe various spin effects. Open and bound heavy quark production can be used to probe gluon TMDs, but also color-octet NRQCD long distance matrix elements. Spin-dependent fragmentation functions can be used too, but are also interesting in themselves. Especially for studies of the small-$x$ and the high-$Q^2$ spin structure the EIC will be essential.

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arXiv2019

Analysis of fine-tuning measures in models with extended Higgs sectors

In the literature measures of fine-tuning have been discussed as one of the tools to assess the feasibility of beyond the Standard Model theories. In this paper we focus on two specific measures and investigate what kind of fine-tuning they actually quantify. First we apply both measures to the two Higgs doublet model, for which one can analyze the numerical results in terms of available analytic expressions. After drawing various conclusions about the fine-tuning measures, we investigate a particular left-right symmetric model for which it has been claimed that already at tree-level it suffers from a high amount of fine-tuning. We will reach a different conclusion, although left-right symmetric models may require a modest amount of fine-tuning if phenomenological constraints are imposed. Our analysis shows that the two considered measures can probe different aspects of fine-tuning and are both useful if applied and interpreted in the appropriate way.

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arXiv2019

Overview of Spin Physics at EIC

The possibilities to measure spin effects at a high-energy Electron-Ion Collider (EIC) are reviewed from a theory point of view. Various types of spin distributions and promising observables are discussed.

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arXiv2019

Comment on 'Winding around non-Hermitian singularities' by Zhong et al., Nat. Commun. 9, 4808 (2018)

In a recent paper entitled "Winding around non-Hermitian singularities" by Zhong et al., published in Nat. Commun. 9, 4808 (2018), a formalism is proposed for calculating the permutations of eigenstates that arise upon encircling (multiple) exceptional points (EPs) in the complex parameter plane of an analytic non-Hermitian Hamiltonian. The authors suggest that upon encircling EPs one should track the eigenvalue branch cuts that are traversed, and multiply the associated permutation matrices accordingly. In this comment we point out a serious shortcoming of this approach, illustrated by an explicit example that yields the wrong result for a specific loop. A more general method that has been published earlier by us and that does not suffer from this problem, is based on using fundamental loops. We briefly explain the method and list its various advantages. In addition, we argue that this method can be verified in a three wave-guide system, which then also unambiguously establishes the noncommutativity associated with encircling multiple EPs.

quant-ph↗

arXiv2018

Non-abelian nature of systems with multiple exceptional points

The defining characteristic of an exceptional point (EP) in the parameter space of a family of operators is that upon encircling the EP eigenstates are permuted. In case one encircles multiple EPs, the question arises how to properly compose the effects of the individual EPs. This was thought to be ambiguous. We show that one can solve this problem by considering based loops and their deformations. The theory of fundamental groups allows to generalize this technique to arbitrary degeneracy structures like exceptional lines in a three-dimensional parameter space. As permutations of three or more objects form a non-abelian group, the next question that arises is whether one can experimentally demonstrate this non-commutative behavior. This requires at least two EPs of a family of operators that have at least 3 eigenstates. A concrete implementation in a recently proposed $\mathcal{PT}$ symmetric waveguide system is suggested as an example of how to experimentally check the composition law and show the non-abelian nature of non-hermitian systems with multiple EPs.

