In light-front dynamics, form factors are traditionally computed with the "good current" $J^+$ within the Drell-Yan frame $q^+=0$. Due to truncations imposed in practical calculations, the from factor may acquire frame dependence, which is often neglected. In this work, we explore the form factors in more general frames, preserving the boost covariance. We find the frame dependence of the elastic form factors for mesons is small in basis light-front holography and related models with two-body Fock space truncation. We suggest to use the difference between form factor results from Drell-Yan frame and the "longitudinal frame" as a metric for the violation of the Lorentz symmetry due to Fock space truncation.
We study the radiative transitions between vector and pseudoscalar quarkonia in the light-front Hamiltonian approach, and investigate the effects of using different current component and different reference frames. In practical calculations with truncated Fock spaces, transition form factors may acquire current component dependence and frame dependence, and such dependences could serve as a measure for the Lorentz symmetry violation. We suggest using the transverse current with $m_j=0$ state of the vector meson, since this procedure employs the dominant spin components of the light-front wavef…
The frame dependence of the pair-term contribution to the electromagnetic form factor of the pion is studied within the Light Front approach. A symmetric ansatz for the pion Bethe-Salpeter amplitude with a pseudo scalar coupling of the constituent to the pion field is used. In this model, the pair term vanishes for the Drell-Yan condition, while it is dominant for momentum transfer along the light-front direction.
The light-quark flavor dependence of the proton sea has been of great interest for many years because of its close connection with non-perturbative effects. One hypothesis is that this dependence arises from the pion cloud of the proton. We apply light cone perturbation theory and experimental constraints to a chiral Lagrangian to compute the relevant Fock-space components of the nucleon wave function with well-defined uncertainties. Existing experimental information regarding the light flavor sea is studied, and predictions for future experimental results are provided. Future experiments have…
We study the structure of the $ρ$-meson within a light-front model with constituent quark degrees of freedom. We calculate electroweak static observables: magnetic and quadrupole moments, decay constant and charge radius. The prescription used to compute the electroweak quantities is free of zero modes, which makes the calculation implicitly covariant. We compare the results of our model with other ones found in the literature. Our model parameters give a decay constant close to the experimental one.
We elaborate the frame dependence of the angular conditions for spin-1 form factors. An extra angular condition is found in addition to the usual angular condition relating the four helicity amplitudes. Investigating the frame-dependence of the angular conditions, we find that the extra angular condition is in general as complicated as the usual one, although it becomes very simple in the $q^+ = 0$ frame involving only two helicity amplitudes. It is confirmed that the angular conditions are identical in frames that are connected by kinematical transformations. The high $Q^2$ behaviors of the p…
We present an extension of the recombination formalism to analyze the effects from the variation of the hadron wavefunctions. The hadron spectra are sensitive to the shape of the wavefunctions. However, when we fit the wavefunction parameters to the physical observables, such as the average charge radius, the final spectra are very similar each other. We discuss our numerical results in comparison with the published PHENIX and STAR data at RHIC. In the hadron spectra, the recombination of thermal partons dominates at intermediate transverse momentum ($P_{T}$ = 2 $\sim$ 5 GeV), and the fragment…
The frame and scale dependence of the pair-term contribution to the electromagnetic form factor of a spin-zero composite system of two-fermions is studied within the Light Front. The form factor is evaluated from the plus-component of the current in the Breit frame, using for the first time a nonconstant, symmetric ansatz for the Bethe-Salpeter amplitude. The frame dependence is analyzed by allowing a nonvanishing plus component of the momentum transfer, while the dynamical scale is set by the masses of the constituents and by mass and size of the composite system. A transverse momentum distri…
