Energy Sum Rules Research Articles

Nucleon Resonance Masses from QCD Sum Rules

We calculate the masses of the nucleon resonances [N+(1440), N-(1535), N- (1650), N+(1710), N+(1880), N-(1895), N+(2100)] using an adaptation of the method of finite energy QCD sum rules (FESR) introduced recently in the determination of the masses of the vector meson resonances. This variation of finite energy sum rules involves as usual integration over a closed contour consisting of a circle of a large radius R and a cut in the complex energy (squared) plane. A specific integration kernel is used, however, which minimizes the integral over the cut. We obtain remarkably stable results over a wide range R, where R is the radius of the integration contour. The sum rule predictions agree well with the experimental values. We make use of the nucleonic correlator discussed in our previous FESR calculation of the nucleon mass.

Nucleon axial coupling constant in a magnetar environment

Using appropriate QCD finite energy sum rules, we discuss the influence of an external magnetic field and baryonic density on the axial-vector coupling constant gA. This scenario corresponds to a magnetar environment. We found that gA decreases both as function of the magnetic field strength and the baryonic density. It turns out that at the nuclear density ρ0 the axial-vector coupling takes the value gA⁎≈0.92. Although gA decreases in general with the magnetic field intensity, gA⁎ does not change in a relevant way with the magnetic field.

Finite energy sum rules for gravitational Regge amplitudes

We develop a framework to derive consistency constraints on gravitational Regge amplitudes based on the finite energy sum rules (FESRs), which directly connect gravitational Regge amplitudes at a finite ultraviolet scale with infrared physics without suffering from super-Planckian physics. For illustration, we consider four-point scattering of an identical massless scalar coupled to gravity. First, we derive multiple FESRs without relying on the s-t-u permutation invariance. We then make use of FESRs, crossing symmetry, and other principles such as unitarity, to derive bounds on the Regge parameters. The bounds result in infrared finite gravitational positivity bounds in four spacetime dimensions.

Axial coupling constant in a magnetic background

The nucleon axial coupling constant ${g}_{A}$ is calculated in the presence of an external uniform magnetic field using finite energy sum rules. The correlation function of proton, neutron and axial-vector currents is calculated both the hadronic and the QCD sector. Once the axial contribution in the form factor is isolated, a double sum rule is considered, i.e., the usual QCD contour integration for the external moments of both the proton and neutron current. The effects of the external magnetic field come mainly through the in-medium current-nucleon coupling constants ${\ensuremath{\lambda}}_{N}(B)$ and the hadronic thresholds ${s}_{0}(B)$ provided by the nucleon-nucleon correlators. As a result, the axial coupling constant decreases in the presence of the magnetic field.

Tests of the Zc -like Laplace sum rule results using finite energy sum rule at NLO

In this note, we use local duality Finite Energy Sum Rule (FESR) to test the validity of the Laplace sum rules (LSR) results truncated at the dimension-six condensates for the estimates of the masses and couplings of the Z_c-like ground states in Ref.1 by taking the example of the D^*D molecule configuration. We confirm the existence of an eventual (D^*D)_1 radial excitation with a mass around 5700 MeV and coupling of 197(25) keV to the current which may mask the eventual Z_c(4430) radial excitation candidate (named (D^*D)_0 in Ref.1) having a relatively small coupling f_{(D^*D)_0}=46(56) keV. We add more explanations on the estimates in Ref.1 from LSR and comment the results in Ref.2.

Using improved operator product expansion in Borel–Laplace sum rules with ALEPH tau decay data, and determination of pQCD coupling

We use improved truncated operator product expansion (OPE) for the Adler function, involving two types of terms with dimension D=6, in the double-pinched Borel–Laplace sum rules and finite energy sum rules for the V + A channel strangeless semihadronic tau decays. The generation of the higher order perturbative QCD terms of the D=0 part of the Adler function is carried out using a renormalon-motivated ansatz incorporating the leading UV renormalon and the first two leading IR renormalons. The trunacted D=0 part of the sum rules is evaluated by two variants of the fixed-order perturbation theory (FO), by principal value of the Borel resummation (PV), and by contour-improved perturbation theory (CI). For the experimental V + A channel spectral function we use the ALEPH tau -decay data. We point out that the truncated FO and PV evaluation methods account correctly for the renormalon structure of the sum rules, while this is not the case for the truncated CI evaluation. We extract the value of the {overline{mathrm{MS}}} coupling alpha _s(m_{tau }^2) = 0.3235^{+0.0138}_{-0.0126} [alpha _s(M_Z^2)=0.1191 pm 0.0016] for the average of the two FO methods and the PV method, which we consider as our main result. If we included in the average also CI extraction, the value would be alpha _s(m_{tau }^2) = 0.3299^{+0.0232}_{-0.0225} [alpha _s(M_Z^2)=0.1199^{+0.0026}_{-0.0028}]. This work is an extension and improvement of our previous work (Ayala et al. in Eur Phys J. C 81(10): 930, 2021, arXiv:2105.00356 [hep-ph]) where we used for the truncated OPE a more naive (and widely used) form and where the extracted values for alpha _s(M_Z^2) were somewhat lower.

