Spectral-function Sum Rules Research Articles

Some remarks on compositeness of * *Supported in part by the National Nature Science Foundations of China (12335002, 12375078, 11975028). H.Q. Zheng and Z. Xiao are also Supported by "the Fundamental Research Funds for the Central Universities"

Recently, the LHCb experimental group found an exotic state from the process. A key question is whether it is just a molecule or may have a confined tetraquark ingredient. To investigate this, different methods were used, including a two-channel ( and ) K-matrix unitarization and a single-channel Flatté-like parametrization method analyzed utilizing the pole counting rule and spectral density function sum rule. These analyses demonstrated that is a molecular state, although the possibility that there may exist an elementary ingredient cannot be excluded, according to an approximate analysis of its production rate.

On the nature of X(3960)

A near-threshold enhancement in the D^{+}_{s}D^{-}_{s} system, dubbed as X(3960), is observed by the LHCb collaboration recently. A combined analysis on chi _{c0}(3930)~(rightarrow D^+ D^-), X(3960)~(rightarrow D^{+}_{s}D^{-}_{s}), and X(3915)~(rightarrow J/psi omega ) is performed using both a K-matrix approach of D_{(s)}bar{D}_{(s)} four-point contact interactions and a model of Flatté-like parameterizations. The use of the pole counting rule and spectral density function sum rule indicate, under current statistics, that this D^{+}_{s}D^{-}_{s} near-threshold state has probably the mixed nature of a cbar{c} confining state and D^{+}_{s}D^{-}_{s} continuum.

X(6900) peak could be a molecular state

The analyses of the LHCb data on $X(6900)$ found in di-$J/\psi$ and $J/\psi \psi(3686)$ systems are performed using a momentum-dependent {Flatt\'{e}}-like parameterization. The use of the pole counting rule and spectral density function sum rule give consistent conclusions that $X(6900)$ may not be a molecule of $J/\psi \psi(3686)$. Nevertheless it is still possible that $X(6900)$ be a molecule of higher states, such as $J/\psi\psi(3770)$, $\chi_{c0}\chi_{c2}$, etc.

Exact sum rules for spectral zeta functions of homogeneous 1D quantum oscillators, revisited *

We survey sum rules for spectral zeta functions of homogeneous 1D Schrödinger operators, that mainly result from the exact Wentzel–Kramers–Brillouin method.

Some remarks on X(6900) * *Supported in part by National Nature Science Foundations of China (11975028, 10925522) and China Postdoctoral Science Foundation (2020M680500)

The analysis of the LHCb data on found in the di- system was performed using a momentum-dependent Flatté-like parameterization. The use of the pole counting rule and spectral density function sum rule provides consistent evidence that both confining and molecular states are possible. Alternatively, the nature of cannot be distinguished if only the di- experimental data with current statistics are available. Nevertheless, we found that the lowest state in the di- system likely has the same quantum numbers as , and is probably not interpreted as a molecular state.

Light-Front Dynamics and the $${{^{3}He}}$$ 3 H e Spectral Function

Two topics are presented. The first one is a novel approach for a Poincare' covariant description of nuclear dynamics based on light-front Hamiltonian dynamics. The key quantity is the light-front spectral function, where both normalization and momentum sum rule can be satisfied at the same time. Preliminary results are discussed for an initial analysis of the role of relativity in the EMC effect in 3He. A second issue, very challenging, is considered in a non-relativistic framework, namely a distorted spin-dependent spectral function for 3He in order to take care of the final state interaction between the observed pion and the remnant in semi-inclusive deep inelastic electron scattering off polarized 3He. The generalization of the analysis within the light-front dynamics is outlined.

Essentials of the σ resonance in meson–meson scattering and spectral functions

We study the roles of resonances in semi-local duality from meson-meson scattering and in the scalar and pseudoscalar spectral function sum rules. The scattering amplitudes and spectral functions are first systematically calculated within chiral perturbation theory (χPT) with explicit η1 field in addition to the pseudo-Goldstone octet π,K,η8 and then unitarized through the N/D approach. In this note, we emphasize the important roles of the σ or f0(500) resonance in these quantities.

