Observation of <i>d</i> → (<i>k</i>)over-bar₁ (1270)μ⁺ν_μ and Test of Lepton Flavor Universality with <i>d</i> → (<i>k</i>)over-bar₁ (1270)<i>l</i>⁺ν<i>_l</i>

By analyzing 7.93 fb(-1) of e(+)e(-) collision data collected at the center-of-mass energy of 3.773 GeV with the BESIII detector operated at the BEPCII collider, we report the observation of the semimuonic decays of D+ -> (K) over bar (1) (1270)(0)mu(+)nu(mu) and D-0 -> K-1 (1270)(-)mu(+)nu(mu) with statistical significances of 12.5 sigma and 6.0 sigma, respectively. Their decay branching fractions are determined to be B[D+ -> (K) over bar (1) (1270)(0)mu(+)nu(mu)] = (2.36 +/- 0.20(-0.27)(+0.18) +/- 0.48) x 10(-3) and B[D-0 -> K-1 (1270)(-)mu(+)nu(mu)] = (0.78 +/- 0.11(-0.09)(+0.05) +/- 0.15) x 10(-3), where the first and second uncertainties are statistical and systematic, respectively, and the third originates from the input branching fraction of (K) over bar (1) (1270)(0) -> (K) over bar (-) pi(+)pi(0) or K-1 (1270)(-) -> K-pi(+)pi(-). Combining our branching fractions with the previous measurements of B[D+ -> (K) over bar (1) (1270)(0)e(+)nu(e)] and B[D-0 -> K-1 (1270)(-)e(+)nu(e)], we determine the branching fraction ratios to be B[D-0 -> K-1 (1270)(-)mu(+)nu(mu)]/B[D-0 -> K-1 (1270)(-)mu+nu(mu)]/B[D-0 -> K-1 (1270)(-)e(+)nu(e)] = 0.74 +/- 0.13(-1.03)(+0.08). Using the branching fractions measured in this work and the world-average lifetimes of the D+ and D-0 mesons, we determine the semimuonic partial decay width ratio to be Gamma[D+ -> (K) over bar (1) (1270)(0)mu(+)nu(mu)]/Gamma[D-0 -> (K) over bar (1) (1270)(-)mu(+)nu(mu)] = 1.22 +/- 0.10(-0.09)(+0.06), which is consistent with unity as predicted by isospin conservation.