Lattice Form Factors Research Articles

New physics effects on Λb→Λc*τν¯τ decays

We benefit from a recent lattice determination of the full set of vector, axial and tensor form factors for the ${\mathrm{\ensuremath{\Lambda}}}_{b}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Lambda}}}_{c}^{*}(2595)\ensuremath{\tau}{\overline{\ensuremath{\nu}}}_{\ensuremath{\tau}}$ and ${\mathrm{\ensuremath{\Lambda}}}_{c}^{*}(2625)\ensuremath{\tau}{\overline{\ensuremath{\nu}}}_{\ensuremath{\tau}}$ semileptonic decays to study the possible role of these two reactions in lepton flavor universality violation studies. Using an effective theory approach, we analyze different observables that can be accessed through the visible kinematics of the charged particles produced in the tau decay, for which we consider the ${\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\nu}}_{\ensuremath{\tau}},{\ensuremath{\rho}}^{\ensuremath{-}}{\ensuremath{\nu}}_{\ensuremath{\tau}}$ and ${\ensuremath{\mu}}^{\ensuremath{-}}{\overline{\ensuremath{\nu}}}_{\ensuremath{\mu}}{\ensuremath{\nu}}_{\ensuremath{\tau}}$ channels. We compare the results obtained in the Standard Model and other schemes containing new physics (NP) interactions, with either left-handed or right-handed neutrino operators. We find a discriminating power between models similar to the one of the ${\mathrm{\ensuremath{\Lambda}}}_{b}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Lambda}}}_{c}$ decay, although somewhat hindered in this case by the larger errors of the ${\mathrm{\ensuremath{\Lambda}}}_{b}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Lambda}}}_{c}^{*}$ lattice form factors. Notwithstanding this, the analysis of these reactions is already able to discriminate between some of the NP scenarios and its potentiality will certainly improve when more precise form factors are available.

Optical demonstration of crystallography and reciprocal space using laser diffraction from Au microdisc arrays.

Crystallography is an invaluable tool in materials science, solid state physics and protein science. Understanding crystallography requires grasping the powerful but abstract concept of reciprocal space. Here a simple but insightful experiment using a laser pointer and Au microdisc arrays to explore and illustrate Bragg diffraction and reciprocal space is demonstrated. The Au microdisc arrays were manufactured using standard semiconductor fabrication techniques. The flexibility of the array design allows the demonstration of basic concepts such as lattice and atomic form factor, but also more advanced ones such as quasicrystal and shape function.

Microscopic Eilenberger theory of Fulde-Ferrell-Larkin-Ovchinnikov states in the presence of vortices

We theoretically investigate the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state by using the microscopic quasi-classical Eilenberger equation. The Pauli paramagnetic effects and the orbital depairing effects due to vortices are treated in an equal footing for three dimensional spherical Fermi surface model and $s$-wave pairing. The field evolution of the LO state is studied in detail, such as the $H$-$T$ phase diagram, spatial structures of the order parameter, the paramagnetic moment, and the internal filed. Field-dependences of various thermodynamic quantities: the paramagnetic moment, entropy, and the zero-energy density of states are calculated. Those quantities are shown to start quickly growing upon entering the LO state. We also evaluate the wave length of the LO modulation, the flux line lattice form factors for small angle neutron scattering, and the NMR spectra to facilitate the identification of the LO state. Two cases of strong and intermediate Pauli paramagnetic effect are studied comparatively. The possibility of the LO phase in Sr$_2$RuO$_4$, CeCoIn$_5$, CeCu$_2$Si$_2$, and the organic superconductors is critically examined and crucial experiments to identify it are proposed.

Opposite-parity contaminations in lattice nucleon form factors

The recently-introduced Parity Expanded Variational Analysis (PEVA) technique allows for the isolation of baryon eigenstates at finite momentum free from opposite-parity contamination. In this paper, we establish the formalism for computing form factors of spin-1/2 states using PEVA. Selecting the vector current, we compare the electromagnetic form factors of the ground state nucleon extracted via this technique to a conventional parity-projection approach. Our results show a statistically significant discrepancy between the PEVA and conventional analyses. This indicates that existing calculations of matrix elements of ground state baryons at finite momentum can be affected by systematic errors of ~20% at physical quark masses. The formalism introduced here provides an effective approach to removing these systematic errors.

