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\documentclass{cimento}

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\usepackage{graphicx}  % got figures? uncomment this
\usepackage[dvipsnames]{xcolor}

\title{Investigating the dark sector with the PADME experiment}
\author{P.~Gianotti\from{ins:x}\\
%        \atque
For the PADME Collaboration\thanks{S. Bertelli, F. Bossi, R. De Sangro, C. Di Giulio, E. Di Meco, D. Domenici, G. Finocchiaro, L.G. Foggetta, M. Garattini, P. Gianotti, M. Mancini, I. Sarra, T. Spadaro, E. Spiriti, C. Taruggi, E. Vilucchi {\it INFN Laboratori Nazionali di Frascati, Italy}, V. Kozhuharov, K. Dimitrova, G. Georgiev, S. Ivanov, Sv. Ivanov, R. Simeonov {\it Sofia University, Bulgaria}, F. Ferrarotto, E. Leonardi, E. Long, G.C. Organtini, G. Piperno, M. Raggi, P. Valente, A. Variola {\it INFN Sez. di Roma and Sapienza University Roma, Italy}, A. Frankenthal {\it Princeton University, USA}, I. Oceano {\it presently DESY Hamburg, Germany}, F. Oliva {\it presently Edingburgh University, UK}. }}
\instlist{\inst{ins:x} INFN, Laboratori Nazionali di Frascati - Frascati, Italy}
%  \inst{ins:y} Dipartimento di Fisica, Universit\`a di Roma - Roma, Italy}
%% When only one author is present, please do not use the command \from{} near the author name.





\begin{document}

\maketitle

\begin{abstract}

In the attempt of justifying some unexplained physics phenomena like dark matter nature or the (g-2)$_\mu$ anomaly, the existence of new light particles with a wide range of properties has been postulated by several theoretical extensions of the Standard Model.  Among the others, a light particle of mass $\sim$ 17 MeV (named X17) decaying in $e^+ e^-$ has been put forward to explain an anomaly observed since 2016 in a series of nuclear physics studies performed by an ATOMKI group of Debrecem in Hungary. If confirmed, this new state will represent a real breakthrough in the search of physics phenomena beyond the Standard Model.

The PADME experiment at the Laboratori Nazionali di Frascati of INFN, searching for a dark photon and/or other dark sector candidates among the annihilation products of a beam of positrons on the electrons of a fixed target, has the unique opportunity to confirm/disprove the particle nature of such an anomaly. In the second half of 2022, the collaboration performed a data taking campaign centered at $\sqrt{s} \sim$ 17 MeV in order to produce on-shell the X17. The collected data are under analysis and this paper presents an overview of the PADME results and perspectives.
\end{abstract}

\section{Introduction}
The nuclear physics group of the ATOMKI institute of Debrecem in Hungary, while studying the de-excitation of several highly energetic states of $^8$Be, $^4$He and $^{12}$C nuclei via Internal Pair Creation (IPC), observed an anomaly in the opening angle and invariant mass distributions of the final state $e^+e^-$ pairs \cite{ref:1,ref:2,ref:3}.
A possible explanation of this effect is the creation, and subsequent decay, of a particle of mass approximately 17 MeV which has been named X17.
Within the particle physics community, a wide debate is ongoing. Many theoretical interpretation of the X17 in terms of a new scalar or vector state have been put forward, and possibly unaccounted Standard Model (SM) effects have been investigated \cite{ref:th1,ref:th2}. On the experimental side, searches have been proposed and/or are taking data with the goal of independently investigate this anomaly. Among the others, the Positron Annihilation into Dark Matter Experiment (PADME) ongoing at the Frascati National Laboratory (LNF) of the Italian Institute for Nuclear Physics (INFN). In the following sections the experimental setup and the scientific program of this initiative are described.

