arXiv subjects

K. Williams

Publications and source records attributed to K. Williams.

At least 19 recordsLinked to original sources

arXiv2024

Bounds on $a_\mu^{\mathrm{HVP,LO}}$ using H\"older's inequalities and finite-energy QCD sum rules

This study establishes bounds on the leading-order (LO) hadronic vacuum polarization (HVP) contribution to the anomalous magnetic moment of the muon ($a_\mu^{\mathrm{HVP,LO}}$, $a_\mu = (g-2)_\mu/2$) by using H\"older's inequality and related inequalities in Finite-Energy QCD sum rules. Considering contributions from light quarks ($u,d,s$) up to five-loop order in perturbation theory within the chiral limit, leading-order light-quark mass corrections, next-to-leading order for dimension-four QCD condensates, and leading-order for dimension-six QCD condensates, the study finds QCD lower and upper bounds as $\left(657.0\pm 34.8\right)\times 10^{-10}\leq a_\mu^{\mathrm{HVP,LO}} \leq \left(788.4\pm 41.8\right)\times10^{-10}\,$.

hep-ph↗

arXiv2024

QCD bounds on leading-order hadronic vacuum polarization contributions to the muon anomalous magnetic moment

QCD bounds on the leading-order (LO) hadronic vacuum polarization (HVP) contribution to the anomalous magnetic moment of the muon ($a_\mu^{\mathrm{HVP,LO}}$, $a_\mu=\left(g-2\right)_\mu/2$) are determined by imposing H\"older inequalities and related inequality constraints on systems of Finite-Energy QCD sum-rules. This novel methodology is complementary to lattice QCD and data-driven approaches to determining $a_\mu^{\mathrm{HVP,LO}}$. For the light-quark ($u,d,s$) contributions up to five-loop order in perturbation theory in the chiral limit, LO in light-quark mass corrections, next-to-leading order in dimension-four QCD condensates, and to LO in dimension-six QCD condensates, we find that $\left(657.0\pm 34.8\right)\times 10^{-10}\leq a_\mu^{\mathrm{HVP,LO}} \leq \left(788.4\pm 41.8\right)\times10^{-10}\,$, bridging the range between lattice QCD and data-driven values.

hep-ph↗

arXiv2017

Design Of The LBNF Beamline

The Long Baseline Neutrino Facility (LBNF) will utilize a beamline located at Fermilab to provide and aim a neutrino beam of sufficient intensity and appropriate energy range toward the Deep Underground Neutrino Experiment (DUNE) detectors, placed deep underground at the SURF Facility in Lead, South Dakota. The primary proton beam (60-120 GeV) will be extracted from the MI-10 section of Fermilab's Main Injector. Neutrinos will be produced when the protons interact with a solid target to produce mesons which will be subsequently focused by magnetic horns into a 194m long decay pipe where they decay into muons and neutrinos. The parameters of the facility were determined taking into account the physics goals, spatial and radiological constraints, and the experience gained by operating the NuMI facility at Fermilab. The Beamline facility is designed for initial operation at a proton-beam power of 1.2 MW, with the capability to support an upgrade to 2.4 MW. LBNF/DUNE obtained CD-1 approval in November 2015. We discuss here the design status and the associated challenges as well as the R&D and plans for improvements before baselining the facility.

physics.acc-ph↗

arXiv2016

Design of the LBNF Beamline Target Station

The Long Baseline Neutrino Facility (LBNF) project will build a beamline located at Fermilab to create and aim an intense neutrino beam of appropriate energy range toward the DUNE detectors at the SURF facility in Lead, South Dakota. Neutrino production starts in the Target Station, which consists of a solid target, magnetic focusing horns, and the associated sub-systems and shielding infrastructure. Protons hit the target producing mesons which are then focused by the horns into a helium-filled decay pipe where they decay into muons and neutrinos. The target and horns are encased in actively cooled steel and concrete shielding in a chamber called the target chase. The reference design chase is filled with air, but nitrogen and helium are being evaluated as alternatives. A replaceable beam window separates the decay pipe from the target chase. The facility is designed for initial operation at 1.2 MW, with the ability to upgrade to 2.4 MW, and is taking advantage of the experience gained by operating Fermilab's NuMI facility. We discuss here the design status, associated challenges, and ongoing R&D and physics-driven component optimization of the Target Station.