Transverse Components of Flux Line Lattice Form Factors in Uniaxial Superconductors

Magnetic field orientation dependence of transverse and longitudinal flux line lattice form factors are theoretically studied in uniaxial superconductors with extremely large anisotropy ratio 60 for some field magnitudes. The form factors are estimated by two methods, the Eilenberger theory and the London theory comparatively. We also compare them to the form factors observed by the small angle neutron scattering experiment on Sr2RuO4. We discuss the cutoff function of extended London theory, and the contributions from the suppression of the pair potential as a function of the field orientation.

|Vub|fromB→πℓνdecays and (2+1)-flavor lattice QCD

We present a lattice-QCD calculation of the $B\to\pi\ell\nu$ semileptonic form factors and a new determination of the CKM matrix element $|V_{ub}|$. We use the MILC asqtad 2+1-flavor lattice configurations at four lattice spacings and light-quark masses down to 1/20 of the physical strange-quark mass. We extrapolate the lattice form factors to the continuum using staggered chiral perturbation theory in the hard-pion and SU(2) limits. We employ a model-independent $z$ parameterization to extrapolate our lattice form factors from large-recoil momentum to the full kinematic range. We introduce a new functional method to propagate information from the chiral-continuum extrapolation to the $z$ expansion. We present our results together with a complete systematic error budget, including a covariance matrix to enable the combination of our form factors with other lattice-QCD and experimental results. To obtain $|V_{ub}|$, we simultaneously fit the experimental data for the $B\to\pi\ell\nu$ differential decay rate obtained by the BaBar and Belle collaborations together with our lattice form-factor results. We find $|V_{ub}|=(3.72\pm 0.16)\times 10^{-3}$ where the error is from the combined fit to lattice plus experiments and includes all sources of uncertainty. Our form-factor results bring the QCD error on $|V_{ub}|$ to the same level as the experimental error. We also provide results for the $B\to\pi\ell\nu$ vector and scalar form factors obtained from the combined lattice and experiment fit, which are more precisely-determined than from our lattice-QCD calculation alone. These results can be used in other phenomenological applications and to test other approaches to QCD.

Pauli paramagnetic effects on mixed-state properties in a strongly anisotropic superconductor: Application toSr2RuO4

We study theoretically the mixed state properties of a strong uniaxially-anisotropic type II superconductor with the Pauli paramagnetic effect, focusing on their behaviors when the magnetic field orientation is tilted from the conduction layer ab plane. On the basis of Eilenberger theory, we quantitatively estimate significant contributions of the Pauli paramagnetic effects on a variety of physical observables, including transverse and longitudinal components of the flux line lattice form factors, magnetization curves, Sommerfeld coefficient, field distributions and magnetic torques. We apply these studies to Sr_2_RuO_4_ and quantitatively explain several seemingly curious behaviors, including the H_c2_ suppression for the ab plane direction, the larger anisotropy ratio and intensity found by the spin-flip small angle neutron scattering, and the first order transition observed recently in magneto-caloric, specific heat and magnetization measurements in a coherent and consistent manner. Those lead us to conclude that Sr_2_RuO_4_ is either a spin-singlet or a spin-triplet pairing with the d-vector components in the ab plane.

Eilenberger and London theories for transverse components of flux line lattice form factors in uniaxial superconductors

We theoretically study the magnetic field orientation dependence of longitudinal and transverse flux line lattice form factors in uniaxial superconductors with anisotropy ratio corresponding to ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$. We discuss influences of the anisotropy ratio of coherence length and differences between the $s$-wave and the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave pairings. The calculations are performed by two methods, the Eilenberger theory and the London theory comparatively, and we study the cutoff function of the extended London theory, which will be helpful in the analysis of the small angle neutron scattering in the vortex states.

