= Solution
\b[The conversion from a measured beam peak to a <particle resonance> <mass> is fixed, but the missing graph supplies neither the peak position nor its width.] Let $T_R$ be the incoming <pion> <kinetic energy> at the peak and $\Delta T$ the <full width at half maximum> after allowing for instrumental resolution. With a stationary <proton> and <natural units>,
$$
s=m_p^2+m_\pi^2+2m_p(m_\pi+T)
=(m_p+m_\pi)^2+2m_pT.
$$
Thus the peak <invariant mass> is
$$
\boxed{M=\sqrt{(m_p+m_\pi)^2+2m_pT_R}.}
$$
The width must also be transformed to the <centre-of-mass frame>. To first order about the peak,
$$
\frac{d\sqrt{s}}{dT}=\frac{m_p}{\sqrt{s}},\qquad
\boxed{\Gamma\simeq\frac{m_p}{M}\Delta T,\qquad
\tau=\frac{\hbar}{\Gamma}.}
$$
For a broad feature, transform the two half-height positions separately: if they are $T_-$ and $T_+$, then the corresponding width in <invariant mass> is $\sqrt{(m_p+m_\pi)^2+2m_pT_+}-\sqrt{(m_p+m_\pi)^2+2m_pT_-}$. An energy-dependent numerator or width can also displace the observed maximum from the <resonance pole> parameter.
The low-<energy> $\pi^+p$ channel is normally dominated by $\Delta^{++}(1232)$, a <Delta baryon> with $Q=2$, $B=1$ and $I=3/2$. As an \b[external reference example, not a reading of the absent plot], $M=1232\,\mathrm{MeV}$ and $\Gamma=117\,\mathrm{MeV}$ give $T_R\simeq190\,\mathrm{MeV}$, $\Delta T\simeq154\,\mathrm{MeV}$ and $\tau\simeq5.63\times10^{-24}\,\mathrm s$.<Delta(1232) particle listing by Particle Data Group>[Breit-Wigner mass near 1232 MeV and width near 117 MeV; these are external comparison values]{ref} The actual graphical estimates remain unavailable. In particular, using the laboratory width directly in $\tau=\hbar/\Delta T$ misses the factor $m_p/M$.
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