Lattice calculation of the pion mass difference $M_{{\pi }^{+}}-M_{{\pi }^0}$ at order $\mathcal{O}({\alpha }_{em})$

Abstract

We present a lattice calculation of the charged/neutral pion mass difference $M_{{\pi }^{+}}-M_{{\pi }^0}$ at order $\mathcal{O}({\alpha }_{em})$ using the gauge configurations produced by the Extended Twisted Mass Collaboration with $N_f=2+1+1$ dynamical quark flavours at three values of the lattice spacing ($a\simeq 0.062,0.082,0.089\mathrm{fm}$) and pion masses in the range $M_{\pi }\simeq 250-500\mathrm{MeV}$. We employ the RM123 method and expand the path-integral around the isospin symmetric point at leading order in the electromagnetic coupling ${\alpha }_{em}$. Making use of the recently proposed RTM scheme, we evaluate the full $\mathcal{O}({\alpha }_{em})$ contribution, with the inclusion of the disconnected diagram. At the physical point, after performing the continuum and infinite volume extrapolation, we obtain the value $M_{{\pi }^{+}}-M_{{\pi }^0}=4.622(95)\mathrm{MeV}$ which is in good agreement with the experimental result $[M_{{\pi }^{+}}-M_{{\pi }^0}{]}^{exp.}=4.5936(5)\mathrm{MeV}$.

arXiv comment13 pages, 5 figures, 1 table

References in corpus (27)

• Leading hadronic contribution to the muon magnetic moment from lattice QCD
• Ab initio calculation of the neutron-proton mass difference
• Chirally improving Wilson fermions - I. O(a) improvement
• Light hadrons from lattice QCD with light (u,d), strange and charm dynamical quarks
• Virtual Photons in Chiral Perturbation Theory
• Chirally improving Wilson fermions II. Four-quark operators
• Finite volume effects for meson masses and decay constants
• Up, down, strange and charm quark masses with Nf = 2+1+1 twisted mass lattice QCD
• Leading isospin breaking effects on the lattice
• QED in finite volume and finite size scaling effect on electromagnetic properties of hadrons
• Bayesian model averaging for analysis of lattice field theory results
• Electromagnetic and strong isospin-breaking corrections to the muon $g-2$ from Lattice QCD+QED
• First lattice calculation of the QED corrections to leptonic decay rates
• Light-meson leptonic decay rates in lattice QCD+QED
• Leading isospin-breaking corrections to pion, kaon and charmed-meson masses with Twisted-Mass fermions
• Finite-Volume Electromagnetic Corrections to the Masses of Mesons, Baryons and Nuclei
• Isospin breaking effects due to the up-down mass difference in Lattice QCD
• Quark masses using twisted mass fermion gauge ensembles
• First lattice calculation of radiative leptonic decay rates of pseudoscalar mesons
• Isospin breaking corrections to meson masses and the hadronic vacuum polarization: a comparative study
• Strange and charm HVP contributions to the muon ($g-2)$ including QED corrections with twisted-mass fermions
• Lattice computation of the electromagnetic contributions to kaon and pion masses
• Lattice QCD Calculation of the Pion Mass Splitting
• Gauge invariant determination of charged hadron masses
• Electromagnetic corrections to leptonic decay rates of charged pseudoscalar mesons: finite-volume effects
• State mixing and masses of the ${\pi }^0$, $\eta$ and ${\eta }^{\prime }$ mesons from $n_f=1+1+1$ lattice QCD+QED
• Rotated twisted-mass: a convenient regularization scheme for isospin breaking QCD and QED lattice calculations

Cited by in corpus (3)

• Forward light-by-light scattering and electromagnetic correction to hadronic vacuum polarization
• Quark mass difference effects in hadronic Fermi matrix elements from first principles
• QED corrections to meson masses