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Laszlo Zalavari - One of the best experts on this subject based on the ideXlab platform.
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Point Particle effective field theory ii relativistic effects and coulomb inverse square competition
Journal of High Energy Physics, 2017Co-Authors: Peter Hayman, C P Burgess, Laszlo Zalavari, Markus Rummel, M P WilliamsAbstract:We apply Point-Particle effective field theory (PPEFT) to compute the leading shifts due to finite-size source effects in the Coulomb bound energy levels of a relativistic spinless charged Particle. This is the analogue for spinless electrons of the contribution of the charge-radius of the source to these levels, and we disagree with standard calculations in several ways. Most notably we find there are two effective interactions with the same dimension that contribute to leading order in the nuclear size. One is the standard charge-radius contribution, while the other is a contact interaction whose leading contribution to $\delta E$ arises linearly in the small length scale, $\epsilon$, characterizing the finite-size effects, and is suppressed by $(Z\alpha)^5$. We argue that standard calculations miss the contributions of this second operator because they err in their choice of boundary conditions at the source for the wave-function of the orbiting Particle. PPEFT predicts how this boundary condition depends on the source's charge radius, as well as on the orbiting Particle's mass. Its contribution turns out to be crucial if the charge radius satisfies $\epsilon \lesssim (Z\alpha)^2 a_B$, with $a_B$ the Bohr radius, since then relativistic effects become important. We show how the problem is equivalent to solving the Schrodinger equation with competing Coulomb, inverse-square and delta-function potentials, which we solve explicitly. A similar enhancement is not predicted for the hyperfine structure, due to its spin-dependence. We show how the charge-radius effectively runs due to classical renormalization effects, and why the resulting RG flow is central to predicting the size of the energy shifts. We discuss how this flow is relevant to systems having much larger-than-geometric cross sections, and the possible relevance to catalysis of reactions through scattering with monopoles.
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Point Particle effective field theory i classical renormalization and the inverse square potential
Journal of High Energy Physics, 2017Co-Authors: Peter Hayman, C P Burgess, Matthew Williams, Laszlo ZalavariAbstract:Singular potentials (the inverse-square potential, for example) arise in many situations and their quantum treatment leads to well-known ambiguities in choosing boundary conditions for the wave-function at the position of the potential's singularity. These ambiguities are usually resolved by developing a self-adjoint extension of the original problem; a non-unique procedure that leaves undetermined which extension should apply in specific physical systems. We take the guesswork out of this picture by using techniques of effective field theory to derive the required boundary conditions at the origin in terms of the effective Point-Particle action describing the physics of the source. In this picture ambiguities in boundary conditions boil down to the allowed choices for the source action, but casting them in terms of an action provides a physical criterion for their determination. The resulting extension is self-adjoint if the source action is real (and involves no new degrees of freedom), and not otherwise (as can also happen for reasonable systems). We show how this effective-field picture provides a simple framework for understanding well-known renormalization effects that arise in these systems, including how renormalization-group techniques can resum non-perturbative interactions that often arise, particularly for non-relativistic applications. In particular we argue why the low-energy effective theory tends to produce a universal RG flow of this type and describe how this can lead to the phenomenon of reaction {\em catalysis}, in which physical quantities (like scattering cross sections) can sometimes be surprisingly large compared to the underlying scales of the source in question. We comment in passing on the possible relevance of these observations to the phenomenon of the catalysis of baryon-number violation by scattering from magnetic monopoles.
