textlessptextgreaterWe compute the leptonic decay constants textlessinline-formulatextgreatertextlessmml:math display=“inline"textgreatertextlessmml:msubtextgreatertextlessmml:mitextgreaterftextless/mml:mitextgreatertextlessmml:msuptextgreatertextlessmml:mitextgreaterDtextless/mml:mitextgreatertextlessmml:motextgreater+textless/mml:motextgreatertextless/mml:msuptextgreatertextless/mml:msubtextgreatertextless/mml:mathtextgreatertextless/inline-formulatextgreater, textlessinline-formulatextgreatertextlessmml:math display=“inline"textgreatertextlessmml:mrowtextgreatertextlessmml:msubtextgreatertextlessmml:mrowtextgreatertextlessmml:mitextgreaterftextless/mml:mitextgreatertextless/mml:mrowtextgreatertextlessmml:mrowtextgreatertextlessmml:msubtextgreatertextlessmml:mrowtextgreatertextlessmml:mitextgreaterDtextless/mml:mitextgreatertextless/mml:mrowtextgreatertextlessmml:mrowtextgreatertextlessmml:mitextgreaterstextless/mml:mitextgreatertextless/mml:mrowtextgreatertextless/mml:msubtextgreatertextless/mml:mrowtextgreatertextless/mml:msubtextgreatertextless/mml:mrowtextgreatertextless/mml:mathtextgreatertextless/inline-formulatextgreater, and textlessinline-formulatextgreatertextlessmml:math display=“inline"textgreatertextlessmml:msubtextgreatertextlessmml:mitextgreaterftextless/mml:mitextgreatertextlessmml:msuptextgreatertextlessmml:mitextgreaterKtextless/mml:mitextgreatertextlessmml:motextgreater+textless/mml:motextgreatertextless/mml:msuptextgreatertextless/mml:msubtextgreatertextless/mml:mathtextgreatertextless/inline-formulatextgreater and the quark-mass ratios textlessinline-formulatextgreatertextlessmml:math display=“inline"textgreatertextlessmml:msubtextgreatertextlessmml:mitextgreatermtextless/mml:mitextgreatertextlessmml:mitextgreaterctextless/mml:mitextgreatertextless/mml:msubtextgreatertextlessmml:mo stretchy=“false"textgreater/textless/mml:motextgreatertextlessmml:msubtextgreatertextlessmml:mitextgreatermtextless/mml:mitextgreatertextlessmml:mitextgreaterstextless/mml:mitextgreatertextless/mml:msubtextgreatertextless/mml:mathtextgreatertextless/inline-formulatextgreater and textlessinline-formulatextgreatertextlessmml:math display=“inline"textgreatertextlessmml:msubtextgreatertextlessmml:mitextgreatermtextless/mml:mitextgreatertextlessmml:mitextgreaterstextless/mml:mitextgreatertextless/mml:msubtextgreatertextlessmml:mo stretchy=“false"textgreater/textless/mml:motextgreatertextlessmml:msubtextgreatertextlessmml:mitextgreatermtextless/mml:mitextgreatertextlessmml:mitextgreaterltextless/mml:mitextgreatertextless/mml:msubtextgreatertextless/mml:mathtextgreatertextless/inline-formulatextgreater in unquenched lattice QCD using the experimentally determined value of textlessinline-formulatextgreatertextlessmml:math display=“inline"textgreatertextlessmml:msubtextgreatertextlessmml:mitextgreaterftextless/mml:mitextgreatertextlessmml:msuptextgreatertextlessmml:mitextgreaterπtextless/mml:mitextgreatertextlessmml:motextgreater+textless/mml:motextgreatertextless/mml:msuptextgreatertextless/mml:msubtextgreatertextless/mml:mathtextgreatertextless/inline-formulatextgreater for normalization. We use the MILC highly improved staggered quark ensembles with four dynamical quark flavors—up, down, strange, and charm—and with both physical and unphysical values of the light sea-quark masses. The use of physical pions removes the need for a chiral extrapolation, thereby eliminating a significant source of uncertainty in