math-ph↗

arXiv2018

Directed flow from C-odd gluon correlations at small $x$

It is shown that odd harmonic azimuthal correlations, including the directed flow $v_1$, in forward two-particle production in peripheral proton-nucleus ($pA$) collisions can arise simply from the radial nuclear profile of a large nucleus. This requires consideration of the C-odd part of the gluonic generalized transverse momentum dependent (GTMD) correlator of nucleons in the nucleus. The gluonic GTMD correlator is the Fourier transform of an off-forward hadronic matrix element containing gluonic field strength tensors that are connected by gauge links. It is parametrized in terms of various gluon GTMD distribution functions (GTMDs). We show (in a gauge invariant way) that for the relevant dipole-type gauge link structure in the small-$x$ limit the GTMD correlator reduces to a generalized Wilson loop correlator. The Wilson loop correlator is parametrized in terms of a single function, implying that in the region of small $x$ there is only one independent dipole-type GTMD, which can have a C-odd part. We show that the odderon Wigner distribution, which is related to this C-odd dipole GTMD by a Fourier transform, generates odd harmonics in the two-particle azimuthal correlations in peripheral $pA$ collisions. We calculate the first odd harmonic $v_1$ for forward production within the color glass condensate framework in the limit of a large number of colors. We find that nonzero odd harmonics are present without breaking the rotational symmetry of the nucleus, arising just from its inhomogeneity in the radial direction. Using a CGC model with a cubic action, we illustrate that percent level $v_1$ can arise from this C-odd mechanism. In contrast, we show that only even harmonics arise in diffractive dijet production in ultra-peripheral $pA$ collisions where this gluon dipole GTMD also appears.

hep-ph↗

arXiv2018

Semi-inclusive production of two back-to-back hadron pairs in $e^+e^-$ annihilation revisited

The cross section for back-to-back hadron pair production in $e^+e^-$ annihilation provides access to the dihadron fragmentation functions (DiFF) needed to extract nucleon parton distribution functions from the semi-inclusive deep inelastic scattering (SIDIS) experiments with two detected final state hadrons. Particular attention is given to the so-called interference DiFF (IFF), which makes it possible to extract the transversity parton distribution of the nucleon in the collinear framework. However, previously unnoticed discrepancies were recently highlighted between the definitions of the IFFs appearing in the collinear kinematics when reconstructed from DiFFs entering the unintegrated fully differential cross sections of SIDIS and $e^+e^-$ annihilation processes. In this work, to clarify this problem we rederive the fully differential cross section for $e^+e^-$ annihilation at the leading-twist approximation. We find a mistake in the definition of the kinematics in the original expression that systematically affects a subset of terms and that leads to two significant consequences. First, the discrepancy between the IFF definitions in the cross sections for SIDIS and $e^+e^-$ annihilation is resolved. Second, the previously derived azimuthal asymmetry for accessing the helicity dependent DiFF $G_1^\perp$ in $e^+e^-$ annihilation vanishes, which explains the nonobservation of this asymmetry in the recent experimental searches by the ${\tt BELLE}$ Collaboration. We discuss the recently proposed alternative option to extract $G_1^\perp$.

hep-ph↗

arXiv2017

Colour unwound - disentangling colours for azimuthal asymmetries in Drell-Yan scattering

It has been suggested that a colour-entanglement effect exists in the Drell-Yan cross section for the 'double T-odd' contributions at low transverse momentum $Q_T$, rendering the colour structure different from that predicted by the usual factorisation formula [1]. These T-odd contributions can come from the Boer-Mulders or Sivers transverse momentum dependent distribution functions. The different colour structure should be visible already at the lowest possible order that gives a contribution to the double Boer-Mulders (dBM) or double Sivers (dS) effect, that is at the level of two gluon exchanges. To discriminate between the different predictions, we compute the leading-power contribution to the low-$Q_T$ dBM cross section at the two-gluon exchange order in the context of a spectator model. The computation is performed using a method of regions analysis with Collins subtraction terms implemented. The results conform with the predictions of the factorisation formula. In the cancellation of the colour entanglement, diagrams containing the three-gluon vertex are essential. Furthermore, the Glauber region turns out to play an important role - in fact, it is possible to assign the full contribution to the dBM cross section at the given order to the region in which the two gluons have Glauber scaling. A similar disentanglement of colour is found for the dS effect.

