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P. J. Mulders

Publications and source records attributed to P. J. Mulders.

At least 19 recordsLinked to original sources

Non-collinearity in di-jet fragmentation in electron-positron scattering

We study fragmentation in electron-positron annihilation assuming a di-jet situation, using variables defined independent of any frame. In a collinear situation some of the variables are centered around zero with the small deviations attributed to intrinsic transverse momenta and large deviations attributed to additional hard subprocesses. Of course there is a gradual transition. Our modest goal is to show that covariantly defined variables are well suited to get a feeling for the magnitude of intrinsic transverse momenta.

hep-ph

The LHCSpin Project

LHCSpin aims at installing a polarized gas target in front of the LHCb spectrometer, bringing, for the first time, polarized physics to the LHC. The project will benefit from the experience achieved with the installation of an unpolarized gas target at LHCb during the LHC Long Shutdown 2. LHCb will then become the first experiment simultaneously running in collider and fixed-target mode with polarized targets, opening a whole new range of explorations to its exceptional spectrometer. LHCSpin will offer a unique opportunity to probe polarized quark and gluon parton distributions in nucleons and nuclei, especially at high $x$ and intermediate $Q^2$, where experimental data are still largely missing. Beside standard collinear parton distribution functions (PDFs), LHCSpin will make it possible to study multidimensional polarized parton distributions that depend also on parton transverse momentum. The study of the multidimensional partonic structure of the nucleon, particularly including polarization effects, can test our knowledge of QCD at an unprecedented level of sophistication, both in the perturbative and nonperturbative regime. At the same time, an accurate knowledge of hadron structure is necessary for precision measurements of Standard Model (SM) observables and discovery of physics beyond the SM. Due to the intricate nature of the strong interaction, it is indispensable to perform the widest possible suite of experimental measurements. It will be ideal to have two new projects complementing each other: a new facility for polarized electron-proton collisions and a new facility for polarized proton-proton collisions. LHCSpin stands out at the moment as the most promising candidate for the second type of project, going beyond the kinematic coverage and the accuracy of the existent experiments, especially on the heavy-quark sector.

hep-ex

Emergent symmetries of the Standard Model

We show how, using multipartite entanglement, the symmetries among bosons and fermions of the Standard Model of particle physics emerge. Fermions belong to tripartite maximally entangled classes starting with basic chiral right and left states. Quarks and leptons belong to different classes, with only leptons appearing as asymptotic states in three space dimensions. The Higgs boson is the scalar mode with a nonvanishing vacuum expectation value, other bosons are as usual linked to symmetry generators.

hep-ph

The 3D entangled structure of the proton; transverse degrees of freedom in QCD, momenta, spins and more

Light-front quantized quark and gluon states (partons) play a dominant role in high energy scattering processes. Initial state hadrons are mixed ensembles of partons, while produced pure partonic states appear as mixed ensembles of hadrons. The transition from collinear hard physics to the 3D structure including partonic transverse momenta is related to confinement which links color and spatial degrees of freedom. We outline ideas on emergent symmetries in the Standard Model and their connection to the 3D structure of hadrons. Wilson loops, including those with light-like Wilson lines such as used in the studies of transverse momentum dependent distribution functions (TMDs) may play a crucial role here, establishing a direct link between transverse spatial degrees of freedom and gluonic degrees of freedom.

hep-ph

The Roots of the Standard Model of Particle Physics

We conjecture how the particle content of the standard model can emerge starting with a supersymmetric Wess-Zumino model in 1+1 dimensions (d = 2) with three real boson and fermion fields. Considering SU(3) transformations, the lagrangian and its ground state are SO(3) invariant. The SO(3) symmetry extends the basic IO(1,1) Poincaré symmetry to IO(1,3) for the asymptotic fields requiring physical states to be singlets under the A_4 symmetry that governs the SO(3) embedding. This is linked to the three-family structure. For the internal symmetries of the asymptotic fields an SU(2) x U(1) symmetry remains, broken down as in the standard model. The boson excitations in d = 4 are identified with electroweak gauge bosons and the Higgs boson. Fermion excitations come in three families of leptons living in E(1,3) Minkowski space or three families of quarks living in E(1,1). Many features of the standard model now emerge in a natural way. The supersymmetric starting point solves the naturalness problem. The underlying left-right symmetry leads to custodial symmetry in the electroweak sector. In the spectrum one has Dirac-type charged leptons and Majorana-type neutrinos. The electroweak behavior of the naturally confined quarks, leads to fractional electric charges and the doublet and singlet structure of left- and right-handed quarks, respectively. Most prominent feature is the link between the number of colors, families and space directions.

