Subtraction Point Research Articles

Renormalization of three-quark operators at two loops in the RI′/SMOM scheme

We consider the renormalization of the three-quark operators without derivatives at next-to-next-to-leading order in QCD perturbation theory at the symmetric subtraction point. This allows us to obtain conversion factors between the MS‾ scheme and the regularization invariant symmetric MOM (RI/SMOM, RI′/SMOM) schemes. The results are presented both analytically in Rξ gauge in terms of a set of master integrals and numerically in Landau gauge. They can be used to reduce the errors in determinations of baryonic distribution amplitudes in lattice QCD simulations.

Two different spectrophotometric methods for simultaneous determination of binary mixture of atenolol and amlodipine in commercial formulation

Two different spectrophotometric methods for simultaneous determination of binary mixture of atenolol and amlodipine in commercial formulation

The subtraction contribution to the muonic-hydrogen Lamb shift: A point for lattice QCD calculations of the polarizability effect

The proton-polarizability contribution to the muonic-hydrogen Lamb shift is a major source of theoretical uncertainty in the extraction of the proton charge radius. An empirical evaluation of this effect, based on the proton structure functions, requires a systematically improvable calculation of the “subtraction function”, possibly using lattice QCD. We consider a different subtraction point, with the aim of accessing the subtraction function directly in lattice calculations. A useful feature of this subtraction point is that the corresponding contribution of the structure functions to the Lamb shift is suppressed. The whole effect is dominated by the subtraction contribution, calculable on the lattice.

Renormalization in Minkowski space–time

The multiplicative and the functional renormalization group methods are applied for the four-dimensional scalar theory in Minkowski space–time. It is argued that the appropriate choice of the subtraction point is more important in Minkowski than in Euclidean space–time. The parameters of the cutoff theory, defined by a subtraction point in the quasi-particle domain, are complex due to the mass-shell contributions and the renormalization group flow becomes much more involved than its Euclidean counterpart.

A New Black Hole Solution in Conformal Dilaton Gravity on a Warped Spacetime

An exact time-dependent solution of a black hole is found in a conformally invariant gravity model on a warped Randall-Sundrum spacetime, by writing the metric . Here, represents the “un-physical” spacetime and ω the dilaton field, which will be treated on equal footing as any renormalizable scalar field. In the case of a five-dimensional warped spacetime, we thereafter write . The dilaton field can be used to describe the different notion the in-going and outside observers have of the Hawking radiation by using different conformal gauge freedom. The disagreement about the interior of the black hole is explained by the antipodal map of points on the horizon. The free parameters of the solution can be chosen in such a way that is singular-free and topologically regular, even for ω → 0 . It is remarkable that the 5D and 4D effective field equations for the metric components and dilaton fields can be written in general dimension n = 4,5. From the exact energy-momentum tensor in Eddington-Finkelstein coordinates, we are able to determine the gravitational wave contribution in the process of evaporation of the black hole. It is conjectured that, in context of quantization procedures in the vicinity of the horizon, unitarity problems only occur in the bulk at large extra-dimension scale. The subtraction point in an effective theory will be in the UV only in the bulk, because the use of a large extra dimension results in a fundamental Planck scale comparable with the electroweak scale.

Moments n = 2 and n = 3 of the Wilson twist-two operators at three loops in the RI′/SMOM scheme

We study the renormalization of the matrix elements of the twist-two non-singlet bilinear quark operators, contributing to the n=2 and n=3 moments of the structure functions, at next-to-next-to-next-to-leading order in QCD perturbation theory at the symmetric subtraction point. This allows us to obtain conversion factors between the MS‾ scheme and the regularization-invariant symmetric momentum subtraction (RI/SMOM, RI′/SMOM) schemes. The obtained results can be used to reduce errors in determinations of moments of structure functions from lattice QCD simulations. The results are given in Landau gauge.

