Breit Frame Research Articles

Nucleon helicity generalized parton distribution at physical pion mass from lattice QCD

The generalized parton distributions (GPDs) offer a window on three-dimensional imaging of the nucleon, providing understanding of how the fundamental properties of the nucleon, such as its mass and spin, arise from the underlying quark and gluon degrees of freedom. In this work, we present the first lattice calculation of the nucleon isovector helicity GPD at physical pion mass, using an a≈0.09 fm lattice ensemble with 2+1+1 flavors of highly improved staggered quarks generated by MILC Collaboration. We perform the GPD calculation in Breit frame using averaged nucleon boost momentum Pz≈2.2 GeV with nonzero momentum transfers in [0.2,1.0] GeV2. Nonperturbative renormalization in RI/MOM scheme is used to obtain the quasi-distribution before matching to the lightcone GPDs. The three-dimensional distribution H˜(x,Q2) is presented, along with the three-dimensional nucleon tomography and impact-parameter–dependent distribution for selected Bjorken x at μ=3 GeV in MS‾ scheme.

Factorized approach to radiative corrections for inelastic lepton-hadron collisions

We propose a factorized approach to QED radiative corrections for inclusive and semi-inclusive deep-inelastic scattering to systematically account for QED and QCD radiation contributions to both processes on equal footing. This is achieved by utilizing factorization to resum logarithmically enhanced QED radiation into universal lepton distribution and fragmentation (or jet) functions. Numerical simulations suggest that the QED effects induced by the rotational distortion of the hadron transverse momentum, arising from the mismatch between the experimental Breit frame and the true photon-hadron frame, can be as large as 50\% for moderate $Q$, and become increasingly important for large transverse momenta. Our framework provides a uniform treatment of radiative effects for extracting three-dimensional hadron structure from high-energy lepton-hadron scattering at current and future facilities, such as the Electron-Ion Collider.

Energy-momentum tensor of the nucleon on the light front: Abel tomography case

We investigate the two-dimensional energy-momentum-tensor (EMT) distributions of the nucleon on the light front, using the Abel transforms of the three-dimensional EMT ones. We explicitly show that the main features of all EMT distributions are kept intact in the course of the Abel transform. We also examine the equivalence between the global and local conditions for the nucleon stability in the three-dimensional Breit frame and in the two-dimensional transverse plane on the light front. We also discuss the two-dimensional force fields inside a nucleon on the light front.

Transverse charge distributions of the nucleon and their Abel images

We investigate the two-dimensional transverse charge distributions of the transversely polarized nucleon. As the longitudinal momentum (${P}_{z}$) of the nucleon increases, the electric dipole moment is induced, which causes the displacement of the transverse charge and magnetization distributions of the nucleon. The induced dipole moment of the proton reaches its maximum value at around ${P}_{z}\ensuremath{\approx}3.2\text{ }\text{ }\mathrm{GeV}$ due to the kinematical reason. We also investigate how the Abel transformations map the three-dimensional charge and magnetization distributions in the Breit frame onto the transverse charge and magnetization ones in the infinite momentum frame.

Large-momentum effective theory

It is an art to match partons defined in the infinite-momentum frame to QCD lattice simulations. Large-momentum effective theory relates properties of Feynman's partons to partons of finite momentum, using asymptotic freedom to match the former's properties in the ultraviolet. Finite-momentum partons are then directly matched to nonperturbative QCD quantities. While reviewing recent developments, this article demonstrates its use in extracting physics from $a\phantom{\rule{0}{0ex}}b$ $i\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}o$ lattice calculations.

Asymmetric jet clustering in deep-inelastic scattering

We propose a new jet algorithm for deep-inelastic scattering (DIS) that accounts for the forward-backward asymmetry in the Breit frame. The Centauro algorithm is longitudinally invariant and can cluster jets with Born kinematics, which enables novel studies of transverse-momentum-dependent observables. Furthermore, we show that spherically-invariant algorithms in the Breit frame give access to low-energy jets from current fragmentation. We propose novel studies in unpolarized, polarized, and nuclear DIS at the future Electron-Ion Collider.

