<p>The recent KLOE measurement <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math display="inline"> <msubsup> <mi>BR</mi> <mtext>KLOE</mtext> <mrow> <mi>η</mi> <mo>→</mo> <mi>π</mi> <mn>0</mn> <mi mathvariant="italic">γγ</mi> </mrow> </msubsup> <mo>=</mo> <mfenced close=")" open="("> <mrow> <mn>0.98</mn> <mo>±</mo> <mn>0</mn> <mo>.</mo> <msub> <mn>11</mn> <mtext>stat</mtext> </msub> <mo>±</mo> <mn>0</mn> <mo>.</mo> <msub> <mn>14</mn> <mtext>syst</mtext> </msub> </mrow> </mfenced> <mo>×</mo> <mn>1</mn> <msup> <mn>0</mn> <mrow> <mo>−</mo> <mn>4</mn> </mrow> </msup> </math></EquationSource> <EquationSource Format="TEX">\( {\textrm{BR}}_{\textrm{KLOE}}^{\eta \to \pi 0\gamma \gamma}=\left(0.98\pm 0.{11}_{\textrm{stat}}\pm 0.{14}_{\textrm{syst}}\right)\times 1{0}^{-4} \)</EquationSource> </InlineEquation> is less than half the current world average, (2<i>.</i>55 ± 0<i>.</i>22) × 10<sup><i>−</i>4</sup>, dominated by MAMI photoproduction data. We show that this ≈ 5<i>.</i>5 <i>σ</i> discrepancy can be resolved by the new leptophobic, nucleon-triggered vector particle <InlineEquation ID="IEq3"> <EquationSource Format="MATHML"><math display="inline"> <msub> <mi>V</mi> <mi mathvariant="script">B</mi> </msub> </math></EquationSource> <EquationSource Format="TEX">\( {V}_{\mathcal{B}} \)</EquationSource> </InlineEquation> with 1<i>.</i>5 GeV ≲ <InlineEquation ID="IEq4"> <EquationSource Format="MATHML"><math display="inline"> <msub> <mi>m</mi> <msub> <mi>V</mi> <mi mathvariant="script">B</mi> </msub> </msub> </math></EquationSource> <EquationSource Format="TEX">\( {m}_{V_{\mathcal{B}}} \)</EquationSource> </InlineEquation> ≲ 5 GeV, coupled via the effective operator <InlineEquation ID="IEq5"> <EquationSource Format="MATHML"><math display="inline"> <mfenced close=")" open="("> <mrow> <mover accent="true"> <mi>N</mi> <mo stretchy="true">¯</mo> </mover> <mi>N</mi> </mrow> </mfenced> <msubsup> <mover accent="true"> <mi>V</mi> <mo stretchy="true">~</mo> </mover> <mi mathvariant="script">B</mi> <mi mathvariant="italic">μν</mi> </msubsup> <msub> <mi>F</mi> <mi mathvariant="italic">μν</mi> </msub> <mi>P</mi> </math></EquationSource> <EquationSource Format="TEX">\( \left(\overline{N}N\right){\overset{\sim }{V}}_{\mathcal{B}}^{\mu \nu}{F}_{\mu \nu}P \)</EquationSource> </InlineEquation>. This interaction modifies the <i>η</i><sup>(</sup><i>′</i><sup>)</sup> → <i>π</i><sup>0</sup> (<i>η</i>)<i>γγ</i> decay rates <i>only</i> in the processes involving an external nucleon current, <i>γp</i> → <i>η</i><sup>(</sup><i>′</i><sup>)</sup><i>p</i> and <i>π</i><sup><i>−</i></sup><i>p</i> → <i>η</i><sup>(</sup><i>′</i><sup>)</sup><i>n</i>, but leaves purely leptonic production channels, such as <i>e</i><sup>+</sup><i>e</i><sup><i>−</i></sup> → <i>ϕ</i> → <i>η</i><sup>(</sup><i>′</i><sup>)</sup><i>γ</i> at KLOE and <i>e</i><sup>+</sup><i>e</i><sup><i>−</i></sup> → <i>J/ψ</i> → <i>γη</i><sup>(</sup><i>′</i><sup>)</sup> at BESIII, Standard-Model-like. The same mechanism predicts a ≈ 10% nucleon-triggered enhancement of the <i>η′</i> → <i>π</i><sup>0</sup><i>γγ</i> decay rate and a negligible shift for <i>η′</i> → <i>ηγγ</i>, together with an A<sup>2</sup>-scaling boost if produced on heavy nuclei instead of protons. <InlineEquation ID="IEq6"> <EquationSource Format="MATHML"><math display="inline"> <msub> <mi>V</mi> <mi mathvariant="script">B</mi> </msub> </math></EquationSource> <EquationSource Format="TEX">\( {V}_{\mathcal{B}} \)</EquationSource> </InlineEquation> can be searched directly in 2 → 3 photoproduction, for example, <InlineEquation ID="IEq7"> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="italic">γp</mi> <mo>→</mo> <msub> <mi>V</mi> <mi mathvariant="script">B</mi> </msub> <msup> <mi>π</mi> <mn>0</mn> </msup> <mi>p</mi> </math></EquationSource> <EquationSource Format="TEX">\( \gamma p\to {V}_{\mathcal{B}}{\pi}^0p \)</EquationSource> </InlineEquation>. An integrated experimental program that compares <i>η</i><sup>(</sup><i>′</i><sup>)</sup> → <i>π</i><sup>0</sup>(<i>η</i>)<i>γγ</i> in the presence of external nucleon currents with purely leptonic production, and conducts direct photoproduction searches for a GeV-scale vector, can decisively confirm or exclude our nucleon-rescaled, leptophobic-vector interpretation of the KLOE-MAMI discrepancy.</p>

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

  • Yaroslav Balytskyi

摘要

The recent KLOE measurement BR KLOE η π 0 γγ = 0.98 ± 0 . 11 stat ± 0 . 14 syst × 1 0 4 \( {\textrm{BR}}_{\textrm{KLOE}}^{\eta \to \pi 0\gamma \gamma}=\left(0.98\pm 0.{11}_{\textrm{stat}}\pm 0.{14}_{\textrm{syst}}\right)\times 1{0}^{-4} \) is less than half the current world average, (2.55 ± 0.22) × 104, 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 B \( {V}_{\mathcal{B}} \) with 1.5 GeV ≲ m V B \( {m}_{V_{\mathcal{B}}} \) ≲ 5 GeV, coupled via the effective operator N ¯ N V ~ B μν F μν P \( \left(\overline{N}N\right){\overset{\sim }{V}}_{\mathcal{B}}^{\mu \nu}{F}_{\mu \nu}P \) . This interaction modifies the η()π0 (η)γγ decay rates only in the processes involving an external nucleon current, γpη()p and πpη()n, but leaves purely leptonic production channels, such as e+eϕη()γ at KLOE and e+eJ/ψγη() at BESIII, Standard-Model-like. The same mechanism predicts a ≈ 10% nucleon-triggered enhancement of the η′π0γγ decay rate and a negligible shift for η′ηγγ, together with an A2-scaling boost if produced on heavy nuclei instead of protons. V B \( {V}_{\mathcal{B}} \) can be searched directly in 2 → 3 photoproduction, for example, γp V B π 0 p \( \gamma p\to {V}_{\mathcal{B}}{\pi}^0p \) . An integrated experimental program that compares η()π0(η)γγ in the presence of external nucleon currents with purely leptonic production, and conducts direct photoproduction searches for a GeV-scale vector, can decisively confirm or exclude our nucleon-rescaled, leptophobic-vector interpretation of the KLOE-MAMI discrepancy.