First-principles study of the structural and optoelectronic properties of ANbO3 (A = Na, K and Rb) in four crystal phases

In the present work structural and optoelectronic properties of alkali niobates ANbO3 (A = Na, K and Rb) are investigated in different crystal structures e.g. cubic, tetragonal, orthorhombic and rhombohedral using generalized gradient approximation (GGA), GGA with Hubbard potential (GGA + U) and modified Becke-Johnson (mBJ) approach. Structural properties show that ferroelectric rhombohedral crystal structure is the most stable structure of these compounds. The anti-ferroelectric and paraelectric are their higher energy crystal structures. The obtained results of the electronic band gaps show that mBJ is the appropriate exchange-correlation approximation for the calculations of electronic and optical properties of these niobates. They are indirect band gap semiconductors, except the ferroelectric rhombohedral and antiferroelectric orthorhombic NaNbO3. The valence band is predominantly contributed by O 2p orbitals and conduction band is made of Nb 4d orbitals. Real and imaginary parts of dielectric function and other optical parameters such as energy loss function, sum rule and refractive index are also investigated.

Determination of perturbative QCD coupling from ALEPH tau decay data using pinched Borel\u2013Laplace and Finite Energy Sum Rules

We present a determination of the perturbative QCD (pQCD) coupling using the V+A channel ALEPH tau -decay data. The determination involves the double-pinched Borel–Laplace Sum Rules and Finite Energy Sum Rules. The theoretical basis is the Operator Product Expansion (OPE) of the V+A channel Adler function in which the higher order terms of the leading-twist part originate from a model based on the known structure of the leading renormalons of this quantity. The applied evaluation methods are contour-improved perturbation theory (CIPT), fixed-order perturbation theory (FOPT), and Principal Value of the Borel resummation (PV). All the methods involve truncations in the order of the coupling. In contrast to the truncated CIPT method, the truncated FOPT and PV methods account correctly for the suppression of various renormalon contributions of the Adler function in the mentioned sum rules. The extracted value of the {overline{mathrm{MS}}} coupling is alpha _s(m_{tau }^2) = 0.3116 pm 0.0073 [alpha _s(M_Z^2)=0.1176 pm 0.0010] for the average of the FOPT and PV methods, which we regard as our main result. On the other hand, if we include in the average also the CIPT method, the resulting values are significantly higher, alpha _s(m_{tau }^2) = 0.3194 pm 0.0167 [alpha _s(M_Z^2)=0.1186 pm 0.0021].

Strong coupling from an improved τ vector isovector spectral function

We combine ALEPH and OPAL results for the spectral distributions measured in $\tau\to\pi^-\pi^0\nu_\tau$, $\tau\to 2\pi^-\pi^+\pi^0\nu_\tau$ and $\tau\to\pi^-3\pi^0\nu_\tau$ decays with (i) recent BaBar results for the analogous $\tau\to K^- K^0\nu_\tau$ distribution and (ii) estimates of the contributions from other hadronic $\tau$-decay modes obtained using CVC and electroproduction data, to obtain a new and more precise non-strange, inclusive vector, isovector spectral function. The BaBar $K^- K^0$ and CVC/electroproduction results provide us with alternate, entirely data-based input for the contributions of all exclusive modes for which ALEPH and OPAL employed Monte-Carlo-based estimates. We use the resulting spectral function to determine $\alpha_s(m_\tau)$, the strong coupling at the $\tau$ mass scale, employing finite energy sum rules. Using the fixed-order perturbation theory (FOPT) prescription, we find $\alpha_s(m_\tau)=0.3077\pm 0.0075$, which corresponds to the five-flavor result $\alpha_s(M_Z)=0.1171\pm 0.0010$ at the $Z$ mass. While we also provide an estimate using contour-improved perturbation theory (CIPT), we point out that the FOPT prescription is to be preferred for comparison with other $\alpha_s$ determinations employing the $\overline{{\rm MS}}$ scheme, especially given the inconsistency between CIPT and the standard operator product expansion recently pointed out in the literature. Additional experimental input on the dominant $2\pi$ and $4\pi$ modes would allow for further improvements to the current analysis.