\section{The PADME experiment}
The scientific program of PADME regards the study of dark matter at accelerators. The main goal of the experiment is to search for a dark photons $A'$ produced in the annihilation of a positron beam with the electrons at rest of a 100 $\mu$m thick active diamond target \cite{ref:padme}. The reaction under study is $e^+ e^- \rightarrow A' \gamma$, with the $A'$ undetected. Therefore, events with a single photon and nothing else in the setup (see fig.\ref{fig1}) have to be selected. Knowing the energy of the incoming positron and measuring the recoil
photon 4-momentum, the missing mass can be computed. In case an $A'$ is produced, a pick at its mass value will appear above the SM background. 
\begin{figure}[h]
\begin{center}
\includegraphics[width=0.7\textwidth]{LayoutMio.png}     
\caption{Layout of the PADME setup. The main detector components are schematically shown (see text for details). In the picture are also drawn the possible trajectories for a $\gamma \gamma$/$\gamma A'$ event (in yellow), for a Bremsstrahlung event (in red), and the path for not interacting positrons (in black).}
\label{fig1}
\end{center}
\end{figure}

Actually, the PADME approach can be sensitive to several other dark matter candidates like Axion-Like-Particles, dark Higgs and eventually the X17 that can be produced resonantly and then detected via its decay in a $e^+ e^-$ pair~\cite{ref:5}.

The PADME detector is sketched in fig. \ref{fig1}. The setup has to detect the products of the interaction of the positron beam with the active diamond target able to count the incoming positrons and to reconstruct their interaction point with a precision below 1 mm both in x and y directions. The charged particles are detected and vetoed by 3 modules of scintillator sticks. Two are installed in vacuum along the opposite sides of a dipole magnet that has the double function of deflecting toward the beam dump the positrons that have not interacted, and to allow the determination of $e^+$ and $e^-$ momenta. The third one is located out of the main vacuum chamber to detect highest energy positrons.
Photons are detected by means of a calorimetric system. This later is composed by two modules: ECAL, a cylindrical array of 616 BGO crystals (energy resolution better than 3\%) arranged with a central hole, and a small angle PbF$_2$ array (SAC) placed exactly behind ECAL hole. This arrangement is necessary to avoid that Bremsstrahlung photons, that are copiously emitted in the forward direction, would blind the main calorimeter whose response time is not fast enough to stand their rate ($\sim$ 40 MHz). On the contrary, the 25 PbF$_2$ crystals, readout by fast PMTs, are perfectly suited to veto these photons in combination with the $e^+$ veto. The setup is completed by a solid state pixel detector, placed on the beam exit, to further improve the experiment beam monitor capability. 

The PADME collaboration had two data taking periods in Winter 2019 and 2020 (Run I and Run II) during which similar statistics were collected ($\sim 5 \times  10^{12} $ Positron on Target - PoT) at 490 and 430 MeV beam energies, respectively. In between these two data collections, major improvements on the beam quality and its transport line were realized to reduce the background the beam induces in the apparatus~\cite{ref:MC}.
Figure \ref{fig2} (Left) shows the energy of two photons final states measured by ECAL in 3 different run conditions (details are in the figure caption). The reduction of the background from Run I to Run II is evident.
\begin{figure}[h]
\begin{center}
\includegraphics[width=0.45\textwidth]{2Photons.png}     
\includegraphics[width=0.4\textwidth]{DataRooFitEffTrendMeasurement_PadmeBiggerSize.png}     
\caption{{\bf Left.} Sum of energies of photon pairs in PADME ECal in three beamline configurations
between Run I and Run II: \\
-- \textcolor{blue}{Blue}, secondary beam; energy 545 MeV; intensity 25k positrons/bunch; bunch length 250 ns; \\
-- \textcolor{red}{Red}, primary beam; energy 490 MeV; intensity 25k positrons/bunch; bunch length 250 ns; \\
-- \textcolor{Green}{Green}, primary beam; energy 430 MeV; intensity 28k positrons/bunch; bunch length 280 ns.\\
{\bf Right.} Theoretical predictions, at the leading order and next-to-leading order approximation for the cross-section  $\sigma(e^+ e^- \rightarrow \gamma \gamma$) a function of the positron energy. The PADME measurement is superimposed along with earlier measurements. Data to theory ratios are shown in the bottom pad~\cite{ref:cs}.}
\label{fig2}
\end{center}
\end{figure}

