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Publications and source records attributed to Lehner, Christoph.
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A study of two-pion scattering for the isospin channels, 𝐼 = 0 and 𝐼 = 2, using lattice QCD is presented. Möbius domain-wall fermions, on top of the Iwasaki-DSDR gauge action for gluons with periodic boundary conditions, are used for the lattice computations, which are carried out on two ensembles of gauge field configurations generated by the RBC and UKQCD Collaborations with physical masses, inverse lattice spacings of 1.023 and 1.378 GeV, and spatial extents of 𝐿 = 4.63 and 4.58 fm, respectively. The all-to-all propagator method is employed to compute a matrix of correlation functions of two-pion operators. The generalized eigenvalue problem (GEVP) is solved for a matrix of correlation functions to extract phase shifts with multiple states—two pions with a nonzero relative momentum, as well as two pions at rest. Our results for phase shifts for both the 𝐼 = 0 and 𝐼 = 2 channels are consistent with the Roy equation and chiral perturbation theory, though at this preliminary stage our errors for 𝐼 = 0 are large. An important outcome of this work is that we are successful in extracting two-pion excited states, which are useful for studying 𝐾 → 𝜋𝜋 decay, on physical-mass ensembles using the GEVP.
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This document is one of a series of white papers from the USQCD Collaboration. Here, we discuss opportunities for Lattice QCD in quark and lepton flavor physics. New data generated at Belle II, LHCb, BES III, NA62, KOTO, and Fermilab E989, combined with precise calculations of the relevant hadronic physics, may reveal what lies beyond the Standard Model. We outline a path toward improvements of the precision of existing Lattice QCD calculations and discuss groundbreaking new methods that allow Lattice QCD to access new observables.
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We compute the renormalisation factors (Z-matrices) of the ΔF = 2 four-quark operators needed for Beyond the Standard Model (BSM) kaon mixing. We work with nf = 2+1 flavours of Domain-Wall fermions whose chiral-flavour properties are essential to maintain a continuum-like mixing pattern. We introduce new RI-SMOM renormalisation schemes, which we argue are better behaved compared to the commonly-used corresponding RI-MOM one. We find that, once converted to MS¯, the Z-factors computed through these RI-SMOM schemes are in good agreement but differ significantly from the ones computed through the RI-MOM scheme. The RI-SMOM Z-factors presented here have been used to compute the BSM neutral kaon mixing matrix elements in the companion paper. In conclusion, we argue that the renormalisation procedure is responsible for the discrepancies observed by different collaborations, we will investigate and elucidate the origin of these differences throughout this work.
In our previous work, the connected and leading disconnected hadronic light-by-light contributions to the muon anomalous magnetic moment (g — 2) have been computed using lattice QCD ensembles corresponding to physical pion mass generated by the RBC/UKQCD Collaboration. However, the calculation is expected to suffer from a significant finite-volume error that scales like 1/L 2 where L is the spatial size of the lattice. In this paper, we demonstrate that this problem is cured by treating the muon and photons in infinite-volume, continuum QED, resulting in a weighting function that is precomputed and saved with affordable cost and sufficient accuracy. We present numerical results for the case when the quark loop is replaced by a muon loop, finding the expected exponential approach to the infinite volume limit and consistency with the known analytic result. Here, we have implemented an improved weighting function which reduces both discretization and finite-volume effects arising from the hadronic part of the amplitude.
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We report a lattice QCD calculation of the hadronic light-by-light contribution to the muon anomalous magnetic moment at a physical pion mass. The calculation includes the connected diagrams and the leading, quark-line-disconnected diagrams. We incorporate algorithmic improvements developed in our previous work. The calculation was performed on the 48 3 × 96 ensemble generated with a physical pion mass and a 5.5 fm spatial extent by the RBC and UKQCD Collaborations using the chiral, domain wall fermion formulation. We find a HLbL μ = 5.35(1.35) × 10 –10 , where the error is statistical only. The finite-volume and finite lattice-spacing errors could be quite large and are the subject of ongoing research. Finally, the omitted disconnected graphs, while expected to give a correction of order 10%, also need to be computed.
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The quark-connected part of the hadronic light-by-light scattering contribution to the muon’s anomalous magnetic moment is computed using lattice QCD with chiral fermions. Here we report several significant algorithmic improvements and demonstrate their effectiveness through specific calculations which show a reduction in statistical errors by more than an order of magnitude. The most realistic of these calculations is performed with a near-physical 171 MeV pion mass on a (4.6 fm) 3 spatial volume using the 32 3 ×64 Iwasaki+DSDR gauge ensemble of the RBC/UKQCD Collaboration.
Measurements of the Λ b → p ℓ - ν ¯ ℓ and Λ b → Λ c ℓ - ν ¯ ℓ decay rates can be used to specify the magnitudes of the Cabibbo-Kobayashi-Maskawa matrix elements Vub and Vcb, provided that the relevant hadronic form factors are known. In this work we present a precise calculation of these form factors using lattice QCD with 2 + 1 flavors of dynamical domain-wall fermions. The b and c quarks are implemented with relativistic heavy-quark actions, allowing us to work directly at the physical heavy-quark masses. The lattice computation is performed for six different pion masses and two different lattice spacings, using gauge-field configurations generated by the RBC and UKQCD Collaborations. The b → u and b → c currents are renormalized with a mostly nonperturbative method. We extrapolate the form factor results to the physical pion mass and the continuum limit, parametrizing the q 2 dependence using z expansions. The form factors are presented in such a way as to enable the correlated propagation of both statistical and systematic uncertainties into derived quantities such as differential decay rates and asymmetries. Using these form factors, we present predictions for the Λ b → p ℓ - ν ¯ ℓ and Λ b → Λ c ℓ - ν ¯ ℓ differential and integrated decay rates. Combined with experimental data, our results enable determinations of |V ub |, |V cb |, and |V ub /V cb | with theory uncertainties of 4.4%, 2.2%, and 4.9%, respectively.