Magnetic effects of QCD parameters from fnite energy sum rules

One of the advantages of the fnite energy sum rules is the fact that every operator in the operator product expansion series can be selected individually by the use of an appropriate kernel function which removes other operator poles. This characteristic is maintained by QCD systems in the presence of external homogeneous magnetic feld, providing interesting information about the magnetic evolution of QCD and hadronic parameters. In this work fnite energy sum rules are applied on QCD in the light quark sector, combining axial and pseudoscalar channels in the presence of an external homogeneous magnetic feld, obtaining the magnetic evolution of the light quark masses, pion mass, the pion decay constant, the gluon condensate and the continuum hadronic threshold.

Renormalons in integrated spectral function moments and αs extractions

Precise extractions of $\alpha_s$ from $\tau\to {\rm (hadrons)}+\nu_\tau$ and from $e^+e^-\to {\rm (hadrons)}$ below the charm threshold rely on finite energy sum rules (FESRs) where the experimental side is given by integrated spectral function moments. Here we study the renormalons that appear in the Borel transform of polynomial moments in the large-$\beta_0$ limit and in full QCD. In large-$\beta_0$, we establish a direct connection between the renormalons and the perturbative behaviour of moments often employed in the literature. The leading IR singularity is particularly prominent and is behind the fate of moments whose perturbative series are unstable, while those with good perturbative behaviour benefit from partial cancellations of renormalon singularities. The conclusions can be extended to QCD through a convenient scheme transformation to the $C$-scheme together with the use of a modified Borel transform which make the results particularly simple; the leading IR singularity becomes a simple pole, as in large-$\beta_0$. Finally, for the moments that display good perturbative behaviour, we discuss an optimized truncation based on renormalisation scheme (or scale) variation. Our results allow for a deeper understanding of the perturbative behaviour of integrated spectral function moments and provide theoretical support for low-$Q^2$ $\alpha_s$ determinations.

Relation between the continuum threshold and the Polyakov loop with the QCD deconfinement transition

Using vector and axial-vector correlators within finite energy sum rules with inputs from a chiral quark model, coupled to the Polyakov loop, with nonlocal vector interactions, we extend our previous work to confirm the equivalence between the continuum threshold $s_0$ and the trace of the Polyakov loop $\Phi$ as order parameters for the deconfinement transition at finite temperature $T$ and quark chemical potential $\mu$. The obtained results are in agreement with our initial conclusion, where we showed that $s_0(T,\mu)$ and $\Phi(T,\mu)$ provide the same information for the QCD deconfinement transition.

Precision Determination of the Light Quark Masses from QCD Finite Energy Sum Rules

The light quark masses are determined from a QCD finite energy sum rule, using the pseudoscalar correlator to six-loop order in perturbative QCD, with the leading vacuum condensates and higher order quark mass corrections included. Both the fixed order perturbation theory (FOPT) method and contour improved perturbation theory (CIPT) method are explored. The results in the latter framework exhibit good convergence and stability in the window s0 = 3.0 5.0 GeV2 for the strange quark and s0 = 1.5 4.0 GeV2 for the up and down quarks; where s0 is the radius of the integration contour in the complex s-plane. The results are: , and the sum is . These proceedings critically explore how the current results - computed precisely in a modern computer language, Mathematica compare to past determinations in literature.

Up- and down-quark masses from QCD sum rules

The QCD up- and down-quark masses are determined from an optimized QCD Finite Energy Sum Rule (FESR) involving the correlator of axial-vector current divergences. In the QCD sector this correlator is known to five loop order in perturbative QCD (PQCD), together with non-perturbative corrections from the quark and gluon condensates. This FESR is designed to reduce considerably the systematic uncertainties arising from the hadronic spectral function. The determination is done in the framework of both fixed order and contour improved perturbation theory. Results from the latter, involving far less systematic uncertainties, are: {overline{m}}_uleft(2 mathrm{GeV}right)=left(2.6pm 0.4right) MeV, {overline{m}}_dleft(2 mathrm{GeV}right)=left(5.3pm 0.4right) MeV, and the sum {overline{m}}_{ud}equiv left({overline{m}}_u+{overline{m}}_dright)/2 , is {overline{m}}_{ud}left(2 mathrm{GeV}right)=left(3.9pm 0.3right) MeV.