Genuine empirical pressure within the proton

A phenomenological extraction of pressure within the proton has recently been performed using JLab CLAS data (arXiv:2104.02031 [nucl-ex]). The extraction used a 3-dimensional Breit frame description in which the initial and final proton states have different momenta. Instead, we obtain the two-dimensional transverse light front pressure densities that incorporate relativistic effects arising from the boosts that cause the initial and final states to differ. The mechanical radius is then determined to be $0.518~ \pm 0.062_{\mathrm{fit}} \pm 0.126_{\mathrm{sys}}~\mathrm{fm}$, which is smaller than the electric charge radius and larger than the light front momentum radius. The forces within the proton are shown to be predominantly repulsive at distances less than $0.43~\pm 0.12~\mathrm{fm}$ from the center, and predominantly attractive further out.

Forces inside the nucleon on the light front from 3D Breit frame force distributions: Abel tomography case

We derive simple relations which express 2D light front force distributions in terms of 3D Breit frame pressure and shear force distributions. Mathematically the relations correspond to invertible Abel transformation and they establish one-to-one mathematical equivalence of 3D Breit frame force distributions and 2D light front ones. The beauty and simplicity of the Abel transformations allow us to derive a number of new relations for light front force distributions. Any knowledge (model calculation, experimental measurement, etc.) about pressure and shear force distributions in Breit frame can be unambiguously transformed into light front force distributions with the help of Abel transformation. Due to the positivity property of the Abel transformation we obtain an important result---the 2D local stability conditions are satisfied automatically if the corresponding 3D stability conditions are fulfilled. In this way we established not only mathematical equivalence of 2D and 3D forces distributions but also their physics equivalence in terms of stability. As an illustration of how the relations work, we calculated the light front force distributions for a large nucleus as a liquid drop, and for large ${N}_{c}$ nucleon as a chiral soliton.

Novel twist-three transverse-spin sum rule for the proton and related generalized parton distributions

We derive a new twist-3 partonic sum rule for the transverse spin of the proton, which involves the well-know quark spin structure function gT(x)=g1(x)+g2(x), the less-studied but known transverse gluon polarization density ΔGT(x), and quark and gluon canonical orbital angular momentum densities associated with transverse polarization. This is the counter part of the sum rule for the longitudinal spin of the proton derived by Jaffe and Manohar previously. We relate the partonic canonical orbital angular momentum densities to a new class of twist-3 generalized parton distribution functions which are potentially measurable in deep-virtual exclusive processes. We also discuss in detail an important technicality related to the transverse polarization in the infinite momentum frame, i.e., separation of intrinsic contributions from the extrinsic ones. We apply our finding to the transverse-space distributions of partons, angular momentum, and magnetic moment, respectively, in a transversely polarized proton.

Forces within hadrons on the light front

In this work, we find the light front densities for momentum and forces, including pressure and shear forces, within hadrons. This is achieved by deriving relativistically correct expressions relating these densities to the gravitational form factors $A(t)$ and $D(t)$ associated with the energy momentum tensor. The derivation begins from the fundamental definition of density in a quantum field theory, namely the expectation value of a local operator within a spatially-localized state. We find that it is necessary to use the light front formalism to define a density that corresponds to internal hadron structure. When using the instant form formalism, it is impossible to remove the spatial extent of the hadron wave function from any density, and -- even within instant form dynamics -- one does not obtain a Breit frame Fourier transform for a properly defined density. Within the front formalism, we derive new expressions for various mechanical properties of hadrons, including the mechanical radius, as well as for stability conditions. The multipole ansatz for the form factors is used as an example to illustrate all of these findings.

Energy-energy correlators in deep inelastic scattering

The energy-energy correlator (EEC) is an event shape observable which probes the angular correlations of energy depositions in detectors at high energy collider facilities. It has been investigated extensively in the context of precision QCD. In this work, we introduce a novel definition of EEC adapted to the Breit frame in deep-inelastic scattering (DIS). In the back-to-back limit, the observable we propose is sensitive to the universal transverse momentum dependent (TMD) parton distribution functions and fragmentation functions, and it can be studied within the traditional TMD factorization formalism. We further show that the new observable is insensitive to experimental pseudorapidity cuts, often imposed in the Laboratory frame due to detector acceptance limitations. In this work the singular distributions for the new observable are obtained in soft collinear effective theory up to $\mathcal{O}(\alpha_s^3)$ and are verified by the full QCD calculations up to $\mathcal{O}(\alpha_s^2)$. The resummation in the singular limit is performed up to next-to-next-to-next-to-leading logarithmic accuracy. After incorporating non-perturbative effects, we present a comparison of our predictions to PYTHIA 8 simulations.