Symmetric point flavor singlet axial vector current renormalization at two loops

We calculate the two loop correction to the quark 2-point function with the non-zero momentum insertion of the flavour singlet axial vector current at the fully symmetric subtraction point for massless quarks in the modified minimal subtraction (MSbar) scheme. The Larin method is used to handle $\gamma^5$ within dimensional regularization at this loop order ensuring that the effect of the chiral anomaly is properly included within the construction.

Bilinear quark operators in the RI/SMOM scheme at three loops

We consider the renormalization of the matrix elements of the bilinear quark operators ψ¯ψ, ψ¯γμψ, and ψ¯σμνψ at next-to-next-to-next-to-leading order in QCD perturbation theory at the symmetric subtraction point. This allows us to obtain conversion factors between the MS‾ scheme and the regularization invariant symmetric momentum subtraction (RI/SMOM) scheme. The obtained results can be used to reduce the errors in determinations of quark masses from lattice QCD simulations. The results are given in Landau gauge.

Quark matter in the perturbation QCD model with a rapidly convergent matching-invariant running coupling

The properties of dense quark matter are investigated in the perturbation theory with a rapidly convergent matching-invariant running coupling. The fast convergence is mainly due to the resummation of an infinite number of known logarithmic terms in a compact form. The only parameter in this model, the ratio of the renormalization subtraction point to the chemical potential, is restricted to be about 2.64 according to the Witten–Bodmer conjecture, which gives the maximum mass and the biggest radius of quark stars to be, respectively, two times the solar mass and 11.7[Formula: see text]km.

Design and application of a system for droplet-size measurement in the field based on micro-distance imaging technology

A measurement system was developed using micro-distance imaging technology to measure droplet sizes in the field. Legible droplet images were acquired with a single-lens reflex camera, a micro-distance lens and illumination source in the proper parameters. The droplets were extracted effectively based on the background subtraction, region-growing repair, shape-factor screening and concave points matching methods. The droplet characterizations, including projective area, diameter and volume were calculated using MATLAB image processing technology. The system displayed droplet sizes and distribution regulation in graphs that were convenient for obtaining experimental regulation. Indoor comparison experiments between the developed system and oil disk method was conducted, and the average relative errors were 6.03%, 5.50% and 6.25% for DV 0.1, DV 0.5, DV 0.9, respectively. Field comparison experiments revealed that the relative error was 5.61% between the developed system and the oil disk method and 6.88% between the developed system and the laser instrument method. Application experiments in the field were conducted and the result revealed that fine droplets had better penetration than coarse droplets in the tree canopy. The system was simple in structure, had a lower cost compared with some instruments and reduced experimental time compared with the image processing methods that use oil disks. It has a good prospect for use.

Renormalization of Chiral Nuclear Forces with Multiple Subtractions in Peripheral Channels

We analyse the renormalization of the of two-nucleon interaction with multiple subtractions in peripheral waves considering two chiral forces at N3LO. Phase shifts at low energies are then computed with several subtraction points below μ=10 fm−1. We show that for most peripheral waves the phase shifts have nearly no dependence on the renormalization scale. In two cases the phase shifts converge slowly as the renormalization scale approaches μ=1 fm−1 and in one case the phase shifts presented oscillations with respect to the subtraction point μ.

Properties of quark matter in a new quasiparticle model with QCD running coupling

The running of the QCD coupling in the effective mass causes thermodynamic inconsistency problem in the conventional quasiparticle model. We provide a novel treatment which removes the inconsistency by an effective bag constant. The chemical potential dependence of the renormalization subtraction point is constrained by the Cauchy condition in the chemical potential space. The stability and microscopic properties of strange quark matter are then studied within the completely self-consistent quasiparticle model, and the obtained equation of state of quark matter is applied to the investigation of strange stars. It is found that our improved model can describe well compact stars with mass about two times the solar mass, which indicates that such massive compact stars could be strange stars.