We propose a new method for the nonperturbative solution of quantum field theories and illustrate its use in the context of a light-front analog to the Greenberg--Schweber model. The method is based on light-front quantization and uses the exponential-operator technique of the many-body coupled-cluster method. The formulation produces an effective Hamiltonian eigenvalue problem in the valence Fock sector of the system of interest, combined with nonlinear integral equations to be solved for the functions that define the effective Hamiltonian. The method avoids the Fock-space truncations usually…
The space-like elastic form factor of heavy-light pseudoscalar mesons is investigated within a light-front constituent quark model in order to evaluate the Isgur-Wise form factor. The relativistic composition of the constituent quark spins is properly taken into account using the Melosh rotations, and various heavy-meson wave function are considered, including the eigenfunctions of an effective light-front mass operator reproducing meson mass spectra. It is shown that in a wide range of values of the recoil the Isgur-Wise form factor exhibits a moderate dependence upon the choice of the heavy-…
We study the form factors of heavy--to--heavy and heavy--to--light weak decays using the light--front relativistic quark model. For the heavy--to--heavy $B \ra D^{(\ast)}$ semileptonic decays we calculate the corresponding Isgur--Wise function for the whole kinematic region. For the heavy--to--light $B\ra P$ and $B\ra V$ semileptonic decays we calculate the form factors at $q^2 = 0$; in particular, we have derived the dependence of the form factors on the $b$--quark mass in the $m_b \ra \infty$ limit. This dependence can not be produced by extrapolating the scaling behavior of the form factors…
A light-front treatment for the scalar and vector meson momentum distribution functions is developed using a model in which the nucleus is treated a static source of radius $R$. The limit $R\to \infty$ corresponds to infinite nuclear matter. In this limit, the scalar mesons are shown to carry a vanishing momentum fraction of the nuclear plus momentum $k^+$, but the vector mesons carry a significant fraction, all occuring at the experimentally inaccessible value of $k^+=0$. This confirms earlier work. A study of the $R$ dependence for sizes of real nuclei shows that a fraction of the scalar and…
Using the Wick-Cutkosky model and an extended version (massive exchange) of it, we have calculated the bound states in a quantum field theoretical approach. In the light-front formalism we have calculated the bound-state mass spectrum and wave functions. Using the Terent'ev transformation we can write down an approximation for the angular dependence of the wave function. After calculating the bound-state spectra we characterized all states found. Similarly, we have calculated the bound-state spectrum and wave functions in the instant-form formalism. We compare the spectra found in both forms o…
Within the framework of the Covariant formulation of Light-Front Dynamics, we develop a general non-perturbative renormalization scheme based on the Fock decomposition of the state vector and its truncation. The explicit dependence of our formalism on the orientation of the light front is essential in order to analyze the structure of the counterterms and bare parameters needed to renormalize the theory. We present here a general strategy to determine the dependence of these quantities on the Fock sectors. We apply our formalism to QED for the two-body (one fermion and one boson) truncation an…
The impact parameter dependence of color charge correlators in the proton is obtained from the light front formalism in light cone gauge. We include NLO corrections due to the $|qqqg\rangle$ Fock state via light-cone perturbation theory. Near the center of the proton, the $b$-dependence of the correlations is very different from a "transverse profile function". The resulting $t$-dependence of exclusive $J/Ψ$ photoproduction transitions from exponential to power law at $|t| \approx 1$ GeV$^2$. This prediction could be tested at upcoming DIS facilities or in nucleus-proton ultraperipheral collis…
We investigate the connection between the Breit and infinite momentum frames and show that when the nucleon matrix element of the time component of the electromagnetic current, which yields G_E in the Breit frame, is boosted to the infinite momentum (or light-front) frame, the quantity F_1 is obtained.