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Point Particle effective field theory i classical renormalization and the inverse square potential
Journal of High Energy Physics, 2017Co-Authors: Peter Hayman, C P Burgess, Laszlo Zalavari, M P WilliamsAbstract:Singular potentials (the inverse-square potential, for example) arise in many situations and their quantum treatment leads to well-known ambiguities in choosing boundary conditions for the wave-function at the position of the potential’s singularity. These ambiguities are usually resolved by developing a self-adjoint extension of the original prob-lem; a non-unique procedure that leaves undetermined which extension should apply in specific physical systems. We take the guesswork out of this picture by using techniques of effective field theory to derive the required boundary conditions at the origin in terms of the effective Point-Particle action describing the physics of the source. In this picture ambiguities in boundary conditions boil down to the allowed choices for the source action, but casting them in terms of an action provides a physical criterion for their determination. The resulting extension is self-adjoint if the source action is real (and involves no new degrees of freedom), and not otherwise (as can also happen for reasonable systems). We show how this effective-field picture provides a simple framework for understanding well-known renormalization effects that arise in these systems, including how renormalization-group techniques can resum non-perturbative interactions that often arise, particularly for non-relativistic applications. In particular we argue why the low-energy effective theory tends to produce a universal RG flow of this type and describe how this can lead to the phenomenon of reaction catalysis, in which physical quantities (like scattering cross sections) can sometimes be surprisingly large compared to the underlying scales of the source in question. We comment in passing on the possible relevance of these observations to the phenomenon of the catalysis of baryon-number violation by scattering from magnetic monopoles.
Y Itoh - One of the best experts on this subject based on the ideXlab platform.
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third and a half order post newtonian equations of motion for relativistic compact binaries using the strong field Point Particle limit
Physical Review D, 2009Co-Authors: Y ItohAbstract:We report our rederivation of the equations of motion for relativistic compact binaries through the third-and-a-half post-Newtonian (3.5 PN) order approximation to general relativity using the strong field Point Particle limit to describe self-gravitating stars instead of the Dirac delta functional. The computation is done in harmonic coordinates. Our equations of motion describe the orbital motion of the binary consisting of spherically symmetric nonrotating stars. The resulting equations of motion fully agree with the 3.5 PN equations of motion derived in the previous works. We also show that the locally defined energy of the star has a simple relation with its mass up to the 3.5 PN order.
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equation of motion for relativistic compact binaries with the strong field Point Particle limit third post newtonian order
Physical Review D, 2004Co-Authors: Y ItohAbstract:An equation of motion for relativistic compact binaries is derived through the third post-Newtonian (3PN) approximation of general relativity. The strong field Point-Particle limit and multipole expansion of the stars are used to solve iteratively the harmonically relaxed Einstein equations. We take into account the Lorentz contraction on the multipole moments defined in our previous works. We then derive a 3PN acceleration of the binary orbital motion of the two spherical compact stars based on a surface integral approach which is a direct consequence of local energy momentum conservation. Our resulting equation of motion admits a conserved energy (neglecting the 2.5PN radiation reaction effect), is Lorentz invariant, and is unambiguous: there exist no undetermined parameters reported in the previous works. We shall show that our 3PN equation of motion agrees physically with the Blanchet-Faye 3PN equation of motion if $\ensuremath{\lambda}=\ensuremath{-}1987/3080,$ where $\ensuremath{\lambda}$ is the parameter which is undetermined within their framework. This value of $\ensuremath{\lambda}$ is consistent with the result of Damour, Jaranowski, and Sch\"afer, who first completed a 3PN iteration of the ADM Hamiltonian in the ADMTT gauge using dimensional regularization.
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equation of motion for relativistic compact binaries with the strong field Point Particle limit the second and half post newtonian order
Physical Review D, 2001Co-Authors: Y Itoh, Toshifumi Futamase, Hideki AsadaAbstract:We study the equation of motion appropriate to an inspiraling binary star system whose constituent stars have strong internal gravity. We use the post-Newtonian approximation with the strong field Point Particle limit by which we can introduce into general relativity a notion of a Pointlike Particle with strong internal gravity without using the Dirac delta distribution. In addition to this limit, to deal with strong internal gravity we express the equation of motion in surface integral forms and calculate these integrals explicitly. As a result we obtain the equation of motion for a binary of compact bodies accurate through the second and half post-Newtonian (2.5 PN) order. This equation is derived in the harmonic coordinate. Our resulting equation perfectly agrees with the Damour-Deruelle 2.5 PN equation of motion. Hence it is found that the 2.5 PN equation of motion is applicable to a relativistic compact binary.
