Breit Frame Research Articles

Next-to-next-to-leading-order nucleon parton distributions from a light-cone quark model dressed with its virtual meson cloud

A detailed study of nucleon parton distribution functions is performed within a radiative Next-to-Next-to Leading Order (NNLO) parton model whose low-scale input is rigidly described by wave functions which include quarks and dressing meson-cloud. The light-front Hamiltonian dynamics fixes the three-quark wave functions and the meson cloud is introduced by means of high-order Fock component in time-ordered perturbation theory in the infinite momentum frame. Non-strange as well as strange mesons-baryon fluctuations are considered ($\pi$, $\rho$, $\omega$, $K$ and $K^*$, together with $N$, $\Delta$, $\Lambda$ and $\Sigma$) and the effects on strange and non-strange parton distributions investigated showing the large effects due to (non-strange) sea asymmetries and the delicate balance of the strange asymmetry. The non-strange and the strange components, the valence as well as the gluon distributions are compared with available experimental data confirming the need of both non-perturbative degrees of freedom and perturbative (NNLO) radiative effects.

ANALYTIC CONTINUATION OF NUCLEONS FORM FACTORS IN TIME-LIKE REGION WITH SKYRME MODEL

Using the Skyrme model for nucleons we test the possibility to obtain time-like form factors by analytic continuation of space-like ones. We present a method based on a direct computation of the space-like form factors in the Breit frame, where they are defined as Fourier transform of electromagnetic current. A Padé approximation of the current is implemented in order to solve the integral. The results are compared to data both in space-like and time-like region.

Elastic and Transition Form Factors of the Δ(1232)

Predictions obtained with a confining, symmetry-preserving treatment of a vector-vector contact interaction at leading-order in a widely used truncation of QCD's Dyson-Schwinger equations are presented for \Delta and \Omega baryon elastic form factors and the \gamma N -> \Delta transition form factors. This simple framework produces results that are practically indistinguishable from the best otherwise available, an outcome which highlights that the key to describing many features of baryons and unifying them with the properties of mesons is a veracious expression of dynamical chiral symmetry breaking in the hadron bound-state problem. The following specific results are of particular interest. The \Delta elastic form factors are very sensitive to m_\Delta. Hence, given that the parameters which define extant simulations of lattice-regularised QCD produce \Delta-resonance masses that are very large, the form factors obtained therewith are a poor guide to properties of the \Delta(1232). Considering the \Delta-baryon's quadrupole moment, whilst all computations produce a negative value, the conflict between theoretical predictions entails that it is currently impossible to reach a sound conclusion on the nature of the \Delta-baryon's deformation in the infinite momentum frame. Results for analogous properties of the \Omega baryon are less contentious. In connection with the N->\Delta transition, the Ash-convention magnetic transition form factor falls faster than the neutron's magnetic form factor and nonzero values for the associated quadrupole ratios reveal the impact of quark orbital angular momentum within the nucleon and \Delta; and, furthermore, these quadrupole ratios do slowly approach their anticipated asymptotic limits.

THREE-ALGEBRA BFSS MATRIX THEORY

We extend the BFSS matrix theory by means of Lie 3-algebra. The extended model possesses the same supersymmetry as the original BFSS matrix theory, and thus as the infinite momentum frame limit of M-theory. We study dynamics of the model by choosing the minimal Lie 3-algebra that includes u(N) algebra. We can solve a constraint in the minimal model and obtain two phases. In one phase, the model reduces to the original matrix model. In another phase, it reduces to a simple supersymmetric model.

The form factors of the nucleons

There has been much activity in the measurement of the elastic electromagnetic proton and neutron form factors in the last decade, and the quality of the data has been greatly improved by performing double-polarization experiments, in comparison with with previous unpolarized cross section data. Here we will review the experimental data base in view of the new results for the proton and the neutron, obtained at MIT-Bates, JLab and MAMI. The rapid evolution of phenomenological models triggered by these high-precision experiments will be discussed. In particular, the possibility that the proton is non-spherical in its ground state, and that the transverse charge density are model independently defined in the infinite momentum frame. Likewise, flavor decomposition of the nucleon form factors into dressed u and d quark form factors, may give information about the quark-diquark structure of the nucleon. The current proton radius “crisis” will also be discussed.

