The Subleading Isgur-Wise Form Factor X3 (v.v') to Order Alpha s in QCD Sum Rules
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Neubert, M.↗
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Results for “sum rules”
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Spin Structure of the Neutron (^3 HE) and the Bjorken Sum Rule
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Meziani, Z.↗
Moldauer's sum rule implies superradiance in compound nuclear reactions
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73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Multipole moments of stellar oscillation modes
The oscillating mass 2(exp l)-pole moment, M(sub nl), of a star in a given (normalized) oscillation mode determines the energy that can be absorbed by the mode in a tidal interaction and the power radiated by the mode in gravitational waves, both of which are proportional to (absolute value of M(sub nl))(exp 2). The coefficients in the expansion of the vector fields del(r(exp l)Y(sub lm)(theta, phi)) in terms of the displacement fields of modes of given l and m are proportional to M(sub nl). This expansion leads to a sum rule sum over n(absolute value of M(sub nl))(exp 2) = constant. For stars of weak to moderate central condensation (such as neutron stars), the f-mode is well approximated by the vector field being expanded, and therefore it takes the lion's share of the sum. Thus the multipole moments of all other modes must be small. In there numerical evaluation, it is necessary to know the shape of the eigenfunctions quite precisly, since a small f-mode contamination can significantly increase the obtained values. This contamination occurs in some `hybrid' numerical computations of neutron star oscillations with relativistic equilibrium stars and Newtonian dynamics (e.g., McDermott et al. 1988). In this case, it is due to a slight inconsistency in the models and leads to a large overestimate of the power radiated in gravitational waves by modes other than the f-mode, although their oscillation periods are nearly unaffected.
Reisenegger, Andreas↗
Computing the dipole polarizability of Ca 48 with increased precision
Here, we compute the electric dipole polarizability of 48 Ca with an increased precision by including more correlations than in previous studies. Employing the coupled-cluster method we go beyond single and double excitations and include leading-order three-particle-three-hole (3p-3h) excitations for the ground state, excited states, and the similarity-transformed operator. We study electromagnetic sum rules, such as the bremsstrahlung sum rule m 0 and the polarizability sum rule αD using interactions from chiral effective field theory. To gauge the quality of our coupled-cluster approximations we perform several benchmarks with the effective interaction hyperspherical harmonics approach in 4 He and with self consistent Green's function in 16 O. We compute the dipole polarizability of 48 Ca employing the chiral interaction N 2 LO sat and the 1.8/2.0 (EM). We find that the effect of 3p-3h excitations in the ground state is small for 1.8/2.0 (EM) but non-negligible for N 2 LO sat . The addition of these new correlations allows us to improve the precision of our 48 Ca calculations and reconcile the recently reported discrepancy between coupled-cluster results based on these interactions and the experimentally determined αD from proton inelastic scattering in 48 Ca. For the computation of electromagnetic and polarizability sum rules, the inclusion of leading-order 3p-3h excitations in the ground state is important, while it is less so for the excited states and the similarity-transformed dipole operator.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Free-free matrix-elements for two-photon opacity
