Two-parameter Fits Research Articles

Indirect constraints on top quark operators from a global SMEFT analysis

We perform a model-independent analysis of top-philic New Physics scenarios, under the assumption that only effective operators involving top quarks are generated at tree level. Within the SMEFT framework, we derive indirect constraints on Wilson Coefficients by combining a large set of low-energy observables: B-meson and kaon decays, meson mixing observables, precision electroweak and Higgs measurements, anomalous magnetic moments, lepton flavour violating processes, lepton flavour universality tests, and measurements of the Cabibbo angle. We consider the renormalization group evolution of the operators and use the one-loop matching of the SMEFT onto the LEFT. The global analysis is then used to perform one-parameter, two-parameter, and global fits, as well as applications to explicit ultraviolet models. We find that the inclusion of measurements from different physics sectors reveals a strong interplay and complementarity among the observables. The resulting constraints are also compared to direct bounds provided by top quark productions at the LHC.

Tomography-based observational measurements of the halo mass function via the submillimeter magnification bias

Aims. The main goal of this paper is to derive observational constraints on the halo mass fuction (HMF) by performing a tomographic analysis of the magnification bias signal on a sample of background submillimeter galaxies. The results can then be compared with those from a non-tomographic study. Methods. We measure the cross-correlation function between a sample of foreground GAMA galaxies with spectroscopic redshifts in the range 0.1 < z < 0.8 (and divided up into four bins) and a sample of background submillimeter galaxies from H-ATLAS with photometric redshifts in the range 1.2 < z < 4.0. We model the weak lensing signal within the halo model formalism and carry out a Markov chain Monte Carlo algorithm to obtain the posterior distribution of all HMF parameters, which we assume to follow the Sheth and Tormen (ST) three-parameter and two-parameter fits. Results. While the observational constraints on the HMF from the non-tomographic analysis are not stringent, there is a remarkable improvement in terms of uncertainty reduction when tomography is adopted. Moreover, with respect to the traditional ST triple of values from numerical simulations, the results from the three-parameter fit predict a higher number density of halos at masses below ∼1012 M⊙ h−1 at 95% credibility. The two-parameter fit yields even more restricting results, with a larger number density of halos below ∼1013 M⊙ h−1 and a lower one above ∼1014 M⊙ h−1, this time at more than 3σ credibility. Our results are therefore in disagreement with the standard N-body values for the ST fit at 2σ and 3σ, respectively.

Combined SMEFT interpretation of Higgs, diboson, and top quark data from the LHC

We present a global interpretation of Higgs, diboson, and top quark production and decay measurements from the LHC in the framework of the Standard Model Effective Field Theory (SMEFT) at dimension six. We constrain simultaneously 36 independent directions in its parameter space, and compare the outcome of the global analysis with that from individual and two-parameter fits. Our results are obtained by means of state-of-the-art theoretical calculations for the SM and the EFT cross-sections, and account for both linear and quadratic corrections in the 1/Λ2 expansion. We demonstrate how the inclusion of NLO QCD and mathcal{O} (Λ−4) effects is instrumental to accurately map the posterior distributions associated to the fitted Wilson coefficients. We assess the interplay and complementarity between the top quark, Higgs, and diboson measurements, deploy a variety of statistical estimators to quantify the impact of each dataset in the parameter space, and carry out fits in BSM-inspired scenarios such as the top-philic model. Our results represent a stepping stone in the ongoing program of model-independent searches at the LHC from precision measurements, and pave the way towards yet more global SMEFT interpretations extended to other high-pT processes as well as to low-energy observables.

Characterizing Solar Energetic Particle Event Profiles with Two-Parameter Fits

The intensity–time profiles of solar energetic ( $E>10~\mbox{MeV}$ ) particle (SEP) events observed at 1 AU reflect a number of physical processes involving solar injection and interplanetary transport. In addition to energy spectral and composition studies, SEP intensity–time profiles are the basis for diagnostic timescales needed for describing and modeling the acceleration and transport of SEPs. We briefly review commonly used timescales and point out the absence of holistic descriptions of the SEP profiles. We define the requirements for such a description and select a modified Weibull function from among three candidates as one which provides a reasonable two-parameter fit for most observed SEP events. In addition to the peak intensity, $I_{\mathrm{p}}$ , each event energy range can be described by shape and duration parameters $\alpha$ and $\beta$ . Fits are applied to the profiles of 14 recent large SEP events observed in three integral energy ranges by the Geostationary Operational Environmental Satellite (GOES) spacecraft. The fits are generally robust, with ${<}\,1\%$ uncertainties in the parameters, but they can be very dependent on the choices of fit end times. We show the fit parameters as functions of energy range and solar source longitude. The fit parameters can be used not only as targets for modeling efforts, but also in space weather applications.

