Hadron Structure Research Articles

Nonlinear Regge trayectories in the context of bottom-up holography

Motivated by the non-holographic phenomenology, where the mesonic constituent mass breaks linearity in Regge trajectories, we discuss how to implement nonlinear Regge trajectories by deforming the static (monoparametric) quadratic dilaton into a non-quadratic one. This deformation adds an extra parameter into the dilaton, which measures the constituent mass effect, accounting for nonlinearity in the hadronic trajectory. We applied this model to the description of the isovector multiplet spectrum. The set of isovector parameters defines a set of hadronic calibration curves for the dilaton slope and linearity deviation parameter, allowing us to extrapolate the model to other vector states, such as heavy-light mesons or vector non-qq¯ hadrons. In other words, this approach allows us to consider the hadronic inner structure by modifying the dilaton profile.

Combining nonperturbative transverse momentum dependence with TMD evolution

Central to understanding the nonperturbative, intrinsic partonic nature of hadron structure are the concepts of transverse momentum dependent (TMD) parton distribution and fragmentation functions. A TMD factorization approach to the phenomenology of semi-inclusive processes that includes evolution, higher orders, and matching to larger transverse momentum is ultimately necessary for reliably connecting with phenomenologically extracted nonperturbative structures, especially when widely different scales are involved. In this paper, we will address some of the difficulties that arise when phenomenological techniques that were originally designed for very high energy applications are extended to studies of hadron structures, and we will solidify the connection between standard high energy TMD implementations and the more intuitive, parton model based approaches to phenomenology that emphasize nonperturbative hadron structure. In the process, we will elaborate on differences between forward and backward TMD evolution, which in the context of this paper, we call ``bottom-up'' and ``top-down'' approaches, and we will explain the advantages of a bottom-up strategy. We will also emphasize and clarify the role of the integral relations that connect TMD and collinear correlation functions. We will show explicitly how they constrain the nonperturbative ``$g$-functions'' of standard Collins-Soper-Sterman implementations of TMD factorization. This paper is especially targeted toward phenomenologists and model builders who are interested in merging specific nonperturbative models and calculations (including lattice QCD) with TMD factorization at large $Q$. Our main result is a recipe for incorporating nonperturbative models into TMD factorization and for constraining their parameters in a way that matches perturbative QCD and evolution.

Accessing pion GPDs through the Sullivan process: is it feasible?

Describing hadronic structure is one of the most intriguing problems in physics. In this respect, generalized parton distributions (GPDs) constitute an outstanding tool, allowing to draw “three dimensional pictures” of hadron’s inside. Starting from contemporary models for pion’s GPDs fulfilling all constraints imposed by QCD, we compute Compton form factors of pions subjected to deeply virtual Compton scattering. We show CFF’s behaviour to be gluon-dominated at EIC’s kinematics. Finally we evaluate lepton-beam-spin asymmetries in the Sullivan process, demonstrating the existence of such and thus triggering optimism about the possibility of probing pion’s 3D structure at electron-ion colliders.

Structure of exotic hadrons by a weak-binding relation with finite-range correction

The composite nature of a shallow bound state is studied by using the weak-binding relation, which connects the compositeness of the bound state with observables. We first show that the previous weak-binding relation cannot be applied to the system with a large effective range. To overcome this difficulty, we introduce the finite-range correction by redefining the typical length scale in the weak-binding relation. A method to estimate the uncertainty of the compositeness is proposed. It is numerically demonstrated that the range correction enlarges the applicable region of the weak-binding relation. Finally, we apply the improved weak-binding relation to the actual hadrons, nuclei, and atomic systems [deuteron, $X(3872)$, $D^{*}_{s0}(2317)$, $D_{s1}(2460)$, $N\Omega$ dibaryon, $\Omega\Omega$ dibaryon, ${}^{3}_{\Lambda}{\rm H}$, and ${}^{4}{\rm He}$ dimer] to discuss their internal structure from the compositeness. We present a reasonable estimation of the compositeness of the deuteron by properly taking into account the uncertainty. The results of $X(3872)$ and the $N\Omega$ dibaryon show that the range correction is important to estimate the compositeness of physical states.