Revisiting the role of grooming in DIS

We introduce a novel grooming procedure, which is an extension of the modified MassDrop tagging algorithm, tailored to the needs of deep inelastic scattering (DIS). The new algorithm, which grooms the event as a whole, takes advantage of the natural separation of current and target fragmentation in the Breit frame, in order to eliminate radiation in the beam and central rapidity regions. We study the groomed invariant mass in DIS and within soft-collinear effective theory we construct a factorization theorem for the cross-section in the back-to-back limit. In this limit we show that, up to a normalization factor, the cross-section does not depend on the incoming hadronic matrix element and we propose this measurement at HERA and the future electron-ion collider (EIC) as a probe to hadronization, precision QCD, and cold nuclear matter effects. We also give an event based definition of the Winner-Take-All axis and comment on possible applications.

TMD factorization for dijet and heavy-meson pair in DIS

We study a transverse momentum dependent (TMD) factorization framework for the processes of dijet and heavy-meson pair production in deep-inelastic-scattering in an electron-proton collider, considering the measurement of the transverse momentum imbalance of the two hard probes in the Breit frame. For the factorization theorem we employ soft-collinear and boosted-heavy-quark effective field theories. The factorized cross-section for both processes is sensitive to gluon unpolarized and linearly polarized TMD distributions and requires the introduction of a new soft function. We calculate the new soft function here at one-loop, regulating rapidity divergences with the δ-regulator. In addition, using a factorization consistency relation and a universality argument regarding the heavy-quark jet function, we obtain the anomalous dimension of the new soft function at two and three loops.

Charge Distributions of Moving Nucleons.

We introduce relativistic charge distributions for targets with arbitrary average momentum, providing a natural interpolation between the usual Breit frame and infinite-momentum frame distributions. Among the remarkable results, we find that Breit frame distributions can be interpreted from a phase-space perspective as internal charge quasidensities in the rest frame of a localized target, without any relativistic correction. Moreover, we show that the unexpected negative center observed in the unpolarized neutron infinite-momentum frame charge distribution results from a magnetization contribution generated by the Wigner rotation.

Transverse energy\u2013energy correlations of jets in the electron\u2013proton deep inelastic scattering at HERA

We study the event shape variables, transverse energy–energy correlation TEEC (cos phi ) and its asymmetry ATEEC (cos phi ) in deep inelastic scattering (DIS) at the electron–proton collider HERA, where phi is the angle between two jets defined using a transverse-momentum (k_T) jet algorithm. At HERA, jets are defined in the Breit frame, and the leading nontrivial transverse energy–energy correlations arise from the 3-jet configurations. With the help of the NLOJET++, these functions are calculated in the leading order (LO) and the next-to-leading order (NLO) approximations in QCD at the electron–proton center-of-mass energy sqrt{s}=314 GeV. We restrict the angular region to -0.8 le cos phi le 0.8, as the forward- and backward-angular regions require resummed logarithmic corrections, which we have neglected in this work. Following experimental jet-analysis at HERA, we restrict the DIS-variables x, y=Q^2/(x s), where Q^2=-q^2 is the negative of the momentum transfer squared q^2, to 0 le x le 1, 0.2 le y le 0.6, and the pseudo-rapidity variable in the laboratory frame (eta ^mathrm{{lab}}) to the range -1 le eta ^mathrm{{lab}} le 2.5. The TEEC and ATEEC functions are worked out for two ranges in Q^2, defined by 5.5,mathrm{GeV}^2 le Q^2 le 80,mathrm{GeV}^2, called the low-Q^2-range, and 150,mathrm{GeV}^2 le Q^2 le 1000,mathrm{GeV}^2, called the high-Q^2-range. We show the sensitivity of these functions on the parton distribution functions (PDFs), the factorization (mu _F) and renormalization (mu _R) scales, and on alpha _s(M_Z^2). Of these the correlations are stable against varying the scale mu _F and the PDFs, but they do depend on mu _R. For the choice of the scale mu _R= sqrt{langle E_Trangle ^2 +Q^2}, advocated in earlier jet analysis at HERA, the shape variables TEEC and ATEEC are found perturbatively robust. These studies are useful in the analysis of the HERA data, including the determination of alpha _s(M_Z^2) from the shape variables.