Current matrix elements and observables for electro- and photo-excitation of baryons from the nucleon are studied in a light-front framework. Relativistic effects are estimated by comparison to a nonrelativistic model, where we use simple basis states to represent the baryon wavefunctions. Sizeable relativistic effects are found for certain transitions, for example, to radial excitations such as that conventionally used to describe to the Roper resonance. A systematic study shows that the violation of rotational covariance of the baryon transition matrix elements stemming from the use of one-b…
A general procedure for obtaining frame-independent, three-dimensional light-front coordinate-space wave functions is introduced. The third spatial coordinate, $\tilde z$ , is the frame independent coordinate conjugate to the light-front momentum coordinate $x={k^+\over P^+}$ which appears in the momentum-space light-front wave functions underlying generalized parton distributions, structure functions, distribution amplitudes, form factors, and other hadronic observables. These causal light-front coordinate-space wave functions are used to derive a general expression for the quark distribution…
We study the light-unflavored mesons as relativistic bound states in the nonperturbative Hamiltonian formalism of the basis light-front quantization (BLFQ) approach. The dynamics for the valence quarks of these mesons is specified by an effective Hamiltonian containing the one-gluon exchange interaction and the confining potentials both introduced in our previous work on heavy quarkonia, supplemented additionally by a pseudoscalar contact interaction. We diagonalize this Hamiltonian in our basis function representation to obtain the mass spectrum and the light-front wave functions (LFWFs). Bas…
The Generalized Parton Distributions (GPDs) of the nucleon are analyzed within the relativistic constituent quark model formulated on the light-front. It is shown that the matrix elements of the plus component of the one-body vector current are plagued by spurious effects related to the dependence on the hyperplane where the nucleon wave function is defined in terms of its constituents. The physical GPDs can be extracted only from the matrix elements of a transverse component of the one-body current. The loss of the polinomiality property is then related to the neglect of the pair creation pro…
We compare the Bakamjian-Thomas (BT) formulation of relativistic few-body systems with light front field theories that maintain closer contact with Feynman diagrams. We find that Feynman diagrams distinguish Melosh rotations and other kinematical quantities belonging to various composite subsystem frames that correspond to different loop integrals. The BT formalism knows only the rest frame of the whole composite system, where everything is evaluated.
The dependence of thermal field theory on the surface of quantization and on the velocity of the heat bath is investigated by working in general coordinates that are arbitrary linear combinations of the Minkowski coordinates. In the general coordinates the metric tensor $g_{\bar{μν}}$ is non-diagonal. The Kubo, Martin, Schwinger condition requires periodicity in thermal correlation functions when the temporal variable changes by an amount $-i\big/(T\sqrt{g_{\bar{00}}})$. Light front quantization fails since $g_{\bar{00}}=0$, however various related quantizations are possible.
The issue of resulting in the same physical observables with different current components, in particular from the minus current, has been challenging in the light-front quark model (LFQM) even for the computation of the two-point functions such as meson decay constants. At the level of one-body current matrix element computation, we show the uniqueness of pseudoscalar and vector meson decay constants using all available components including the minus component of the current in the LFQM consistent with the Bakamjian-Thomas construction. Regardless of the current components, the polarization ve…
The 't Hooft model, i.e. the two-dimensional quantum chromodynamics in the limit of infinite number of colors, is interpolated by an angle parameter $δ$ between $δ=0$ for the instant form dynamics (IFD) and $δ=π/4$ for the light-front dynamics (LFD). With this parameter $δ$, we formulate the interpolating mass gap equation which takes into account the non-trivial vacuum effect on the bare fermion mass to find the dressed fermion mass. Our interpolating mass gap solutions link the IFD and LFD results with the $δ$ parameter. We find the interpolation angle independent characteristic energy funct…
The instant form and the front form of relativistic dynamics proposed by Dirac in 1949 can be linked by an interpolation angle parameter $δ$ spanning between the instant form dynamics (IFD) at $δ=0$ and the front form dynamics which is now known as the light-front dynamics (LFD) at $δ=π/4$. We present the formal derivation of the interpolating quantum electrodynamics (QED) in the canonical field theory approach and discuss the constraint fermion degree of freedom which appears uniquely in the LFD. The constraint component of the fermion degrees of freedom in LFD results in the instantaneous co…
We demonstrate the equivalence of the light-front and equal-time formulations of pionic corrections to nucleon properties. As a specific example, we consider the self-energy of a nucleon dressed by pion loops, for both pseudovector and pseudoscalar pion-nucleon couplings. We derive the leading and next-to-leading nonanalytic behavior of the self-energy on the light-front, and show explicitly their equivalence in the rest frame and infinite momentum frame in equal-time quantization, as well as in a manifestly covariant formulation.