Chiral dynamics in form factors, spectral-function sum rules, meson-meson scattering and semilocal duality

In this work, we perform the one-loop calculation of the scalar and pseudoscalar form factors in the framework of $U(3)$ chiral perturbation theory with explicit tree level exchanges of resonances. The meson-meson scattering calculation from Guo and Oller [Phys. Rev. D 84, 034005 (2011)] is extended as well. The spectral functions of the nonet scalar-scalar ($SS$) and pseudoscalar-pseudoscalar ($PP$) correlators are constructed by using the corresponding form factors. After fitting the unknown parameters to the scattering data, we discuss the resonance content of the resulting scattering amplitudes. We also study spectral-function sum rules in the $SS\ensuremath{-}SS$, $PP\ensuremath{-}PP$, and $SS\ensuremath{-}PP$ sectors as well as semilocal duality from scattering. The former relate the scalar and pseudoscalar spectra between themselves while the latter mainly connects the scalar spectrum with the vector one. Finally we investigate these items as a function of ${N}_{C}$ for ${N}_{C}>3$. All these results pose strong constraints on the scalar dynamics and spectroscopy that are discussed. They are successfully fulfilled by our meson-meson scattering amplitudes and spectral functions.

Spectral-function sum rules in supersymmetry breaking models

The technique of Weinberg's spectral-function sum rule is a powerful tool for a study of models in which global symmetry is dynamically broken. It enables us to convert information on the short-distance behavior of a theory to relations among physical quantities which appear in the low-energy picture of the theory. We apply such technique to general supersymmetry breaking models to derive new sum rules.

Interesting features of scalar and pseudoscalar spectral function sum rules within aU(3) chiral framework

We compute the scalar and pseudoscalar spectral functions by using their form factors calculated within the unitarized U(3) chiral perturbation theory (�PT). The extrapolation to larger values of NC and the spectral function sum rules are discussed as well. Some interesting features of the scalar spectral functions are revealed.

Bulk spectral function sum rule in QCD-like theories with a holographic dual

We derive the sum rule for the spectral function of the stress-energy tensor in the bulk (uniform dilatation) channel in a general class of strongly coupled field theories. This class includes theories holographically dual to a theory of gravity coupled to a single scalar field, representing the operator of the scale anomaly. In the limit when the operator becomes marginal, the sum rule coincides with that in QCD. Using the holographic model, we verify explicitly the cancellation between large and small frequency contributions to the spectral integral required to satisfy the sum rule in such QCD-like theories.

Vacuum energy and spectral function sum rules

We reformulate the problem of the cancellation of the ultraviolet divergencies of the vacuum energy, particularly important at the cosmological level, in terms of a saturation of spectral function sum rules which leads to a set of conditions on the spectrum of the fundamental theory. We specialize the approach to both Minkowski and de Sitter space-times and investigate some examples.

Numerical renormalization group approach to Green’s functions for quantum impurity models

We present a novel technique for the calculation of dynamical correlation functions of quantum impurity systems in equilibrium with Wilson's numerical renormalization group. Our formulation is based on a complete basis set of the Wilson chain. In contrast to all previous methods, it does not suffer from overcounting of excitation. By construction, it always fulfills sum rules for spectral functions. Furthermore, it accurately reproduces local thermodynamic expectation values, such as occupancy and magnetization, obtained directly from the numerical renormalization group calculations.

Nonperturbative bound on high multiplicity cross sections inφ4theory in three dimensions from lattice simulation

We have looked for evidence of large cross sections at large multiplicities in weakly coupled scalar field theory in three dimensions. We use spectral function sum rules to derive bounds on total cross sections where the sum can be expresed in terms of a quantity which can be measured by Monte Carlo simulation in Euclidean space. We find that high multiplicity cross sections remain small for energies and multiplicities for which large effects had been suggested.