DIS physics at the EIC and LHeC and connections to the future LHC and $\nu$A programs

Deeply-inelastic scattering (DIS) stands to enter a golden age with the prospect of precision programs at the Electron-Ion Collider (EIC) and Large Hadron-electron Collider (LHeC). While these programs will be of considerable importance to resolving longstanding issues in (non)perturbative QCD as well as hadronic and nuclear structure, they will also have valuable implications for a wider range of physics at the Energy and Intensity Frontiers, including at the High-Luminosity LHC (HL-LHC) and future \nu AνA facilities. In this plenary contribution, we highlight a number of salient examples of the potential HEP impact from the complementary EIC and LHeC programs drawn from their respective Yellow Report and Whitepaper. Interested readers are encouraged to consult the extensive studies and literature from which these examples are taken for more detail.

Shadow generalized parton distributions: a practical approach to the deconvolution problem of DVCS

Deeply virtual Compton scattering (DVCS) attracts a lot of interest due to its sensitivity to generalized parton distributions (GPDs) which provide a rich access to the partonic structure of hadrons. However, the practical extraction of GPDs for this channel requires a deconvolution procedure, whose feasibility has been disputed. We provide a practical approach to this problem based on a next-to-leading order analysis and a careful study of evolution effects, by exhibiting shadow GPDs with arbitrarily small imprints on DVCS observables at current and future experimental facilities. This shows that DVCS alone will not allow for a model independent extraction of GPDs and a multi-channel analysis is required for this purpose.

Global Analysis of SSAs and the Impact of the EIC and SoLID on Tensor Charge Extractions

Single transverse-spin asymmetries (SSAs) give great insight into the 3-dimensional structure of hadrons. We report on the first global QCD analysis of SSAs in semi-inclusive deep-inelastic scattering, electron-positron annihilation, Drell-Yan, and single-inclusive proton-proton collisions. One byproduct of the analysis is an extraction of the transversity function, from which the nucleon tensor charges can be computed, and we find, for the first time, agreement with lattice QCD for these quantities. Based on this analysis, we perform an impact study of future data on extractions of the nucleon tensor charges.

Ultraperipheral collisions and low-x physics

Ultraperipheral collisions at the LHC and RHIC offer the highest currently available energy for photon-nucleon and photon-nucleus collisions. Thus they are a valuable tool for studying the gluonic structure of hadrons and nuclei at small x. We discuss recent theoretical work towards understanding such exclusive processes at NLO accuracy in QCD perturbation theory. These theoretical advances are also immediately relevant for understanding the physics of deep inelastic scattering at small x. We also discuss experimental results in ultraperipheral collisions, most prominently for exclusive vector meson production.

Transverse Single Spin Asymmetries of Heavy Flavor Electrons and Charged Pions in 200 GeV $p+p^{\uparrow}$ Collisions at Midrapidity

Transverse single spin asymmetries of particles produced in p+p^{\uparrow}p+p↑ collisions provide insight on the partonic spin and momentum structure of hadrons; heavy flavor electrons provide access to initial state spin-momentum correlations of gluons in the proton, while charged pions provide access to initial and final state transverse spin effects. Charged particles are measured at midrapidity at PHENIX using the silicon vertex detector and central arm spectrometer, made of an electromagnetic calorimeter, a ring-imaging Cherenkov detector, and drift and pad chambers. Recent results for both electron and charged pion measurements from the 2015 running period will be presented.

The NICA-SPD project: a new tool to investigate the hadron structure

SPD is an international Collaboration gathering around the Spin Physics Detector at the Nuclotron-based Ion Collider FAcility (NICA), presently under construction at the Joint Institute per Nuclear Research, in Dubna. The project is briefly presented with special focus to the opportunities opened by the collision of high luminosity polarized proton and deuteron beams with total energy up to $\sqrt{s}$=27 GeV. Examples of the foreseen research program are highlighted, in connection with the spin structure of light nuclei, the proton gluon content and the spin dependence of the nucleon-nucleon interaction. The unicity of NICA-SPD makes the future results complementary to the studies that have been or will be performed at other polarized hadron machines in different energy domains.

