Multipolar transitions excited by twisted photons in heavy quarkonia

Abstract In this study, we investigate the excitation of multipole transitions in quarkonium systems by high-energy photons carrying orbital angular momentum. We derive explicit expressions for the amplitude and probability of photoexcitation incorporating the dynamics of the quarkonium center of mass. It is shown that the leading contribution to the transitions induced by twisted photons comes from the multipole $$j=|m_\gamma |$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mrow> <mml:mi>j</mml:mi> <mml:mo>=</mml:mo> <mml:mo>|</mml:mo> </mml:mrow> <mml:msub> <mml:mi>m</mml:mi> <mml:mi>γ</mml:mi> </mml:msub> <mml:mrow> <mml:mo>|</mml:mo> </mml:mrow> </mml:mrow> </mml:math> and $$m_\gamma =l'-l$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>m</mml:mi> <mml:mi>γ</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:msup> <mml:mi>l</mml:mi> <mml:mo>′</mml:mo> </mml:msup> <mml:mo>-</mml:mo> <mml:mi>l</mml:mi> </mml:mrow> </mml:math> in the long-wave approximation. Despite the fact that similar transitions can be excited by plane-wave photons, twisted photons with $$|m_\gamma |&gt;1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mrow> <mml:mo>|</mml:mo> </mml:mrow> <mml:msub> <mml:mi>m</mml:mi> <mml:mi>γ</mml:mi> </mml:msub> <mml:mrow> <mml:mo>|</mml:mo> <mml:mo>&gt;</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:mrow> </mml:math> enable the isolation of higher multipoles offering a unique spectroscopic tool. The fulfillment of the derived selection rules imposes constraints on the parameters of the wave packet of the quarkonium center of mass, since, in general, the angular momentum can be transferred to the center of mass. As a case study, we examine the octupole transitions $$1^{3}G_3 \rightarrow 3^{3}P_0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mn>1</mml:mn> <mml:mn>3</mml:mn> </mml:msup> <mml:msub> <mml:mi>G</mml:mi> <mml:mn>3</mml:mn> </mml:msub> <mml:mo>→</mml:mo> <mml:msup> <mml:mn>3</mml:mn> <mml:mn>3</mml:mn> </mml:msup> <mml:msub> <mml:mi>P</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:mrow> </mml:math> and $$ 1^{3}F_3 \rightarrow 3^{3}S_1 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mn>1</mml:mn> <mml:mn>3</mml:mn> </mml:msup> <mml:msub> <mml:mi>F</mml:mi> <mml:mn>3</mml:mn> </mml:msub> <mml:mo>→</mml:mo> <mml:msup> <mml:mn>3</mml:mn> <mml:mn>3</mml:mn> </mml:msup> <mml:msub> <mml:mi>S</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:mrow> </mml:math> in the charmonium system. We also compare the probabilities of excitation of this multipole transition by plane-wave and twisted photons with different polarizations.