Note on finite temperature sum rules for vector and axial-vector spectral functions

An updated analysis of vector and axial-vector spectral functions is presented. The resonant contributions to the spectral integrals are shown to be expressible as multiples of 4 pi^2 f_pi^2, encoding the scale of spontaneous chiral symmetry breaking in QCD. Up to order T^2 this behavior carries over to the case of finite temperature.

High-energy theorems at large N

Sum rules for products of two, three and four quantum chromodynamics (QCD) currents arederived using chiral symmetry at infinite momentum in thelarge-N limit. These exact relations among meson decayconstants, axial-vector couplings and masses determine theasymptotic behaviour of an infinite number of QCD correlators.The familiar spectral function sum rules for products of twoQCD currents are among the relations derived. With thisprecise knowledge of asymptotic behaviour, an infinite numberof large-N QCD correlators can be constructed usingdispersion relations. A detailed derivation is given of theexact large-N pion vector form factor and forwardpion-pion scattering amplitudes.

Physical spectrum of conformalSU(N)gauge theories

We investigate the physical spectrum of vector-like $\mathrm{SU}(N)$ gauge theories with infrared coupling close to but above the critical value for a conformal phase transition. We use dispersion relations, the momentum dependence of the dynamical fermion mass and resonance saturation. We argue that the second spectral function sum rule is substantially affected by the continuum contribution, allowing for a reduction of the axial-vector--vector mass splitting with respect to QCD-like theories. Possible consequences for technicolor theories are described.

Energy weighted sum rules for spectral functions in nuclear matter.

The energy weighted sum rule of single-particle spectral functions in nuclear matter is studied. The spectral functions include the influence of short-range correlations as generated by the Reid potential in the framework of the self-consistent Green's function method. For the range of momenta studied, the sum rule is rather accurately fulfilled numerically (within 5%). It is observed that the high-energy tail of the particle part of the spectral function exhausts most of the sum rule, which confirms the need for the appearance of single-particle strength at very high energies.

Tau decay and spin-one resonances.

The implications of the recent measurement of the decay {tau}{sup {minus}}{r_arrow}{nu}{sub {tau}}{ital {bar K}}{pi}{pi} are analyzed in the resonance dominance picture. With flavor SU(3) symmetry, the observed {ital {bar K}}{sub 1} resonance production in {tau}{sup {minus}}{r_arrow}{nu}{sub {tau}}{ital {bar K}}{pi}{pi} requires {tau}{sup {minus}}{r_arrow}{nu}{sub {tau}}{ital a1}{sup {minus}} dominance in the nonstrange axial-vector channel. Then the spectral function sum rule cannot be saturated with {rho}, {pi}, and {ital a}{sub 1}. The inclusion of the first excited vector meson brings back a consistent picture and improves the {pi}{sup +}-{pi}{sup 0} mass difference calculation.

Vacuum alignment in composite technicolor standard models

We consider the question of vacuum alignment in the recently proposed “composite technicolor standard models” (CTSMs). In these models, explicit chiral symmetry breaking due to masses of electroweak-singlet “ultrafermions” is communicated to the quarks and leptons by a chiral condensate produced by strong “ultracolor” gauge interactions. In these models the ultracolor vacuum alignment is determined by the competition between ultrafermion masses and “flavor” gauge boson exchange. In order for these models to work, the gauge contribution to the effective potential is assumed to dominate the contribution from ultrafermion masses and stabilize the desired vacuum. Using spectral function sum rules and a vector-meson saturation approximation known to work well in QCD, we determine the gauge contribution to the effective potential for perturbative flavor gauge boson couplings in the limit where the number of ultracolors is large. We find that the flavor gauge interactions do not favor the vacuum required by CTSMs for weak couplings. While realistic models require nonperturbative values of the flavor gauge couplings, we interpret this as evidence against the vacuum required by CTSMs.