Subtractive Renormalization of the NJL model *

In this work, we apply a subtractive renormalization method to the SU(2) Nambu-Jona-Lasinio (NJL) model in Born approximation and compare the results obtained here with those achieved by the standard momentum cutoff regularization. We have computed the dynamical quark mass, the chiral condensate, the pion mass and the quark-antiquark T-matrix as a function of the cutoff Λ and the subtraction scale ξ. We have shown that both approaches give similar results and the dependence of the physical quantities on the subtraction point ξ is much weaker than the dependence on the cutoff Λ.

Improved fD(s)∗, fB(s)∗ and fBc from QCD Laplace sum rules

Anticipating future precise measurements of the D- and B-like (semi)leptonic and hadronic decays for alternative determinations of the CKM mixing angles, we pursue our program on the D- and B-like mesons by improving the estimates of [Formula: see text] and [Formula: see text] (analogue to [Formula: see text]) by using the well-established (inverse) Laplace sum rules (LSR) and/or their suitable ratios less affected by the systematics, which are known to N2LO pQCD and where the complete [Formula: see text] nonperturbative condensate contributions are included. The convergence of the PT series is analyzed by an estimate of the N3LO terms based on geometric growth of the coefficients. In addition to the standard LSR variable [Formula: see text] and the QCD continuum threshold [Formula: see text] stability criteria, we extract our optimal results by also requiring stability on the variation of the arbitrary QCD subtraction point [Formula: see text] which reduces the errors in the analysis. We complete the study of the open bottom states by an estimate of [Formula: see text]. Our results summarized in Tables 3 and 4 are compared with some other recent sum rules and lattice estimates.

Running of the contact interactions in chiral N3LO potentials from subtractive renormalization

In this work a subtracted kernel renormalization procedure (SKM) is applied to the chiral NN potential up to next-to-next-to-next-to-leading-order (N3 LO) to obtain the running of the renormalized contact strengths with the subtraction scale μ and the phase shifts for all uncoupled waves with contact interaction (S,P,D). We use two potentials constructed within the framework of Weinberg's approach to ChEFT, which provide a very accurate description of NN scattering data below laboratory energies E ∼ 350 MeV, namely Epelbaum, Glöckle and Meissner (N3LO-EGM) and Entem and Machleidt (N3LO-EM). For both potentials, we consider a large cutoff (30 fm-1) and analyze the phases and the running of the contact strengths with the subtraction point μ by making a fit of the K-matrix with five subtractions to the K-matrix from the Nijmegen II potential at low energies (E ≤ 20 MeV).

Novel Ratio Subtraction and Isoabsorptive Point Methods for Determination of Ambroxol Hydrochloride and Doxycycline in their Combined Dosage Form: Development and Validation

Purpose: To develop and validate two innovative spectrophotometric methods used for the simultaneous determination of ambroxol hydrochloride and doxycycline in their binary mixture.Methods: Ratio subtraction and isoabsorptive point methods were used for the simultaneous determination of ambroxol hydrochloride and doxycycline in their binary mixture. Linear correlations were obtained in the concentration range of 6 - 40 and 4 - 32 μg mL-1 for ambroxol hydrochloride and doxycycline, respectively. Ratio subtraction method was utilized for determination of ambroxol hydrochloride at 246.5 nm while isoabsorptive point method was employed for doxycycline at 244 nm (using methanol as a solvent) in mixtures as well as in their combined dosage form (Ambrodoxy capsules).Results: The proposed methods were successfully applied to the analysis of the pharmaceutical capsules containing the two analytes. Recovery for ambroxol hydrochloride and doxycycline in capsules was 99.49 and 99.96 %, respectively. The relative standard deviation (% RSD) for the assay of the capsules was < 1 %. Validation of the two methods was assessed according to International Council on Harmonization (ICH) guidelines regarding linearity, accuracy, precision, specificity and range. The results of the proposed methods compared favorably with those obtained by a reported chemometricsassisted ultraviolet (UV)-spectroscopic method.Conclusion: The proposed methods are rapid, selective, simple and accurate. They also represent suitable alternatives to the chromatographic methods currently used for the analysis of the pharmaceutical mixtures in various dosage forms.Keywords: Ambroxol, Doxycycline, Ratio subtraction method, Isoabsorptive point method, Binary mixture, Spectrophotometry

