Light-cone Formalism Research Articles

Light-cone gauge cubic interaction vertices for massless fields in AdS(4)

In the framework of light-cone formulation of relativistic dynamics, arbitrary spin massless fields propagating in the four-dimensional AdS space are studied. For such fields, the complete list of light-cone gauge cubic interaction vertices is obtained. Realization of relativistic symmetries on space of light-cone gauge massless AdS fields is also obtained. The light-cone gauge vertices for massless AdS fields take simple form similar to the one for massless fields in the flat space.

Heavy meson photoproduction in peripheral AA collisions

The exclusive photoproduction of the heavy vector mesons $\psi$'s and $Y$'s is investigated in peripheral lead-lead collisions for the energies available at the LHC, $\sqrt{s}=2.76$ TeV and $\sqrt{s}=5.02$ TeV. In order to evaluate the robustness of the light-cone color dipole formalism, previously tested in the ultraperipheral regime. It was calculated the rapidity distribution as well as the nuclear modification factor ($R_{AA}$) for the three centrality classes: 30%-50%, 50%-70% and 70%-90%. The transition from ultraperipheral to peripheral regime was carried out sophisticating the photon flux description and the photonuclear cross section, taking into account the effective interaction area. In our calculations, three scenarios were considered: (scenario 1) the direct application of the usual photon flux and of the photonuclear cross section without any relevant change in relation to the UPC's, (scenario 2) the application of an effective photon flux keeping the photonuclear cross section unchanged and (scenario 3) where it was also considered an effective photonuclear cross section. The results obtained from the three scenarios were compared with the ALICE measurements (only $J/\psi$ at the moment), showing a better agreement with the data in the more complete approach (scenario 3), mainly in the more central regions (30%-50% and 50%-70%) where the incertainty is smaller.

Continuous spin fields of mixed-symmetry type

We propose a description of continuous spin massless fields of mixed-symmetry type in Minkowski space at the level of equations of motion. It is based on the appropriately modified version of the constrained system originally used to describe massless bosonic fields of mixed-symmetry type. The description is shown to produce generalized versions of triplet, metric-like, and light-cone formulations. In particular, for scalar continuous spin fields we reproduce the Bekaert-Mourad formulation and the Schuster-Toro formulation. Because a continuous spin system inevitably involves infinite number of fields, specification of the allowed class of field configurations becomes a part of its definition. We show that the naive choice leads to an empty system and propose a suitable class resulting in the correct degrees of freedom. We also demonstrate that the gauge symmetries present in the formulation are all Stueckelberg-like so that the continuous spin system is not a genuine gauge theory.

Photoproduction of Upsilon states in ultraperipheral collisions at the LHC

The exclusive photoproduction of upsilon states is investigated in the context of ultra-peripheral collisions at the LHC energies. Predictions are presented for their production in proton-proton, proton-nucleus and nucleus-nucleus collisions at the energies available at the LHC run 2. The theoretical framework considered in the analysis is the light-cone color dipole formalism, which includes consistently parton saturation effects and nuclear shadowing corrections. For PbPb collisions we consider both the coherent and incoherent contributions.

On the equivalence among stress tensors in a gauge-fluid system

In this paper, we bring out the subtleties involved in the study of a first-order relativistic field theory with auxiliary field variables playing an essential role. In particular, we discuss the nonisentropic Eulerian (or Hamiltonian) fluid model. Interactions are introduced by coupling the fluid to a dynamical Maxwell (U(1)) gauge field. This dynamical nature of the gauge field is crucial in showing the equivalence, on the physical subspace, of the stress tensor derived from two definitions, i.e. the canonical (Noether) one and the symmetric one. In the conventional equal-time formalism, we have shown that the generators of the space–time transformations obtained from these two definitions agree modulo the Gauss constraint. This equivalence in the physical sector has been achieved only because of the dynamical nature of the gauge fields. Subsequently, we have explicitly demonstrated the validity of the Schwinger condition. A detailed analysis of the model in lightcone formalism has also been done where several interesting features are revealed.

