Off forward non- s -channel helicity conserving contributions to exclusive vector quarkonium production from the spin dependent BFKL Pomeron

A novel contribution to off forward, exclusive vector quarkonium production, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:msup><a:mrow><a:mi>γ</a:mi></a:mrow><a:mrow><a:mo stretchy="false">(</a:mo><a:mo>*</a:mo><a:mo stretchy="false">)</a:mo></a:mrow></a:msup><a:mo>+</a:mo><a:mi>p</a:mi><a:mo stretchy="false">→</a:mo><a:mi>V</a:mi><a:mo>+</a:mo><a:mi>p</a:mi></a:mrow></a:math>, at high energy is derived which corresponds to a <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:mi>t</f:mi></f:math>-channel exchange of a Balitsky-Fadin-Kuraev-Lipatov (BFKL) hard Pomeron, with a helicity flip of the proton. This “spin-dependent BFKL Pomeron” is required in a consistent expansion in powers of the momentum transfer <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:mrow><h:mi>t</h:mi><h:mo>≈</h:mo><h:mo>−</h:mo><h:msubsup><h:mrow><h:mi mathvariant="bold">Δ</h:mi></h:mrow><h:mrow><h:mo>⊥</h:mo></h:mrow><h:mrow><h:mn>2</h:mn></h:mrow></h:msubsup></h:mrow></h:math> beyond first order. The spin-dependent Pomeron violates <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>s</k:mi></k:math>-channel helicity conservation at <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi mathvariant="script">O</m:mi><m:mo stretchy="false">(</m:mo><m:msubsup><m:mi mathvariant="normal">Δ</m:mi><m:mo>⊥</m:mo><m:mn>2</m:mn></m:msubsup><m:mo stretchy="false">)</m:mo></m:math>, and beyond. Expanding to leading twist only, it corresponds to generalized parton distributions <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:msub><s:mi>E</s:mi><s:mi>g</s:mi></s:msub><s:mo stretchy="false">(</s:mo><s:mi>x</s:mi><s:mo>,</s:mo><s:mi>t</s:mi><s:mo stretchy="false">)</s:mo></s:math> for vanishing skewness. We derive explicit expressions for the eikonal BFKL amplitudes, to all orders in dipole size times momentum transfer, for all helicity configurations of the particles in the initial and final states. We also provide numerical estimates of the helicity flip two gluon exchange amplitude at moderate <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:mi>x</w:mi></w:math> from a light cone quark model of the proton. The spin dependent BFKL Pomeron could, in principle, be discovered via double spin asymmetries in <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:mrow><y:mi>e</y:mi><y:mo>+</y:mo><y:mi>p</y:mi><y:mo stretchy="false">→</y:mo><y:mi>e</y:mi><y:mo>+</y:mo><y:mi>p</y:mi><y:mo>+</y:mo><y:mi>J</y:mi><y:mo>/</y:mo><y:mi>ψ</y:mi></y:mrow></y:math> with a transversely polarized proton and longitudinally polarized electron in the initial state.