Pseudoscalar Currents Research Articles

Three-loop matching coefficients for heavy flavor-changing currents and the phenomenological applications

Within the framework of non-relativistic QCD (NRQCD) factorization, we compute the matching coefficients between full Quantum Chromodynamics (QCD) and NRQCD for the heavy flavor-changing vector, axial-vector, scalar and pseudo-scalar currents up to next-to-next-to-next-to-leading order (N3LO). We accomplish the analytical expressions for the three-loop renormalization constants and the corresponding anomalous dimensions for all of the four NRQCD currents with two different heavy flavors. The three-loop QCD corrections to the matching coefficients turn out to be significantly larger than lower order corrections. By employing the scale relation, we approximately simulate the N3LO correction to the wave functions at the origin for the vector {B}_c^{ast } meson and the pseudo-scalar Bc meson from the known result for the equal-mass heavy quarkonium in potential NRQCD (pNRQCD). We find large cancellations at the third order between the matching coefficients and the wave functions at the origin, and obtain the convergent decay constants of {B}_c^{ast } and Bc up to N3LO. We present the complete perturbative QCD predictions for the decay constants, leptonic decay widths, and branching ratios of the beauty-charmed mesons.

The chiral Lagrangian with three flavors and large-N_c sum rules

We reconsider the chiral Lagrangian with three-flavor baryon fields. A systematic analysis of all low-energy constants (LEC) that contribute to the axial-vector and pseudoscalar currents in the baryon octet and decuplet fields at next-to-leading order in the inverse number of colors (1/N_c) of QCD is performed. We study the correlation function consisting of axial-vector and scalar currents as well. While there are 4 LEC relevant at leading chiral order, the number of relevant LEC at subleading order is 23. For those a leading order large-N_c analysis predicts 3 and 18 sum rules respectively. At the next accuracy level the number of sum rules is reduced to 2 and 8. Our results are illustrated by a tree-level analysis of available axial-vector coupling constants and strong decay widths of the baryon decuplet states.

Next-to-next-to-leading order matching of beauty-charmed meson Bc and Bc* decay constants

We present the next-to-next-to-leading order (NNLO) quantum chromodynamics (QCD) corrections to the decay constants for both the pseudoscalar ${B}_{c}$ meson and the vector ${B}_{c}^{*}$ meson in the nonrelativistic QCD (NRQCD) effective theory. The explicit NNLO calculations prove that the ${B}_{c}$ decay constant from the pseudoscalar current is identical with the ${B}_{c}$ decay constant from the axial-vector current. The NNLO result for the vector decay constant of ${B}_{c}^{*}$ meson is novel. Combining this result with the latest extraction of the NRQCD long-distance matrix elements of ${B}_{c}$ and ${B}_{c}^{*}$ meson, we calculate and show the theoretical predictions for the branching ratios of the leptonic decays ${B}_{c}^{+}/{B}_{c}^{*+}\ensuremath{\rightarrow}{l}^{+}{\ensuremath{\nu}}_{l}$ with ${l}^{+}=({e}^{+},{\ensuremath{\mu}}^{+},{\ensuremath{\tau}}^{+})$. In addition, the novel anomalous dimension for the flavor-changing heavy quark vector current in the NRQCD effective theory is helpful to investigate the threshold behaviors of the two different heavy quarks.

Singlet and nonsinglet three-loop massive form factors

We consider Quantum Chromodynamics with external vector, axial-vector, scalar and pseudo-scalar currents and compute three-loop corrections to the corresponding vertex function taking into account massive quarks. We consider all non-singlet contributions as well as those singlet contributions where the external current couples to a massive quark loop. We apply a semi-numerical method which is based on expansions around singular and regular kinematical points. They are matched at intermediate values of the squared partonic center-of-mass energy $s$ which allows to cover the whole kinematic range for negative and positive values of $s$. Our method permits a systematic increase of the precision by varying the expansion depth and the choice of the intermediate matching points. In our current set-up we have at least seven significant digits for the finite contribution of all form factors. We present our results as a combination of series expansions and interpolation functions which allows for a straightforward use in practical applications.

Three-loop nonsinglet matching coefficients for heavy quark currents

We compute the matching coefficients between QCD and non-relativistic QCD for external vector, axial-vector, scalar and pseudo-scalar currents up to three-loop order. We concentrate on the non-singlet contributions and present precise numerical results with an accuracy of about ten digits. For the vector current the results from arXiv:1401.3004 are confirmed, increasing the accuracy by several orders of magnitude.

