Up and Down Quark Masses and Corrections to Dashen's Theorem from Lattice QCD and Quenched QED

Kaon electromagnetic form factors in dispersion theory

The electromagnetic form factors of charged and neutral kaons are strongly constrained by their low-energy singularities, in the isovector part from two-pion intermediate states and in the isoscalar contribution in terms of ω and ϕ residues. The former can be predicted using the respective π π → K ¯ K partial-wave amplitude and the pion electromagnetic form factor, while the latter parameters need to be determined from electromagnetic reactions involving kaons. We present a global analysis of time- and spacelike data that implements all of these constraints. The results enable manifold applications: kaon charge radii, elastic contributions to the kaon electromagnetic self energies and corrections to Dashen's theorem, kaon boxes in hadronic light-by-light (HLbL) scattering, and the ϕ region in hadronic vacuum polarization (HVP). Our main results are: ⟨ r 2 ⟩ c = 0.359 ( 3 ) fm 2 , ⟨ r 2 ⟩ n = - 0.060 ( 4 ) fm 2 for the charged and neutral radii, ϵ = 0.63 ( 40 ) for the elastic contribution to the violation of Dashen's theorem, a μ K -box = - 0.48 ( 1 ) × 10 - 11 for the charged kaon box in HLbL scattering, and a μ HVP [ K + K - , ≤ 1.05 GeV ] = 184.5 ( 2.0 ) × 10 - 11 , a μ HVP [ K S K L , ≤ 1.05 GeV ] = 118.3 ( 1.5 ) × 10 - 11 for the HVP integrals around the ϕ resonance. The global fit to K ¯ K gives M ¯ ϕ = 1019.479 ( 5 ) MeV , Γ ¯ ϕ = 4.207 ( 8 ) MeV for the ϕ resonance parameters including vacuum-polarization effects.

ε ' / ε in the Standard Model at the Dawn of the 2020s

We reanalyse the ratio ε ' / ε in the Standard Model (SM) using most recent hadronic matrix elements from the RBC-UKQCD collaboration in combination with most important NNLO QCD corrections to electroweak penguin contributions and the isospin-breaking corrections. We illustrate the importance of the latter by using their latest estimate from chiral perturbation theory (ChPT) based on the octet approximation for lowest-lying mesons and a very recent estimate in the nonet scheme that takes into account the contribution of η 0 . We find ( ε ' / ε ) SM ( 8 ) = ( 17.4 ± 6.1 ) × 10 - 4 and ( ε ' / ε ) SM ( 9 ) = ( 13.9 ± 5.2 ) × 10 - 4 , respectively. Despite a very good agreement with the measured value ( ε ' / ε ) exp = ( 16.6 ± 2.3 ) × 10 - 4 , the large error in ( ε ' / ε ) SM still leaves room for significant new physics (BSM) contributions to this ratio. We update the 2018 master formula for ( ε ' / ε ) BSM valid in any extension beyond the SM without additional light degrees of freedom. We provide new values of the penguin parameters B 6 ( 1 / 2 ) ( μ ) and B 8 ( 3 / 2 ) ( μ ) at the μ -scales used by the RBC-UKQCD collaboration and at lower scales O ( 1 GeV ) used by ChPT and Dual QCD (DQCD). We present semi-analytic formulae for ( ε ' / ε ) SM in terms of these parameters and Ω ^ eff that summarizes isospin-breaking corrections to this ratio. We stress the importance of lattice calculations of the O ( α em ) contributions to the hadronic matrix elements necessary for the removal of renormalization scheme dependence at O ( α em ) in the present analyses of ε ' / ε .

Leading isospin-breaking corrections to meson masses on the lattice

We present a study of the isospin-breaking (IB) corrections to pseudoscalar (PS) meson masses using the gauge configurations produced by the ETM Collaboration with Nf = 2+1+1 dynamical quarks at three lattice spacings varying from 0.089 to 0.062 fm. Our method is based on a combined expansion of the path integral in powers of the small parameters [see formula in PDF] and αem, where [see formula in PDF] is the renormalized quark mass and αem the renormalized fine structure constant. We obtain results for the pion, kaon and Dmeson mass splitting; for the Dashen’s theorem violation parameters ϵγ(MM, 2 GeV), ϵπ0 ϵK0(MS, 2 GeV) for the light quark masses [see formula in PDF] for the flavour symmetry breaking parameters R(MS, 2 GeV) and Q(MS, 2 GeV) and for the strong IB effects on the kaon decay constants.

Topological susceptibility with a single light quark flavour

One of the historical suggestions to tackle the strong CP problem is to take the up quark mass to zero while keeping md finite. The θ angle is then supposed to become irrelevant, i.e. the topological susceptibility vanishes. However, the definition of the quark mass is scheme-dependent and identifying the mu = 0 point is not trivial, in particular with Wilson-like fermions. More specifically, up to our knowledge there is no theoretical argument guaranteeing that the topological susceptibility exactly vanishes when the PCAC mass does.

We will present our recent progresses on the empirical check of this property using Nf = 1 + 2 flavours of clover fermions, where the lightest fermion is tuned very close to [see formula in PDF] and the mass of the other two is kept of the order of magnitude of the physical ms. This choice is indeed expected to amplify any unknown non-perturbative effect caused by mu ≠ md. The simulation is repeated for several βs and those results, although preliminary, give a hint about what happens in the continuum limit.

Isospin Breaking Corrections to the HVP with Domain Wall Fermions

We present results for the QED and strong isospin breaking corrections to the hadronic vacuum polarization using Nf = 2 + 1 Domain Wall fermions. QED is included in an electro-quenched setup using two different methods, a stochastic and a perturbative approach. Results and statistical errors from both methods are directly compared with each other.

η→3π: Study of the Dalitz Plot and Extraction of the Quark Mass Ratio Q

The η→3π amplitude is sensitive to the quark mass difference m_{u}-m_{d} and offers a unique way to determine the quark mass ratio Q^{2}≡(m_{s}^{2}-m_{ud}^{2})/(m_{d}^{2}-m_{u}^{2}) from experiment. We calculate the amplitude dispersively and fit the KLOE Collaboration data on the charged mode, varying the subtraction constants in the range allowed by chiral perturbation theory. The parameter-free predictions obtained for the neutral Dalitz plot and the neutral-to-charged branching ratio are in excellent agreement with experiment. Our representation of the transition amplitude implies Q=22.0±0.7.