A constituent parton picture of hadrons with logarithmic confinement arises naturally in light-front QCD when the hamiltonian is computed using a perturbative renormalization group; however, rotational symmetry is not manifest as a simple kinematic symmetry. Relevant operators must typically be fine-tuned when a perturbative renormalization group is used, and in light-front field theory such operators contain functions of longitudinal momenta. We explore the possibility that a gluon mass operator with simple longitudinal momentum dependence may improve approximate kinematic rotational symmetry…
The Pomeron Regge trajectory underlies the dynamics dependence of hadronic total cross sections and diffractive reactions at high energies. The physics of the Pomeron is closely related to the gluon distribution function and the gluon gravitational form factor of the target hadron. In this article we examine the scale dependence of the nonperturbative gluon distribution in the nucleon and the pion which was derived in a previous article [Phys. Rev. D 104, 114005 (2021)] in the framework of holographic light-front QCD and the Veneziano model. We argue that the QCD evolution of the gluon distrib…
Through the development of a parallel code called TMSWIFT, an extensive light-front quantization study of the nonperturbative spectrum of the bound state $(μ^+μ^-)$, true muonium, has been performed. Using Padé approximants, it has been possible to extract continuum and infinite-cutoff limits for the singlet and triplet states for a range of values of the coupling constant $α$. This data set allows for an investigation of the $α$ dependence of the light-front spectra, the results of which are compared to standard calculations. Decay constants have also been obtained. Improved calculations have…
We study parton distributions for two partons, a quark and a gluon, in the light-front dressed quark model, with focus on correlations between the two partons. The model calculation leads to sizable spin-spin and spin-kinematic correlations of interest for studies of double parton scattering (DPS) in high-energy collisions. In particular, we find that the transverse dependence of the double parton distributions (DPDs) does not factorize within the model. The results gives insight to the strengths of correlations in different kinematical regions, which can help in constructing input DPDs in cro…
We study the analytic structure of light-front wave functions (LFWFs) and its consequences for hadron form factors using an explicitly Lorentz-invariant formulation of the front form. The normal to the light front is specified by a general null vector $ω^μ.$ The LFWFs with definite total angular momentum are eigenstates of a {\it kinematic} angular momentum operator and satisfy all Lorentz symmetries. They are analytic functions of the invariant mass squared of the constituents $M^2_0= (\sum k^μ)^2$ and the light-cone momentum fractions $x_i= {k_i\cd ω/ p \cd ω}$ multiplied by invariants const…
In light-front dynamics, the regularization of amplitudes by traditional cutoffs imposed on the transverse and longitudinal components of particle momenta corresponds to restricting the integration volume by a non-rotationally invariant domain. The result depends not only on the size of this domain (i.e., on the cutoff values), but also on its orientation determined by the position of the light-front plane. Explicitly covariant formulation of light front dynamics allows us to parameterize the latter dependence in a very transparent form. If we decompose the regularized amplitude in terms of in…
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. 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. It is important that the transf…
The color transparency (CT) of a hadron, propagating with reduced absorption in a nucleus, is a fundamental property of QCD (quantum chromodynamics) reflecting its internal structure and effective size when it is produced at high transverse momentum, $Q$. CT has been confirmed in many experiments, such as semi-exclusive hard electroproduction, $e A \to e' πX$ for mesons produced at $Q^2 > 3 ~ {\rm GeV}^2$. However, a recent JLab (Jefferson Laboratory) measurement for a proton electroproduced in carbon $e\, {\rm C}\to e' p X$, where $X$ stands for the inclusive sum of all produced final states,…
We analyze the current matrix elements in the general collinear (Breit) frames and find the relation between the ordinary (or canonical) helicity amplitudes and the light-front helicity amplitudes. Using the conservation of angular momentum, we derive a general angular condition which should be satisfied by the light-front helicity amplitudes for any spin system. In addition, we obtain the light-front parity and time-reversal relations for the light-front helicity amplitudes. Applying these relations to the spin-1 form factor analysis, we note that the general angular condition relating the fi…