hep-ph

Operator Structure of TMDs

The focus of this talk is on the transverse components of parton momenta. Like for collinear parton distribution functions (PDFs), we are also in the case of transverse momentum dependent (TMD) PDFs, talking about forward matrix elements. While the collinear PDFs describe only spin-spin correlations, the TMD PDFs (or in short TMDs) include spin-momentum correlations, including also time-reversal-odd (T-odd) correlations. The latter are important in the description of single spin asymmetries. In this way TMDs open up new ways of studying the spin structure of hadrons or they can be used as tools that incorporate hadronic structure also in non-collinear situations. The operator structure of TMDs within QCD, in particular the structure of Wilson lines, is more complex than that for collinear functions leading to various ways of breaking of universality. This breaking of universality, however, can be handled within QCD.

hep-ph

Spin Physics and Transverse Structure

Spin is a welcome complication in the study of partonic structure that has led to new insights, even if theoretically and experimentally not all dust has settled, in particular on quark flavor dependence and gluon spin. At the same time it opened new questions on angular momentum and effects of transverse structure. In this talk the focus is on the role of the transverse momenta of partons. Like for collinear parton distribution functions (PDFs), we are also in the case of transverse momentum dependent (TMD) PDFs, talking about forward matrix elements. TMD PDFs (or in short TMDs) extend collinear PDFs with only spin-spin correlations to PDFs that include spin-momentum correlations, including also time-reversal-odd (T-odd) correlations, relevant for the description of single spin asymmetries. In this way TMDs open up new ways of studying the spin structure. Their operator structure within QCD, however, is more complex leading to various ways of breaking of universality.

hep-ph

Transverse momentum dependent (TMD) parton distribution functions: status and prospects

We provide a concise overview on transverse momentum dependent (TMD) parton distribution functions, their application to topical issues in high-energy physics phenomenology, and their theoretical connections with QCD resummation, evolution and factorization theorems. We illustrate the use of TMDs via examples of multi-scale problems in hadronic collisions. These include transverse momentum q_T spectra of Higgs and vector bosons for low q_T, and azimuthal correlations in the production of multiple jets associated with heavy bosons at large jet masses. We discuss computational tools for TMDs, and present an application of a new tool, TMDlib, to parton density fits and parameterizations.

hep-ph

Operator analysis of $p_T$-widths of TMDs

Transverse momentum dependent (TMD) parton distribution functions (PDFs), TMDs for short, are defined as the Fourier transform of matrix elements of nonlocal combinations of quark and gluon fields. The nonlocality is bridged by gauge links, which for TMDs have characteristic paths (future or past pointing), giving rise to a process dependence that breaks universality. It is possible, however, to construct sets of universal TMDs of which in a given process particular combinations are needed with calculable, process-dependent, coefficients. This occurs for both T-odd and T-even TMDs, including also the {\it unpolarized} quark and gluon TMDs. This extends the by now well-known example of T-odd TMDs that appear with opposite sign in single-spin azimuthal asymmetries in semi-inclusive deep inelastic scattering or in the Drell-Yan process. In this paper we analyze the cases where TMDs enter multiplied by products of two transverse momenta, which includes besides the $p_T$-broadening observable, also instances with rank two structures. To experimentally demonstrate the process dependence of the latter cases requires measurements of second harmonic azimuthal asymmetries, while the $p_T$-broadening will require measurements of processes beyond semi-inclusive deep inelastic scattering or the Drell-Yan process. Furthermore, we propose specific quantities that will allow for theoretical studies of the process dependence of TMDs using lattice QCD calculations.

hep-ph

TMDlib and TMDplotter: library and plotting tools for transverse-momentum-dependent parton distributions

Transverse-momentum-dependent distributions (TMDs) are central in high-energy physics from both theoretical and phenomenological points of view. In this manual we introduce the library, TMDlib, of fits and parameterisations for transverse-momentum-dependent parton distribution functions (TMD PDFs) and fragmentation functions (TMD FFs) together with an online plotting tool, TMDplotter. We provide a description of the program components and of the different physical frameworks the user can access via the available parameterisations.

hep-ph

Color effects for transverse momentum dependent parton distribution functions in hadronic processes

In the Drell-Yan process (DY) a quark and an antiquark, coming from two different protons, produce a colorless virtual photon. In the proton description, we include transverse momentum dependent parton distribution functions (TMD PDFs), which go beyond the ordinary collinear PDFs. As such, we become sensitive to polarization modes of the partons and protons that one cannot probe without accounting for transverse momenta of partons, in particular when one looks at azimuthal asymmetries. Matrix elements used in the description of hadronic processes, such as DY, require the inclusion of gauge links, coming from gluon contributions in the process, which are path-ordered exponentials tracing the color flow. In processes with two hadrons in the initial state the color flow between different parts of the process causes entanglement. We show that in the process of color disentangling each gauge link remains sensitive to this color flow. After disentanglement, we find that particular combinations of TMDs require a different numerical color factor than one might have expected. Such color factors will even play a role for azimuthal asymmetries in the simplest hadronic processes such as the DY process.

