Tests for gluonium or other non- $q \bar{q}$ admixtures in the $f (1270)$

SU(3) and SU(6) suggest

Γ (f \to π π) = 112 - 115

MeV for a quark-antiquark state, while the observed value is 148±17 MeV. This small discrepancy permits a non-

q \bar{q}

admixture ("

gg

") in the

f : | f 〉 = cos θ | q \bar{q} 〉 + sin θ | g g 〉

. We examine the possibility that the orthogonal state

f^{⊥} = - sin θ | q \bar{q} 〉 + cos θ | g g 〉

decouples from

π π

, and find

{sin}^{2} θ = {0.15}_{- 0.06}^{+ 0.05}

. Consequences include a diminished predicted rate for

f \to γ γ

, in qualitative accord with experiment; a mass formula

f^{⊥} - A_{2} = {cot}^{2} θ (A_{2} - f)

yielding

f^{⊥}

in the range 1.45-1.87

{G e V / c}^{2}

; and predictions for

f^{(⊥)}

spectra as produced in

γ γ \to f^{(⊥)}

\frac{J}{ψ} \to f^{(⊥)} + γ

and detected in

f \to K \bar{K}, ρ γ, or γ γ

. The width of

f^{⊥}

is estimated to be no more than 40 MeV under these assumptions.

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Tests for gluonium or other non-qq¯admixtures in thef(1270)