previous calculations. Four different lattice spacings ranging from textlessinline-formulatextgreatertextlessmml:math display=“inline"textgreatertextlessmml:mitextgreateratextless/mml:mitextgreatertextlessmml:motextgreater≈textless/mml:motextgreatertextlessmml:mntextgreater0.06textless/mml:mntextgreatertextless/mml:mathtextgreatertextless/inline-formulatextgreater to 0.15 fm are included in the analysis to control the extrapolation to the continuum limit. Our primary results are textlessinline-formulatextgreatertextlessmml:math display=“inline"textgreatertextlessmml:mrowtextgreatertextlessmml:msubtextgreatertextlessmml:mrowtextgreatertextlessmml:mitextgreaterftextless/mml:mitextgreatertextless/mml:mrowtextgreatertextlessmml:mrowtextgreatertextlessmml:msuptextgreatertextlessmml:mrowtextgreatertextlessmml:mitextgreaterDtextless/mml:mitextgreatertextless/mml:mrowtextgreatertextlessmml:mrowtextgreatertextlessmml:motextgreater+textless/mml:motextgreatertextless/mml:mrowtextgreatertextless/mml:msuptextgreatertextless/mml:mrowtextgreatertextless/mml:msubtextgreatertextlessmml:motextgreater=textless/mml:motextgreatertextlessmml:mntextgreater212.6textless/mml:mntextgreatertextlessmml:mo stretchy=“false"textgreater(textless/mml:motextgreatertextlessmml:mntextgreater0.4textless/mml:mntextgreatertextlessmml:mo stretchy=“false"textgreater)textless/mml:motextgreatertextlessmml:mo stretchy=“false"textgreater(textless/mml:motextgreatertextlessmml:mrowtextgreatertextlessmml:mfrac linethickness=“0"textgreatertextlessmml:mrowtextgreatertextlessmml:motextgreater+textless/mml:motextgreatertextlessmml:mntextgreater1.0textless/mml:mntextgreatertextless/mml:mrowtextgreatertextlessmml:mrowtextgreatertextlessmml:motextgreater−textless/mml:motextgreatertextlessmml:mntextgreater1.2textless/mml:mntextgreatertextless/mml:mrowtextgreatertextless/mml:mfractextgreatertextless/mml:mrowtextgreatertextlessmml:mo stretchy=“false"textgreater)textless/mml:motextgreatertextlessmml:mtexttextgreater textless/mml:mtexttextgreatertextlessmml:mtexttextgreater textless/mml:mtexttextgreatertextlessmml:mitextgreaterMeVtextless/mml:mitextgreatertextless/mml:mrowtextgreatertextless/mml:mathtextgreatertextless/inline-formulatextgreater, textlessinline-formulatextgreatertextlessmml:math display=“inline"textgreatertextlessmml:mrowtextgreatertextlessmml:msubtextgreatertextlessmml:mrowtextgreatertextlessmml:mitextgreaterftextless/mml:mitextgreatertextless/mml:mrowtextgreatertextlessmml:mrowtextgreatertextlessmml:msubtextgreatertextlessmml:mrowtextgreatertextlessmml:mitextgreaterDtextless/mml:mitextgreatertextless/mml:mrowtextgreatertextlessmml:mrowtextgreatertextlessmml:mitextgreaterstextless/mml:mitextgreatertextless/mml:mrowtextgreatertextless/mml:msubtextgreatertextless/mml:mrowtextgreatertextless/mml:msubtextgreatertextlessmml:motextgreater=textless/mml:motextgreatertextlessmml:mntextgreater249.0textless/mml:mntextgreatertextlessmml:mo stretchy=“false"textgreater(textless/mml:motextgreatertextlessmml:mntextgreater0.3textless/mml:mntextgreatertextlessmml:mo stretchy=“false"textgreater)textless/mml:motextgreatertextlessmml:mo stretchy=“false"textgreater(textless/mml:motextgreatertextlessmml:mrowtextgreatertextlessmml:mfrac linethickness=“0"textgreatertextlessmml:mrowtextgreatertextlessmml:motextgreater+textless/mml:motextgreatertextlessmml:mntextgreater1.1textless/mml:mntextgreatertextless/mml:mrowtextgreatertextlessmml:mrowtextgreatertextlessmml:motextgreater−textless/mml:motextgreatertextlessmml:mntextgreater1.5textless/mml:mntextgreatertextless/mml:mrowtextgreatertextless/mml:mfractextgreatertextless/mml:mrowtextgreatertextlessmml:mo