Quark and gluon momentum fractions in the pion and in the kaon

Abstract

We present results on the momentum fraction carried by quarks and gluons in the pion and the kaon. We employ three gauge ensembles generated with $N_f=2+1+1$ Wilson twisted-mass clover-improved fermions with physical quark masses. We perform, for the first time, a continuum extrapolation directly at the physical pion. We find that the total momentum fraction carried by quarks is $\langle x \rangle_{q, R}^{\pi}= 0.575(79)$ and $\langle x \rangle_{q,R}^{K} = 0.683(50)$ and by gluons $\langle x \rangle_{g, R}^{\pi}=0.402(53)$ and $\langle x \rangle_{g, R}^{K}=0.422(67)$ in the pion and in the kaon, respectively, in the $\overline{\mathrm{MS}}$ scheme and at the renormalization scale of 2 GeV. Having computed both the quark and gluon contributions in the continuum limit, we verify the momentum sum, finding 0.984(89) for the pion and 1.13(11) for the kaon.