physics.acc-ph↗

arXiv2012

Maximal unbalanced families

A family of subsets of the set {1,2,...,n} is said to be unbalanced if the convex hull of its characteristic vectors misses the diagonal in the n-cube.The purpose of this article is to develop the combinatorics of maximal unbalanced families. Specifically, we will prove lower and upper bounds on the number of maximal unbalanced families of subsets of an n-element set -- both bounds are of the form 2^{C n^2} for some C > 0. These families correspond to the chambers of a hyperplane arrangement, the restricted all-subset arrangement, that has arisen in various forms in physics, economics and psychometrics. In particular, our bounds answer a question posed in thermal field theory concerning the order of the number of chambers of this arrangement.

math.CO↗

arXiv2009

New HiggsBounds from LEP and the Tevatron

We review the program HiggsBounds that tests theoretical predictions of models with arbitrary Higgs sectors against the exclusion bounds obtained from the Higgs searches at LEP and the Tevatron. We explicitly list the bounds that have been added after the first release of HiggsBounds.

hep-ph↗

arXiv2009

A new detailed examination of white dwarfs in NGC3532 and NGC2287

We present the results of a photometric and spectroscopic study of the white dwarf candidate members of the intermediate age open clusters NGC3532 and NGC2287. Of the nine objects investigated, it is determined that six are probable members of the clusters, four in NGC3532 and two in NGC2287. For these six white dwarfs we use our estimates of their cooling times together with the cluster ages to constrain the lifetimes and masses of their progenitor stars. We examine the location of these objects in initial mass-final mass space and find that they now provide no evidence for substantial scatter in initial mass-final mass relation as suggested by previous investigations. Instead, we demonstrate that, when combined with current data from other solar metalicity open clusters and the Sirius binary system, they hint at an IFMR that is steeper in the initial mass range 3M$_{\odot}$$\simless$M$_{\rm init}$$\simless$4M$_{\odot}$ than at progenitor masses immediately lower and higher than this. This form is generally consistent with the predictions of stellar evolutionary models and can aid population synthesis models in reproducing the relatively sharp drop observed at the high mass end of the main peak in the mass distribution of white dwarfs.

astro-ph.SR↗

arXiv2008

SDSS J142625.71+575218.3: The First Pulsating White Dwarf with a Large Detectable Magnetic Field

We report the discovery of a strong magnetic field in the unique pulsating carbon-atmosphere white dwarf SDSS J142625.71+575218.3. From spectra gathered at the MMT and Keck telescopes, we infer a surface field of B_s ~1.2 MG, based on obvious Zeeman components seen in several carbon lines. We also detect the presence of a Zeeman-splitted He I 4471 line, which is an indicator of the presence of a non-negligible amount of helium in the atmosphere of this Hot DQ star. This is important for understanding its pulsations, as nonadabatic theory reveals that some helium must be present in the envelope mixture for pulsation modes to be excited in the range of effective temperature where the target star is found. Out of nearly 200 pulsating white dwarfs known today, this is the first example of a star with a large detectable magnetic field. We suggest that SDSS J142625.71+575218.3 is the white dwarf equivalent of a roAp star.

astro-ph↗

arXiv2006

Higher-Order Corrected Higgs Bosons in FeynHiggs 2.5

Large higher-order corrections enter the Higgs boson sector of the MSSM via Higgs-boson self-energies. Their effects have to be taken into account for the correct treatment of loop-corrected Higgs-boson mass eigenstates as external (on-shell) or internal particles in Feynman diagrams. We review how the loop corrections, including momentum dependence and imaginary contributions, are correctly taken into account for external (on-shell) Higgs boson and how effective couplings can be derived. The proceedures are implemented in the code FeynHiggs 2.5.

hep-ph↗

arXiv2004

The White Dwarf Luminosity Function: The Shape of Things to Come

We describe a new survey for cool white dwarfs that supplements Sloan Digital Sky Survey photometry with USNO proper motions and follow-up spectroscopy. To date we have discovered and spectroscopically confirmed 80 new moderate temperature and cool white dwarfs. We have also found a handful of high-velocity white dwarfs and we expect a sizable fraction of these to be thick disk or possibly halo objects. Our survey is designed to find ~10,000 new white dwarfs, although only ~60 will be among the faintest white dwarfs (M(V) >= 16), where most of the age-sensitivity resides. We discuss an extension of our survey to V ~ 22.