COSMOGENIC NEUTRINOS CHALLENGE THE COSMIC-RAY PROTON DIP MODEL

ABSTRACT The origin and composition of ultra-high-energy cosmic rays (UHECRs) remain a mystery. The proton dip model describes their spectral shape in the energy range above 109 GeV by pair production and photohadronic interactions with the cosmic microwave background. The photohadronic interactions also produce cosmogenic neutrinos peaking around 109 GeV. We test whether this model is still viable in light of recent UHECR spectrum measurements from the Telescope Array experiment and upper limits on the cosmogenic neutrino flux from IceCube. While two-parameter fits have been already presented, we perform a full scan of the three main physical model parameters: source redshift evolution, injected proton maximal energy, and spectral index. We find qualitatively different conclusions compared to earlier two-parameter fits in the literature: a mild preference for a maximal energy cutoff at the sources instead of the Greisen–Zatsepin–Kuzmin cutoff, hard injection spectra, and strong source evolution. The predicted cosmogenic neutrino flux exceeds the IceCube limit for any parameter combination. As a result, the proton dip model is challenged at more than 95% C.L. This is strong evidence against this model independent of mass composition measurements.

Inequality of Chances as a Symmetry Phase Transition

We propose a model for Lorenz curves. It provides two-parameter fits to data on incomes, electric consumption, life expectation and rate of survival after cancer. Graphs result from the condition of maximum entropy and from the symmetry of statistical distributions. Differences in populations composing a binary system (poor and rich, young and old, etc.) bring about chance inequality. Symmetrical distributions insure equality of chances, generate Gini coefficients Gi £ ⅓, and imply that nobody gets more than twice the per capita benefit. Graphs generated by different symmetric distributions, but having the same Gini coefficient, intersect an even number of times. The change toward asymmetric distributions follows the pattern set by second-order phase transitions in physics, in particular universality: Lorenz plots reduce to a single universal curve after normalisation and scaling. The order parameter is the difference between cumulated benefit fractions for equal and unequal chances. The model also introduces new parameters: a cohesion range describing the extent of apparent equality in an unequal society, a poor-rich asymmetry parameter, and a new Gini-like indicator that measures unequal-chance inequality and admits a theoretical expression in closed form.

Universality in the energy spectrum of medium-sized quantum dots

In a two-dimensional parabolic quantum dot charged with $N$ electrons, Thomas-Fermi theory states that the ground-state energy satisfies the following nontrivial relation: ${E}_{\text{gs}}/(\ensuremath{\hbar}\ensuremath{\omega})\ensuremath{\approx}{N}^{3/2}{f}_{\text{gs}}({N}^{1/4}\ensuremath{\beta})$, where the coupling constant, $\ensuremath{\beta}$, is the ratio between Coulomb and oscillator $(\ensuremath{\hbar}\ensuremath{\omega})$ characteristic energies and ${f}_{\text{gs}}$ is a universal function. We perform extensive configuration-interaction calculations in order to verify that the exact energies of relatively large quantum dots approximately satisfy the above relation. In addition, we show that the number of energy levels for intraband and interband (excitonic and biexcitonic) excitations of the dot follows a simple exponential dependence on the excitation energy whose exponent, $1/\ensuremath{\Theta}$, satisfies also an approximate scaling relation \'a la Thomas-Fermi, $\ensuremath{\Theta}/(\ensuremath{\hbar}\ensuremath{\omega})\ensuremath{\approx}{N}^{\ensuremath{-}\ensuremath{\gamma}}g({N}^{1/4}\ensuremath{\beta})$. We provide an analytic expression for ${f}_{\text{gs}}$ based on two-point Pad\'e approximants and two-parameter fits for the $g$ functions.

Renormalization of the singular attractive1∕r4potential

We study the radial Schr\"odinger equation for a particle of mass $m$ in the field of a singular attractive ${g}^{2}∕{r}^{4}$ potential with particular emphasis on the bound-states problem. Using the regularization method of Beane et al. [Phys. Rev. A 64, 042103 (2001)], we solve analytically the corresponding ``renormalization-group flow'' equation. We find in agreement with previous studies that its solution exhibits a limit cycle behavior and has infinitely many branches. We show that a continuous choice for the solution corresponds to a given fixed number of bound states and to low-energy phase shifts that vary continuously with energy. We study in detail the connection between this regularization method and a conventional method modifying the short-range part of the potential with an infinitely repulsive hard core. We show that both methods yield bound-states results in close agreement even though the regularization method of Beane et al. does not include explicitly any new scale in the problem. We further illustrate the use of the regularization method in the computation of electron bound states in the field of neutral polarizable molecules without dipole moment. We find the binding energy of $s$-wave polarization bound electrons in the field of ${\mathrm{C}}_{60}$ molecules to be 17 meV for a scattering length corresponding to a hard-core radius of the size of the molecule radius $(\ensuremath{\sim}3.37\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}})$. This result can be further compared with recent two-parameter fits using the Lennard-Jones potential yielding binding energies ranging from 3 to 25 meV.