stretchy=“false"textgreater)textless/mml:motextgreatertextlessmml:mtexttextgreater textless/mml:mtexttextgreatertextlessmml:mtexttextgreater textless/mml:mtexttextgreatertextlessmml:mitextgreaterMeVtextless/mml:mitextgreatertextless/mml:mrowtextgreatertextless/mml:mathtextgreatertextless/inline-formulatextgreater, and textlessinline-formulatextgreatertextlessmml:math display=“inline"textgreatertextlessmml:mrowtextgreatertextlessmml:msubtextgreatertextlessmml:mrowtextgreatertextlessmml:mitextgreaterftextless/mml:mitextgreatertextless/mml:mrowtextgreatertextlessmml:mrowtextgreatertextlessmml:msubtextgreatertextlessmml:mrowtextgreatertextlessmml:mitextgreaterDtextless/mml:mitextgreatertextless/mml:mrowtextgreatertextlessmml:mrowtextgreatertextlessmml:mitextgreaterstextless/mml:mitextgreatertextless/mml:mrowtextgreatertextless/mml:msubtextgreatertextless/mml:mrowtextgreatertextless/mml:msubtextgreatertextlessmml:mo stretchy=“false"textgreater/textless/mml:motextgreatertextlessmml:msubtextgreatertextlessmml:mrowtextgreatertextlessmml:mitextgreaterftextless/mml:mitextgreatertextless/mml:mrowtextgreatertextlessmml:mrowtextgreatertextlessmml:msuptextgreatertextlessmml:mrowtextgreatertextlessmml:mitextgreaterDtextless/mml:mitextgreatertextless/mml:mrowtextgreatertextlessmml:mrowtextgreatertextlessmml:motextgreater+textless/mml:motextgreatertextless/mml:mrowtextgreatertextless/mml:msuptextgreatertextless/mml:mrowtextgreatertextless/mml:msubtextgreatertextlessmml:motextgreater=textless/mml:motextgreatertextlessmml:mntextgreater1.1712textless/mml:mntextgreatertextlessmml:mo stretchy=“false"textgreater(textless/mml:motextgreatertextlessmml:mntextgreater10textless/mml:mntextgreatertextlessmml:mo stretchy=“false"textgreater)textless/mml:motextgreatertextlessmml:mo stretchy=“false"textgreater(textless/mml:motextgreatertextlessmml:mrowtextgreatertextlessmml:mfrac linethickness=“0"textgreatertextlessmml:mrowtextgreatertextlessmml:motextgreater+textless/mml:motextgreatertextlessmml:mntextgreater29textless/mml:mntextgreatertextless/mml:mrowtextgreatertextlessmml:mrowtextgreatertextlessmml:motextgreater−textless/mml:motextgreatertextlessmml:mntextgreater32textless/mml:mntextgreatertextless/mml:mrowtextgreatertextless/mml:mfractextgreatertextless/mml:mrowtextgreatertextlessmml:mo stretchy=“false"textgreater)textless/mml:motextgreatertextless/mml:mrowtextgreatertextless/mml:mathtextgreatertextless/inline-formulatextgreater, where the errors are statistical and total systematic, respectively. The errors on our results for the charm decay constants and their ratio are approximately 2–4 times smaller than those of the most precise previous lattice calculations. We also obtain textlessinline-formulatextgreatertextlessmml:math display=“inline"textgreatertextlessmml:mrowtextgreatertextlessmml:msubtextgreatertextlessmml:mrowtextgreatertextlessmml:mitextgreaterftextless/mml:mitextgreatertextless/mml:mrowtextgreatertextlessmml:mrowtextgreatertextlessmml:msuptextgreatertextlessmml:mrowtextgreatertextlessmml:mitextgreaterKtextless/mml:mitextgreatertextless/mml:mrowtextgreatertextlessmml:mrowtextgreatertextlessmml:motextgreater+textless/mml:motextgreatertextless/mml:mrowtextgreatertextless/mml:msuptextgreatertextless/mml:mrowtextgreatertextless/mml:msubtextgreatertextlessmml:mo