The modern era of light kaonic atom experiments

This review covers the modern era of experimental kaonic atom studies, encompassing 20 years of activity, defined by breakthroughs in technological developments which allowed performing a series of long-awaited precision measurements. Kaonic atoms are atomic systems where an electron is replaced by a negatively charged kaon, containing the strange quark, which interacts in the lowest orbits with the nucleus also by the strong interaction. As a result, their study offers the unique opportunity to perform experiments equivalent to scattering at vanishing relative energy. This allows one to study the strong interaction between the antikaon and the nucleon or the nucleus “at threshold,” namely, at zero relative energy, without the need of ad hoc extrapolation to zero energy, as in scattering experiments. The fast progress achieved in performing precision light kaonic atom experiments, which also solved long-pending inconsistencies with theoretical calculations generated by old measurements, relies on the development of novel cryogenic targets, x-ray detectors, and the availability of pure and intense charged kaon beams, which propelled an unprecedented progress in the field. Future experiments, based on new undergoing technological developments, will further boost the kaonic atom studies, thus fostering a deeper understanding of the low-energy strong interaction extended to the second family of quarks.

Figure 1

Density dependence of $K^{-}p$ atom x-ray yields. In this work the shift and width were taken to be ${ϵ}_{1s}=300\mathrm{eV}$, ${\mathrm{\Gamma }}_{1s}=550\mathrm{eV}$, and ${\mathrm{\Gamma }}_{2p}=1\mathrm{meV}$. ${\rho }_{\mathrm{STP}}$ denotes the density at the standard temperature and pressure. The liquid hydrogen density (LHD) corresponds to $\sim 790$ ${\rho }_{\mathrm{STP}}$. The gas target density used in the KpX experiment, the first experiment to employ a cryogenic gaseous target, was $\sim 10$ ${\rho }_{\mathrm{STP}}$ (1.3% LHD). In the SIDDHARTA experiment ([11]) a gas target density of $\sim 14.5$ ${\rho }_{\mathrm{STP}}$ (1.8% LHD) was used. Adapted from [90].

Figure 2

Cascade processes for kaonic hydrogen, starting when the kaon is captured in a highly excited state, down to the $1s$ ground state, which is shifted due to strong interaction and broadened due to nuclear absorption of the kaon by the proton. The shift and width of the $2p$ state due to strong interaction are negligible.

Figure 3

DAΦNE accelerator complex layout. Adapted from [120].

Figure 4

J-PARC accelerator layout, showing the existing facilities in red and the proposed upgrades in blue. Adapted from [108].

Figure 5

Configuration of the K1.8BR beam line in the Hadron Hall of J-PARC. Adapted from [1].

Figure 6

Schematic view of the beam line spectrometer. The setup consists of a beam line spectrometer, a cylindrical spectrometer system (CDS), trigger counters (BHD and T0), beam line chambers (BLC1 and BLC2), and a kaon identification counter (AC). The beam line magnets, composed of an SQDQD system, consist of beam sweeping dipole magnets (D4 and D5), quadrupole magnets (Q7 and Q8), and a sextupole magnet (S3). Adapted from [1].

Figure 7

(Left) The structure of a CCD. (Right) A sketch showing how the charge below a pixel is transferred.

Figure 8

(Left) Particle interactions and charge collection in a CCD detector. (Right) An example of an x-ray signal (inside the circle) in a CCD picture exposed during a data-taking run.

Figure 9

SDD structure with implanted JFET (S = source, G = gate, D = drain) and reset mechanism via a clear contact. Adapted from [91].

Figure 10

Subdetector unit with two SDD chips, each with three individual cells, used in the SIDDHARTA experiment.

Figure 11

Layout of the new $2\times 4$ SDD array: (left) SDD chip mounted on a ceramic carrier and aluminum cooling block, with indication of the pixel structure; (center) backside of the ceramic carrier with eight holes to allow for bonding connections of each anode to the CUBE amplifier; (right) amplified bonding layout for one anode CUBE arrangement.