hep-ph↗

arXiv2016

Probing Gluon TMDs at a Future EIC

Gluon TMDs can be accessed through the analysis of azimuthal asymmetries for heavy quark pair and dijet production in electron-proton collisions, similarly to the way quark TMDs are commonly extracted from semi-inclusive deep-inelastic scattering data. We calculate the upper bounds for these observables, showing in which kinematic regions they are large enough to be measured in future experiments at an Electron-Ion Collider. Moreover, we study their behavior in the small-$x$ region, adopting a McLerran-Venugopalan model for unpolarized and linearly polarized gluon distributions. By comparison with related observables at RHIC and LHC, we expect to gather information on the process dependence of the gluon TMDs and to test our prediction of a sign change of the gluon Sivers function and two other $T$-odd gluon distributions.

hep-ph↗

arXiv2016

Gluon TMDs in quarkonium production

Quarkonium production offers good possibilities to study gluon TMDs. In this proceedings contribution this topic is explored for the linearly polarized gluons inside unpolarized hadrons and unpolarized gluons inside transversely polarized hadrons. It is argued that $χ_{b0/2}$ and $η_b$ production at LHC are best to study the effects of linearly polarized gluons in hadronic collisions, by means of angular independent ratios of ratios of cross sections. This can be directly compared to $\cos 2ϕ$ asymmetries in heavy quark pair and dijet production in DIS at a future high-energy Electron-Ion Collider (EIC), which probe the same TMDs. In the small-$x$ limit this corresponds to the Weizsäcker-Williams (WW) gluon distributions, which should show a change in behavior for transverse momenta around the saturation scale. Together with investigations of the dipole (DP) gluon distributions, this can provide valuable information about the polarization of the Color Glass Condensate if sufficiently small $x$ are reached. Quarkonia can also be useful in the study of single transverse spin asymmetries. For transversely polarized hadrons the gluon distribution can be asymmetric, which is referred to as the Sivers effect. It leads to single spin asymmetries in for instance $J/ψ$ (pair) production at AFTER@LHC, which probe the WW or $f$-type gluon Sivers TMD. It allows for a test of a sign-change relation w.r.t. the gluon Sivers TMD probed at an EIC in open heavy quark pair production. Single spin asymmetries in backward inclusive $C$-odd quarkonium production, such as $J/ψ$ production, may offer probes of the DP or $d$-type gluon Sivers TMD at small $x$-values in the polarized proton, which in that limit corresponds to a correlator of a single Wilson loop, describing the spin-dependent odderon.

hep-ph↗

arXiv2016

Gluon and Wilson loop TMDs for hadrons of spin $\leq$ 1

In this paper we consider the parametrizations of gluon transverse momentum dependent (TMD) correlators in terms of TMD parton distribution functions (PDFs). These functions, referred to as TMDs, are defined as the Fourier transforms of hadronic matrix elements of nonlocal combinations of gluon fields. The nonlocality is bridged by gauge links, which have characteristic paths (future or past pointing), giving rise to a process dependence that breaks universality. For gluons, the specific correlator with one future and one past pointing gauge link is, in the limit of small $x$, related to a correlator of a single Wilson loop. We present the parametrization of Wilson loop correlators in terms of Wilson loop TMDs and discuss the relation between these functions and the small-$x$ `dipole' gluon TMDs. This analysis shows which gluon TMDs are leading or suppressed in the small-$x$ limit. We discuss hadronic targets that are unpolarized, vector polarized (relevant for spin-$1/2$ and spin-$1$ hadrons), and tensor polarized (relevant for spin-$1$ hadrons). The latter are of interest for studies with a future Electron-Ion Collider with polarized deuterons.