Nucleon axial-vector and pseudoscalar form factors and PCAC relations

We use a continuum quark+diquark approach to the nucleon bound-state problem in relativistic quantum field theory to deliver parameter-free predictions for the nucleon axial and induced pseudoscalar form factors, $G_A$ and $G_P$, and unify them with the pseudoscalar form factor $G_5$ or, equivalently, the pion-nucleon form factor $G_{\pi NN}$. We explain how partial conservation of the axial-vector current and the associated Goldberger-Treiman relation are satisfied once all necessary couplings of the external current to the building blocks of the nucleon are constructed consistently; in particular, we fully resolve the seagull couplings to the diquark-quark vertices associated with the axial-vector and pseudoscalar currents. Among the results we describe, the following are worth highlighting. A dipole form factor defined by an axial charge $g_A=G_A(0)=1.25(3)$ and a mass-scale $M_A = 1.23(3) m_N$, where $m_N$ is the nucleon mass, can accurately describe the pointwise behaviour of $G_A$. Concerning $G_P$, we obtain the pseudoscalar charge $g_p^\ast = 8.80(23)$, and find that the pion pole dominance approach delivers a reliable estimate of the directly computed result. Our computed value of the pion-nucleon coupling constant, $g_{\pi NN}/m_N =14.02(33)/{\rm GeV}$ is consistent with recent precision determinations.

Charged lepton flavor violation associated with heavy quark production in deep inelastic lepton-nucleon scattering via scalar exchange

We study charged lepton flavor violation (CLFV) associated with heavy quark pair production in lepton-nucleon deep-inelastic scattering ℓiN → ℓjq overline{q} X. Here ℓi and ℓj denote the initial and final leptons; N and X are respectively the initial nucleon and arbitrary final hadronic system. We employ a model Lagrangian in which a scalar and pseudoscalar mediator generates the CLFV. We derive heavy quark structure functions for scalar and pseudoscalar currents and compute momentum distributions of the final lepton for the process. Our focus is on the heavy quark mass effects in the final lepton momentum distribution. We clarify the necessity of inclusion of the heavy quark mass to obtain reliable theory predictions for the CLFV signal searches in the deep-inelastic scattering.

Subleading contributions to the nuclear scalar isoscalar current

We extend our recent analyses of the nuclear vector, axial-vector and pseudoscalar currents and derive the leading one-loop corrections to the two-nucleon scalar current operator in the framework of chiral effective field theory using the method of unitary transformation. We also show that the scalar current operators at zero momentum transfer are directly related to the quark mass dependence of the nuclear forces.

Two-Point Fermionic Correlators in External Constant Uniform Magnetic Field

The results of calculation of two-point correlation functions of fermionic currents in a constant uniform magnetic field are presented. The off-diagonal correlation functions including the tensor current (namely, the scalar-tensor and pseudoscalar-tensor) are calculated in addition to the correlators of scalar, pseudoscalar, vector, and axial-vector fermionic currents. The tensor fermionic current is a part of the Pauli term in the Lagrangian, which is responsible for the electromagnetic interaction of the fermion through an anomalous magnetic moment. In particular, if we take this interaction into account, we modify the frequency of axion-photon oscillations. In the future, it is planned to investigate this feature in details.

Nucleon Matrix Elements of the Antisymmetric Quark Tensor.

If physics beyond the standard model enters well above the electroweak scale, its low-energy effects are described by standard model effective field theory. Already, at dimension 6, many operators involve the antisymmetric quark tensor q[over ¯]σ^{μν}q, whose matrix elements are difficult to constrain from experiment, Ward identities, or low-energy theorems, in contrast to the corresponding vector and axial-vector or even scalar and pseudoscalar currents. However, with normalizations determined from lattice QCD, analyticity and unitarity often allow one to predict the momentum dependence in a large kinematic range. Starting from recent results in the meson sector, we extend this method to the nucleon case and, in combination with pole dominance, provide a comprehensive assessment of the current status of the nucleon form factors of the quark tensor.

Two-Point One-Loop Fermionic Amplitudes in Constant Homogeneous Magnetic Field

Two-point one-loop fermionic amplitudes modifiled by a constant homogeneous magnetic fileld are studied. In addition to the amplitudes resulted after an insertion of scalar, pseudoscalar, vector and axial-vector fermionic currents, we calculate similar amplitudes with the tensor and (pseudo)scalar vertices. The crossed-field limit of these amplitudes is presented. The tensor current is a fermionic part of the Pauli Lagrangian relevant for the electromagnetic interaction of fermions through the anomalous magnetic moment and its contribution to the photon polarization operator is briefly discussed.

Heavy quark form factors at three loops in the planar limit

We compute the color-planar and complete light quark non-singlet contributions to the heavy quark form factors in the case of the axialvector, scalar and pseudoscalar currents at three loops in perturbative QCD. We evaluate the master integrals applying a new method based on differential equations for general bases, which is applicable for all first order factorizing systems. The analytic results are expressed in terms of harmonic polylogarithms and real-valued cyclotomic harmonic polylogarithms.

