Quark and gluon momentum fractions in the pion from $N_f=2+1+1$ lattice QCD

We perform the first full decomposition of the pion momentum into its gluon and quark contributions. We employ an ensemble generated by the Extended Twisted Mass Collaboration with <math display="inline"><msub><mi>N</mi><mi>f</mi></msub><mo>=</mo><mn>2</mn><mo>+</mo><mn>1</mn><mo>+</mo><mn>1</mn></math> Wilson twisted mass clover fermions at maximal twist tuned to reproduce the physical pion mass. We present our results in the <math display="inline"><mover accent="true"><mi>MS</mi><mo stretchy="true">¯</mo></mover></math> scheme at 2 GeV. We find <math display="inline"><mrow><mo stretchy="false">⟨</mo><mi>x</mi><msub><mrow><mo stretchy="false">⟩</mo></mrow><mrow><mi>u</mi><mo>+</mo><mi>d</mi></mrow></msub><mo>=</mo><mn>0.601</mn><mo stretchy="false">(</mo><mn>28</mn><mo stretchy="false">)</mo></mrow></math>, <math display="inline"><mo stretchy="false">⟨</mo><mi>x</mi><msub><mo stretchy="false">⟩</mo><mi>s</mi></msub><mo>=</mo><mn>0.059</mn><mo stretchy="false">(</mo><mn>13</mn><mo stretchy="false">)</mo></math>, <math display="inline"><mo stretchy="false">⟨</mo><mi>x</mi><msub><mo stretchy="false">⟩</mo><mi>c</mi></msub><mo>=</mo><mn>0.019</mn><mo stretchy="false">(</mo><mn>05</mn><mo stretchy="false">)</mo></math>, and <math display="inline"><mo stretchy="false">⟨</mo><mi>x</mi><msub><mo stretchy="false">⟩</mo><mi>g</mi></msub><mo>=</mo><mn>0.52</mn><mo stretchy="false">(</mo><mn>11</mn><mo stretchy="false">)</mo></math> for the separate contributions, respectively, whose sum saturates the momentum sum rule.