While the particle-number-conserving convolution formalism established in the Drell-Yan-West reference frame is frequently used to compute exclusive amplitudes in the light-front quantization, this formalism is limited to only those frames where the light-front helicities are not changed and the good (plus) component of the current remains unmixed. For an explicit demonstration of such criteria, we present the relations between the current matrix elements in the two typical reference frames used for calculations of the exclusive amplitudes, i.e. the Drell-Yan-West and Breit frames and investig…
A consistent treatment of $B\rightarrow πl ν$ decay is given on the light-front. The $B$ to $π$ transition form factors are calculated in the entire physical range of momentum transfer for the first time. The valence-quark contribution is obtained using relativistic light-front wave functions. Higher quark-antiquark Fock-state of the $B$-meson bound state is represented effectively by the $|B^*π\rangle$ configuration, and its effect is calculated in the chiral perturbation theory. Wave function renormalization is taken into account consistently. The $|B^*π\rangle$ contribution dominates near t…
We study the semileptonic decay of the $B_c (0^-)$ to charmonia through the bottom-to-charm-quark electroweak current in the framework of basis light-front quantization. Explicitly, we calculate the weak transition form factors for processes of $B_c$ decaying into $η_c$ or $J/ψ$ based on the corresponding initial and final valence light-front wave functions both obtained from the basis light-front quantization. We also present the corresponding differential decay width and branching ratios, as well as the branching ratios for decays into the $η_c'$ and the $ψ'$. We observe unphysical frame dep…
The relation between equal-time and light-front wave functions is studied using models for which the four-dimensional solution of the Bethe-Salpeter wave function can be obtained. The popular prescription of defining the longitudinal momentum fraction using the instant-form free kinetic energy and third component of momentum is found to be incorrect except in the non-relativistic limit. The only presently known way to obtain light-front wave functions from rest-frame, instant-form wave functions is to boost the latter wave functions to the infinite momentum frame. Despite this fact, we prove a…
The ladder kernel of the Bethe-Salpeter equation is amended by introducing a different flavor dependence of the dressing functions in the heavy-quark sector. Compared with earlier work this allows for the simultaneous calculation of the mass spectrum and leptonic decay constants of light pseudoscalar mesons, the $D_u$, $D_s$, $B_u$, $B_s$ and $B_c$ mesons and the heavy quarkonia $η_c$ and $η_b$ within the same framework at a physical pion mass. The corresponding Bethe-Salpeter amplitudes are projected onto the light front and we reconstruct the distribution amplitudes of the mesons in the full…
In this paper we study the relation between the light-front (infinite momentum) and rest-frame descriptions of quarkonia. While the former is more convenient for high-energy production, the latter is usually used for the evaluation of charmonium properties. In particular, we discuss the dynamics of a relativistically moving system with nonrelativistic internal motion and give relations between rest frame and light-front potentials used for the description of quarkonium states. We consider two approximations, first the small coupling regime, and next the nonperturbative small binding energy app…
In this thesis, we have investigated the higher twist structure functions in the recently developed method based on light-front Hamiltonian QCD. Because of various special properties of light-front QCD, this is a more intuitive approach towards deep inelastic scattering but has a well defined field theoretic calculational procedure. Because our method is different from the conventional one, we have obtained various new results. Also, it is easier to explore many aspects which are difficult to understand in the conventional way. The structure functions, twist four $F_L$ and $g_T$ contain non-tr…
