High Momentum Limit Research Articles

Nuclear short-range correlations and the zero-energy eigenstates of the Schrödinger equation

We present a systematic analysis of the nuclear two- and three-body short-range correlations and their relations to the zero-energy eigenstates of the Schr\"odinger equation. To this end we analyze the doublet and triplet coupled-cluster amplitudes in the high momentum limit, and show that they obey universal equations independent of the number of nucleons and their state. Furthermore, we find that these coupled-cluster amplitudes coincide with the zero-energy Bloch-Horowitz operator. These results illuminate the relations between the nuclear many-body theory and the generalized contact formalism, introduced to describe the nuclear two-body short range correlations, and they might also be helpful for general coupled-cluster computations as the asymptotic part of the amplitudes is given and shown to be universal.

Bowen\u2013York model solution redux

Initial value problem in general relativity is often solved numerically; with only a few exceptions one of which is the “model” solution of Bowen and York where an analytical form of the solution is available. The solution describes a dynamical, time-asymmetric, gravitating system with mass and linear momentum. Here we revisit this solution and correct an error which turns out to be important for identifying the energy-content of the solution. Depending on the linear momentum, the ratio of the non-stationary part of the initial energy to the total ADM energy takes values between [0, 0.592). This non-stationary part is expected to be turned into gravitational waves during the evolution of the system to possibly settle down to a black hole with mass and linear momentum. In the ultra-relativistic case (the high momentum limit), the maximum amount of gravitational wave energy is 59.2% of the total ADM energy. We also give a detailed account of the general solution of the Hamiltonian constraint.

The generating functional of correlation functions as a high-momentum limit of a Wilson action

It is well known that a Wilson action reduces to the generating functional of connected correlation functions as we take the momentum cutoff to zero. For a fixed point Wilson action, this implies that for momenta large compared with the cutoff, the action reduces to the generating functional. We elaborate on this simple observation.

Horndeski extension of the minimal theory of quasidilaton massive gravity

The minimal theory of quasidilaton massive gravity allows for a stable self-accelerating de Sitter solution in a wide range of parameters. On the other hand, in order for the theory to be compatible with local gravity tests, the fifth force due to the quasidilaton scalar needs to be screened at local scales. The present paper thus extends the theory by inclusion of a cubic Horndeski term in a way that (i) respects the quasidilaton global symmetry, that (ii) maintains the physical degrees of freedom in the theory being three, that (iii) can accommodate the Vainshtein screening mechanism and that still (iv) allows for a stable self-accelerating de Sitter solution. After adding the Horndeski term (and a k-essence type nonlinear kinetic term as well) to the precursor action, we switch to the Hamiltonian language and find a complete set of independent constraints. We then construct the minimal theory with three physical degrees of freedom by carefully adding a pair of constraints to the total Hamiltonian of the precursor theory. Switching back to the Lagrangian language, we study cosmological solutions and their stability in the minimal theory. In particular, we show that a self-accelerating de Sitter solution is stable for a wide range of parameters. Furthermore, as in the minimal theory of massive gravity, the propagation speed of the massive gravitational waves in the high momentum limit precisely agrees with the speed of light.

Exploring correlations in the CGC wave function: Odd azimuthal anisotropy

We extend the CGC approach to calculation of the double inclusive gluon production by including high-density effect in the CGC wave function of the projectile (proton). Our main result is that these effects lead to the appearance of odd harmonics in the two-particle correlation C(k,p). We find that in the high momentum limit, |k|,|p|>>Q_s, this results in a positive c_1{2}. Additionally when the magnitudes of the two momenta are approximately equal, |k|/|p| ~ 1, the density effects also generate a positive third harmonic c_3{2}, which translates into a non-vanishing v_3 when the momenta of the trigger and associated particle are in the same momentum bin. The sign of c_3{2} becomes negative when |k|/|p|>1.1 suggesting an interesting experimental signature.

Effects of intrinsic noise on a cubic autocatalytic reaction-diffusion system.

Starting from our recent chemical master equation derivation of the model of an autocatalytic reaction-diffusion chemical system with reactions U+2V→[over λ_{0}]3V and V→[over μ]P, U→[over ν]Q, we determine the effects of intrinsic noise on the momentum-space behavior of its kinetic parameters and chemical concentrations. We demonstrate that the intrinsic noise induces n→n molecular interaction processes with n≥4, where n is the number of participating molecules of type U or V. The momentum dependences of the reaction rates are driven by the fact that the autocatalytic reaction (inelastic scattering) is renormalized through the existence of an arbitrary number of intermediate elastic scatterings, which can also be interpreted as the creation and subsequent decay of a three body composite state σ=ϕ_{u}ϕ_{v}^{2}, where ϕ_{i} corresponds to the fields representing the densities of U and V. Finally, we discuss the difference between representing σ as a composite or an elementary particle (molecule) with its own kinetic parameters. In one dimension, we find that while they show markedly different behavior in the short spatiotemporal scale, high-momentum (UV) limit, they are formally equivalent in the large spatiotemporal scale, low momentum (IR) regime. On the other hand, in two dimensions and greater, due to the effects of fluctuations, there is no way to experimentally distinguish between a fundamental and composite σ. Thus, in this regime, σ behaves as an entity unto itself, suggesting that it can be effectively treated as an independent chemical species.