Transverse magnetic field and chiral-nonchiral transition in vortex states for nearlyB∥abin chiralp-wave superconductors

On the basis of Eilenberger theory, we study the vortex state when a magnetic field is applied nearly parallel to the $ab$ plane in a chiral $p$-wave superconductor with a large anisotropy ratio of $ab$ and $c$, as in ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$. We quantitatively estimate the field dependence of the pair potential, magnetization, and flux-line lattice form factor, and study the transition from the chiral ${p}_{\ensuremath{-}}$ state at low fields to the nonchiral ${p}_{y}$ state at high fields. Even for exactly parallel fields to the $ab$ plane, transverse fields exist in the chiral state. The chiral-nonchiral transition disappears when the magnetic field orientation is tilted within ${1}^{\ensuremath{\circ}}$ from the $ab$ plane. This may be a reason why the experimental detection of this transition is difficult.

Field Evolution of the Fulde–Ferrell–Larkin–Ovchinnikov State in a Superconductor with Strong Pauli Effects

The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase in the vortex lattice state is quantitatively studied using the selfconsistent Eilenberger theory in three-dimensional (3D) space. We estimate free energy to determine the FFLO phase diagram in the H-T plane and stable FFLO wave number in the isotropic system with the 3D Fermi sphere and s-wave pairing. To facilitate the experimental identification of the FFLO state, we investigate the field evolution of NMR spectra and flux line lattice form factors obtained in neutron scattering in the FFLO vortex states. Possible applications of our results to experimental data on CeCoIn5 are mentioned.

Fluctuations and order of antiferromagnetism induced by paramagnetic pair breaking in superconducting vortex lattices

Effects of the strong Pauli-paramagnetic pair breaking (PPB) on the vortex lattice in $d$-wave superconductors are theoretically studied by putting emphasis on consequences of the PPB-induced antiferromagnetic (AFM) ordering in the spatial modulation in the vortex lattice. It is shown that the PPB-induced AFM fluctuation in the superconducting state leads to an enhancement of the vortex lattice form factor which is a measure of spatial variations of the internal magnetic field and that the enhancement becomes more remarkable as an AFM instability is approached. It is also demonstrated that the PPB-induced AFM ordering is assisted by the vortex-lattice modulation, and thus, that the resulting AFM order is spatially modulated, while it is not localized in the vortex cores but coexistent with the nonvanishing superconducting order parameter. These results are discussed in connection with two phenomena observed in CeCoIn${}_{5}$, the anomalous field dependence of the vortex lattice form factor and the AFM order appearing inside the high-field and low-temperature superconducting phase.

Vortex lattices in type-II superconductors studied by small-angle neutron scattering

Here we review recent small-angle scattering studies of the vortex lattice in a range of type-II superconductors carried out by our group. Emphasis is placed on providing examples of the kind of information which can be obtained by such measurements, focusing in particular on studies of the vortex lattice structure and form factor in LuNi2B2C, TmNi2B2C, CeCoIn5 and Ba(Fe0.93Co0.07)2As2.

Flux distribution in vortex lattice states in d-wave and paramagnetic superconductors

Roles of field-induced antiferromagnetic (AFM) fluctuation in the vortex lattice in d-wave superconductors with strong Pauli paramagnetic depairing (PD) are studied with a focus on the heavy-fermion superconductor CeCoIn5. Based on the Ginzburg-Landau approach, we calculate the field dependence of the vortex lattice form factor (VLFF) which reflects the magnetic flux distribution in the vortex lattice. It is found that, in a magnetic field perpendicular to the two-dimensional plane (H || c), the strong AFM fluctuation near Hc2(0) enhances the VLFF in high fields and that this enhancement is remarkable when the AFM moment is perpendicular to H (m ⊥ H). The obtained result in m ⊥ H well explains an anomalous field dependence of the VLFF obtained in neutron scattering experiments on CeCoIn5, which suggests the necessity of taking account of the AFM fluctuation and the possibility that the configuration m ⊥ H is realized in H || c.

Paramagnetic effects in vortex lattice field distribution in strongly type-II superconductors

We present an analysis of the magnetic field distribution in the Abrikosov lattice of high-$\ensuremath{\kappa}$ superconductors with singlet pairing in the case where the critical field is mainly determined by the Pauli limit and the superfluid currents partly come from the paramagnetic interaction of electron spins with the local magnetic field. The derivation is performed in the frame of the generalized Clem variational method which is valid not too close to the critical field and furthermore with the Abrikosov-type theory in the vicinity of it. The found vortex lattice form factor increases with increasing field and then falls down at approach of the upper critical field where the superconducting state is suppressed.