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equation of motion for relativistic compact binaries with the strong field Point Particle limit formulation the first post newtonian order and multipole terms
Physical Review D, 2000Co-Authors: Y Itoh, Toshifumi Futamase, Hideki AsadaAbstract:We derive the equation of motion for the relativistic compact binaries in the post-Newtonian approximation taking explicitly their strong internal gravity into account. For this purpose we adopt the method of the Point Particle limit where the equation of motion is expressed in terms of the surface integrals. We examine carefully the behavior of the surface integrals in the derivation. As a result, we obtain the Einstein-Infeld-Hoffman equation of motion at the first post-Newtonian (1PN) order, and a part of the 2PN order which depends on the quadrupole moments and the spins of component stars. Hence, it is found that the equation of motion in the post-Newtonian approximation is valid for compact binaries by a suitable definition of the mass, spin, and quadrupole moment.
C P Burgess - One of the best experts on this subject based on the ideXlab platform.
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fall to the centre in atom traps and Point Particle eft for absorptive systems
Journal of High Energy Physics, 2018Co-Authors: Ryan Plestid, C P Burgess, D H J OdellAbstract:Polarizable atoms interacting with a charged wire do so through an inverse-square potential, V = −g/r2. This system is known to realize scale invariance in a nontrivial way and to be subject to ambiguities associated with the choice of boundary condition at the origin, often termed the problem of ‘fall to the center’. Point-Particle effective field theory (PPEFT) provides a systematic framework for determining the boundary condition in terms of the properties of the source residing at the origin. We apply this formalism to the charged-wire/polarizable-atom problem, finding a result that is not a self-adjoint extension because of absorption of atoms by the wire. We explore the RG flow of the complex coupling constant for the dominant low-energy effective interactions, finding flows whose character is qualitatively different when g is above or below a critical value, gc. Unlike the self-adjoint case, (complex) fixed Points exist when g > gc, which we show correspond to perfect absorber (or perfect emitter) boundary conditions. We describe experimental consequences for wire-atom interactions and the possibility of observing the anomalous breaking of scale invariance.
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Point Particle effective field theory ii relativistic effects and coulomb inverse square competition
Journal of High Energy Physics, 2017Co-Authors: Peter Hayman, C P Burgess, Laszlo Zalavari, Markus Rummel, M P WilliamsAbstract:We apply Point-Particle effective field theory (PPEFT) to compute the leading shifts due to finite-size source effects in the Coulomb bound energy levels of a relativistic spinless charged Particle. This is the analogue for spinless electrons of the contribution of the charge-radius of the source to these levels, and we disagree with standard calculations in several ways. Most notably we find there are two effective interactions with the same dimension that contribute to leading order in the nuclear size. One is the standard charge-radius contribution, while the other is a contact interaction whose leading contribution to $\delta E$ arises linearly in the small length scale, $\epsilon$, characterizing the finite-size effects, and is suppressed by $(Z\alpha)^5$. We argue that standard calculations miss the contributions of this second operator because they err in their choice of boundary conditions at the source for the wave-function of the orbiting Particle. PPEFT predicts how this boundary condition depends on the source's charge radius, as well as on the orbiting Particle's mass. Its contribution turns out to be crucial if the charge radius satisfies $\epsilon \lesssim (Z\alpha)^2 a_B$, with $a_B$ the Bohr radius, since then relativistic effects become important. We show how the problem is equivalent to solving the Schrodinger equation with competing Coulomb, inverse-square and delta-function potentials, which we solve explicitly. A similar enhancement is not predicted for the hyperfine structure, due to its spin-dependence. We show how the charge-radius effectively runs due to classical renormalization effects, and why the resulting RG flow is central to predicting the size of the energy shifts. We discuss how this flow is relevant to systems having much larger-than-geometric cross sections, and the possible relevance to catalysis of reactions through scattering with monopoles.