Mini-review on QCD spectral sum rules

Taking the example of the most popular and well-established Borel / Laplace / Exponential sum rule (LSR), I shortly review some of its recent applications in hadron physics namely the estimates of non-perturbative condensates, the determination of the light and heavy quark masses, the extraction of the heavy-light decay constants, the estimates of charmonium and bottomium molecule masses and the properties of scalar gluonium. In addition to the standard τ (sum rule variable) and tc (QCD continuum threshold) stablity criteria, I introduce a new stability criterion versus the arbitrary QCD subtraction point μ for extracting the optimal results when radiative QCD corrections are included. Future improvements on further uses of QCD spectral sum rules (QSSR) are commented.

Improved light quark masses from pseudoscalar sum rules

Using ratios of the inverse Laplace transform sum rules within stability criteria for the subtraction point μ in addition to the ones of the usual τ spectral sum rule variable and continuum threshold tc, we extract the π(1300) and K(1460) decay constants to order αs4 of perturbative QCD by including power corrections up to dimension-six condensates, tachyonic gluon mass for an estimate of large order PT terms, instanton and finite width corrections. Using these inputs with enlarged generous errors, we extract, in a model-independent and conservative ways, the sum of the scale-independent renormalization group invariant (RGI) quark masses (mˆu+mˆq):q≡d,s and the corresponding running masses (m¯u+m¯q) evaluated at 2 GeV. By giving the value of the ratio mu/md, we deduce the running quark masses m¯u,d,s and condensate 〈u¯u¯〉 and the scale-independent mass ratios: 2ms/(mu+md) and ms/md. Using the positivity of the QCD continuum contribution to the spectral function, we also deduce, from the inverse Laplace transform sum rules, for the first time to order αs4, new lower bounds on the RGI masses which are translated into the running masses at 2 GeV and into upper bounds on the running quark condensate 〈u¯u¯〉. Our results summarized in Table 3 and compared with our previous results and with recent lattice averages suggest that precise phenomenological determinations of the sum of light quark masses require improved experimental measurements of the π(1.3) and K(1.46) hadronic widths and/or decay constants which are the dominant sources of errors in the analysis.

Revisiting [formula omitted] and [formula omitted] from HQET spectral sum rules

Using recent values of the QCD (non-) perturbative parameters given in Table 1, we reconsider the extraction of fB and the on-shell mass Mb from HQET Laplace spectral sum rules known to N2LO PT series and including dimension 7 condensates in the OPE. We especially study the convergence of the PT series, the effects on “different spectral sum rules data” of the continuum threshold and subtraction point varied in a larger range than in the existing literature and include in the error an estimate of the N3LO PT series based on a geometric growth of the PT series. We obtain the Renormalization Group Invariant (RGI) universal coupling: fˆB∞=0.416(60)GeV3/2 in the static limit Mb→∞ and the physical decay constant including 1/Mb corrections: fBhqet=199(29)MeV. Using the ratio of sum rules, we obtain, to order αs2, the running mass m¯b(m¯b)=4213(59)MeV. The previous results are in good agreement with the ones from QCD spectral sum rules (QSSR) in full QCD to the same order from the same channel Narison (2013) [1]: fBqcd=206(7)MeV and m¯b(m¯b)qcd=4236(69)MeV.

Power corrections to symmetric point vertices in Gribov-Zwanziger theory

The 3-point vertices of QCD are examined at the symmetric subtraction point at one loop in the Landau gauge in the presence of the Gribov mass, gamma. They are expanded in powers of gamma^2 up to dimension four in order to determine the order of the leading correction. As well as analysing the pure Gribov-Zwanziger Lagrangian, its extensions to include localizing ghost masses are also examined. For comparison a pure gluon mass term is also considered.