Recent opacity measurements have inspired a close study of the two-photon contributions to the opacity of hot plasmas. The absorption and emission of radiation is controlled by dipole matrix-elements of electrons in an atom or ion. This paper describes two independent methods to calculate matrix-elements needed for the two-photon opacity and tests the results by the f-sum rule. The usual f-sum rule is extended to a matrix f-sum that offers a rigorous test for bound-bound, bound-free and free-free transitions. An additional higher-order sum-rule for the two-photon transition amplitudes is described. In this work, we obtain a simple parametric representation of a key plasma density effect on the matrix-elements. The perturbation theory calculation of two-photon cross-sections is compared to an independent method based on the solution of the time-dependent Schroedinger equation for an atom or ion in a high-frequency electromagnetic field. This is described as a high frequency Stark effect or AC Stark effect. Two-photon cross sections calculated with the AC Stark code agree with perturbation theory to within about 5%. In addition to this cross check, the AC Stark code is well suited to evaluating important questions such as the variation of two-photon opacity for different elements.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Experimental Study of the 3 He and Neutron Spin Structure at Low Q 2 and The Upgrade of the JLab Polarized 3 He Target
In the scattering process off a nuclear or nucleon target, the Gerasimov-Drell-Hearn (GDH) sum rule for real photons (Q 2 =0 where Q 2 ≡ -q 2 with q the photon's 4-momentum) relates static properties of the target particle's ground state to dynamic properties of all its excited states. On the other side of the Q 2 spectrum, the Bjorken sum rule holds in the Bjorken limit Q 2 → ∞. Bjorken sum rule relates the final structure functions of the proton and neutron to the nucleon axial coupling constant in weak decay. These two sum rules belong to domains where calculations are achievable but use different degrees of freedom: hadronic degrees of freedom at low Q 2 versus partonic degrees of freedom at intermediate Q 2 . Meanwhile, different methods have been used to connect the two sum rules at finite Q 2 values: Chiral Perturbation Theory is used to expand the GDH sum rule while Operator Product Expansion is used to expand the Bjorken sum rule. In recent decades, improvements in polarized beam and polarized target techniques have made it possible to test theoretical predictions in the intermediate Q 2 region. During the Jefferson Lab (JLab) Hall A E97110 experiment, a precise measurement of polarized cross sections was performed at 0.02 < Q 2 < 0.3 GeV 2 using a polarized 3 He target as an effective polarized neutron target. The measured data allowed us to test predictions of Chiral Perturbation Theory at very low Q 2 . Furthermore, an extrapolation to the real photon point Q 2 =0 tests the GDH sum rule on the neutron. In order to reach the small angles necessary for the low Q 2 range, a new septum magnet was installed in Hall A for this experiment. Unfortunately, the magnet was mis-wired during initial running. There were therefore two periods for this experiment: the first period had the defective magnet due to mis-wiring; while in the second period, the magnet had been fixed and was working properly. The cross sections and the asymmetries for the first period must be extracted using a difficult and unusual method employing focal plane variables in the spectrometer. In the work described in this thesis, the target-plane and focal-plane method will be established first and confirmed by elastic scattering cross section measurements from carbon foil and 3 He targets. Cross sections and asymmetries of inelastic scattering were then extracted using the same method, which constitute the main physics results of this thesis. Preliminary results on ITT , the integral of the polarized cross section, were also extracted and are presented in this thesis. In addition to the data analysis of E97110, this thesis includes instrumentation work performed on the polarized 3 He target at JLab. For the 12 GeV program of JLab, the polarized 3 He target is being upgraded to satisfy new experimental requirements. The new target is a convection-based cell with two transfer tubes rather than a single transfer tube as in the former 6 GeV design. The first stage of the target upgrade aims to produce a 40 cm long, 10 amg target that can withstand 30 μA of electron beam current with an in-beam polarization of 55%, doubling the figure-of-merit from the 6 GeV time. Several studies were conducted at the Test Lab of JLab on the new convection cell. Work and improvement done on the Pulse Nuclear Magnetic Resonance (NMR) polarimetry and its test results will be presented. As this thesis is written, the target is being installed in Hall C of JLab in preparation for a 6-month long running from November 2019 to May 2020.