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Point Particle effective field theory i classical renormalization and the inverse square potential
Journal of High Energy Physics, 2017Co-Authors: Peter Hayman, C P Burgess, Matthew Williams, Laszlo ZalavariAbstract:Singular potentials (the inverse-square potential, for example) arise in many situations and their quantum treatment leads to well-known ambiguities in choosing boundary conditions for the wave-function at the position of the potential's singularity. These ambiguities are usually resolved by developing a self-adjoint extension of the original problem; a non-unique procedure that leaves undetermined which extension should apply in specific physical systems. We take the guesswork out of this picture by using techniques of effective field theory to derive the required boundary conditions at the origin in terms of the effective Point-Particle action describing the physics of the source. In this picture ambiguities in boundary conditions boil down to the allowed choices for the source action, but casting them in terms of an action provides a physical criterion for their determination. The resulting extension is self-adjoint if the source action is real (and involves no new degrees of freedom), and not otherwise (as can also happen for reasonable systems). We show how this effective-field picture provides a simple framework for understanding well-known renormalization effects that arise in these systems, including how renormalization-group techniques can resum non-perturbative interactions that often arise, particularly for non-relativistic applications. In particular we argue why the low-energy effective theory tends to produce a universal RG flow of this type and describe how this can lead to the phenomenon of reaction {\em catalysis}, in which physical quantities (like scattering cross sections) can sometimes be surprisingly large compared to the underlying scales of the source in question. We comment in passing on the possible relevance of these observations to the phenomenon of the catalysis of baryon-number violation by scattering from magnetic monopoles.
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Point Particle effective field theory i classical renormalization and the inverse square potential
Journal of High Energy Physics, 2017Co-Authors: Peter Hayman, C P Burgess, Laszlo Zalavari, M P WilliamsAbstract:Singular potentials (the inverse-square potential, for example) arise in many situations and their quantum treatment leads to well-known ambiguities in choosing boundary conditions for the wave-function at the position of the potential’s singularity. These ambiguities are usually resolved by developing a self-adjoint extension of the original prob-lem; a non-unique procedure that leaves undetermined which extension should apply in specific physical systems. We take the guesswork out of this picture by using techniques of effective field theory to derive the required boundary conditions at the origin in terms of the effective Point-Particle action describing the physics of the source. In this picture ambiguities in boundary conditions boil down to the allowed choices for the source action, but casting them in terms of an action provides a physical criterion for their determination. The resulting extension is self-adjoint if the source action is real (and involves no new degrees of freedom), and not otherwise (as can also happen for reasonable systems). We show how this effective-field picture provides a simple framework for understanding well-known renormalization effects that arise in these systems, including how renormalization-group techniques can resum non-perturbative interactions that often arise, particularly for non-relativistic applications. In particular we argue why the low-energy effective theory tends to produce a universal RG flow of this type and describe how this can lead to the phenomenon of reaction catalysis, in which physical quantities (like scattering cross sections) can sometimes be surprisingly large compared to the underlying scales of the source in question. We comment in passing on the possible relevance of these observations to the phenomenon of the catalysis of baryon-number violation by scattering from magnetic monopoles.
S. Balachandar - One of the best experts on this subject based on the ideXlab platform.
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An Assessment of the Drag Models in the Case of a Shock Interacting With a Fixed Bed of Point Particles
Journal of Fluids Engineering, 2020Co-Authors: Rahul Koneru, S. BalachandarAbstract:Abstract In this work, three-dimensional Euler–Lagrange (EL) Point-Particle simulations of a shock wave interacting with a fixed bed of Particles are carried out. The results from the Particle-resolved (PR) simulations are used to assess the performance of the Point-Particle drag models during short time scales. We demonstrate that in a one-way coupled regime, the Point-Particle simulations recover the dominant gas dynamic features of the flow and are in a good agreement with the exact Riemann solution of a shock traveling through a sudden area contraction. Although the PR simulations are inviscid, we show that a dissipative drag is necessary to predict the mean behavior of the gas. As a model for the inviscid shock-induced (SI) drag two different models are presented in lieu of the quasi-steady drag. Finally, two-way coupled simulations are performed at four different Particle volume fractions {0.10, 0.15, 0.20, 0.25} and three different incident shock Mach numbers {1.22, 1.66, 3.0} and compared against the data from PR inviscid simulations. At a lower Mach number (1.22), averaged flow quantities from the two-way coupled simulations agree well with the PR simulations. As the Mach number increases, we observe that the discrepancies between the Point-Particle and the PR simulations grow. A sensitivity analysis of the drag models involved reveals a strong influence of the inviscid-unsteady force on the gas quantities especially in the case of a strong shock interacting with a dense bed of Particles. The use of Mach correlation beyond the subcritical regime coupled with the model for volume fraction correction is identified as a probable cause for the additional drag.
