| Summary: | The color transparency (CT) of a hadron, propagating with reduced absorption in a nucleus, is a fundamental property of QCD (quantum chromodynamics) reflecting its internal structure and effective size when it is produced at high transverse momentum, <i>Q</i>. CT has been confirmed in many experiments, such as semi-exclusive hard electroproduction, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>e</mi><mi>A</mi><mo>→</mo><msup><mi>e</mi><mo>′</mo></msup><mi>π</mi><mi>X</mi></mrow></semantics></math></inline-formula>, for mesons produced at <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>Q</mi><mn>2</mn></msup><mo>></mo><mn>3</mn><mspace width="3.33333pt"></mspace><msup><mrow><mi>GeV</mi></mrow><mn>2</mn></msup></mrow></semantics></math></inline-formula>. However, a recent JLab (Jefferson Laboratory) measurement for a proton electroproduced in carbon <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>e</mi><mspace width="0.166667em"></mspace><mi mathvariant="normal">C</mi><mo>→</mo><msup><mi>e</mi><mo>′</mo></msup><mi>p</mi><mi>X</mi></mrow></semantics></math></inline-formula>, where <i>X</i> stands for the inclusive sum of all produced final states, fails to observe CT at <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>Q</mi><mn>2</mn></msup></semantics></math></inline-formula> up to 14.2 GeV<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mn>2</mn></msup></semantics></math></inline-formula>. In this paper, the onset of CT is determined by comparing the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>Q</mi><mn>2</mn></msup></semantics></math></inline-formula>-dependence of the hadronic cross sections for the initial formation of a small color-singlet configuration using the generalized parton distributions from holographic light-front QCD. A critical dependence on the hadron’s twist, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>τ</mi></semantics></math></inline-formula>, the number of hadron constituents, is found for the onset of CT, with no significant effects from the nuclear medium. This effect can explain the absence of proton CT in the present kinematic range of the JLab experiment. The proton is predicted to have a “two-stage” color transparency with the onset of CT differing for the spin-conserving (twist-3, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>τ</mi><mo>=</mo><mn>3</mn></mrow></semantics></math></inline-formula>) Dirac form factor with a higher onset in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>Q</mi><mn>2</mn></msup></semantics></math></inline-formula> for the spin-flip Pauli (twist-4) form factor. In contrast, the neutron is predicted to have a “one-stage” color transparency with the onset at higher <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>Q</mi><mn>2</mn></msup></semantics></math></inline-formula> because of the dominance of its Pauli form factor. The model also predicts a strong dependence at low energies on the flavor of the quark current coupling to the hadron.
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