Production-dependent interpretation of the KLOE-MAMI η → π0γγ tension via the nucleon-triggered leptophobic vector $$ {V}_{\mathcal{B}} $$

A bstract The recent KLOE measurement $$ {\textrm{BR}}_{\textrm{KLOE}}^{\eta \to \pi 0\gamma \gamma}=\left(0.98\pm 0.{11}_{\textrm{stat}}\pm 0.{14}_{\textrm{syst}}\right)\times 1{0}^{-4} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>BR</mml:mi> <mml:mtext>KLOE</mml:mtext> <mml:mrow> <mml:mi>η</mml:mi> <mml:mo>→</mml:mo> <mml:mi>π</mml:mi> <mml:mn>0</mml:mn> <mml:mi>γγ</mml:mi> </mml:mrow> </mml:msubsup> <mml:mo>=</mml:mo> <mml:mfenced> <mml:mrow> <mml:mn>0.98</mml:mn> <mml:mo>±</mml:mo> <mml:mn>0</mml:mn> <mml:mo>.</mml:mo> <mml:msub> <mml:mn>11</mml:mn> <mml:mtext>stat</mml:mtext> </mml:msub> <mml:mo>±</mml:mo> <mml:mn>0</mml:mn> <mml:mo>.</mml:mo> <mml:msub> <mml:mn>14</mml:mn> <mml:mtext>syst</mml:mtext> </mml:msub> </mml:mrow> </mml:mfenced> <mml:mo>×</mml:mo> <mml:mn>1</mml:mn> <mml:msup> <mml:mn>0</mml:mn> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> </mml:msup> </mml:math> is less than half the current world average, (2 . 55 ± 0 . 22) × 10 − 4 , dominated by MAMI photoproduction data. We show that this ≈ 5 . 5 σ discrepancy can be resolved by the new leptophobic, nucleon-triggered vector particle $$ {V}_{\mathcal{B}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>V</mml:mi> <mml:mi>B</mml:mi> </mml:msub> </mml:math> with 1 . 5 GeV ≲ $$ {m}_{V_{\mathcal{B}}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>m</mml:mi> <mml:msub> <mml:mi>V</mml:mi> <mml:mi>B</mml:mi> </mml:msub> </mml:msub> </mml:math> ≲ 5 GeV, coupled via the effective operator $$ \left(\overline{N}N\right){\overset{\sim }{V}}_{\mathcal{B}}^{\mu \nu}{F}_{\mu \nu}P $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mfenced> <mml:mrow> <mml:mover> <mml:mi>N</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mi>N</mml:mi> </mml:mrow> </mml:mfenced> <mml:msubsup> <mml:mover> <mml:mi>V</mml:mi> <mml:mo>~</mml:mo> </mml:mover> <mml:mi>B</mml:mi> <mml:mi>μν</mml:mi> </mml:msubsup> <mml:msub> <mml:mi>F</mml:mi> <mml:mi>μν</mml:mi> </mml:msub> <mml:mi>P</mml:mi> </mml:math> . This interaction modifies the η ( ′ ) → π 0 ( η ) γγ decay rates only in the processes involving an external nucleon current, γp → η ( ′ ) p and π − p → η ( ′ ) n , but leaves purely leptonic production channels, such as e + e − → ϕ → η ( ′ ) γ at KLOE and e + e − → J/ψ → γη ( ′ ) at BESIII, Standard-Model-like. The same mechanism predicts a ≈ 10% nucleon-triggered enhancement of the η′ → π 0 γγ decay rate and a negligible shift for η′ → ηγγ , together with an A 2 -scaling boost if produced on heavy nuclei instead of protons. $$ {V}_{\mathcal{B}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>V</mml:mi> <mml:mi>B</mml:mi> </mml:msub> </mml:math> can be searched directly in 2 → 3 photoproduction, for example,