Light-front analysis of the Casimir effect

The Casimir force between conducting plates at rest in an inertial frame is usually computed in equal-time quantization, the natural choice for the given boundary conditions. We show that the well-known result obtained in this way can also be obtained in light-front quantization. This differs from a light-front analysis where the plates are at "rest" in an infinite momentum frame, rather than an inertial frame; in that case, as shown by Lenz and Steinbacher, the result does not agree with the standard result. As is usually done, the analysis is simplified by working with a scalar field and periodic boundary conditions, in place of the complexity of quantum electrodynamics. The two key ingredients are a careful implementation of the boundary conditions, following the work of Almeida et al. on oblique light-front coordinates, and computation of the ordinary energy density, rather than the light-front energy density. The analysis demonstrates that the physics of the effect is independent of the coordinate choice, as it must be.

Interpolating scattering amplitudes between the instant form and the front form of relativistic dynamics

Among the three forms of relativistic Hamiltonian dynamics proposed by Dirac in 1949, the instant form and the front form can be interpolated by introducing an interpolation angle between the ordinary time $t$ and the light-front time $(t+z/c)/\sqrt{2}$. Using this method, we introduce the interpolating scattering amplitude that links the corresponding time-ordered amplitudes between the two forms of dynamics and provide the physical meaning of the kinematic transformations as they allow the invariance of each individual time-ordered amplitude for an arbitrary interpolation angle. In particular, it exhibits that the longitudinal boost is kinematical only in the front form dynamics, or the light-front dynamics (LFD), but not in any other interpolation angle dynamics. It also shows that the disappearance of the connected contributions to the current arising from the vacuum occurs when the interpolation angle is taken to yield the LFD. Since it doesn't require the infinite momentum frame (IMF) to show this disappearance and the proof is independent of reference frames, it resolves the confusion between the LFD and the IMF. The well-known utility of IMF usually discussed in the instant form dynamics is now also extended to any other interpolation angle dynamics using our interpolating scattering amplitudes.

Determination of the parameters of a color neutral 3D color glass condensate model

We consider a version of the McLerran-Venugopalan model by Lam and Mahlon where confinement is implemented via colored noise in the infrared. This model does not assume an infinite momentum frame, hence the boosted nuclei are not infinitely thin. Instead, the nuclei have a finite extension in the longitudinal direction and therefore depend on the longitudinal coordinate. In this fully three dimensional framework an x dependence of the gluon distribution function emerges naturally. In order to fix the parameters of the model, we calculate the gluon distribution function and compare it with the JR09 parametrization of the data. We explore the parameter space of the model to attain a working framework that can be used to calculate the initial conditions in heavy ion collisions.

Heisenberg uncertainty relations for photons

The idea to base the uncertainty relation for photons on the electromagnetic energy distribution in space enabled us to derive a sharp inequality that expresses the uncertainty relation [Phys. Rev. Lett. {\bf 108}, 140401 (2012)]. An alternative version of the uncertainty relation derived in this paper is closer in spirit to the original Heisenberg relation because it employs the analog of the position operator for the photon---the center of energy operator. The noncommutativity of the components of the center of energy operator results in the increase of the bound $3/2\,\hbar$ in the standard Heisenberg uncertainty relation in three dimensions. This difference diminishes with the increase of the photon energy. In the limiting case of infinite momentum frame, the lower bound in the Heisenberg uncertainty relations for photons is the same as in nonrelativistic quantum mechanics.

Particle production at HERA

Results on particle production in deep-inelastic scattering in ep collision at HERA, obtained with the H1 and ZEUS detectors, are presented. The underlying parton dynamics is investigated by studying the transverse momentum distribution of charged particles and comparing the measurements with various Monte Carlo generators using different approaches to simulate the parton cascade. In this context also results on forward jet production are discussed. The underlying parton dynamics is also studied using prompt photon production in both DIS and photoproduction regimes. The production is compared to theoretical calculations and Monte Carlo predictions. In the context of hadronisation, studies are presented of the scaled momentum distribution for charged hadrons and for K S 0 and Λ particles in the current fragmentation region of the Breit frame. The data are compared to models and to next-to-leading order QCD calculations. In addition, differential cross sections for K S 0 production in the laboratory and Breit frame are investigated and compared to Monte Carlo predictions, which are used to study the flavour decomposition and strangeness suppression factor. K S 0 production is also compared to the production of charged particles and to the production rate of the DIS events.