stretchy=“false"textgreater/textless/mml:motextgreatertextlessmml:msubtextgreatertextlessmml:mrowtextgreatertextlessmml:mitextgreaterftextless/mml:mitextgreatertextless/mml:mrowtextgreatertextlessmml:mrowtextgreatertextlessmml:msuptextgreatertextlessmml:mrowtextgreatertextlessmml:mitextgreaterπtextless/mml:mitextgreatertextless/mml:mrowtextgreatertextlessmml:mrowtextgreatertextlessmml:motextgreater+textless/mml:motextgreatertextless/mml:mrowtextgreatertextless/mml:msuptextgreatertextless/mml:mrowtextgreatertextless/mml:msubtextgreatertextlessmml:motextgreater=textless/mml:motextgreatertextlessmml:mntextgreater1.1956textless/mml:mntextgreatertextlessmml:mo stretchy=“false"textgreater(textless/mml:motextgreatertextlessmml:mntextgreater10textless/mml:mntextgreatertextlessmml:mo stretchy=“false"textgreater)textless/mml:motextgreatertextlessmml:mo stretchy=“false"textgreater(textless/mml:motextgreatertextlessmml:mrowtextgreatertextlessmml:mfrac linethickness=“0"textgreatertextlessmml:mrowtextgreatertextlessmml:motextgreater+textless/mml:motextgreatertextlessmml:mntextgreater26textless/mml:mntextgreatertextless/mml:mrowtextgreatertextlessmml:mrowtextgreatertextlessmml:motextgreater−textless/mml:motextgreatertextlessmml:mntextgreater18textless/mml:mntextgreatertextless/mml:mrowtextgreatertextless/mml:mfractextgreatertextless/mml:mrowtextgreatertextlessmml:mo stretchy=“false"textgreater)textless/mml:motextgreatertextless/mml:mrowtextgreatertextless/mml:mathtextgreatertextless/inline-formulatextgreater, updating our previous result, and determine the quark-mass ratios textlessinline-formulatextgreatertextlessmml:math display=“inline"textgreatertextlessmml:mrowtextgreatertextlessmml:msubtextgreatertextlessmml:mrowtextgreatertextlessmml:mitextgreatermtextless/mml:mitextgreatertextless/mml:mrowtextgreatertextlessmml:mrowtextgreatertextlessmml:mitextgreaterstextless/mml:mitextgreatertextless/mml:mrowtextgreatertextless/mml:msubtextgreatertextlessmml:mo stretchy=“false"textgreater/textless/mml:motextgreatertextlessmml:msubtextgreatertextlessmml:mrowtextgreatertextlessmml:mitextgreatermtextless/mml:mitextgreatertextless/mml:mrowtextgreatertextlessmml:mrowtextgreatertextlessmml:mitextgreaterltextless/mml:mitextgreatertextless/mml:mrowtextgreatertextless/mml:msubtextgreatertextlessmml:motextgreater=textless/mml:motextgreatertextlessmml:mntextgreater27.35textless/mml:mntextgreatertextlessmml:mo stretchy=“false"textgreater(textless/mml:motextgreatertextlessmml:mntextgreater5textless/mml:mntextgreatertextlessmml:mo stretchy=“false"textgreater)textless/mml:motextgreatertextlessmml:mo stretchy=“false"textgreater(textless/mml:motextgreatertextlessmml:mrowtextgreatertextlessmml:mfrac linethickness=“0"textgreatertextlessmml:mrowtextgreatertextlessmml:motextgreater+textless/mml:motextgreatertextlessmml:mntextgreater10textless/mml:mntextgreatertextless/mml:mrowtextgreatertextlessmml:mrowtextgreatertextlessmml:motextgreater−textless/mml:motextgreatertextlessmml:mntextgreater7textless/mml:mntextgreatertextless/mml:mrowtextgreatertextless/mml:mfractextgreatertextless/mml:mrowtextgreatertextlessmml:mo stretchy=“false"textgreater)textless/mml:motextgreatertextless/mml:mrowtextgreatertextless/mml:mathtextgreatertextless/inline-formulatextgreater and textlessinline-formulatextgreatertextlessmml:math