Figure 12

The three kaonic-hydrogen x-ray transition measurements carried out at CERN and the Rutherford Laboratory, in the late 1970s through the early 1980s. In these measurements a liquid hydrogen target was used.

Figure 13

The major components of the KpX experimental apparatus. A beam of negatively charged kaons of $600\mathrm{MeV}/c$ was utilized from the KEK 12 GeV-PS at the K3 beam line, the momenta degraded by a carbon block, after which they were injected into the hydrogen target. Kaons were identified by three lucite Čerenkov (LCs) counters sandwiched with the beam defining counters $B2$ and $B3$. Two charged pions emitted from the $K^{-}p$ reaction were tracked by two cylindrical MWPCs $C1$ and $C2$ and triggered by the cylindrical hodoscope counters $T1$ and $T2$. The contaminating $e^{\pm }$ tracks were rejected by outermost water Čerenkov counters. To achieve a maximum solid angle for x rays, 60 Si(Li) crystals were directly exposed to the gaseous hydrogen target, whose density was $\rho \sim 10{\rho }_{\mathrm{STP}}$. From [81].

Figure 14

The x-ray spectrum obtained by the KpX experiment. The inset is a close-up spectrum of the region of interest, together with the fit result. From [82].

Figure 15

The shift and width obtained by the KpX experiment are compared with the results of three previous measurements ([36]; [83]; [24]) and with some of the analyses of the low-energy $\overline{K}N$ scattering data ([88]; [107]; [93]). The DEAR result ([20]) is also reported.

Figure 16

Schematic view of the DEAR experimental setup; only the right outer lead wall shielding is shown.

Figure 17

The measured kaonic-hydrogen x-ray spectrum in the DEAR experiment. The kaonic-hydrogen transitions (indicated by boxes) and the electronic excitations coming from setup materials are visible. The fit functions (total and components) are shown. Upper-right inset: zoom of the kaonic-hydrogen $K_{\alpha }$ transition region with the continuous background; the iron $K_{\alpha }$ and the kaonic-hydrogen $K_{\alpha }$ lines are disentangled. Lower-left inset: zoom of the silicon peak region with the aluminum, silicon, and calcium escape peaks. From [20].

Figure 18

The DEAR kaonic-hydrogen x-ray spectrum after continuous and structured background subtraction: (a) results of analysis I; (b) results of analysis II. The fitting curves of the various kaonic-hydrogen lines are shown. From [20].

Figure 19

Energy spectrum of kaonic nitrogen. The arrows show the positions of the kaonic nitrogen x-ray lines: the $7\to 6$ transition at 4.6 keV, the $6\to 5$ transition at 7.6 keV, and the $5\to 4$ transition at 14.0 keV. The peaks at 1.4, 1.7, 3.6, 4.5, 4.9, 11.5, 14.2, and 15.7 keV are the $\mathrm{Al}\text{−}{K}_{\alpha }$, $\mathrm{Si}\text{−}{K}_{\alpha }$, $\mathrm{Ca}\text{−}{K}_{\alpha }$, $\mathrm{Ti}\text{−}{K}_{\alpha }$, $\mathrm{Ti}\text{−}{K}_{\beta }$, Au (L complex), $\mathrm{Sr}\text{−}{K}_{\alpha }$, and $\mathrm{Zr}\text{−}{K}_{\alpha }$ lines, respectively. In the inset, the fit of the $6\to 5$ (at 7.6 keV) transition is reported. From [79].

Figure 20

Fit of the (a) ($K^{-}\mathrm{N}$) $7\to 6$ (at 4.6 keV) and the (b) ($K^{-}\mathrm{N}$) $5\to 4$ (at 14.0 keV) kaonic nitrogen transitions. The kaonic peaks and the fluorescence lines of titanium and strontium are clearly separated. From [79].

