QCD inequalities for hadron interactions

We derive generalisations of the Weingarten--Witten QCD mass inequalities for particular multi-hadron systems. For systems of any number of identical pseudo-scalar mesons of maximal isospin, these inequalities prove that interactions between the constituent mesons must be repulsive and that no bound states can form in these channels. Similar constraints in less symmetric systems are also extracted. These results are compatible with experimental results (where known) and recent lattice QCD calculations, and also lead to a more stringent bound on the nucleon mass than previously derived, $m_N \ge 3/2 m_\pi$.Comment: 5 pages, 2 figure

Lattice QCD study of mixed systems of pions and kaons

The different ground state energies of N-pion and M-kaon systems for N+M <=12 are studied in lattice QCD. These energies are then used to extract the various two- and three- body interactions that occur in these systems. Particular attention is paid to additional thermal states present in the spectrum because of the finite temporal extent. These calculations are performed using one ensemble of 2+1 flavor anisotropic lattices with a spatial lattice spacing a_s ~ 0.125 fm, an anisotropy factor {\xi}=a_s/a_t=3.5, and a spatial volume L^3 ~ (2.5 fm)^3. The quark masses used correspond to pion and kaon masses of m_{\pi} ~ 383 MeV and m_K ~ 537 MeV, respectively. The isospin and strangeness chemical potentials of these systems are found to be in the region where chiral perturbation theory and hadronic models predict a phase transition between a pion condensed phase and a kaon condensed phase

Λb→Λℓ+ℓ−\Lambda_b \to \Lambda \ell^+ \ell^- form factors, differential branching fraction, and angular observables from lattice QCD with relativistic bb quarks

Using $(2+1)$-flavor lattice QCD, we compute the 10 form factors describing the $\Lambda_b \to \Lambda$ matrix elements of the $b \to s$ vector, axial vector, and tensor currents. The calculation is based on gauge field ensembles generated by the RBC and UKQCD Collaborations with a domain-wall action for the $u$, $d$, and $s$ quarks and the Iwasaki gauge action. The $b$ quark is implemented using an anisotropic clover action, tuned nonperturbatively to the physical point, and the currents are renormalized with a mostly nonperturbative method. We perform simultaneous chiral, continuum, and kinematic extrapolations of the form factors through modified $z$ expansions. Using our form factor results, we obtain precise predictions for the $\Lambda_b \to \Lambda(\to p^+ \pi^-) \mu^+ \mu^-$ differential branching fraction and angular observables in the Standard Model.Comment: 33 pages, 9 figures, form factor parameters included as ancillary file

Composite Vector Particles in External Electromagnetic Fields

Lattice quantum chromodynamics (QCD) studies of electromagnetic properties of hadrons and light nuclei, such as magnetic moments and polarizabilities, have proven successful with the use of background field methods. With an implementation of nonuniform background electromagnetic fields, properties such as charge radii and higher electromagnetic multipole moments (for states of higher spin) can be additionally obtained. This can be achieved by matching lattice QCD calculations to a corresponding low-energy effective theory that describes the static and quasi-static response of hadrons and nuclei to weak external fields. With particular interest in the case of vector mesons and spin-1 nuclei such as the deuteron, we present an effective field theory of spin-1 particles coupled to external electromagnetic fields. To constrain the charge radius and the electric quadrupole moment of the composite spin-1 field, the single-particle Green's functions in a linearly varying electric field in space are obtained within the effective theory, providing explicit expressions that can be used to match directly onto lattice QCD correlation functions. The viability of an extraction of the charge radius and the electric quadrupole moment of the deuteron from the upcoming lattice QCD calculations of this nucleus is discussed.Comment: 38 page

Baryon properties in meson mediums from lattice QCD

We present results for the ground-state mass shifts of octet baryons due to the presence of a medium of pions or kaons from a lattice QCD calculation performed at a single value of the quark mass, corresponding to a pion mass of $m_\pi$ ~ 390 MeV, and a spatial volume V ~ (4fm)^3. We use a canonical approach in which correlators are formed using a single baryon propagator and a fixed number of meson propagators, up to n=9. From the ground-state energies we calculate two- and three-body interaction parameters. We also extract combinations of low-energy constants by comparing our results to tree level chiral perturbation theory at non-zero isospin/kaon chemical potential.Comment: 7 pages, 3 figures, Proceedings of the 31st International Symposium on Lattice Field Theory (Lattice 2013), July 29 - August 3, 2013, Mainz, German

Signal/noise enhancement strategies for stochastically estimated correlation functions

We develop strategies for enhancing the signal/noise ratio for stochastically sampled correlation functions. The techniques are general and offer a wide range of applicability. We demonstrate the potential of the approach with a generic two-state system, and then explore the practical applicability of the method for single hadron correlators in lattice quantum chromodynamics. In the latter case, we determine the ground state energies of the pion, proton, and delta baryon, as well as the ground and first excited state energy of the rho meson using matrices of correlators computed on an exemplary ensemble of anisotropic gauge configurations. In the majority of cases, we find a modest reduction in the statistical uncertainties on extracted energies compared to conventional variational techniques. However, in the case of the delta baryon, we achieve a factor of three reduction in statistical uncertainties. The variety of outcomes achieved for single hadron correlators illustrates an inherent dependence of the method on the properties of the system under consideration and the operator basis from which the correlators are constructed.Comment: 40 pages, 21 figures; revisions made to the abstract and Section VI C, one additional figure and five tables added; published versio