Heavy quark form factors at two loops

We compute the two-loop QCD corrections to the heavy quark form factors in case of the vector, axial-vector, scalar and pseudo-scalar currents up to second order in the dimensional parameter $\epsilon = (4-D)/2$. These terms are required in the renormalization of the higher order corrections to these form factors.

Three-loop massive form factors: complete light-fermion and large-Nc corrections for vector, axial-vector, scalar and pseudo-scalar currents

We compute the three-loop QCD corrections to the massive quark form factors with external vector, axial-vector, scalar and pseudo-scalar currents. All corrections with closed loops of massless fermions are included. The non-fermionic part is computed in the large-Nc limit, where only planar Feynman diagrams contribute.

Two-Point Correlators of Fermionic Currents in External Magnetic Field

We study the two-point correlation functions under an influence of the constant homogeneous magnetic field. In addition to the correlators of scalar, pseudoscalar, vector and axial-vector fermionic currents, we calculate the non-diagonal one including the tensor and pseudoscalar currents. The tensor current is a fermionic part of the Pauli Lagrangian relevant for the electromagnetic interaction of fermions through the anomalous magnetic moment. Its contribution to the photon polarization operator is briefly discussed.

Heavy-quark Form Factors at Two Loops in Perturbative QCD

We present the results for heavy quark form factors at two-loop order in perturbative QCD for different currents, namely vector, axial-vector, scalar and pseudo-scalar currents, up to second order in the dimensional regularization parameter. We outline the necessary computational details, ultraviolet renormalization and corresponding universal infrared structure.

Renormalization of local quark-bilinear operators forNf=3flavors of stout link nonperturbative clover fermions

The renormalization factors of local quark-bilinear operators are computed non-perturbatively for $N_f=3$ flavors of SLiNC fermions, with emphasis on the various procedures for the chiral and continuum extrapolations. The simulations are performed at a lattice spacing $a=0.074$ fm, and for five values of the pion mass in the range of 290-465 MeV, allowing a safe and stable chiral extrapolation. Emphasis is given in the subtraction of the well-known pion pole which affects the renormalization factor of the pseudoscalar current. We also compute the inverse propagator and the Green's functions of the local bilinears to one loop in perturbation theory. We investigate lattice artifacts by computing them perturbatively to second order as well as to all orders in the lattice spacing. The renormalization conditions are defined in the RI$'$-MOM scheme, for both the perturbative and non-perturbative results. The renormalization factors, obtained at different values of the renormalization scale, are translated to the ${\bar{\rm MS}}$ scheme and are evolved perturbatively to 2 GeV. Any residual dependence on the initial renormalization scale is eliminated by an extrapolation to the continuum limit. We also study the various sources of systematic errors. Particular care is taken in correcting the non-perturbative estimates by subtracting lattice artifacts computed to one loop perturbation theory using the same action. We test two different methods, by subtracting either the ${\cal O}(g^2\,a^2)$ contributions, or the complete (all orders in $a$) one-loop lattice artifacts.

The ρ and A mesons in strong abelian magnetic field in [formula omitted] lattice gauge theory

We calculated correlators of vector, axial and pseudoscalar currents in external strong abelian magnetic field according to SU(2) gluodynamics. The masses of neutral ρ and A mesons with various spin projections to the axis parallel to the external magnetic field B have been calculated. We found that the masses of neutral mesons with zero spin s=0 decrease in increasing magnetic field, while the masses of the ρ and A mesons with spin s=±1 increase in the mentioned field. Also we performed extrapolation and renormalization of masses on the lattice.

Neutral ρ meson in a strong magnetic field in the SU(2) lattice gauge theory

The correlation functions of vector and pseudoscalar currents have been calculated in the external strong magnetic field in SU(2) lattice gluodynamics. The masses of the neutral ρ meson with different spin projections s = 0, ±1 to the axis parallel to the external magnetic field B have been calculated. The ρ meson mass with zero spin s = 0 decreases with the growth of the magnetic field and the ρ meson masses with s = ±1 increase with the magnetic field.

Determination of theΔ(1232)axial and pseudoscalar form factors from lattice QCD

We present a lattice QCD calculation of the $\ensuremath{\Delta}(1232)$ matrix elements of the axial-vector and pseudoscalar currents. The decomposition of these matrix elements into the appropriate Lorentz invariant form factors is carried out, and the techniques to calculate the form factors are developed and tested using quenched configurations. Results are obtained for $2+1$ domain wall fermions and within a hybrid scheme with domain wall valence and staggered sea quarks. Two Goldberger-Treiman--type relations connecting the axial to the pseudoscalar effective couplings are derived. These and further relations based on the pion-pole dominance hypothesis are examined using the lattice QCD results, finding support for their validity. Using lattice QCD results on the axial charges of the nucleon and the $\ensuremath{\Delta}$, as well as the nucleon-to-$\ensuremath{\Delta}$ transition coupling constant, we perform a combined chiral fit to all three quantities and study their pion mass dependence as the chiral limit is approached.