Chiral symmetry breaking and the spin content of hadrons

From the parton distributions in the infinite momentum frame, one finds that only about 30% of the nucleon spin is carried by spins of the valence quarks, which gave rise to the term “spin crisis”. Similar results hold for the lowest mesons, as it follows from the lattice simulations. We define the spin content of a meson in the rest frame and use a complete and orthogonal q̄q chiral basis and a unitary transformation from the chiral basis to the 2S+1LJ basis. Then, given a mixture of different allowed chiral representations in the meson wave function at a given resolution scale, one can obtain its spin content at this scale. To obtain the mixture of the chiral representations in the meson, we measure in dynamical lattice simulations a ratio of couplings of interpolators with different chiral structure. For the ρ meson, we obtain practically the 3S1 state with no trace of the spin crisis. Then a natural question arises: which definition does reflect the spin content of a hadron?

Direct test of the gauge-gravity correspondence for Matrix theory correlation functions

We study correlation functions in (0+1)-dimensional maximally supersymmetric U(N) Yang-Mills theory, which was proposed by Banks et al. as a non-perturbative definition of 11-dimensional M-theory in the infinite-momentum frame. We perform first-principle calculations using Monte Carlo simulations, and compare the results against the predictions obtained previously based on the gauge-gravity correspondence from 10 dimensions. After providing a self-contained review on these predictions, we present clear evidence that the predictions in the large-N limit actually hold even at small N such as N=2 and 3. The predicted behavior seems to continue to the far infrared regime, which goes beyond the naive range of validity of the 10D supergravity analysis. This suggests that the correlation functions also contain important information on the M-theory limit.

Chiral symmetry breaking and the spin content of the ρ and [formula omitted] mesons

Using interpolators with different SU(2)L×SU(2)R transformation properties we study the chiral symmetry and spin contents of the ρ and ρ′ mesons in lattice simulations with dynamical quarks. A ratio of couplings of the q¯γiτq and q¯σ0iτq interpolators to a given meson state at different resolution scales tells one about the degree of chiral symmetry breaking in the meson wave function at these scales. Using a Gaussian gauge invariant smearing of the quark fields in the interpolators, we are able to extract the chiral content of mesons up to the infrared resolution of ∼1 fm. In the ground state ρ meson the chiral symmetry is strongly broken with comparable contributions of both the (0,1)+(1,0) and (1/2,1/2)b chiral representations with the former being the leading contribution. In contrast, in the ρ′ meson the degree of chiral symmetry breaking is manifestly smaller and the leading representation is (1/2,1/2)b. Using a unitary transformation from the chiral basis to the LJ2S+1 basis, we are able to define and measure the angular momentum content of mesons in the rest frame. This definition is different from the traditional one which uses parton distributions in the infinite momentum frame. The ρ meson is practically a S13 state with no obvious trace of a “spin crisis”. The ρ′ meson has a sizeable contribution of the D13 wave, which implies that the ρ′ meson cannot be considered as a pure radial excitation of the ρ meson.

Frame dependence ofHe3transverse(e,e′)response functions at intermediate momentum transfers

The transverse electron scattering response function of 3He was recently studied by us in the quasi-elastic peak region for momentum transfers q between 500 and 700 MeV/c. Those results, obtained using the Active Nucleon Breit frame (ANB), are here supplemented by calculations in the laboratory, Breit and ANB frames using the two-fragment model discussed in our earlier work on the frame dependence of the the longitudinal response function R_L(q,omega). We find relatively frame independent results and good agreement with experiment especially for the lower momentum transfers. This agreement occurs when we neglect an omega-dependent piece of the one-body current relativistic correction. An inclusion of this term leads however to a rather pronounced frame dependence at q=700 MeV/c. A discussion of this term is given here. This report also includes a correction to our previous ANB results for R_T(q,omega).

QCD factorization forΛb0→Λc+π−

We prove that in the limit ${m}_{b},{m}_{c}\ensuremath{\rightarrow}\ensuremath{\infty}$, with ${m}_{c}/{m}_{b}$ fixed, factorization holds at order ${\ensuremath{\alpha}}_{s}$ for the decay ${\ensuremath{\Lambda}}_{b}^{0}\ensuremath{\rightarrow}{\ensuremath{\Lambda}}_{c}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$. This proof is done in the infinite-momentum frame in which the momenta of $\ensuremath{\pi}$, ${\ensuremath{\Lambda}}_{c}$, and ${\ensuremath{\Lambda}}_{b}$ go to infinity. Our result is renormalization-scale- and scheme-independent at $\mathcal{O}({\ensuremath{\alpha}}_{s})$. This is the same as the QCD factorization for $B\ensuremath{\rightarrow}D\ensuremath{\pi}$.