Application of the local-bulk partitioning and competitive binding models to interpret preferential interactions of glycine betaine and urea with protein surface.

Two thermodynamic models have been developed to interpret the preferential accumulation or exclusion of solutes in the vicinity of biopolymer surface and the effects of these solutes on protein processes. The local-bulk partitioning model treats solute (and water) as partitioning between the region at/or near the protein surface (the local domain) and the bulk solution. The solvent exchange model analyzes a 1:1 competition between water and solute molecules for independent surface sites. Here we apply each of these models to interpret thermodynamic data for the interactions of urea and the osmoprotectant glycine betaine (N,N,N-trimethylglycine; GB) with the surface exposed in unfolding the marginally stable lacI HTH DNA binding domain. The partition coefficient K(P) quantifying accumulation of urea at this protein surface (K(P) approximately equal 1.1) is only weakly dependent on urea concentration up to 6 M urea. However, K(P) quantifying exclusion of GB from the vicinity of this protein surface increases from 0.83 (extrapolated to 0 M GB) to 1.0 (indicating that local and bulk GB concentrations are equal) at 4 M GB (activity > 40 M). We interpret the significant concentration dependence of K(P) for GB, predicted to be general for excluded, nonideal solutes such as GB, as a modest (8%) attenuation of the GB concentration dependence of solute nonideality in the local domain relative to that in the bulk solution. Above 4 M, K(P) for the interaction of GB with the surface exposed in protein unfolding is predicted to exceed unity, which explains the maximum in thermal stability observed for RNase and lysozyme at 4 M GB (Santoro, M. M., Liu, Y. F., Khan, S. M. A., Hou, L. X., and Bolen, D. W. (1992) Biochemistry 31, 5278-5283). Both thermodynamic models provide good two-parameter fits to GB and urea data for lacI HTH unfolding over a wide concentration range. The solute partitioning model allows for a full spectrum of attenuation effects in the local domain, encompasses the cases treated by the competitive binding model, and provides a somewhat better two-parameter fit of effects of high GB concentration on lacI HTH stability. Parameters of this fit should be applicable to isothermal and thermal unfolding data for all proteins with similar compositions of surface exposed in unfolding.

Screening effect in the 6Li(p, 3He) 4He and 7Li(p, α) 4He fusion reactions for solid targets

The electronic screening effect on the penetrability of the Coulomb barrier is evaluated for 6Li(p, 3He) 4He and 7Li(p, α) 4He fusion reactions through the so-called enhancement factor ƒ. The ƒ s experimental values of ƒ for the two reactions involving solid targets are extracted from published cross sections. For the two inverse reactions involving gaseous targets ƒ g values are also extracted. A model of interacting p and Li in a solid medium which predicts theoretical ƒ s values is presented. Numerical evaluations of ƒ s are made for the astrophysical energy range under numerous assumptions. Analytical two-parameter fits are derived. Values of the electron screening potential energy U 0 are evaluated and compared to those deduced from experimental data.

Effective charge parameters for 7Li, 11B, 12C, 14N, and 16O projectiles traversing Kapton targets

Some recent measurements of the stopping powers of Kapton foils for 0.2–2.1 MeV/u 7Li, 11B, 12C, 14N, and 16O projectiles have been subjected to analysis in terms of modified Bethe-Bloch theory so as to extract values of projectile effective charge parameters. Although one-parameter and two-parameter fits were attempted, only the former provided meaningful results. The one-parameter fits showed excellent internal consistency, and reasonable consistency with results obtained in a recent similar analysis of nickel and Havar stopping powers for the same projectiles.

Mean excitation energies of Al 2O 3 and SiO 2 extracted from alpha particle stopping power measurements

Previously reported measurements of the stopping powers of Al 2O 3 and SiO 2 for 0.2–2 MeV and 5.48 MeV alpha particles have been analyzed for extraction of values of parameters from modified Bethe-Bloch theory. Two-parameter fits were conducted for values of mean excitation energy and one of two available Barkas-effect parameters. Resulting mean excitation energies lay below additivity-based predictions, whereas Barkas-effect parameters essentially coincided with values prescribed by the formalism.