Ton, Nguyen↗
Realizing infrared power-law liquids in the cuprates from unparticle interactions
Recent photoemission experiments reveal that the excitations along the nodal region in the strange metal phase of the cuprates, rather than corresponding to poles in the single-particle Green function, exhibit power-law scaling as a function of frequency and temperature. Because such power-law scaling is indicative of a scale-invariant sector, as a first step, we perturbatively evaluate the electron self-energy due to interactions with scale-invariant unparticles. We focus on a G 0 W-type diagram with an interaction W mediated by a bosonic scalar unparticle. In this work, we find that in the high-temperature limit, the imaginary part of the self-energy Im$\Sigma$ is linear in temperature. In the low-temperature limit, Im$\Sigma$ exhibits the same power law in both temperature and frequency, with an exponent that depends on the scaling dimension of an unparticle operator. Such behavior is qualitatively consistent with the experimental observations. We then expand the unparticle propagator into coherent and incoherent contributions and study how the incoherent part violates the density of states (DOS) and density-density correlation function sum rules (f-sum rule). Such violations, in principle, can be observed experimentally. Our work indicates that the physical mechanism for the origin of the power-law scaling is the incoherent background, which is generated from the Mott-scale physics.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
The spin structure of the nucleon
We review the present understanding of the spin structure of protons and neutrons, the fundamental building blocks of nuclei collectively known as nucleons. The field of nucleon spin provides a critical window for testing Quantum Chromodynamics (QCD), the gauge theory of the strong interactions since it involves fundamental aspects of hadron structure, and it can be probed in detail in experiments, particularly deep inelastic lepton scattering on polarized targets. QCD was initially probed in high energy deep inelastic lepton scattering with unpolarized beams and targets. With time, interest shifted from testing perturbative QCD to illuminating the nucleon structure itself. In fact, the spin degrees of freedom of hadrons provides an essential and detailed verification of both perturbative and nonperturbative QCD dynamics. Nucleon spin was initially thought of coming mostly from the spin of its quark constituents, based on intuition from the parton model. However, the first experiments showed that this expectation was incorrect. It is now clear that nucleon physics is much more complex, involving quark orbital angular momenta as well as gluonic and sea quark contributions. Thus, the nucleon spin structure remains a most active aspect of QCD research, involving important advances such as the developments of generalized parton distributions (GPD) and transverse momentum distributions (TMD). Elastic and inelastic lepton-proton scattering, as well as photoabsorption experiments provide various ways to investigate non-perturbative QCD. Fundamental sum rules --such as the Bjorken sum rule for polarized photoabsorption on polarized nucleons-- are also in the non-perturbative domain. This realization triggered a vigorous program to link the low energy effective hadronic description of the strong interactions to fundamental quarks and gluon degrees of freedom of QCD. This has also led to the development of holographic QCD ideas based on the AdS/CFT or gauge/gravity correspondence, a novel approach providing a well-founded semiclassical approximation to QCD. Any QCD-based model of the nucleon's spin and dynamics must also successfully account for the observed spectroscopy of hadrons. Analytic calculations of the hadron spectrum, a long sought goal of QCD research, has now being realized using light-front holography and superconformal quantum mechanics, a formalism consistent with the results from nucleon spin studies. We begin this review with a phenomenological description of nucleon structure in general and of its spin structure in particular, aimed to engage non-specialist readers. A fundamental tool is Dirac's front form and light-front quantization which provides a frame-independent, relativistic description of hadron structure and dynamics, the derivation of spin-sum rules, and a direct connection to the QCD Lagrangian. Next, we discuss the nucleon spin structure at high energy, including topics such as GPDs and TMDs, as well as nucleon spin observables sensitive to final-state interactions such as the Sivers effect. We then discuss experimental and theoretical advances in the nonperturbative domain --in particular the development of light-front holographic QCD and superconformal quantum mechanics, its predictions for the spin content of nucleons, the computation of PDFs and of hadron masses.
74 ATOMIC AND MOLECULAR PHYSICS↗
Dynamical constraints on RG flows and cosmology