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Toward Particle-resolved accuracy in Euler–Lagrange simulations of multiphase flow using machine learning and pairwise interaction extended Point-Particle (PIEP) approximation
Theoretical and Computational Fluid Dynamics, 2020Co-Authors: S. Balachandar, W C Moore, G. AkikiAbstract:This study presents two different machine learning approaches for the modeling of hydrodynamic force on Particles in a Particle-laden multiphase flow. Results from Particle-resolved direct numerical simulations (PR-DNS) of flow over a random array of stationary Particles for eight combinations of Particle Reynolds number ( $${\mathrm {Re}}$$ Re ) and volume fraction ( $$\phi $$ ϕ ) are used in the development of the models. The first approach follows a two-step process. In the first flow prediction step, the perturbation flow due to a Particle is obtained as an axisymmetric superposable wake using linear regression. In the second force prediction step, the force on a Particle is evaluated in terms of the perturbation flow induced by all its neighbors using the generalized Faxén form of the force expression. In the second approach, the force data on all the Particles from the PR-DNS simulations are used to develop an artificial neural network (ANN) model for direct prediction of force on a Particle. Due to the unavoidable limitation on the number of fully resolved Particles in the PR-DNS simulations, direct force prediction with the ANN model tends to over-fit the data and performs poorly in the prediction of test data. In contrast, due to the millions of grid Points used in the PR-DNS simulations, accurate flow prediction is possible, which then allows accurate prediction of Particle force. This hybridization of multiphase physics and machine learning is particularly important, since it blends the strength of each, and the resulting pairwise interaction extended Point-Particle model cannot be developed by either physics or machine learning alone.
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a hybrid Point Particle force model that combines physical and data driven approaches
Journal of Computational Physics, 2019Co-Authors: W C Moore, S. Balachandar, Georges AkikiAbstract:Abstract This study improves upon the physics-based pairwise interaction extended Point-Particle (PIEP) model. The PIEP model leverages our physical understanding to predict fluid mediated interactions between solid Particles [1] , [2] . By considering the relative location of neighboring Particles, the PIEP model is able to provide better predictions than existing drag models. While the current physical PIEP model is a powerful tool, its assumptions lead to increased error in flows with higher Particle volume fractions. To reduce this error, a regression algorithm makes direct use of the results of direct numerical simulations (DNS) of an array of monodisperse solid Particles subjected to uniform ambient flow at varying Reynolds numbers. The resulting statistical model and the physical PIEP model are superimposed to construct a hybrid, physics-based data-driven PIEP model. It must be noted that the performance of a pure data-driven approach without the model-form provided by the physical PIEP model is substantially inferior. The hybrid model's predictive capabilities are analyzed using additional DNS data that was not part of training the data-driven model. In every case tested, the hybrid models resulting from the regression were capable of (1) improving upon the physical PIEP model's prediction and (2) recovering underlying relevant physics from the DNS data. As the Particle volume fraction increases, the physical PIEP model loses the ability to approximate the forces experienced by the Particles, but the statistical model continues to produce accurate approximations.
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self induced velocity correction for improved drag estimation in euler lagrange Point Particle simulations
Journal of Computational Physics, 2019Co-Authors: S. Balachandar, Mandar LakhoteAbstract:Abstract In Euler–Lagrange (EL) simulations the force on each Particle is obtained from a Point-Particle model, which is then coupled back to the fluid momentum. The feedback force modifies the flow at the Particle location and it is important to evaluate the resulting self-induced velocity disturbance, since the Point-Particle models are based on the undisturbed flow. An exact solution of the Oseen's equation for flow generated by a steady Gaussian feedback force was obtained, which along with the corresponding finite Reynolds number numerical simulations, provided a steady model for the self-induced velocity disturbance. The unsteady problem of a time dependent Gaussian feedback force was then theoretically investigated in the zero Reynolds number limit. The corresponding finite Reynolds number unsteady results were obtained using companion numerical simulations. Based on these results an unsteady model for predicting the self-induced velocity disturbance was developed. The two main non-dimensional quantities affecting the self-induced velocity disturbance are the Reynolds number based on Gaussian width Re σ and the non-dimensional feedback force F ˜ . The resulting self-induced velocity correction model is general and can be applied in a variety of EL Point-Particle simulations, with the time history of Re σ and F ˜ as input. The quasi-steady and unsteady versions of the model were tested in the context of a freely settling Particle. The unsteady model was shown to predict the self-induced velocity disturbance to reasonable accuracy for a wide range of Reynolds and Stokes numbers. Issues pertaining to practical implementation and limitations are discussed.