hep-ph

Universality of TMD correlators

In a high-energy scattering process with hadrons in the initial state, color is involved. Transverse momentum dependent distribution functions (TMDs) describe the quark and gluon distributions in these hadrons in momentum space with the inclusion of transverse directions. Apart from the (anti)-quarks and gluons that are involved in the hard scattering process, additional gluon emissions by the hadrons have to be taken into account as well, giving rise to Wilson lines or gauge links. The TMDs involved are sensitive to the process under consideration and hence potentially nonuniversal due to these Wilson line interactions with the hard process; different hard processes give rise to different Wilson line structures. We will show that in practice only a finite number of universal TMDs have to be considered, which come in different linear combinations depending on the hard process under consideration, ensuring a generalized universality. For quarks this gives rise to three Pretzelocity functions, whereas for gluons a richer structure of functions arises.

hep-ph

Wilson Lines off the Light-cone in TMD PDFs

Transverse Momentum Dependent (TMD) parton distribution functions (PDFs) also take into account the transverse momentum ($p_T$) of the partons. The $p_T$-integrated analogues can be linked directly to quark and gluon matrix elements using the operator product expansion in QCD, involving operators of definite twist. TMDs also involve operators of higher twist, which are not suppressed by powers of the hard scale, however. Taking into account gauge links that no longer are along the light-cone, one finds that new distribution functions arise. They appear at leading order in the description of azimuthal asymmetries in high-energy scattering processes. In analogy to the collinear operator expansion, we define a universal set of TMDs of definite rank and point out the importance for phenomenology.

hep-ph

Color entanglement for azimuthal asymmetries in the Drell-Yan process

In the resummation of collinear gluons emitted together with active partons from the hadrons in the Drell-Yan process (DY) effects of color entanglement become important when the transverse directions are taken into account. It is then no longer possible to write the cross section as the convolution of two soft correlators and a hard part. We show that the color entanglement introduces additional color factors that must be taken into account in the extraction of transverse momentum dependent parton distribution functions (TMD PDFs) from azimuthal asymmetries. Examples where such effects matter are the extraction of the double Sivers and double Boer-Mulders asymmetries. Furthermore, we will argue why this color entanglement is a basic ingredient already in the tree-level description of azimuthal asymmetries.

hep-ph

Generalized Universality of Definite Rank Gluon Transverse Momentum Dependent Correlators

Transverse momentum dependent (TMD) parton correlators describing the partonic structure of hadrons contain gauge links, required by color gauge invariance. The required gauge links enter in the matrix elements that contain the parton fields and depend on the color flow in the hard process. The correlators are expanded in terms of transverse momentum dependent parton distribution functions, referred to as TMD PDFs, or in short TMDs. In this paper, we introduce gluon TMDs of definite rank, by making an expansion of the TMD gluon correlator with the help of irreducible tensors built from the transverse momenta. The process dependence is isolated in gauge link dependent gluonic pole factors multiplying the TMDs. It is important to account for the different possibilities in the color structure within the matrix elements, leading to multiple TMDs at a given rank. In this way we are able to write the leading tree level result for a hard process in terms of process dependent gluon correlators which are expressed in a finite set of universal TMDs. We tabulate the gluonic pole factors for various gauge links, among them those that are relevant for 2 to 2 processes.

hep-ph

Universality of Quark and Gluon TMD Correlators

Transverse Momentum Dependent (TMD) parton distribution functions (PDFs), in short referred to as TMDs, also take into account the transverse momentum (pT) of the partons. Just as the pT-integrated analogues we want to link them to quark and gluon matrix elements using Operator Product Expansion methods in QCD, involving operators of definite twist. The TMDs also involve operators of higher twist, which are not suppressed by powers of the hard scale, however. Using the expression for TMDs involving nonlocal matrix elements of quark and gluon fields there is a gauge link dependence, which also introduces an inherent process dependence. Using transverse moments, which are specific pT-weightings, we can establish the link with quark and gluon fields including the higher twist ones. We introduce (a finite number of) universal TMDs of definite rank and show how the process dependent TMDs can be written as combinations of these universal functions.

hep-ph

Universality of TMD distribution functions

We introduce transverse momentum dependent parton distribution functions (TMDs) for gluons with definite rank. The rank refers to the azimuthal dependence corresponding to the tensorial structure in transverse momenta multiplying universal functions only depending on $x$ and $p_T^2$. In this way only a finite number of functions of definite rank remains for a target with the maximal rank depending on its spin. Gauge links, required for color gauge invariance, enter in the explicit description of the matrix elements corresponding to these TMDs and account for their process dependence. In this way a general gauge link dependent function is expressed in the universal set, where all process (i.e. gauge link) dependence is isolated in gluonic pole factors multiplying the universal TMDs of definite rank.

hep-ph

Universality of TMD distribution functions of definite rank

Transverse momentum dependent (TMD) distribution and fragmentation functions are described as Fourier transforms of matrix elementscontaining nonlocal combinations of quark and gluon fields. These matrix elements also contain a gauge link operator with a process dependent path, of which the process dependence that can be traced back to the color flow in the process. Expanding into irreducible tensors built from the transverse momenta $p_\st$, we can define a universal set of TMD correlators of definite rank with a well-defined operator structure.

hep-ph