Virtual photon emission in leptonic decays of charged pseudoscalar mesons

We study the radiative leptonic decays $P\to\ell\nu_\ell\,\ell^{\prime\,+}\ell^{\prime\,-}$, where $P$ is a pseudoscalar meson and $\ell$ and $\ell^\prime$ are charged leptons. In such decays the emitted photon is off-shell and, in addition to the "point-like" contribution in which the virtual photon is emitted either from the lepton or the meson treated as a point-like particle, four structure-dependent (SD) form factors contribute to the amplitude. We present a strategy for the extraction of the SD form factors and implement it in an exploratory lattice computation of the decay rates for the four channels of kaon decays ($\ell,\ell^\prime=e,\mu$). It is the SD form factors which describe the interaction between the virtual photon and the internal hadronic structure of the decaying meson, and in our procedure we separate the SD and point-like contributions to the amplitudes. We demonstrate that the form factors can be extracted with good precision and, in spite of the unphysical quark masses used in our simulation ($m_\pi\simeq 320\,$MeV and $m_K\simeq 530\,$MeV), the results for the decay rates are in reasonable semiquantitative agreement with experimental data (for the channels where these exist). Following this preparatory work, the emphasis of our future work will be on obtaining results at physical quark masses and on the control of the systematic uncertainties associated with discretisation and finite-volume errors.

Unveiling the proton structure via transverse-momentum-dependent gluon distributions

We present exploratory studies of the proton content via unpolarized and polarized transverse-momentum-dependent gluon distributions in the proton at leading twist. We make use of an enhanced spectator-model approach to encode in our densities both small- and moderate-$x$ effects. These studies are relevant to the investigation of the inner structure of hadrons via tomographic analyses at new-generation colliding machines.

Hadron structure at small-x via unintegrated gluon densities

Inclusive as well as exclusive emissions in forward and central directions of rapidity are widely recognized as excellent channels to access the proton structure at small x. In this regime, to describe nucleons structure, it is necessary to use kT -unintegrated distributions. In particular, at large transverse momenta, the x-evolution of the so-called unintegrated gluon distribution is driven by the Balitsky-Fadin-Kuraev-Lipatov equation, within the framework of the high-energy factorization (HEF). Recent analyses on the diffractive electroproduction of ρ mesons have corroborated the underlying assumption that the small-size dipole scattering mechanism is at work, thus validating the use of the HEF formalism. Nonetheless, a significant sensitivity of polarized cross sections to intermediate values of the meson transverse momenta, where, in the case of inclusive emissions, a description at the hand of the transverse momentum dependent (TMD) factorization starts to be the most appropriate framework, has been observed. In this work, we will review the formal description of the UGD within the BFKL approach and present some UGD models that have been proposed, then we will describe the state of the art of some recent phenomenological analyses.

Highlights of pion and kaon structure from continuum analyses

One of the biggest challenges in contemporary physics is understanding the origin and dynamics of the internal structure of hadrons which, at a fundamental level, is described by quantum chromodynamics (QCD). Taking great prominence amongst hadrons are pions and kaons which, despite being the lightest hadrons in nature, their very existence is intimately connected to those mechanisms responsible for almost all of the mass of the visible matter. In this manuscript we discuss many aspects of the pion and kaon structure via light front wave functions and generalized parton distributions, and a collection of other distributions and structural properties that are inferred therefrom.

Factorization for azimuthal asymmetries in SIDIS at next-to-leading power

Differential measurements of the semi-inclusive deep inelastic scattering (SIDIS) process with polarized beams provide important information on the three-dimensional structure of hadrons. Among the various observables are azimuthal asymmetries that start at subleading power, and which give access to novel transverse momentum dependent distributions (TMDs). Theoretical predictions for these distributions are currently based on the parton model rather than a rigorous factorization based analysis. Working under the assumption that leading power Glauber interactions do not spoil factorization at this order, we use the Soft Collinear Effective Theory to derive a complete factorization formula for power suppressed hard scattering effects in SIDIS. This yields generalized definitions of the TMDs that depend on two longitudinal momentum fractions (one of them only relevant beyond tree level), and a complete proof that only the same leading power soft function appears and can be absorbed into the TMD distributions at this order. We also show that perturbative corrections can be accounted for with only one new hard coefficient. Factorization formulae are given for all spin dependent structure functions which start at next-to-leading power. Prospects for improved subleading power predictions that include resummation are discussed.