A subset of Run II data were used to perform the most precise measurement of the cross-section $\sigma(e^+ e^- \rightarrow \gamma \gamma(\gamma))$ below 1 GeV to date [see fig.~\ref{fig2} (Right)]. This measurement represents an important milestone for the collaboration for several reasons: first, this cross-section  is linearly correlated to the cross-section of associate production of a dark photon, and therefore it is the natural step to define a solid ground for the single photon analysis; second, this is the first measurement at beam energies below 500 MeV with precision better than 20\%, and the only one in this energy range detecting the two final state photons. Thanks to this last point, the measurement can be used to fix limits for new physics contributions to SM. 

\section{Resonant production of X17}
\begin{figure}[t]
\begin{center}
\includegraphics[width=0.8\textwidth]{PADMEScan.png}     
\caption{Number of positrons on target collected by PADME in Run III as a function of the center of mass energy (positron beam momentum is also indicated). The vertical light-blue line indicates the best fit to the mass of X17 performed using all the ATOMKI data (from ref.~\cite{ref:arxiv}).}
\label{fig3}
\end{center}
\end{figure}
As mentioned in the Introduction, if the ``ATOMKI anomaly'' is due by a new particle, PADME is in the ideal position to contribute understanding its nature. In fact, LNF is the only laboratory in the world owing a positron beam that can be tuned to produce resonantly the X17. The experimental technique, extensively described in ref \cite{ref:5}, consists  in studying the process $e^+ e^- \rightarrow X17 \rightarrow e^+ e^- $ varying the beam energy in the interval [265 -- 297] MeV, corresponding to a scan in the c.m. energy range [16.46 -- 17.42] MeV. The X17 signal should appear as a bump above the SM background in the distribution of the measured number of $e^+ e^- $ pairs.



\begin{figure}[h]
\begin{center}
\includegraphics[width=0.45\textwidth]{limitiVector.jpg}     
\includegraphics[width=0.45\textwidth]{limitiAxial.jpg}
\caption{Expected sensitivities of PADME Run III on the coupling of a X17 vector boson ({\bf Left}) and pseudo-scalar ({\bf Right}) for 2 different values of beam energy spread (orange lines). Regions already excluded by other experiments are also shown (from ref.\cite{ref:5}).}
\label{fig4}
\end{center}
\end{figure}

In the second half of 2022, the PADME collaboration performed a data taking (Run III) to conduct the above mentioned set of measurements.
For each of the 47 different energy values, 10$^{10}$ PoT were collected, 5 of them below the resonance value and 1 above, as shown in fig.~\ref{fig3}. The off-resonance points serve to validate the analysis strategy before unblinding the signal region. The expected limits at PADME, given the statistics accumulated, are shown in fig.~\ref{fig4}.

\section{Conclusions}
The PADME experiment is sensitive to any new particle produced in $e^+ e^-$ collisions in the tens of MeV energy scale: dark photons, low mass dark Higgs, leptonic gauge bosons. This peculiarity turned out to be ideal to investigate the particle interpretation (X17) put forward to explain the nature of an anomaly observed in the study of several nuclei excited states. A dedicated data taking to produce resonantly the X17 has been conducted in the second half of 2022 and currently the data analysis is ongoing.

%\acknowledgments
%The author acknowledge XXX, YYY.

\begin{thebibliography}{0}
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%\bibitem{ref:apo} \BY{Einstein A. \atque Fermi E.}
 % \IN{Phys. Rev. A}{13}{1999}{12};
%  \SAME{69}{999}{1666}.
%\bibitem{ref:pul} \BY{Newton I.}
%  preprint INFN 8181.
%\bibitem{ref:bra} \BY{Bragg~B.}
%  \TITLE{Complete Works}, in \TITLE{Workers Playtime}, edited by \NAME{Tizio A. \atque Caio B.} (Unexeditor, Bologna) 1997, pp.~1-10.

\end{thebibliography}

\end{document}
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