Figure 21

Schematic drawing of the E570 experimental setup. The $z$ axis is the beam direction, the $x$ axis is the horizontal axis (the left of the beam view is positive), and the $y$ axis is the vertical one (the top is positive). The $650\text{−}\mathrm{MeV}/c$ negatively charged kaon beam is degraded by carbon layers and stopped in a superfluid liquid helium-4 target. Characteristic x rays generated from a kaonic-helium atom are measured by SDDs installed downstream of the target. LC: Lucite Cerenkov counter. $T1$ and $T0$: scintillation counters. BLC: beam line drift chamber. VDC: vertex drift chamber. PDC: proton drift chamber. TC: scintillation counter for the VDC. PA and PB: scintillation counters for the PDC.

Figure 22

Closeup of the E570 experimental setup (see the Fig. 21 caption).

Figure 23

The SDD kaonic helium-4 spectra (top) without and (bottom) with stopped $K^{-}$-triggered events. From [99].

Figure 24

Schematic view of the SIDDHARTA setup. From [11].

Figure 25

Timing spectrum of a SDD. The spectrum is referred to as a dataset with target filled with helium-3. The peak corresponds to the time difference between the coincidence of the two scintillators of the kaon monitor and the x-ray events in the SDDs (triple coincidence). The peak region contains the kaon induced signals and background. The time window indicated by arrows was selected to identify synchronous events with charged kaons. The continuous asynchronous background was reduced by this timing cut. From [13].

Figure 26

Kaon identification using the timing of the coincidence signals in the kaon detector with respect to the rf signal of 368.7 MHz from DAΦNE. From [11].

Figure 27

The global simultaneous fit of the x-ray energy spectra of hydrogen and deuterium data. (a) Residuals of the measured kaonic-hydrogen x-ray spectrum after subtraction of the fitted background, clearly displaying the kaonic-hydrogen $K$-series transitions. The fit components of the $K^{-}p$ transitions are also shown, where the sum of the functions is drawn for the higher transitions (greater than $K_{\beta }$). (b), (c) Measured energy spectra with the fit lines. Fit components of the background x-ray lines and a continuous background are also shown. The dot-dashed vertical line indicates the e.m. value of the kaonic-hydrogen $K_{\alpha }$ energy. From [11].

Figure 28

Comparison of the experimental results for the strong-interaction $1s$ energy level shift and width of kaonic hydrogen: KEK-PS KpX ([82]), DEAR ([20]), and SIDDHARTA ([11]). The error bars correspond to quadratically added statistical and systematic errors.

Figure 29

X-ray energy spectra of the SDDs, where data of all the selected SDDs were summed: (a) data taken with the x-ray tube in the calibration runs, and (b) data uncorrelated to the kaon triggers in the production runs. The peak positions of the titanium, copper, and gold fluorescence x-ray lines in (b) were used to determine the uncertainty on the energy calibration and the energy dependence of the energy resolution. From [13].

Figure 30

The shift in the x-ray peak position of the Mn $K_{\alpha }$ line (5.9 keV) as a function of (a) time and (b) rate. The origin of the vertical axis is the average of the data. With correction of the time and rate dependences, a stability of $\pm 0.5\mathrm{eV}$ was obtained. From [12].