High energy bosons do not propagate

We discuss the propagation of bosons (scalars, gauge fields and gravitons) at high energy in the context of the spectral action. Using heat kernel techniques, we find that in the high-momentum limit the quadratic part of the action does not contain positive powers of the derivatives. We interpret this as the fact that the two-point Green functions vanish for nearby points, where the proximity scale is given by the inverse of the cutoff.

Direct qqq force in high momentum limit of QCD for proton physics

An explicit construction of the proton wave function is outlined in the high momentum limit of QCD dominated by a direct qqq force, one generated by hooking the ends of a ggg vertex to 3 distinct q ¯ g q vertices, thus making up a Y-shaped diagram (see Fig. 1). The high degree of S 3 symmetry thus involved ensures that the qqq wave function is a mixture of 56 , 0 + and 20 , 1 + components, rather than the traditional 56 , 0 + and 70 , 0 + type. Some results of this paradigm shift are offered.

Four-point functions and kaon decays in a minimal AdS/QCD model

We study the predictions of holographic QCD for various observable four-point quark-flavor current-current correlators. The dual 5-dimensional bulk theory we consider is a $SU(3{)}_{L}\ifmmode\times\else\texttimes\fi{}SU(3{)}_{R}$ Yang-Mills theory in a slice of $\mathrm{Ad}{\mathrm{S}}_{5}$ spacetime with boundaries. Particular UV and IR boundary conditions encode the spontaneous breaking of the dual 4D global chiral symmetry down to the $SU(3{)}_{V}$ subgroup. We explain in detail how to calculate the 4D four-point quark-flavor current-current correlators using the 5D holographic theory, including interactions. We use these results to investigate predictions of holographic QCD for the $\ensuremath{\Delta}I=1/2$ rule for kaon decays and the ${B}_{K}$ parameter. The results agree well in comparison with experimental data, with an accuracy of 25% or better. The holographic theory automatically includes the contributions of the meson resonances to the four-point correlators. The correlators agree well in the low-momentum and high-momentum limit, in comparison with chiral perturbation theory and perturbative QCD results, respectively.

Spin dynamics of qqq wave function on light front in high momentum limit of QCD: Role of qqq force

The contribution of a spin-rich qqq force (in conjunction with pairwise qq forces) to the analytical structure of the qqq wave function is worked out in the high momentum regime of QCD where the confining interaction may be ignored, so that the dominant effect is Coulombic. A distinctive feature of this study is that the spin-rich qqq force is generated by a ggg vertex (a genuine part of the QCD Lagrangian) wherein the 3 radiating gluon lines end on as many quark lines, giving rise to a (Mercedes-Benz type) Y-shaped diagram. The dynamics is that of a Salpeter-like equation (3D support for the kernel) formulated covariantly on the light front, a la Markov–Yukawa Transversality Principle (MYTP) which warrants a 2-way interconnection between the 3D and 4D Bethe–Salpeter (BSE) forms for 2 as well as 3 fermion quarks. With these ingredients, the differential equation for the 3D wave function ϕ receives well-defined contributions from the qq and qqq forces. In particular a negative eigenvalue of the spin operator iσ1·σ2×σ3 which is an integral part of the qqq force, causes a characteristic singularity in the differential equation, signalling the dynamical effect of a spin-rich qqq force not yet considered in the literature. The potentially crucial role of this interesting effect vis-a-vis the so-called ‘spin anomaly’ of the proton, is a subject of considerable physical interest.

Spectral properties of rotating electrons in quantum dots and their relation to quantumHall liquids

The exact diagonalization technique is used to study many-particle properties of interactingelectrons with spin, confined in a two-dimensional harmonic potential. The single-particle basis islimited to the lowest Landau level. The results are analysed as a function of the total angularmomentum of the system. Only at angular momenta corresponding to the filling factors 1,1/3,1/5, etc is the system fully polarized. The lowest energy states exhibit spin waves, domains,and localization, depending on the angular momentum. Vortices exist only at excitedpolarized states. The high angular momentum limit shows localization of electrons andseparation of the charge and spin excitations.

Pion form factor under MYTP on light front

An explicit construction of the proton wave function is outlined in the high momentum limit of QCD dominated by a direct qqq force, one generated by hooking the ends of a ggg vertex to 3 distinct q¯gq vertices, thus making up a Y-shaped diagram (see Fig. 1). The high degree of S3 symmetry thus involved ensures that the qqq wave function is a mixture of 56,0+ and 20,1+ components, rather than the traditional 56,0+ and 70,0+ type. Some results of this paradigm shift are offered.