display=“inline"textgreatertextlessmml:mrowtextgreatertextlessmml:msubtextgreatertextlessmml:mrowtextgreatertextlessmml:mitextgreatermtextless/mml:mitextgreatertextless/mml:mrowtextgreatertextlessmml:mrowtextgreatertextlessmml:mitextgreaterctextless/mml:mitextgreatertextless/mml:mrowtextgreatertextless/mml:msubtextgreatertextlessmml:mo stretchy=“false"textgreater/textless/mml:motextgreatertextlessmml:msubtextgreatertextlessmml:mrowtextgreatertextlessmml:mitextgreatermtextless/mml:mitextgreatertextless/mml:mrowtextgreatertextlessmml:mrowtextgreatertextlessmml:mitextgreaterstextless/mml:mitextgreatertextless/mml:mrowtextgreatertextless/mml:msubtextgreatertextlessmml:motextgreater=textless/mml:motextgreatertextlessmml:mntextgreater11.747textless/mml:mntextgreatertextlessmml:mo stretchy=“false"textgreater(textless/mml:motextgreatertextlessmml:mntextgreater19textless/mml:mntextgreatertextlessmml:mo stretchy=“false"textgreater)textless/mml:motextgreatertextlessmml:mo stretchy=“false"textgreater(textless/mml:motextgreatertextlessmml:mrowtextgreatertextlessmml:mfrac linethickness=“0"textgreatertextlessmml:mrowtextgreatertextlessmml:motextgreater+textless/mml:motextgreatertextlessmml:mntextgreater59textless/mml:mntextgreatertextless/mml:mrowtextgreatertextlessmml:mrowtextgreatertextlessmml:motextgreater−textless/mml:motextgreatertextlessmml:mntextgreater43textless/mml:mntextgreatertextless/mml:mrowtextgreatertextless/mml:mfractextgreatertextless/mml:mrowtextgreatertextlessmml:mo stretchy=“false"textgreater)textless/mml:motextgreatertextless/mml:mrowtextgreatertextless/mml:mathtextgreatertextless/inline-formulatextgreater. When combined with experimental measurements of the decay rates, our results lead to precise determinations of the Cabibbo-Kobayashi-Maskawa matrix elements textlessinline-formulatextgreatertextlessmml:math display=“inline"textgreatertextlessmml:mo stretchy=“false"textgreatertextbartextless/mml:motextgreatertextlessmml:msubtextgreatertextlessmml:mitextgreaterVtextless/mml:mitextgreatertextlessmml:mrowtextgreatertextlessmml:mitextgreaterutextless/mml:mitextgreatertextlessmml:mitextgreaterstextless/mml:mitextgreatertextless/mml:mrowtextgreatertextless/mml:msubtextgreatertextlessmml:mo stretchy=“false"textgreatertextbartextless/mml:motextgreatertextlessmml:motextgreater=textless/mml:motextgreatertextlessmml:mntextgreater0.22487textless/mml:mntextgreatertextlessmml:mo stretchy=“false"textgreater(textless/mml:motextgreatertextlessmml:mntextgreater51textless/mml:mntextgreatertextlessmml:mo stretchy=“false"textgreater)textless/mml:motextgreatertextlessmml:mo stretchy=“false"textgreater(textless/mml:motextgreatertextlessmml:mntextgreater29textless/mml:mntextgreatertextlessmml:mo stretchy=“false"textgreater)textless/mml:motextgreatertextlessmml:mo stretchy=“false"textgreater(textless/mml:motextgreatertextlessmml:mntextgreater20textless/mml:mntextgreatertextlessmml:mo stretchy=“false"textgreater)textless/mml:motextgreatertextlessmml:mo stretchy=“false"textgreater(textless/mml:motextgreatertextlessmml:mntextgreater5textless/mml:mntextgreatertextlessmml:mo stretchy=“false"textgreater)textless/mml:motextgreatertextless/mml:mathtextgreatertextless/inline-formulatextgreater, textlessinline-formulatextgreatertextlessmml:math display=“inline"textgreatertextlessmml:mo stretchy=“false"textgreatertextbartextless/mml:motextgreatertextlessmml:msubtextgreatertextlessmml:mitextgreaterVtextless/mml:mitextgreatertextlessmml:mrowtextgreatertextlessmml:mitextgreaterctextless/mml:mitextgreatertextlessmml:mitextgreaterdtextless/mml:mitextgreatertextless/mml:mrowtextgreatertextless/mml:msubtextgreatertextlessmml:mo