Light-cone observables and gauge-invariance in the geodesic light-cone formalism

The remarkable properties of the geodesic light-cone (GLC) coordinates allow analytic expressions for the light-cone observables, providing a new non-perturbative way for calculating the effects of inhomogeneities in our Universe. However, the gauge-invariance of these expressions in the GLC formalism has not been shown explicitly. Here we provide this missing part of the GLC formalism by proving the gauge-invariance of the GLC expressions for the light-cone observables, such as the observed redshift, the luminosity distance, and the physical area and volume of the observed sources. Our study provides a new insight on the properties of the GLC coordinates and it complements the previous work by the GLC collaboration, leading to a comprehensive description of light propagation in the GLC representation.

New approach to the resummation of logarithms in Higgs-boson decays to a vector quarkonium plus a photon

We present a calculation of the rates for Higgs-boson decays to a vector heavy-quarkonium state plus a photon, where the heavy quarkonium states are the J/psi and the Upsilon(nS) states, with n=1, 2, or 3. The calculation is carried out in the light-cone formalism, combined with nonrelativistic QCD factorization, and is accurate at leading order in m_Q^2/m_H^2, where m_Q is the heavy-quark mass and m_H is the Higgs-boson mass. The calculation contains corrections through next-to-leading order in the strong-coupling constant alpha_s and the square of the heavy-quark velocity v, and includes a resummation of logarithms of m_H^2/m_Q^2 at next-to-leading logarithmic accuracy. We have developed a new method, which makes use of Abel summation, accelerated through the use of Pade approximants, to deal with divergences in the resummed expressions for the quarkonium light-cone distribution amplitudes. This approach allows us to make definitive calculations of the resummation effects. Contributions from the order-alpha_s and order-v^2 corrections to the light-cone distribution amplitudes that we obtain with this new method differ substantially from the corresponding contributions that one obtains from a model light-cone distribution amplitude [M. Koenig and M. Neubert, J. High Energy Phys. 08 (2015) 012]. Our results for the real parts of the direct-process amplitudes are considerably smaller than those from one earlier calculation [G. T. Bodwin, H. S. Chung, J.-H. Ee, J. Lee, and F. Petriello, Phys. Rev. D 90, 113010 (2014)], reducing the sensitivity to the Higgs-boson--heavy-quark couplings, and are somewhat smaller than those from another earlier calculation [M. Koenig and M. Neubert, J. High Energy Phys. 08 (2015) 012]. However, our results for the standard-model Higgs-boson branching fractions are in good agreement with those in M. Koenig and M. Neubert, J. High Energy Phys. 08 (2015) 012.

Transverse Momentum Distribution in Ψ(1S,2S) Photoproduction in PP and AA Collisions at the LHC

The exclusive photoproduction of the heavy vector mesons [Formula: see text] is investigated in the context of ultra-peripheral collisions proton-proton and nucleus-nucleus for the energies available at the LHC run 2. Using the light-cone color dipole formalism, it was calculated the transverse momentum distribution in the central rapidity region, in which it is expected major contribution for the process.

Exceptional versus superPoincaré algebra as the defining symmetry of maximal supergravity

We describe how one may use either the superPoincar\'e algebra or the exceptional algebra to construct maximal supergravity theories in the light-cone formalism. The d=4 construction shows both symmetries albeit in a non-linearly realized manner. In d=11, we find that we have to choose which of these two symmetries to use, in constructing the theory. In order to understand the other "unused" symmetry, one has to perform a highly non-trivial field redefinition. We argue that this shows that one cannot trust counterterm arguments that do not take the full symmetry of the theory into account. Finally we discuss possible consequences for Superstring theory and M-theory.

Quarkonium photoproduction inppandAAcollisions at the LHC

In this contribution we report on the investigations of the exclusive production of quarkonium states in proton-proton and nucleus-nucleus reactions at the LHC using the theoretical framework of the light-cone dipole formalism. In particular, we discuss the rapidity distribution for J /ψ , ψ (2S ) and ϒ(1S ) states and the transverse momentum distribution for the J /ψ meson. The numerical calculations are compared to recent experimental results and prediction are done for future LHC runs in the ultraperipheral channel.

