Current-Component Independent Transition Form Factors for Semileptonic and Rare 
 D
 ⟶
 π
 
 
 K
 
 
 Decays in the Light-Front Quark Model

<jats:p>We investigate the exclusive semileptonic and rare <jats:inline-formula> <math xmlns="http://www.w3. org/1998/Math/MathML" id="M2"> <mi>D</mi> <mo>⟶</mo> <mi>π</mi> <mfenced open="(" close=")"> <mrow> <mi>K</mi> </mrow> </mfenced> </math> </jats:inline-formula> decays within the standard model together with the light-front quark model (LFQM) constrained by the variational principle for the QCD-motivated effective Hamiltonian. The form factors are obtained in the <jats:inline-formula> <math xmlns="http://www.w3. org/1998/Math/MathML" id="M3"> <msup> <mrow> <mi>q</mi> </mrow> <mrow> <mo>+</mo> </mrow> </msup> <mo>=</mo> <mn>0</mn> </math> </jats:inline-formula> frame and then analytically continue to the physical timelike region. Together with our recent analysis of the current-component independent form factors <jats:inline-formula> <math xmlns="http://www.w3. org/1998/Math/MathML" id="M4"> <msub> <mrow> <mi>f</mi> </mrow> <mrow> <mo>±</mo> </mrow> </msub> <mfenced open="(" close=")"> <mrow> <msup> <mrow> <mi>q</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> </mfenced> </math> </jats:inline-formula> for the semileptonic decays, we present the current-component independent tensor form factor <jats:inline-formula> <math xmlns="http://www.w3. org/1998/Math/MathML" id="M5"> <msub> <mrow> <mi>f</mi> </mrow> <mrow> <mi>T</mi> </mrow> </msub> <mfenced open="(" close=")"> <mrow> <msup> <mrow> <mi>q</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> </mfenced> </math> </jats:inline-formula> for the rare decays to make the complete set of hadronic matrix elements regulating the semileptonic and rare <jats:inline-formula> <math xmlns="http://www.w3. org/1998/Math/MathML" id="M6"> <mi>D</mi> <mo>⟶</mo> <mi>π</mi> <mfenced open="(" close=")"> <mrow> <mi>K</mi> </mrow> </mfenced> </math> </jats:inline-formula> decays in our LFQM. The tensor form factor <jats:inline-formula> <math xmlns="http://www.w3. org/1998/Math/MathML" id="M7"> <msub> <mrow> <mi>f</mi> </mrow> <mrow> <mi>T</mi> </mrow> </msub> <mfenced open="(" close=")"> <mrow> <msup> <mrow> <mi>q</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> </mfenced> </math> </jats:inline-formula> are obtained from two independent sets <jats:inline-formula> <math xmlns="http://www.w3. org/1998/Math/MathML" id="M8"> <mfenced open="(" close=")"> <mrow> <msubsup> <mrow> <mi>J</mi> </mrow> <mrow> <mi>T</mi> </mrow> <mrow> <mo>+</mo> <mrow> <mo>⊥</mo> </mrow> </mrow> </msubsup> <mrow> <mo>,</mo> </mrow> <msubsup> <mrow> <mi>J</mi> </mrow> <mrow> <mi>T</mi> </mrow> <mrow> <mo>+</mo> <mrow> <mo>−</mo> </mrow> </mrow> </msubsup> </mrow> </mfenced> </math> </jats:inline-formula> of the tensor current <jats:inline-formula> <math xmlns="http://www.w3. org/1998/Math/MathML" id="M9"> <msubsup> <mrow> <mi>J</mi> </mrow> <mrow> <mi>T</mi> </mrow> <mrow> <mi>u</mi> <mi>v</mi> </mrow> </msubsup> </math> </jats:inline-formula> . As in our recent analysis of <jats:inline-formula> <math xmlns="http://www.w3. org/1998/Math/MathML" id="M10"> <msub> <mrow> <mi>f</mi> </mrow> <mrow> <mo>−</mo> </mrow> </msub> <mfenced open="(" close=")"> <mrow> <msup> <mrow> <mi>q</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> </mfenced> </math> </jats:inline-formula>, we show that <jats:inline-formula> <math xmlns="http://www.w3. org/1998/Math/MathML" id="M11"> <msub> <mrow> <mi>f</mi> </mrow> <mrow> <mi>T</mi> </mrow> </msub> <mfenced open="(" close=")"> <mrow> <msup> <mrow> <mi>q</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> </mfenced> </math> </jats:inline-formula> obtained from the two different sets of the current components gives the identical result in the valence region of the <jats:inline-formula> <math xmlns="http://www.w3. org/1998/Math/MathML" id="M12"> <msup> <mrow> <mi>q</mi> </mrow> <mrow> <mo>+</mo> </mrow> </msup> <mo>=</mo> <mn>0</mn> </math> </jats:inline-formula> frame without involving the explicit zero modes and the instantaneous contributions. The implications of the zero modes and the instantaneou