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pairwise interaction extended Point Particle model for Particle laden flows
Journal of Computational Physics, 2017Co-Authors: Georges Akiki, W C Moore, S. BalachandarAbstract:Abstract In this work we consider the pairwise interaction extended Point-Particle (PIEP) model for Euler–Lagrange simulations of Particle-laden flows. By accounting for the precise location of neighbors the PIEP model goes beyond local Particle volume fraction, and distinguishes the influence of upstream, downstream and laterally located neighbors. The two main ingredients of the PIEP model are (i) the undisturbed flow at any Particle is evaluated as a superposition of the macroscale flow and a microscale flow that is approximated as a pairwise superposition of perturbation fields induced by each of the neighboring Particles, and (ii) the forces and torque on the Particle are then calculated from the undisturbed flow using the Faxen form of the force relation. The computational efficiency of the standard Euler–Lagrange approach is retained, since the microscale perturbation fields induced by a neighbor are pre-computed and stored as PIEP maps. Here we extend the PIEP force model of Akiki et al. [3] with a corresponding torque model to systematically include the effect of perturbation fields induced by the neighbors in evaluating the net torque. Also, we use DNS results from a uniform flow over two stationary spheres to further improve the PIEP force and torque models. We then test the PIEP model in three different sedimentation problems and compare the results against corresponding DNS to assess the accuracy of the PIEP model and improvement over the standard Point-Particle approach. In the case of two sedimenting spheres in a quiescent ambient the PIEP model is shown to capture the drafting-kissing-tumbling process. In cases of 5 and 80 sedimenting spheres a good agreement is obtained between the PIEP simulation and the DNS. For all three simulations, the DEM-PIEP was able to recreate, to a good extent, the results from the DNS, while requiring only a negligible fraction of the numerical resources required by the fully-resolved DNS.
Peter Hayman - One of the best experts on this subject based on the ideXlab platform.
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Point-Particle Catalysis
Frontiers in Physics, 2019Co-Authors: Peter Hayman, Cliff BurgessAbstract:We use the Point-Particle effective field theory (PPEFT) framework to describe Particle-conversion mediated by a flavour-changing coupling to a Point-Particle. We do this for a toy model of two non-relativistic scalars coupled to the same Point-Particle, on which there is a flavour-violating coupling. It is found that the Point-Particle couplings all must be renormalized with respect to a radial cut-off near the origin, and it is an invariant of the flow of the flavour-changing coupling that is directly related to Particle-changing cross-sections. At the same time, we find an interesting dependence of those cross-sections on the ratio k_out/k_in of the outgoing and incoming momenta, which can lead to a 1/k_in enhancement in certain regimes. We further connect this model to the case of a single-Particle non-self-adjoint (absorptive) PPEFT, as well as to a PPEFT of a single Particle coupled to a two-state nucleus. These results could be relevant for future calculations of any more complicated reactions, such as nucleus-induced electron-muon conversions, monopole catalysis of baryon number violation, as well as nuclear transfer reactions.