Partons in the chiral periphery of the nucleon

We introduce transverse densities in the study of parton dynamics in the proton's peripheral region. We calculate these densities using chiral perturbation theory (χPT) and parametrize the long distance structure of the nucleon in a model independent framework in which we identify chiral (b ∼ O(1/Mπ)) and molecular (b ∼ O(M2N/(M3π))) parametrical regions. Through the light cone formulation of the nucleon's electromagnetic current in χPT, one calculates transverse densities from local products of light cone wave functions of a pion- nucleon system. These products are understood as 2-dimensional parton distributions and as such are universal in processes that probe the nucleon's periphery. This universality and also that of the corresponding transverse density can be tested and used in experimental and phenomenological studies of reactions such as high energy proton-nucleon/nucleus collisions and in electron proton scattering as well as in low Q2 extraction of baryonic form factors.

Quark angular momentum in a spectator model

We investigate the quark angular momentum in a model with the nucleon being a quark and a spectator. Both scalar and axial-vector spectators are included. We perform the calculations in the light-cone formalism where the parton concept is well defined. We calculate the quark helicity and canonical orbital angular momentum. Then we calculate the gravitational form factors which are often related to the kinetic angular momentums, and find that even in a no gauge field model we cannot identify the canonical angular momentums with half the sum of gravitational form factors. In addition, we examine the model relation between the orbital angular momentum and pretzelosity, and find it is violated in the axial-vector case.

Extended two-dimensional characteristic framework to study nonrotating black holes

We develop a numerical solver that extends the computational framework considered in [Phys. Rev. D 65, 084016 (2002)] to include scalar perturbations of nonrotating black holes. The nonlinear Einstein-Klein-Gordon equations for a massless scalar field minimally coupled to gravity are solved in two spatial dimensions. The numerical procedure is based on the ingoing light-cone formulation for an axially and reflection-symmetric spacetime. The solver is second-order accurate and was validated in different ways. We use for calibration an auxiliary 1D solver with the same initial and boundary conditions and the same evolution algorithm. We reproduce the quasinormal modes for the massless scalar field harmonics $\ensuremath{\ell}=0$, 1, and 2. For these same harmonics, in the linear approximation, we calculate the balance of energy between the black hole and the world tube. As an example of nonlinear harmonic generation, we show the distortion of a marginally trapped two-surface approximated as a q-boundary and based upon the harmonic $\ensuremath{\ell}=2$. Additionally, we study the evolution of the $\ensuremath{\ell}=8$ harmonic in order to test the solver in a spacetime with a complex angular structure. Further applications and extensions are briefly discussed.

Generalized form factors of the nucleon in a light-cone spectator-diquark model

We investigate the generalized form factors of the nucleon in a light-cone spectator-diquark model. Compared to the form factors, the generalized form factors contain some more information of the structure of the nucleon. In our calculation, both the scalar and the axial-vector spectator diquark are taken into account. As a relation between the spin in the instant form and that in the light-cone form, the Melosh--Wigner rotation effect is included for both the quark and the axial-vector diquark. We also provide numerical results from our model calculations, and the results are comparable with those from lattice QCD.

Gravitational interactions of higher-spin fermions

Abstract We investigate the cubic interactions of a massless higher-spin fermion with gravity in flat space and present covariant 2 − s − s vertices, compatible with the gauge symmetries of the system, preserving parity. This explicit construction relies on the BRST deformation scheme that assumes locality and Poincaré invariance. Consistent nontrivial cubic deformations exclude minimal gravitational coupling and may appear only with a number of derivatives constrained in a given range. Derived in an independent manner, our results do agree with those obtained from the light-cone formulation or inspired by string theory. We also show that none of the Abelian vertices deform the gauge transformations, while all the non-Abelian ones are obstructed in a local theory beyond the cubic order.