Winding solutions for the two-particle system in gravity

We use a computer to follow the evolution of two gravitating particles in a (2 + 1)-dimensional closed universe. In a closed universe there is enough energy to produce a Gott-pair, i.e. a pair of particles with tachyonic centre of mass, from regular initial data. We study such a pair and find that they can wind around each other with ever increasing momentum. As was shown by 't Hooft, the universe must crunch before any closed timelike curve can be traversed. We study the two-particle system and quantize it, long before this crunch happens, in the high-momentum limit. We find that both the relevant configuration variable and its conjugate momentum become discretized.

Geometric Bremsstrahlung in the Early Universe

We discuss photon emission from particles decelerlated by the cosmic expansion. This can be interpretated as a kind of bremsstrahlung induced by the Universe geometry. In the high momentum limit its transition probability does not depend on detailed behavior of the expansion.

Analytical treatment of the quadratic and nonrelativistic Renner-Teller effect for a triatomic molecule in a Π electronic state

This work completes our analytical treatment of the quadratic and non-relativistic Renner-Teller effect and deals with a situation (intermediate limit case, ILC) placed between the recently studied first and second limit cases (FLC, high energy limit, and SLC, high energy and high angular momentum limit, respectively). In the ILC the second order ordinary differential equation in the complex plane that results from a recently reported matrix-integral transformation is also of singular perturbation type, as also occurred in the FLC and SLC, but the method of matched asymptotic expansions cannot be applied in the same extent. However, thanks to the calculation of the non-adiabatic transition probability based on results of an earlier semiclassical study, it has been possible to achieve a fairly deep insight into this problem. To the best of our knowledge this is the first time that the semiclassical non-adiabatic transition probability has been determined, the results being valid for a wide interval of ener...

Analytical treatment of the quadratic and nonrelativistic Renner-Teller effect for a triatomic molecule in a Π electronic state

This work presents an analytical approach to the Renner-Teller effect in the high energy and high angular momentum limit from a quantal viewpoint, and deals with a linear triatomic molecule in a π electronic state within the harmonic oscillator approach, ignoring the spin-orbit coupling. The second order ordinary differential equation in the complex plane that results from a recently reported matrix-integral transformation is of singular perturbation type like that of the high energy limit, but it cannot be solved fully employing the matched asymptotic expansions method

Renormalization group at finite temperature

The renormalization-group equation in quantum field theory at finite temperature is investigated. Owing to the freedom of the renormalization procedure, one can scale the temperature as well as the momentum in choices of renormalization points. The result is an extended version of the renormalization group at zero temperature. Its Lie differential form defines two types of sets of renormalization-group coefficients. Several examples of the applications include the high-momentum limit (deep-inelastic limit), the high-temperature limit, the low-temperature limit, and the critical behavior near a phase transition point.

Short-ranged correlations and the ferromagnetic electron gas

A discussion of the various properties of pair correlation functions of a magnetic electron gas is presented. The cusp conditions obeyed by the many-electron wave functions for a pair of electrons with parallel and antiparallel spins in close proximity are expressed as derivative conditions on the corresponding parallel-and antiparallel-spin pair correlation functions. In particular, it is shown that in a fully ferromagnetic gas the parallel spin correlations determine the correlation energy whereas in the paramagnetic case, this function is of less importance in comparison to the antiparallel-spin correlation function. In the high-momentum limit, it is found that the momentum distribution of electrons is dominated by antiparallel-spin correlations in the partially magnetic case whereas in the fully ferromagnetic case, it is dominated by parallel-spin correlations but is smaller by a factor of ${q}^{\ensuremath{-}2}$. A calculation of the parallel-spin correlation function for the ferromagnetic gas in perturbation theory is presented. A model for the exchange correlation energy of the system which takes into account the exact conditions given here is proposed. Corresponding results for the two-dimensional electron gas are also stated.

Covariant Harmonic Oscillators and the Quark Model

An attempt is made to give a physical interpretation to the phenomenological wave function of Yukawa, which gives a correct nucleon form factor in the symmetric quark model. This wave function is first compared with the Bethe-Salpeter wave function. It is shown that they have similar Lorentz-contraction properties in the high-momentum limit. A hyperplane harmonic oscillator is then introduced. It is shown that the Yukawa wave function, which is defined over the entire four-dimensional Euclidean space, can be interpreted in terms of the three-dimensional hyperplane oscillators. It is shown further that this wave function satisfies a Lorentz-invariant differential equation from which excited harmonic-oscillator states can be constructed, and from which a gauge-invariant electromagnetic interaction can be generated.

Relation between the coupling constant and three-particle production in S-matrix theory

Three particle production in the high angular momentum limit is related to the residue at the pole of the elastic amplitude. If there is no three particle production there can be no pole. Unitarity forces the coupling constant to be real. The results depend only on unitarity, crossing, and Mandelstam analyticity.