Sum rules connecting low-energy observables to high-energy physics are an interesting way to probe the mechanism of inflation and its ultraviolet origin. Unfortunately, such sum rules have proven difficult to study in a cosmological setting. Motivated by this problem, we investigate a precise analogue of inflation in anti-de Sitter spacetime, where it becomes dual to a slow renormalization group flow in the boundary quantum field theory. This dual description provides a firm footing for exploring the constraints of unitarity, analyticity, and causality on the bulk effective field theory. We derive a sum rule that constrains the bulk coupling constants in this theory. In the bulk, the sum rule is related to the speed of radial propagation, while on the boundary, it governs the spreading of nonlocal operators. When the spreading speed approaches the speed of light, the sum rule is saturated, suggesting that the theory becomes free in this limit. We also discuss whether similar results apply to inflation, where an analogous sum rule exists for the propagation speed of inflationary fluctuations.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
The light-front gauge-invariant energy-momentum tensor
In this study, we provide for the first time a complete parametrization for the matrix elements of the generic asymmetric, non-local and gauge-invariant canonical energy-momentum tensor, generalizing therefore former works on the symmetric, local and gauge-invariant kinetic energy-momentum tensor also known as the Belinfante-Rosenfeld energy-momentum tensor. We discuss in detail the various constraints imposed by non-locality, linear and angular momentum conservation. We also derive the relations with two-parton generalized and transverse-momentum dependent distributions, clarifying what can be learned from the latter. In particular, we show explicitly that two-parton transverse-momentum dependent distributions cannot provide any model-independent information about the parton orbital angular momentum. On the way, we recover the Burkardt sum rule and obtain similar new sum rules for higher-twist distributions.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Impact of new physics on the JUNO-long-baseline synergy in the neutrino mass ordering determination
The determination of the neutrino mass ordering is one of the flagship goals in particle physics. A well-known and powerful synergy emerges when combining high-precision measurements of the effective atmospheric mass-squared splitting from electron antineutrino disappearance in reactor experiments with that from muon (anti)neutrino disappearance in accelerator-based long-baseline experiments. To fully exploit this synergy, percent-level precision in the atmospheric mass splitting is required—a target that JUNO is expected to achieve within a few months of data taking. This motivated the formulation of a mass ordering sum rule for neutrino disappearance channels, which shows that by combining data from T2K and NOvA with JUNO after one year of operation, the neutrino mass ordering can be determined at the 3𝜎 confidence level. Since JUNO has recently started taking data, it is timely to ask whether this sum rule remains robust in the presence of new physics. We identify the necessary conditions for new physics to affect the sum rule and demonstrate that, in some cases, such effects could lead to an incorrect inference of the mass ordering. As concrete examples, we consider scalar nonstandard interactions (SNSI) and neutrinos coupled to an ultralight scalar field. We find that, for SNSI, current constraints render any modification of the sum rule negligible, whereas in the latter case, the inference of the ordering requires caution. Nevertheless, these effects can be disentangled, illustrating how the sum rule can also be used to search for new physics.
Alves, Gustavo F. S. [Fermi National Accelerator L↗
Impact of New Physics on the JUNO-Long-Baseline Synergy in Neutrino Mass Ordering Determination
The determination of the neutrino mass ordering is one of the flagship goals in particle physics. A well-known and powerful synergy emerges when combining high-precision measurements of the effective atmospheric mass-squared splitting from electron antineutrino disappearance in reactor experiments with that from muon (anti)neutrino disappearance in accelerator-based long-baseline experiments. To fully exploit this synergy, percent-level precision in the atmospheric mass splitting is required-a target that JUNO is expected to achieve within a few months of data taking. This motivated the formulation of a mass ordering sum rule for neutrino disappearance channels, which shows that by combining data from T2K and NOvA with JUNO after one year of operation, the neutrino mass ordering can be determined at the $3σ$ confidence level. Since JUNO has recently started taking data, it is timely to ask whether this sum rule remains robust in the presence of new physics. We identify the necessary conditions for new physics to affect the sum rule and demonstrate that, in some cases, such effects could lead to an incorrect inference of the mass ordering. As concrete examples, we consider Scalar Non-Standard Interactions (SNSI) and neutrinos coupled to an ultralight scalar field. We find that, for SNSI, current constraints render any modification of the sum rule negligible, whereas in the latter case, the inference of the ordering requires caution. Nevertheless, these effects can be disentangled, illustrating how the sum rule can also be used to search for new physics.
