Measurement of the tau -> 3pi eta nu Branching Fraction and a Search for a Second-Class Current in the tau -> eta'(958) pi nu Decay

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The Novosibirsk function is defined as f ⁡ ( m ) = A ​ exp ​ ( − 0.5 ​ { ln 2 ​ [ 1 + Λ ​ τ ⋅ ( m − m 0 ) ] / τ 2 + τ 2 } ) f(m)=A\;{\rm exp}(-0.5\left\{{\rm ln}^{2}\left[1+\mathchar 28931\relax\tau\cdot(m-m_{0})\right]/\tau^{2}+\tau^{2}\right\}) , where Λ = sinh ⁡ ( τ ​ ln ​ 4 ) / ( σ ​ τ ​ ln ​ 4 ) \mathchar 28931\relax=\sinh(\tau\sqrt{{\rm ln}4})/(\sigma\tau\sqrt{{\rm ln}4}) , the peak position is m 0 m_{0} , the width is σ \sigma and τ \tau is the tail parameter

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The functional form of the P-wave Breit-Wigner function is identical to the nominal Breit-Wigner function except that the width Γ f 1 \Gamma_{f_{1}} is modified by a ( p ⁡ ( x ) / p ⁡ ( 0 ) ) 3 (p(x)/p(0))^{3} factor. The momentum terms p ⁡ ( x ) p(x) and p ⁡ ( 0 ) p(0) are the momenta of the outgoing particles in a two-body decay ( f 1 → π − ​ a 0 + ​ ( 980 ) f_{1}\rightarrow\pi^{-}a_{0}^{+}(980) ) evaluated at the current ( x x ) and peak ( m f 1 m_{f_{1}} ) mass values

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