Fundamental properties of the proton in light-front zero modes

For a proton in the infinite momentum frame, its wave function contains a zero-momentum part (light-front zero-modes) originated from the modification of the QCD vacuum in the presence of the valence quarks, exhibiting a light-front long-range order in the quantum state. This “non-travelling” component of the proton contributes to its fundamental properties, including the mass and spin, as well as the naive-time-reversal-odd correlations between transverse momentum and spin. The large momentum effective theory (LaMET) provides a theoretical approach to study the physical properties of the proton's zero-mode “condensate” through lattice simulations.

Transverse spin sum rule of the proton

The transversely-polarized state of a proton with arbitrary momentum is not an eigenstate of transverse angular momentum operator. The latter does not commute with the QCD Hamiltonian. However, the expectation value of the transverse angular momentum in the state is well-defined and grows proportionally to the energy of the particle. The transverse spin content of the proton is analyzed in terms of the QCD angular momentum structure. In particular, we reconfirm that the generalized parton distributions H+E provide the leading-twist transverse angular momentum densities of quarks and gluons in the infinite momentum frame.

Charm fragmentation functions in the Nambu–Jona-Lasinio model

We derive the fragmentation function (FF), which describes the probability for a charm quark to emit a $D$ meson with a certain momentum fraction, in the Nambu-Jona-Lasinio (NJL) model. The corresponding elementary FF is calculated with the quark-meson coupling determined in the NJL model involving charm quarks. The FF in the infinite momentum frame is constructed through the jet process governed by the elementary FF, and then evolved to the charm scale, at which it is defined. To prepare the FF suitable for an analysis of $D$ meson production at CLEO, we further match the above FF to that in the finite momentum frame at one loop in QCD. It is shown that the charm quark FF including the finite momentum effects leads to theoretical results in agreement with the CLEO data.

Einstein-Podolsky-Rosen Paradox and Quantum Entanglement at Subnucleonic Scales.

In 1935, Einstein, Podolsky, and Rosen (EPR) formulated an apparent paradox of quantum theory [Phys. Rev. 47, 777 (1935)PHRVAO0031-899X10.1103/PhysRev.47.777]. They considered two quantum systems that were initially allowed to interact and were then later separated. A measurement of a physical observable performed on one system then had to have an immediate effect on the conjugate observable in the other system-even if the systems were causally disconnected. The authors viewed this as a clear indication of the inconsistency of quantum mechanics. In the parton model of the nucleon formulated by Bjorken, Feynman, and Gribov, the partons (quarks and gluons) are viewed by an external hard probe as independent. The standard argument is that, inside the nucleon boosted to an infinite-momentum frame, the parton probed by a virtual photon with virtuality Q is causally disconnected from the rest of the nucleon during the hard interaction. Yet, the parton and the rest of the nucleon have to form a color-singlet state due to color confinement and so have to be in strongly correlated quantum states-we thus encounter the EPR paradox at the subnucleonic scale. In this Letter, we propose a resolution of this paradox based on the quantum entanglement of partons. We devise an experimental test of entanglement and carry it out using data on proton-proton collisions from the Large Hadron Collider. Our results provide a strong direct indication of quantum entanglement at subnucleonic scales.

Singularities in twist-3 quark distributions

We find in one-loop calculations and spectator models that twist-3 GPDs exhibit discontinuities. In the forward limit these discontinuities grow into Dirac delta functions which are essential to satisfy the sum rules involving twist-3 PDFs. We calculate twist-3 quasi-PDFs as a function of longitudinal momentum and identify the Dirac delta function terms with momentum components in the nucleon state that do not scale as the nucleon is boosted to the infinite momentum frame.