Observation of ${\pi }^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}$ photoproduction in ultraperipheral heavy-ion collisions at $\sqrt{s_{\mathit{NN}}}=200$ GeV at the STAR detector

We present a measurement of ${\pi }^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}$ photonuclear production in ultraperipheral $\mathrm{Au}-\mathrm{Au}$ collisions at $\sqrt{s_{{}_{NN}}}=200$ GeV from the STAR experiment. The ${\pi }^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}$ final states are observed at low transverse momentum and are accompanied by mutual nuclear excitation of the beam particles. The strong enhancement of the production cross section at low transverse momentum is consistent with coherent photoproduction. The ${\pi }^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}$ invariant mass spectrum of the coherent events exhibits a broad peak around $1540\pm 40$ $\mathrm{MeV}/c^2$ with a width of $570\pm 60$ $\mathrm{MeV}/c^2$, in agreement with the photoproduction data for the ${\rho }^0(1700)$. We do not observe a corresponding peak in the ${\pi }^{+}{\pi }^{-}$ final state and measure an upper limit for the ratio of the branching fractions of the ${\rho }^0(1700)$ to ${\pi }^{+}{\pi }^{-}$ and ${\pi }^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}$ of $2.5\%$ at $90\%$ confidence level. The ratio of ${\rho }^0(1700)$ and ${\rho }^0(770)$ coherent production cross sections is measured to be $13.4\pm {0.8}_{\mathrm{stat}.}\pm {4.4}_{\mathrm{syst}.}\%$.

Figure 1

Schematic view of the photonuclear production of a vector meson $V$ in an ultraperipheral $\mathrm{Au}-\mathrm{Au}$ collision and its subsequent decay into four charged pions. The meson production in the fusion processes of photon ${\gamma }^{*}$ and Pomeron $\mathbb{P}$ is accompanied by mutual Coulomb excitation of the beam ions. The processes are independent, as indicated by the dotted line.

Figure 2

Distribution of the ${\pi }^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}$ transverse momentum $p_T=\left|{\sum }_{i=1}^4{\mathrm{p⃗}}_{T,i}\right|$. The solid circles are the measured points with the statistical errors. The hatched histogram shows the expected distribution from simulation of coherent photoproduction (cf. Sec. 3). The strong enhancement at low transverse momenta is attributable to coherently produced ${\pi }^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}$. This unique signature is used in the event selection, which requires $p_T<150$ $\mathrm{MeV}/c$ (arrow). The remaining background is estimated from $+2$- or $-2$-charged four-prong combinations, by normalizing ($\mathrm{factor}=1.186\pm 0.054$) their $p_T$ distribution (gray histogram) to that of the neutral four prongs in the region of $p_T>250$ $\mathrm{MeV}/c$ (vertical line), yielding the open histogram (see section 4).

Figure 3

Invariant mass distribution of two-pion subsystems. The solid circles show the measured ${\pi }^{+}{\pi }^{-}$ invariant mass spectrum for the selected four-prong sample (four entries per event) with statistical errors. The open circles represent the mass spectrum of the like-sign pion pairs (two entries per event). The unlike-sign mass distribution exhibits an enhancement with respect to the like-sign pairs in the ${\rho }^0(770)$ region. The histograms show the prediction from simulation assuming the relative $S$-wave decay ${\rho }^{\prime }\to {\rho }^0(770)\hspace{0.5em}{f}_0(600)$.

Figure 4

Invariant mass distribution of two-pion subsystems. The open circles show the measured invariant mass spectrum of the lightest ${\pi }^{+}{\pi }^{-}$ pair in the event with the bars indicating the statistical errors. The filled circles represent the invariant mass distribution of the ${\pi }^{+}{\pi }^{-}$ that is recoiling against the lightest pair. The spectrum exhibits a clear peak in the ${\rho }^0(770)$ region. The histograms show the prediction from simulation assuming the relative $S$-wave decay ${\rho }^{\prime }\to {\rho }^0(770)\hspace{0.5em}{f}_0(600)$.

Figure 5

Invariant mass distribution of coherently produced ${\pi }^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}$. The filled circles are the measured points with the statistical errors, the gray histogram is the background estimated from charged four prongs (cf. Fig. 2). The thick black line shows the fit of a modified $S$-wave Breit-Wigner on top of a second-order polynomial background [thin black line; cf. Eq. (5)], taking into account the detector acceptance in the region $\left|y\right|<1$ (rising dashed line). The dotted curve represents the signal curve without background.

Figure 6

Invariant mass distribution of coherently produced ${\pi }^{+}{\pi }^{-}$ pairs. The solid circles are the measured points with statistical errors. The thick black line shows the fit taking into account the detector acceptance in the region $\left|y\right|<1$. The noninterfering combinatorial background is represented by the thin black line, which is a fit to the like-sign invariant mass distribution scaled by a factor estimated from the $p_T$ distribution (gray histogram). The dotted curve shows the Breit-Wigner without background; the dashed line shows the interfering background component that is assumed to be mass-independent. The dash-dotted curve is the Söding interference term of the two [31].

Figure 7

High-mass region of the $m_{{\pi }^{+}{\pi }^{-}}$ spectrum with tighter cuts applied to suppress background. The filled circles are the measured values with statistical errors. No significant enhancement is seen in the region around 1540 $\mathrm{MeV}/c^2$, where the ${\pi }^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}$ invariant mass spectrum exhibits a peak. The thick solid line shows the fit of a modified $S$-wave Breit-Wigner [cf. Eq. (5)] with parameters fixed to the values extracted from the fit of the ${\pi }^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}$ invariant mass distribution on top of an $S$-wave Breit-Wigner that describes the tail of the ${\rho }^0(770)$ (thin solid line), taking into account the detector acceptance. The dashed curve represents the signal curve without the ${\rho }^0$ tail.