Alves, Gustavo F.S. [Fermilab; Northwestern U.; Sa↗
Twist analysis of the spin-orbit correlation in QCD
We present a QCD analysis of the twist-three parton distribution functions associated with the spin-orbit correlation of quarks and gluons in spin-$\frac{1}{2}$ and spin-0 hadrons. We derive exact non-perturbative identities decomposing the spin-orbit correlations into the Wandzura-Wilczek part and the genuine twist-three part. In the spin-$\frac{1}{2}$ case, the result is partially related to the kinematical twist-three part of the g T (x) distribution familiar in the context of transverse spin physics. We use these identities to obtain a novel longitudinal momentum sum rule which may be regarded as the momentum version of the Jaffe-Manohar spin sum rule. We explore the physical interpretation of the sum rule and make a connection to the color Lorentz forces and their associated potential energies.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Born’s rule as signature of a superclassical current algebra
We present a new tool for calculating the interference patterns and particle trajectories of a double-, three- and N-slit system on the basis of an emergent sub-quantum theory developed by our group throughout the last years. The quantum itself is considered as an emergent system representing an off-equilibrium steady state oscillation maintained by a constant throughput of energy provided by a classical zero-point energy field. We introduce the concept of a “relational causality” which allows for evaluating structural interdependences of different systems levels, i.e. in our case of the relations between partial and total probability density currents, respectively. Combined with the application of 21st century classical physics like, e.g., modern nonequilibrium thermodynamics, we thus arrive at a “superclassical” theory. Within this framework, the proposed current algebra directly leads to a new formulation of the guiding equation which is equivalent to the original one of the de Broglie–Bohm theory. By proving the absence of third order interferences in three-path systems it is shown that Born’s rule is a natural consequence of our theory. Considering the series of one-, double-, or, generally, of N-slit systems, with the first appearance of an interference term in the double slit case, we can explain the violation of Sorkin’s first order sum rule, just as the validity of all higher order sum rules. Moreover, the Talbot patterns and Talbot distance for an arbitrary N-slit device can be reproduced exactly by our model without any quantum physics tool. -- Highlights: •Calculating the interference patterns and particle trajectories of a double-, three- and N-slit system. •Deriving a new formulation of the guiding equation equivalent to the de Broglie–Bohm one. •Proving the absence of third order interferences and thus explaining Born’s rule. •Explaining the violation of Sorkin’s order sum rules. •Classical simulation of Talbot patterns and exact reproduction of Talbot distance for N slits.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
The role of fluid-wall interactions on confined liquid diffusion using Mori theory
The dynamics of fluid confined in a nano-channel with smooth walls have been studied through velocity autocorrelation function within the memory function approach by incorporating the atomic level interactions of fluid with the confining wall. Expressions for the second and fourth sum rules of velocity autocorrelation have been derived for nano-channel which involves fluid-fluid and fluid-wall interactions. These expressions, in addition, involve pair correlation function and density profiles. The numerical contributions of fluid-wall interaction to sum rules are found to play a very significant role, specifically at smaller channel width. Results obtained for velocity autocorrelation and self-diffusion coefficient of a fluid confined to different widths of the nanochannel have been compared with the computer simulation results. The comparison shows a good agreement except when the width of the channel is of the order of two atomic diameters, where it becomes difficult to estimate sum rules involving the triplet correlation’s contribution.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Tree-level Unitarity in $$ \textrm{SU}{(2)}_L\times \textrm{U}{(1)}_Y\times \textrm{U}{(1)}_{Y^{\prime }} $$ Models
Abstract In models with a U(1) gauge extension beyond the Standard Model, one can derive sum rules for the couplings of the theory that are a consequence of tree-level unitarity. In this paper, we provide a comprehensive list of coupling sum rules for a general$$ \textrm{SU}{(2)}_L\times \textrm{U}{(1)}_Y\times \textrm{U}{(1)}_{Y^{\prime }} $$ SU 2 L × U 1 Y × U 1 Y ′ gauge theory coupled to an arbitrary set of fermion and scalar multiplets. These results are of particular interest for models of dark matter that employ an extended gauge sector mediated by a new (dark)Z ′ gauge boson. For the case of a minimal extension of the Standard Model with a$$ \textrm{U}{(1)}_{Y^{\prime }} $$ U 1 Y ′ gauge boson, we clarify the definitions of the weak mixing angle and the electroweakρparameter. We demonstrate the utility of a generalizedρparameter (denoted byρ ′ ) whose definition naturally follows from the unitarity sum rules developed in this paper.
Physics↗
Direct ab initio calculation of the 4 He nuclear electric dipole polarizability
The calculation of nuclear electromagnetic sum rules by directly diagonalizing the nuclear Hamiltonian in a large basis is numerically challenging and has not been performed for A>2 nuclei. With the significant progress of high performance computing, we show that calculating sum rules using numerous discretized continuum states obtained by directly diagonalizing the ab initio no-core shell model Hamiltonian is achievable numerically. Specifically, we calculate the 4 He electric dipole (E1) polarizability, that is an inverse energy weighted sum rule, employing the Daejeon16 NN interaction. We demonstrate that the calculations are numerically tractable as the dimension of the basis increases and are convergent. Our results for the 4 He electric dipole polarizability are consistent with the most recent experimental data and are compared with those of other theoretical studies employing different techniques and various interactions.
Astronomy & Astrophysics↗