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Point Particle effective field theory ii relativistic effects and coulomb inverse square competition
Journal of High Energy Physics, 2017Co-Authors: Peter Hayman, C P Burgess, Laszlo Zalavari, Markus Rummel, M P WilliamsAbstract:We apply Point-Particle effective field theory (PPEFT) to compute the leading shifts due to finite-size source effects in the Coulomb bound energy levels of a relativistic spinless charged Particle. This is the analogue for spinless electrons of the contribution of the charge-radius of the source to these levels, and we disagree with standard calculations in several ways. Most notably we find there are two effective interactions with the same dimension that contribute to leading order in the nuclear size. One is the standard charge-radius contribution, while the other is a contact interaction whose leading contribution to $\delta E$ arises linearly in the small length scale, $\epsilon$, characterizing the finite-size effects, and is suppressed by $(Z\alpha)^5$. We argue that standard calculations miss the contributions of this second operator because they err in their choice of boundary conditions at the source for the wave-function of the orbiting Particle. PPEFT predicts how this boundary condition depends on the source's charge radius, as well as on the orbiting Particle's mass. Its contribution turns out to be crucial if the charge radius satisfies $\epsilon \lesssim (Z\alpha)^2 a_B$, with $a_B$ the Bohr radius, since then relativistic effects become important. We show how the problem is equivalent to solving the Schrodinger equation with competing Coulomb, inverse-square and delta-function potentials, which we solve explicitly. A similar enhancement is not predicted for the hyperfine structure, due to its spin-dependence. We show how the charge-radius effectively runs due to classical renormalization effects, and why the resulting RG flow is central to predicting the size of the energy shifts. We discuss how this flow is relevant to systems having much larger-than-geometric cross sections, and the possible relevance to catalysis of reactions through scattering with monopoles.
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Point Particle effective field theory i classical renormalization and the inverse square potential
Journal of High Energy Physics, 2017Co-Authors: Peter Hayman, C P Burgess, Matthew Williams, Laszlo ZalavariAbstract:Singular potentials (the inverse-square potential, for example) arise in many situations and their quantum treatment leads to well-known ambiguities in choosing boundary conditions for the wave-function at the position of the potential's singularity. These ambiguities are usually resolved by developing a self-adjoint extension of the original problem; a non-unique procedure that leaves undetermined which extension should apply in specific physical systems. We take the guesswork out of this picture by using techniques of effective field theory to derive the required boundary conditions at the origin in terms of the effective Point-Particle action describing the physics of the source. In this picture ambiguities in boundary conditions boil down to the allowed choices for the source action, but casting them in terms of an action provides a physical criterion for their determination. The resulting extension is self-adjoint if the source action is real (and involves no new degrees of freedom), and not otherwise (as can also happen for reasonable systems). We show how this effective-field picture provides a simple framework for understanding well-known renormalization effects that arise in these systems, including how renormalization-group techniques can resum non-perturbative interactions that often arise, particularly for non-relativistic applications. In particular we argue why the low-energy effective theory tends to produce a universal RG flow of this type and describe how this can lead to the phenomenon of reaction {\em catalysis}, in which physical quantities (like scattering cross sections) can sometimes be surprisingly large compared to the underlying scales of the source in question. We comment in passing on the possible relevance of these observations to the phenomenon of the catalysis of baryon-number violation by scattering from magnetic monopoles.
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Point Particle effective field theory i classical renormalization and the inverse square potential
Journal of High Energy Physics, 2017Co-Authors: Peter Hayman, C P Burgess, Laszlo Zalavari, M P WilliamsAbstract:Singular potentials (the inverse-square potential, for example) arise in many situations and their quantum treatment leads to well-known ambiguities in choosing boundary conditions for the wave-function at the position of the potential’s singularity. These ambiguities are usually resolved by developing a self-adjoint extension of the original prob-lem; a non-unique procedure that leaves undetermined which extension should apply in specific physical systems. We take the guesswork out of this picture by using techniques of effective field theory to derive the required boundary conditions at the origin in terms of the effective Point-Particle action describing the physics of the source. In this picture ambiguities in boundary conditions boil down to the allowed choices for the source action, but casting them in terms of an action provides a physical criterion for their determination. The resulting extension is self-adjoint if the source action is real (and involves no new degrees of freedom), and not otherwise (as can also happen for reasonable systems). We show how this effective-field picture provides a simple framework for understanding well-known renormalization effects that arise in these systems, including how renormalization-group techniques can resum non-perturbative interactions that often arise, particularly for non-relativistic applications. In particular we argue why the low-energy effective theory tends to produce a universal RG flow of this type and describe how this can lead to the phenomenon of reaction catalysis, in which physical quantities (like scattering cross sections) can sometimes be surprisingly large compared to the underlying scales of the source in question. We comment in passing on the possible relevance of these observations to the phenomenon of the catalysis of baryon-number violation by scattering from magnetic monopoles.
