We present a lattice QCD calculation of the transverse-momentum-dependent wave function (TMDWF) of the pion using large-momentum effective theory. Numerical simulations are based on one ensemble with flavors of highly improved staggered quarks with lattice spacing from the MILC collaboration, and one with flavor clover fermions and tree-level Symanzik gauge action generated by the CLS collaboration with . As a key ingredient, the soft function is first obtained by incorporating the one-loop perturbative contributions and a proper normalization. Based on this and the equal-time quasi-TMDWF simulated on the lattice, we extract the TMDWF. The results for both lattice ensembles are compatible and a comparison with a phenomenological parametrization is made. Our studies provide a first attempt of ab initio calculation of TMDWFs which will eventually lead to crucial theory inputs for making predictions for exclusive processes under QCD factorization.
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"value": "We present a lattice QCD calculation of the transverse-momentum-dependent wave function (TMDWF) of the pion using large-momentum effective theory. Numerical simulations are based on one ensemble with <math><mrow><mn>2</mn><mo>+</mo><mn>1</mn><mo>+</mo><mn>1</mn></mrow></math> flavors of highly improved staggered quarks with lattice spacing <math><mi>a</mi><mo>=</mo><mn>0.121</mn><mtext> </mtext><mtext> </mtext><mi>fm</mi></math> from the MILC collaboration, and one with <math><mrow><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math> flavor clover fermions and tree-level Symanzik gauge action generated by the CLS collaboration with <math><mi>a</mi><mo>=</mo><mn>0.098</mn><mtext> </mtext><mtext> </mtext><mi>fm</mi></math>. As a key ingredient, the soft function is first obtained by incorporating the one-loop perturbative contributions and a proper normalization. Based on this and the equal-time quasi-TMDWF simulated on the lattice, we extract the TMDWF. The results for both lattice ensembles are compatible and a comparison with a phenomenological parametrization is made. Our studies provide a first attempt of ab initio calculation of TMDWFs which will eventually lead to crucial theory inputs for making predictions for exclusive processes under QCD factorization."
}
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