Figure 31

X-ray energy spectra of different SIDDHARTA target data in the synchronous time window. (a) Deuterium ($2.50\mathrm{g}/\mathrm{l}$), (b) helium-3 ($0.96\mathrm{g}/\mathrm{l}$), (c) helium-4 ($1.65\mathrm{g}/\mathrm{l}$), and (d) helium-4 ($2.15\mathrm{g}/\mathrm{l}$). Several kaonic atom x-ray peaks are indicated by numbers for the deuterium target data: (1) kaonic carbon ($K^{-}\mathrm{C}$) $8\to 6$ and $6\to 5$, (2) kaonic oxygen ($K^{-}\mathrm{O}$) $7\to 6$, (3) kaonic nitrogen ($K^{-}\mathrm{N}$) $6\to 5$, (4) ($K^{-}\mathrm{N}$) $7\to 5$, (5) ($K^{-}\mathrm{O}$) $8\to 6$ and $6\to 5$, ($K^{-}\mathrm{C}$) $5\to 4$, and kaonic aluminum ($K^{-}\mathrm{Al}$) $8\to 7$ transitions. The fit lines in the energy spectra are also shown. The dotted lines show the fit functions of the other kaonic atom x-ray lines produced in the Kapton foils and the aluminum frames. The solid lines show the fit functions of the kaonic-helium x-ray lines in (b), (c), and (d). The background was fitted with a second order polynomial function. The positions of the kaonic-helium x-ray lines in (b), (c), and (d) are indicated by arrows. Adapted from [17].

Figure 32

Comparison of experimental results for the strong-interaction shift of the kaonic helium-4 $2p$ level. The plots exhibit results for the three old experiments ([122]; [9]; [6]) and the recent two experiments E570 ([99]) and SIDDHARTA publishing two values using different datasets in 2009 ([10]) and in 2011 ([13]). The error bars correspond to quadratically added statistical and systematic errors.

Figure 33

X-ray spectrum of the exploratory kaonic deuterium measurement. The continuous background fit component is already subtracted. The fit was performed with fixed $Kd$ transition shift and width ($-805$, 750 eV) and fixed yield ratios of the $K$ transitions. The integrated luminosity was $100{\mathrm{pb}}^{-1}$. The lines from kaonic x rays generated by kaons stopping in the window foils as well as the fluorescence lines excited by background are labeled. Note the excess of events in the region of a possible signal. From [16].

Figure 34

Sketch of the (left) SIDDHARTA-2 and the (right) E57 cryogenic target cells.

Figure 35

The SIDDHARTA-2 setup with the cryogenic target cell surrounded by the SDDs and the Veto-2 system within the vacuum chamber, while the Veto-1 device is surrounding the chamber on the outside.

Figure 36

Simulated SIDDHARTA-2 kaonic deuterium spectrum, assuming a shift ${ϵ}_{1s}=-800\mathrm{eV}$ and width ${\mathrm{\Gamma }}_{1s}=750\mathrm{eV}$ of the $1s$ state, as well as a $K_{\alpha }$ yield of ${10}^{-3}$. The spectrum was simulated for an integrated luminosity of $800{\mathrm{pb}}^{-1}$.

Figure 37

Layout of the E57 setup with the cylindrical spectrometer system within a 0.7 T solenoid and in the center the cryogenic target with the novel SDD arrays.

Figure 38

Simulated E57 kaonic deuterium spectrum, assuming a shift ${ϵ}_{1s}=-800\mathrm{eV}$ and width ${\mathrm{\Gamma }}_{1s}=750\mathrm{eV}$ of the $1s$ state, as well as a $K_{\alpha }$ yield of ${10}^{-3}$.

Figure 39

A cross-section top view of the J-PARC E62 experimental setup. The inset shows a birds-eye view around TES and the helium target cell. A set of beam detectors, a cryogenic liquid helium-3 and helium-4 target system, and the NIST’s TES x-ray spectrometer system are shown. From [18].

Figure 40

Expected spectrum in the J-PARC E62 experiment. The red lines represent various x-ray components, and the blue dotted line represents a fit of the spectrum assuming as an example a constant background. From [18].

Figure 41

Real part of the best fit $K^{-}\mathrm{Ni}$ optical potential based on the single-nucleon amplitudes plus a phenomenological multinucleon amplitude $B(\rho /{\rho }_0{)}^{\alpha }$. Shown for comparison as short-dashed lines is a purely phenomenological potential ([49]). Adapted from [53].