Proton spin in a light-cone chiral quark model

We discuss the spin structure of the proton in a light-cone treatment of the chiral quark model. Based on the fact that the quark helicity ($\ensuremath{\Delta}q$) measured in polarized deep inelastic scattering experiments is actually the quark spin defined in the light-cone formalism rather than the quark spin ($\ensuremath{\Delta}{q}_{QM}$) defined in the conventional quark model (or in the rest frame of the nucleon), we calculate the $x$ dependence of the polarized quark distribution functions $\ensuremath{\Delta}q(x)$, and the polarized structure functions ${g}_{1}(x)$. Special attention is focused on the Melosh-Wigner rotation due to the transversal motions of quarks inside the nucleon and Melosh-Wigner rotation effects on the bare quark input. It is shown that our results match the experimental data well.

Search for double charmonium decays of theP-wave spin-triplet bottomonium states

Using a sample of 158 million $\Upsilon(2S)$ events collected with the Belle detector, we search for the first time for double charmonium decays of the $P$-wave spin-triplet bottomonium states ($\Upsilon(2S) \to \gamma \chi_{bJ}$, $\chi_{bJ} \to \jpsi \jpsi$, $\jpsi \psp$, $\psp \psp$ for J=0, 1, and 2). No significant $\chi_{bJ}$ signal is observed in the double charmonium mass spectra, and we obtain the following upper limits, $\BR(\chi_{bJ} \to \jpsi \jpsi)<7.1\times 10^{-5}$, $2.7\times 10^{-5}$, $4.5\times 10^{-5}$, $\BR(\chi_{bJ} \to \jpsi \psp)<1.2\times 10^{-4}$, $1.7\times 10^{-5}$, $4.9\times 10^{-5}$, $\BR(\chi_{bJ} \to \psp \psp)<3.1\times 10^{-5}$, $6.2\times 10^{-5}$, $1.6\times 10^{-5}$ for J=0, 1, and 2, respectively, at the 90% confidence level. These limits are significantly lower than the central values (with uncertainties of 50% to 70%) predicted using the light cone formalism but are consistent with calculations using the NRQCD factorization approach.

Cubic interaction vertices for fermionic and bosonic arbitrary spin fields

Using the light-cone gauge approach to relativistic field dynamics, we study arbitrary spin fermionic and bosonic fields propagating in flat space of dimension greater than or equal to four. Generating functions of parity invariant cubic interaction vertices for totally symmetric and mixed-symmetry massive and massless fields are obtained. For the case of totally symmetric fields, we derive restrictions on the allowed values of spins and the number of derivatives. These restrictions provide a complete classification of parity invariant cubic interaction vertices for totally symmetric fermionic and bosonic fields. As an example of application of the light-cone formalism, we obtain simple expressions for the Yang–Mills and gravitational interactions of massive arbitrary spin fermionic fields. For some particular cases, using our light-cone cubic vertices, we discuss the corresponding manifestly Lorentz invariant and on-shell gauge invariant cubic vertices.

Relativistic corrections to the exclusive decays ofC-even bottomonia intoS-wave charmonium pairs

Within the nonrelativistic quantum chromodynamics (NRQCD) factorization formalism, we compute the relativistic corrections to the exclusive decays of bottomonia with even charge conjugation parity into $S$-wave charmonium pairs at leading order in the strong coupling constant. Relativistic corrections are resummed for a class of color-singlet contributions to all orders in the charm-quark velocity $v_c$ in the charmonium rest frame. Almost every process that we consider in this work has negative relativistic corrections ranging from -20 to -35,%. Among the various processes, the relativistic corrections of the next-to-leading order in $v_c$ to the decay rate for $\chi_{b2}\to \eta_c(mS)+\eta_c(nS)$ with $m,$ $n=1$ or 2 are very large. In every case, the resummation of the relativistic corrections enhances the rate in comparison with the next-to-leading-order results. We compare our results with available predictions based on the NRQCD factorization formalism. The NRQCD predictions are significantly smaller than those based on the light-cone formalism by an or two orders of magnitudes.

Partial Hamiltonian reduction of relativistic extended objects in light-cone gauge

The elimination of the non-transversal field in the standard light-cone formulation of higher-dimensional extended objects is formulated as a Hamiltonian reduction.