Test of semilocal duality in a large NC framework

In this paper we test the semi-local duality based on the method of Ref.[1] for calculating final-state interactions at varying number of colors ($N_C$). We compute the amplitudes by dispersion relations that respect analyticity and coupled channel unitarity, as well as accurately describing experiment. The $N_C$ dependence of the $\pi\pi\to\pi\pi$ scattering amplitudes is obtained by comparing these amplitudes to the one of chiral perturbation theory. The semi-local duality is investigated by varying $N_C$. Our results show that the semi-local duality is not violated when $N_C$ is large. At large $N_C$, the contributions of the $f_2(1270)$, the $f_0(980)$ and the $f_0(1370)$ cancel that of the $\rho(770)$ in the finite energy sum rules, while the $f_0(500)$ has almost no effect. This gives further credit to the method developed in Ref.[1] for investigating the $N_C$ dependence of hadron-hadron scattering with final-state interactions. This study is also helpful to understand the structure of the scalar mesons.

Structure of pion photoproduction amplitudes

We derive and apply the finite energy sum rules to pion photoproduction. We evaluate the low energy part of the sum rules using several state-of-the-art models. We show how the differences in the low energy side of the sum rules might originate from different quantum number assignments of baryon resonances. We interpret the observed features in the low energy side of the sum rules with the expectation from Regge theory. Finally, we present a model, in terms of a Regge-pole expansion, that matches the sum rules and the high-energy observables.

Investigation of the light four-quark states with exotic JPC=0−−

We study the exotic $J^{PC}=0^{--}$ four-quark states in Laplace sum rules (LSR) and finite energy sum rules (FESR). We use the vector tetraquark-like currents as interpolating currents in the correlator, from which the $1^{+-}$ states are also studied. In the mass extraction, we use the standard stability criterion with respect to the Borel parameters and the QCD continuum thresholds and consider the effect of the violation of factorization in estimating the high dimensional condensates as a source of uncertainties. The obtained mass prediction $1.66\pm0.14$ GeV is much lower than the previous sum rule predictions obtained using the scalar currents. Our result favours the four-quark interpretation of the possible $\rho\pi$ dominance in the $D^0$ decay. We also discuss the possible decay patterns of these exotic four-quark states.

Comparison between the continuum threshold and the Polyakov loop as deconfinement order parameters

We study the relation between the continuum threshold as function of the temperature $s_0(T)$ within finite energy sum rules and the trace of the Polyakov loop $\Phi$ in the framework of a nonlocal SU(2) chiral quark model, establishing a contact between both deconfinement order parameters at finite temperature $T$ and chemical potential $\mu$. In our analysis, we also include the order parameter for the chiral symmetry restoration, the chiral quark condensate. We found that $s_0$ and $\Phi$ providing us the same information for the deconfinement transition, both for the zero and finite chemical potential cases. At zero density, the critical temperatures for both quantities coincide exactly and, at finite $\mu$ both order parameters provide evidence for the appearance of a quarkyonic phase.

Tests of quark–hadron duality in τ-decays

An exhaustive number of QCD finite energy sum rules for [Formula: see text]-decay together with the latest updated ALEPH data is used to test the assumption of global duality. Typical checks are the absence of the dimension d = 2 condensate, the equality of the gluon condensate extracted from vector or axial vector spectral functions, the Weinberg sum rules, the chiral condensates of dimensions d = 6 and d = 8, as well as the extraction of some low-energy parameters of chiral perturbation theory. Suitable pinched linear integration kernels are introduced in the sum rules in order to suppress potential quark–hadron duality violations and experimental errors. We find no compelling indications of duality violations in hadronic [Formula: see text]-decay in the kinematic region above s [Formula: see text] 2.2 GeV2 for these kernels.

Quark–hadron duality: Pinched kernel approach

Hadronic spectral functions measured by the ALEPH collaboration in the vector and axial-vector channels are used to study potential quark–hadron duality violations (DV). This is done entirely in the framework of pinched kernel finite energy sum rules (FESR), i.e. in a model independent fashion. The kinematical range of the ALEPH data is effectively extended up to s = 10 GeV2 by using an appropriate kernel, and assuming that in this region the spectral functions are given by perturbative QCD. Support for this assumption is obtained by using e[Formula: see text] e[Formula: see text] annihilation data in the vector channel. Results in both channels show a good saturation of the pinched FESR, without further need of explicit models of DV.