A general effective field theory description of b → sℓ+ℓ− lepton universality ratios

We construct an expression for a general lepton flavour universality (LFU) ratio, RX, in b→sℓ+ℓ− decays in terms of a series of hadronic quantities which can be treated as nuisance parameters. This expression allows to include any LFU ratio in global fits of b→sℓ+ℓ− short-distance parameters, even in the absence of a precise knowledge of the corresponding hadronic structure. The absence of sizeable LFU violation and the approximate left-handed structure of the Standard Model amplitude imply that only a very limited set of hadronic parameters hamper the sensitivity of RX to a possible LFU violation of short-distance origin. A global b→sℓ+ℓ− combination is performed including the measurement of RpK for the first time, resulting in a significance of new physics of 4.2σ. In light of this, we evaluate the impact on the global significance of new physics using a set of experimentally promising non-exclusive RX measurements that LHCb can perform, and find that they can significantly increase the discovery potential of the experiment.

Application of the weak-binding relation with range correction

The weak-binding relation is a useful tool to study the internal structure of hadrons from the observable quantities. We introduce the range correction in the weak-binding relation for the system having a sizable magnitude of the effective range, and show that the applicability of the weak-binding relation can be enlarged by the range correction. Thanks to the low-energy universality, the weak-binding relation can be used to study the structure of shallow bound states in any systems with different length scales. We apply the weak-binding relation to actual systems, including hadrons, hypernuclei, and atoms and show the importance of the range correction.

Electron-Hadron Colliders: EIC, LHeC and FCC-eh

Electron-hadron colliders are the ultimate tool for high-precision quantum chromodynamics studies and provide the ultimate microscope for probing the internal structure of hadrons. The electron is an ideal probe of the proton structure because it provides the unmatched precision of the electromagnetic interaction, as the virtual photon or vector bosons probe the proton structure in a clean environment, the kinematics of which is uniquely determined by the electron beam and the scattered lepton, or the hadronic final state accounting appropriately for radiation. The Hadron Electron Ring Accelerator HERA (DESY, Hamburg, Germany) was the only electron-hadron collider ever operated (1991–2007) and advanced the knowledge of quantum chromodynamics and the proton structure, with implications for the physics studied in RHIC (BNL, Upton, NY) and the LHC (CERN, Geneva, Switzerland). Recent technological advances in the field of particle accelerators pave the way to realize next-generation electron-hadron colliders that deliver higher luminosity and enable collisions in a much broader range of energies and beam types than HERA. Electron-hadron colliders combine challenges from both electron and hadron machines besides facing their own distinct challenges derived from their intrinsic asymmetry. This review paper will discuss the major features and milestones of HERA and will examine the electron-hadron collider designs of the Electron-Ion Collider (EIC) currently under construction at BNL, the CERN’s Large Hadron electron Collider (LHeC), at an advanced stage of design and awaiting approval, and the Future Circular lepton-hadron Collider (FCC-eh).

Computing light-front wave functions without light-front quantization: A large-momentum effective theory approach

Light-front wave functions play a fundamental role in the light-front quantization approach to QCD and hadron structure. However, a naive implementation of the light-front quantization suffers from various subtleties including the well-known zero-mode problem, the associated rapidity divergences which mixes ultraviolet divergences with infrared physics, as well as breaking of spatial rotational symmetry. We advocate that the light-front quantization should be viewed as an effective theory in which small ${k}^{+}$ modes have been effectively ``integrated out,'' with an infinite number of renormalization constants. Instead of solving light-front quantized field theories directly, we make the large momentum expansion of the equal-time Euclidean correlation functions in instant quantization as an effective way to systematically calculate light-front correlations, including the light-front wave function amplitudes. This large-momentum effective theory accomplishes an effective light-front quantization through lattice QCD calculations. We demonstrate our approach using an example of a pseudoscalar meson wave function.

Proton decay matrix elements on the lattice at physical pion mass

Proton decay is a major prediction of grand-unified theories (GUT) and its observation would indicate baryon number violation that is required for baryogenesis. Many decades of searching for proton decay have constrained its rate and ruled out some of the simplest GUT models. Apart from the baryon number-violating interactions, this rate also depends on transition amplitudes between the protons and mesons or leptons produced in the decay, which are matrix elements of three-quark operators. We report the nonperturbative calculation of these matrix elements for the most studied two-body decay channels into a meson and antilepton done on a lattice with physical light and strange quark masses and lattice spacings $a\ensuremath{\approx}0.14\text{ }\text{ }\mathrm{fm}$ and 0.20 fm. We perform nonperturbative renormalization and excited state analysis to control associated systematic effects. Our results largely agree with previous lattice calculations done with heavier quark masses and thus remove ambiguity in ruling out some simple GUT theories due to quark mass dependence of hadron structure.