Design of an antenna system for the collection of singlet excitation energy. Exciton diffusion among concentrated 9,10-diphenylanthracene centers in polystyrene

Fluorescence decay kinetics of 9,10-diphenylanthracene (DPA) were examined at (DPA) = 16 to 181 mM in spin-cast polystyrene films of approx. 2000-A thickness. Exponential decays with lifetimes ranging from 6.94 ns at low concentration to 6.34 ns at 180 mM were observed in unquenched systems. In the presence of tetrabromo-o-benzoquinone (TBBQ), added at 12.0 mM as a quenching probe, the decay kinetics were modified. At very low concentrations of DPA, nearly pure Foerster kinetics were observed. Extrapolation of behavior to (DPA) = 0 gave a critical transfer radius for Foerster transfer from DPA to TBBQ of 28 A. Calculations from spectral data gave 29 A. As the concentration of DPA increased, quenching became progressively more efficient and the time dependence of decay showed evidence of excitation diffusion by hopping from DPA site to DPA site. Diffusion coefficients were evaluated by two-parameter fits of decays to curves predicted from the Yokota-Tanimoto theory based on a Pade approximant. Values of the diffusion coefficient increased with (DPA) to 7.9 x 10/sup -6/ cm/sup 2//s at (DPA) = 180 mM. The corresponding diffusion length is 55 A. The meaning of the results to the construction of an antenna system for collection of photonic energymore » into photochemical reaction centers is discussed.« less

Observations of the hard X-ray spectrum of the impulsive phase of solar flares

view Abstract Citations (35) References (24) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Observations of the hard X-ray spectrum of the impulsive phase of solar flares. Elcan, M. J. Abstract The impulsive solar hard X-ray spectrum provides a direct diagnostic on the impulsive energy release of the flare. The data from the hard X-ray (14-342 keV) spectrometer on OSO 7 have been examined for events covering a wide energy range to determine the photon spectrum more precisely. This resulted in a sample of 38 events. The data have been fitted with either single- or double-power laws, and with an exponential spectrum, as from thermal bremsstrahlung. The chi-squared statistic between two-parameter fits strongly favors the exponential fit, particularly at peak intensity when the widest energy range is sampled. This result supports a single-temperature thermal source of the impulsive solar hard X-rays with temperatures in the range 4.7-31 keV and emission measures in the range from 8.4 x 10 to the 43rd to 6.0 x 10 to the 46th per cu cm. The temperature reaches a single maximum and then rapidly decays, but the emission measure usually increases throughout, even after temperature maximum, for data with 10-s resolution. Publication: The Astrophysical Journal Pub Date: December 1978 DOI: 10.1086/182840 Bibcode: 1978ApJ...226L..99E Keywords: Solar Flares; Solar Temperature; Solar X-Rays; X Ray Spectra; Bremsstrahlung; Oso-7; Plasma Diagnostics; Thermal Energy; Solar Physics; Solar Flares:X-Ray Spectra full text sources ADS |

Titrimetric applications of multiparametric curve-fitting : Part 1. Potentiometric titrations of weak bases with strong acids at extreme dilutions

A multiparametric curve-fitting procedure is described for locating the equivalence point of a potentiometric titration and is applied to data obtained in titrations of acetate ion with hydrochloric acid over a wide range of concentrations (down to 6.5 · 10 -5 M acetate). It does not depend on the existence of a point of inflection on the titration curve, and therefore yields useful results in titrations of this very weak base at concentrations well below that at which the point of maximal slope disappears. Three parameters are involved: the concentration of the base being titrated, the concentration dissociation constant K a of its conjugate acid in the medium employed, and the apparent activity coefficient y H + of hydrogen ion in that medium, and all three of these must be evaluated when a new supporting electrolyte is employed. In 3.0 M potassium chloride at 24°, the apparent activity coefficient of hydrogen ion is 1.746 0, and this value permits data obtained in titrations of other or unknown bases in this medium to be interpreted by two-parameter fits. The value of K a for acetic acid in this medium is 1.313 4 · 10 -5 M; by means of these two numerical values routine titrations of acetate in this medium can be interpreted by one-parameter fits. It is possible to locate the equivalence point with an accuracy and a precision that cannot be approached by other techniques and even to obtain useful and reliable results under conditions so unfavorable that other techniques fail completely.

Analysis of response data for several organic scintillators

Data on the scintillation response (light output) of anthracene, stilbene, NE-213, NE-102 and Pilot-B to electrons and protons and of Ne-230 to electrons and deuterons reported recently by Smith et al. 1) have been fitted by the method of least squares to the L(E) = S ∫ 0 E dε[1+kB( dE dx +C dE dx ) 2] −1 where E is the initial particle energy, d E/d x is the specific energy loss, and S, kB and C are the adjustable parameters. Required values of d E/d x were computed from available data 16,17). Scintillation efficiencies S were deduced from the electron data for which d E/d x≈0. One-parameter ( kB variable, C = 0) and two-parameter ( kB and C variable) fits for the heavy-particle data were obtained and compared with other results reported in the literature.