hep-ph↗

arXiv2016

Asymmetries in Heavy Quark Pair and Dijet Production at an EIC

Asymmetries in heavy quark pair and dijet production in electron-proton collisions allow studies of gluon TMDs in close analogy to studies of quark TMDs in semi-inclusive DIS. Here we present expressions for azimuthal asymmetries for both unpolarized and transversely polarized proton cases and consider the maximal asymmetries allowed. The latter are found to be rather sizeable, except in certain kinematic limits which are pointed out. In addition, we consider the small-x limit and expectations from a McLerran-Venugopalan model for unpolarized and linearly polarized gluons and from a perturbative, large transverse momentum calculation for the T-odd gluon TMDs. Comparison to related observables at RHIC and LHC is expected to provide valuable information about the process dependence of the gluon TMDs. In particular this will offer the possibility of a sign change test of the gluon Sivers TMD and two other T-odd gluon TMDs. This provides additional motivation for studies of azimuthal asymmetries in heavy quark pair and dijet production at a future Electron-Ion Collider.

hep-ph↗

arXiv2016

Single spin asymmetries from a single Wilson loop

We study the leading-power gluon transverse momentum dependent distributions (TMDs) of relevance to the study of asymmetries in the scattering off transversely polarized hadrons. Next-to-leading-order perturbative calculations of these TMDs show that at large transverse momentum they have common dynamical origins, but that in the limit of small longitudinal momentum fraction $x$ only one origin remains. We find that in this limit only the dipole-type gluon TMDs survive and become identical to each other. At small $x$ they are all given by the expectation value of a single Wilson loop inside the transversely polarized hadron, the so-called spin-dependent odderon. This universal origin of transverse spin asymmetries at small $x$ is of importance to current and future experimental studies, paving the way to a better understanding of the role of gluons in the three-dimensional structure of spin-polarized protons.

hep-ph↗

arXiv2016

Gluon TMD studies at EIC

A high-energy Electron-Ion Collider (EIC) would offer a most promising tool to study in detail the transverse momentum distributions of gluons inside hadrons. This applies to unpolarized as well as linearly polarized gluons inside unpolarized protons, and to left-right asymmetric distributions of gluons inside transversely polarized protons, the so-called gluon Sivers effect. The inherent process dependence of these distributions can be studied by comparing to similar, but often complementary observables at LHC.

hep-ph↗

arXiv2015

Linearly polarized gluon effects in unpolarized collisions

Linear polarization of gluons inside unpolarized hadrons affects the transverse momentum distribution of produced spin-0 particles, such as of the Higgs or (pseudo-)scalar quarkonium states at LHC. Despite the currently unknown amount of linear gluon polarization, a range of predictions can be obtained, using TMD evolution, which indicates that their effect is on the few percent level in Higgs production, but can be much larger in quarkonium production. Together with asymmetries in open charm or bottom production in electro-production at an Electron-Ion Collider, the size and sign of the linear gluon polarization could be extracted experimentally. These processes also allow to test the behavior expected at small $x$ in and outside the saturation region.

hep-ph↗

arXiv2015

The gluon Sivers distribution: status and future prospects

This is a review of what is currently known about the gluon Sivers distribution and of what are the opportunities to learn more about it. Because single transverse spin asymmetries in $p^\uparrow \, p \to π\, X$ provide only indirect information about the gluon Sivers function through the relation with the quark-gluon and tri-gluon Qiu-Sterman functions, current data from hadronic collisions at RHIC have not yet been translated into a solid constraint on the gluon Sivers function. SIDIS data, including the COMPASS deuteron data, allow for a gluon Sivers contribution that is of the natural size expected from large $N_c$ arguments, which is ${\cal O}(1/N_c)$ times the nonsinglet quark Sivers contribution. Several very promising processes to measure the gluon Sivers effect directly have been put forward, which apart from ongoing and future investigations at RHIC, would strongly favor experiments at AFTER@LHC and a possible future Electron-Ion Collider. Due to the inherent process dependence of TMDs, the gluon Sivers TMD probed in the various processes are not necessarily the same, but rather can be different linear combinations of two universal gluon Sivers functions that have different behavior under charge conjugation and that therefore satisfy different theoretical constraints. For this reason both hadronic and DIS type of collisions are essential in the study of the role of gluons in transversely polarized protons.

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