Light-cone superspace BPS theory

The BPS bound is formulated in light-cone superspace for the N = 4 super-Yang–Mills theory. As a consequence of the superalgebra all momenta are shown to be expressed as a quadratic form in the relevant supertransformations, and these forms are used to derive the light-cone superspace BPS equations. Finally, the superfield expressions are expanded out to component form, and the Wu–Yang monopole boosted to the infinite momentum frame is shown to be a solution.

Measurement of charm and beauty jets in deep inelastic scattering at HERA

Measurements of cross sections for events with charm and beauty jets in deep inelastic scattering at HERA are presented. Events with jets of transverse energy E_T^jet > 6 GeV and pseudorapidity -1.0 < eta^jet < 1.5 in the laboratory frame are selected in the kinematic region of photon virtuality Q^2 > 6 GeV^2 and inelasticity variable 0.07 < y < 0.625. Measurements are also made requiring a jet in the Breit frame with E_T^*jet > 6 GeV. The data were collected with the H1 detector in the years 2006 and 2007 corresponding to an integrated luminosity of 189 pb^-1. The numbers of charm and beauty jets are determined using variables reconstructed using the H1 vertex detector with which the impact parameters of the tracks to the primary vertex and the position of secondary vertices are measured. The measurements are compared with QCD predictions and with previous measurements where heavy flavours are identified using muons.

Photon parton distributions in nuclei and the EMC effect

Photons, as well as quarks and gluons, are constituents of the infinite momentum frame (IMF) wave function of an energetic particle. They are mostly equivalent photons whose amplitude follows from the Lorentz transformation of the particle rest frame Coulomb field into the IMF and from the conservation of the electromagnetic current. We evaluate in a model independent way the dominant photon contribution $\ensuremath{\propto}{\ensuremath{\alpha}}_{\mathrm{em}}({Z}^{2}/{A}^{4/3})\mathrm{ln}(1/{R}_{A}{m}_{N}x)$ to the nuclear structure functions as well as the term $\ensuremath{\propto}{\ensuremath{\alpha}}_{\mathrm{em}}Z/A$. In addition we show that the definition of $x$ consistent with the exact kinematics of $\mathit{eA}$ scattering (with exact sum rules) works in the same direction as the nucleus field of equivalent photons. Combined, these effects account for the bulk of the hadronic European Muon Collaboration (EMC) effect for $x\ensuremath{\leqslant}0.5$ where Fermi motion effects are small. In particular, for these $x$ the hadronic mechanism contribution to the EMC effect does not exceed $~3%$ for all nuclei. Also, the $A$ dependence of the hadronic mechanism of the EMC effect for $x&gt;0.5$ is significantly modified.

Higher-q Quasi-elastic 3He Transverse (e,e′) Response in a Two-Fragment Model

Recently (Efros et al. in Phys Rev C81:034001, 2010) we have computed the 3He transverse response in the quasielastic region for momentum transfers up to 700 MeV/c using the AV18 potential with the UrbanaIX three body potential. These calculations were carried out in the active nucleon Breit (ANB) frame. Owing to the use of the ANB frame the disagreement of the conventional non-relativistic calculations with experiment has been removed for q values up to 500 MeV/c. However, for higher q values some disagreement still persists. In order to further study the issue we present here results for RT (q, ω) computed in the Breit and Lab frames with the use of the two-fragment model.

Inclusive dijet cross sections in neutral current deep inelastic scattering at HERA

Single- and double-differential inclusive dijet cross sections in neutral current deep inelastic ep scattering have been measured with the ZEUS detector using an integrated luminosity of 374 pb^-1. The measurement was performed at large values of the photon virtuality, Q^2, between 125 and 20000 GeV^2. The jets were reconstructed with the k_T cluster algorithm in the Breit reference frame and selected by requiring their transverse energies in the Breit frame, E_T,B^jet, to be larger than 8 GeV. In addition, the invariant mass of the dijet system, M_jj, was required to be greater than 20 GeV. The cross sections are described by the predictions of next-to-leading-order QCD.