The Wick-Cutkosky model is investigated using the framework of the Nakanishi Perturbative Integral Representation projected in the Light-Front hyperplane for an s-wave amplitude. We developed a new technique based on sucessive integration by parts of the Nakanishi Representation which enabled us to transform one of the integrations into a sum. With a set of boundary conditions it was possible to guess the format of the solution, which was in fact a distribution. The eigenequations obtained were the same as the originals of Cutkosky \cite{CutPR54}. Finally, a numerical check confirmed that the …
We present a calculation of the effective cross section $σ_{eff}$, an important ingredient in the description of double parton scattering in proton-proton collisions. Our theoretical approach makes use of a Light-Front quark model as framework to calculate the double parton distribution functions at low-resolution scale. QCD evolution is implemented to reach the experimental scale. The obtained $σ_{eff}$, when averaged over the longitudinal momentum fractions of the interacting partons, $x_i$, is consistent with the present experimental scenario. However the result of the complete calculation …
The dressed-electron eigenstate of Feynman-gauge QED is computed in light-front quantization with a Fock-space truncation to include at most the one-photon/one-electron sector. The theory is regulated by the inclusion of three massive Pauli-Villars (PV) particles, one PV electron and two PV photons. In particular, the chiral limit is investigated, and the correct limit is found to require two PV photons, not just one as previously thought. The renormalization and covariance of the electron current are also analyzed. We find that the plus component is well behaved and use its spin-flip matrix e…
Double parton scattering, occurring in high energy hadron-hadron collisions, e.g. at the LHC, is usually investigated through model dependent analyses of the so called effective cross section $σ_{eff}$. We present a dynamic approach to this fundamental quantity making use of a Light-Front model treatment. Within such a framework $σ_{eff}$ is initially evaluated at low energy scale using the model and then, through QCD evolution, at high energy scale to reach the experimental conditions. Our numerical outcomes are consistent with the present experimental analyses of data in kinematical region w…
Spontaneous breaking of chiral symmetry is discussed in the light-cone framework. The essential ingredient is an infinite number of constituents near zero light-cone momentum. These high (light-cone) energy degrees of freedom freeze out and leave behind some explicit symmetry breaking in the low (light-cone) energy effective Hamiltonian. Connections with Regge theory and soft pion theorems are discussed. Taking the order parameter to be the 4-th component of a chiral 4-vector, the effect of the spontaneous symmetry breaking on meson masses and decay width is calculated and compared with experi…
We obtain the leading-twist valence quark transverse-momentum-dependent parton distribution functions (TMD PDFs) for the proton within the basis light-front quantization (BLFQ) framework. Our results are consistent with lattice QCD calculations and our previous results for the collinear limit. We also obtain consistency with the Soffer-type bounds. Within our approach, we find that six T-even TMDs in the leading twist are all independent of each other, and previously found model-dependent relations do not hold. This is a promising sign that our results are representative of future, more extens…
Universidade Federal Rural da Amazônia（亚马逊联邦农村大学）；Universidade Cruzeiro do Sul / Universidade Cidade de São Paulo（克鲁塞罗苏尔大学 / 圣保罗城市大学）；Instituto Tecnológico de Aeronáutica（航空技术学院）
In this paper, we study the question of quantization of quantum field theories in a general light-front frame. We quantize scalar, fermion as well as gauge field theories in a systematic manner carrying out the Hamiltonian analysis carefully. The decomposition of the fields into positive and negative frequency terms needs to be done carefully after which we show that the (anti) commutation relations for the quantum operators become frame independent. The frame dependence is completely contained in the functions multiplying these operators in the field decomposition. We derive the propagators f…
We analyze the off-shell scattering amplitudes in the framework of the light-front perturbation theory. It is shown that the previously derived recursion relation between tree level off-shell amplitudes in this formalism actually resums whole classes of graphs into a Wilson line. More precisely, we establish a correspondence between the light-front methods for the computation of the off-shell amplitudes and the approach which makes use of the matrix elements of straight infinite Wilson lines, which are manifestly gauge invariant objects. Furthermore, since it is needed to explicitly verify the…