stretchy=“false"textgreatertextbartextless/mml:motextgreatertextlessmml:motextgreater=textless/mml:motextgreatertextlessmml:mntextgreater0.217textless/mml:mntextgreatertextlessmml:mo stretchy=“false"textgreater(textless/mml:motextgreatertextlessmml:mntextgreater1textless/mml:mntextgreatertextlessmml:mo stretchy=“false"textgreater)textless/mml:motextgreatertextlessmml:mo stretchy=“false"textgreater(textless/mml:motextgreatertextlessmml:mntextgreater5textless/mml:mntextgreatertextlessmml:mo stretchy=“false"textgreater)textless/mml:motextgreatertextlessmml:mo stretchy=“false"textgreater(textless/mml:motextgreatertextlessmml:mntextgreater1textless/mml:mntextgreatertextlessmml:mo stretchy=“false"textgreater)textless/mml:motextgreatertextless/mml:mathtextgreatertextless/inline-formulatextgreater and textlessinline-formulatextgreatertextlessmml:math display=“inline"textgreatertextlessmml:mo stretchy=“false"textgreatertextbartextless/mml:motextgreatertextlessmml:msubtextgreatertextlessmml:mitextgreaterVtextless/mml:mitextgreatertextlessmml:mrowtextgreatertextlessmml:mitextgreaterctextless/mml:mitextgreatertextlessmml:mitextgreaterstextless/mml:mitextgreatertextless/mml:mrowtextgreatertextless/mml:msubtextgreatertextlessmml:mo stretchy=“false"textgreatertextbartextless/mml:motextgreatertextlessmml:motextgreater=textless/mml:motextgreatertextlessmml:mntextgreater1.010textless/mml:mntextgreatertextlessmml:mo stretchy=“false"textgreater(textless/mml:motextgreatertextlessmml:mntextgreater5textless/mml:mntextgreatertextlessmml:mo stretchy=“false"textgreater)textless/mml:motextgreatertextlessmml:mo stretchy=“false"textgreater(textless/mml:motextgreatertextlessmml:mntextgreater18textless/mml:mntextgreatertextlessmml:mo stretchy=“false"textgreater)textless/mml:motextgreatertextlessmml:mo stretchy=“false"textgreater(textless/mml:motextgreatertextlessmml:mntextgreater6textless/mml:mntextgreatertextlessmml:mo stretchy=“false"textgreater)textless/mml:motextgreatertextless/mml:mathtextgreatertextless/inline-formulatextgreater, where the errors are from this calculation of the decay constants, the uncertainty in the experimental decay rates, structure-dependent electromagnetic corrections, and, in the case of textlessinline-formulatextgreatertextlessmml:math display=“inline"textgreatertextlessmml:mo stretchy=“false"textgreatertextbartextless/mml:motextgreatertextlessmml:msubtextgreatertextlessmml:mitextgreaterVtextless/mml:mitextgreatertextlessmml:mrowtextgreatertextlessmml:mitextgreaterutextless/mml:mitextgreatertextlessmml:mitextgreaterstextless/mml:mitextgreatertextless/mml:mrowtextgreatertextless/mml:msubtextgreatertextlessmml:mo stretchy=“false"textgreatertextbartextless/mml:motextgreatertextless/mml:mathtextgreatertextless/inline-formulatextgreater, the uncertainty in textlessinline-formulatextgreatertextlessmml:math display=“inline"textgreatertextlessmml:mo stretchy=“false"textgreatertextbartextless/mml:motextgreatertextlessmml:msubtextgreatertextlessmml:mitextgreaterVtextless/mml:mitextgreatertextlessmml:mrowtextgreatertextlessmml:mitextgreaterutextless/mml:mitextgreatertextlessmml:mitextgreaterdtextless/mml:mitextgreatertextless/mml:mrowtextgreatertextless/mml:msubtextgreatertextlessmml:mo stretchy=“false"textgreatertextbartextless/mml:motextgreatertextless/mml:mathtextgreatertextless/inline-formulatextgreater, respectively.textless/ptextgreater