astro-ph↗

arXiv2001

Wilson loop evaluations in the stochastic vacuum model

The stochastic vacuum model description of a heavy meson is discussed in the context of a gauge invariant approach where Wilson loop expectation values appear naturally in the O($v^2$) spin-orbit Hamiltonian. These expectation values have been derived elsewhere, however by a procedure whose legitimacy is now placed in question. Here they are derived by standard functional methods with a result that is identical to the previous one. In addition, a full spin-independent Hamiltonian reduction to O($v^2$) is carried out.

hep-ph↗

arXiv1999

Revisiting the Eichten - Feinberg - Gromes Q \bar{Q} Spin-Orbit Interaction

Invariant and covariant forms of the quark-antiquark interaction derived by the method of Eichten and Feinberg are considered. Relations between the various terms imposed by Lorentz transformation constraints, here called Gromes relations, are found to exist in neither case. Details of the Gromes relation proper are reconsidered and inconsistencies found that lead to a violation of covariance.

hep-ph↗

arXiv1998

The minimum area, the flux tube, and Thomas precession

Quark confinement in Buchmüller's picture of a rotating flux tube is reconsidered in the context of a minimum area evaluation of the Wilson loop. The question is asked whether resulting spin independent dynamics are consistent with Thomas precessional spin dependence leading from electric confinement. The answer appears to be in the negative; self-consistency of the picture found in the literature is examined and explained in simple classical terms, with illustrations.

hep-ph↗

arXiv1997

Nonperturbative QCD Vacuum Effects in Nonlocal Quark Dynamics

A straightforward calculation reveals the essentially nonlocal character of the leading heavy $Q\bar{Q}$ interaction arising from nonperturbative gluon field correlations in the model of a fluctuating QCD vacuum. In light of this quarkonium spin splitting ratio predictions which have supported the scalar confinement ansatz are reconsidered as a specific example of possible consequences for spectroscopy.

hep-ph↗

arXiv1996

Salpeter amplitudes in a Wilson-loop context

The bound state problem for a gauge invariant quark-antiquark system is considered in the instantaneous rest frame. Focus here is on the long range non-perturbative interaction. A two-time Green's function is constructed for Salpeter amplitudes. The corresponding Schrödinger equation is found to be in the Salpeter form with a Wilson-loop term as the instantaneous kernel.

hep-ph↗

arXiv1995

Fermion Confinement by a Relativistic Flux Tube

We formulate the description of the dynamic confinement of a single fermion by a flux tube. The range of applicability of this model extends from the relativistic corrections of a slowly moving quark to the ultra-relativistic motion in a heavy-light meson. The reduced Salpeter equation, also known as the no-pair equation, provides the framework for our discussion. The Regge structure is that of a Nambu string with one end fixed. Numerical solutions are found giving very good fits to heavy-light meson masses. An Isgur-Wise function with a zero recoil slope of $ξ'(1)\simeq -1.26 $ is obtained.

hep-ph↗

arXiv1995

On the validity of the reduced Salpeter equation

We adapt a general method to solve both the full and reduced Salpeter equations and systematically explore the conditions under which these two equations give equivalent results in meson dynamics. The effects of constituent mass, angular momentum state, type of interaction, and the nature of confinement are all considered in an effort to clearly delineate the range of validity of the reduced Salpeter approximations. We find that for $J\not{\hspace*{-1.0mm}=}0$ the solutions are strikingly similar for all constituent masses. For zero angular momentum states the full and reduced Salpeter equations give different results for small quark mass especially with a large additive constant coordinate space potential. We also show that $\frac{1}{m}$ corrections to heavy-light energy levels can be accurately computed with the reduced equation.

hep-ph↗

arXiv1995

Flux Tubes in Effective Field Theory

Quark-antiquark bound states are examined in the long-range strong-coupling limit with the minimal area law of lattice gauge theory assumed as input. Matrix element relations are established which in the effective theory obtain dynamical equations equivalent to a formulation of the flux-tube model.

hep-ph↗