Lattice QCD Calculation of the Pion Mass Splitting

Abstract

We use the infinite volume reconstruction method to calculate the charged/neutral pion mass difference. The hadronic tensor is calculated on lattice QCD and then combined with an analytic photon propagator, and the mass splitting is calculated with exponentially-suppressed finite volume errors. The calculation is performed using six gauge ensembles generated with $2+1$-flavor domain wall fermions, and five ensembles are at the physical pion mass. Both Feynman and Coulomb gauge are adopted in the calculation and result in a good agreement when the lattice spacing approaches zero. After performing the continuum extrapolation and examining the residual finite-volume effects, we obtain the pion mass splitting $\Delta m_{\pi }=4.534(42)(43)\mathrm{MeV}$, which agrees well with experimental measurements.

arXiv comment10 pages, 5 figures

References in corpus (29)

• Ab initio calculation of the neutron-proton mass difference
• Domain wall QCD with physical quark masses
• A new class of variance reduction techniques using lattice symmetries
• Leading isospin breaking effects on the lattice
• Covariant approximation averaging
• Electromagnetic mass splittings of the low lying hadrons and quark masses from 2+1 flavor lattice QCD+QED
• First lattice calculation of the QED corrections to leptonic decay rates
• QED Corrections to Hadronic Processes in Lattice QCD
• Light-meson leptonic decay rates in lattice QCD+QED
• Domain Wall QCD with Near-Physical Pions
• Finite-Volume QED Corrections to Decay Amplitudes in Lattice QCD
• Determination of light quark masses from the electromagnetic splitting of pseudoscalar meson masses computed with two flavors of domain wall fermions
• Twenty-first Century Lattice Gauge Theory: Results from the QCD Lagrangian
• Leading isospin-breaking corrections to pion, kaon and charmed-meson masses with Twisted-Mass fermions
• First-principles calculation of electroweak box diagrams from lattice QCD
• Isospin splittings of meson and baryon masses from three-flavor lattice QCD + QED
• Isospin breaking corrections to meson masses and the hadronic vacuum polarization: a comparative study
• QED self energies from lattice QCD without power-law finite-volume errors
• Lattice computation of the electromagnetic contributions to kaon and pion masses
• Full QED+QCD Low-Energy Constants through Reweighting
• Long-distance Contributions to Neutrinoless Double Beta Decay ${\pi }^{-}\to {\pi }^{+}ee$
• Lattice QCD calculation of the electroweak box diagrams for the kaon semileptonic decays
• Lattice QCD calculation of the pion charge radius using a model-independent method
• Field sparsening for the construction of the correlation functions in lattice QCD
• Isospin splittings in the decuplet baryon spectrum from dynamical QCD+QED
• QED effects in the pseudoscalar meson sector
• Multi-Grid Lanczos
• Finite-volume effects in long-distance processes with massless leptonic propagators
• State mixing and masses of the ${\pi }^0$, $\eta$ and ${\eta }^{\prime }$ mesons from $n_f=1+1+1$ lattice QCD+QED

Cited by in corpus (6)

• Width effects of broad new resonances in loop observables and application to $(g-2{)}_{\mu }$
• First-principle calculation of ${\eta }_c\to 2\gamma$ decay width from lattice QCD
• Lattice QCD calculation of $K\to \ell {\nu }_{\ell }{\ell }^{\prime +}{\ell }^{\prime -}$ decay width
• Lattice QCD calculation of light sterile neutrino contribution in $0\nu 2\beta$ decay
• Lattice calculation of the pion mass difference $M_{{\pi }^{+}}-M_{{\pi }^0}$ at order $\mathcal{O}({\alpha }_{em})$
• Isospin Mass Differences of the $B$, $D$ and $K$