Antiferromagnetic ordering induced by paramagnetic depairing in unconventional superconductors

Antiferromagnetic (AFM) (or spin-density wave) quantum critical fluctuation enhanced just below H_c2(0) have been often observed in d-wave superconductors with a strong Pauli paramagnetic depairing (PD) including CeCoIn_5. It is shown here that such a tendency of field-induced AFM ordering is a consequence of strong PD and should appear particularly in superconductors with a gap node along the AFM modulation. Two phenomena seen in CeCoIn_5, the anomalous vortex lattice form factor and the AFM order in the Fulde-Ferrell-Larkin-Ovchinnikov state, are explained based on this peculiar PD effect.

Nucleon and γN → Δ lattice form factors in a constituent quark model

A covariant quark model, based both on the spectator formalism and on vector meson dominance, and previously calibrated by the physical data, is here extended to the unphysical region of the lattice data by means of one single extra adjustable parameter—the constituent quark mass in the chiral limit. We calculated the nucleon (N) and the γN → Δ form factors in the universe of values for that parameter described by quenched lattice QCD. A qualitative description of the nucleon and γN → Δ form factors lattice data is achieved for light pions.

Flux line lattice form factor and paramagnetic effects in type II superconductors

Based on the quasiclassical Eilenberger theory, we investigate the vortex structure in type II superconductors with strong Pauli-paramagnetic contributions due to the Zeeman effect. We quantitatively study how the paramagnetic effect suppresses the superconductivity, and evaluate the flux line lattice (FLL) form factor from the calculated internal field distribution both in the s-wave and d-wave pairings. When the paramagnetic effects are strong, the intensity of the FLL form factor increases toward Hc2 as a function of an applied field, instead of exponential decay. This anomalous field dependence is due to the induced paramagnetic moments around the vortex core. We discuss the anomalous field-dependence of the FLL form factor observed by the small angle neutron scattering in CeCoIn5.

External momentum, volume effects, and the nucleon magnetic moment

We analyze the determination of volume effects for correlation functions that depend on an external momentum. As a specific example, we consider finite volume nucleon current correlators, and focus on the nucleon magnetic moment. Because the multipole decomposition relies on $SO(3)$ rotational invariance, the structure of such finite volume corrections is unrelated to infinite volume multipole form factors. One can deduce volume corrections to the magnetic moment only when a zero-mode photon coupling vanishes, as occurs at next-to-leading order in heavy baryon chiral perturbation theory. To deduce such finite volume corrections, however, one must assume continuous momentum transfer. In practice, volume corrections with momentum transfer dependence are required to address the extraction of the magnetic moment, or other observables that arise in momentum-dependent correlation functions. Additionally, we shed some light on a puzzle concerning differences in lattice form factor data at equal values of momentum transfer squared.

Superconducting Vortices in CeCoIn 5 : Toward the Pauli-Limiting Field

Many superconducting materials allow the penetration of magnetic fields in a mixed state in which the superfluid is threaded by a regular lattice of Abrikosov vortices, each carrying one quantum of magnetic flux. The phenomenological Ginzburg-Landau theory, based on the concept of characteristic length scales, has generally provided a good description of the Abrikosov vortex lattice state. We conducted neutron-scattering measurements of the vortex lattice form factor in the heavy-fermion superconductor cerium-cobalt-indium (CeCoIn5) and found that this form factor increases with increasing field-opposite to the expectations within the Abrikosov-Ginzburg-Landau paradigm. We propose that the anomalous field dependence of the form factor arises from Pauli paramagnetic effects around the vortex cores and from the proximity of the superconducting state to a quantum critical point.

Vortex states in superconductors with strong Pauli-paramagnetic effect

Using the quasiclassical theory, we analyze the vortex structure of strong-paramagnetic superconductors.There, induced paramagnetic moments are accumulated exclusively around the vortex core. We quantitatively evaluate the significant paramagnetic effect in the H-dependence of various quantities, such as low temperature specific heat, Knight shift, magnetization and the flux line lattice (FLL) form factor. The anomalous H-dependence of the FLL form factor observed by the small angle neutron scattering in CeCoIn_5 is attributable to the large paramagnetic contribution.