The proton radius puzzle

The FAMU (Fisica degli Atomi Muonici) experiment has the goal to measure precisely the proton Zemach radius, thus contributing to the solution of the so-called proton radius puzzle. To this aim, it makes use of a high-intensity pulsed muon beam at RIKEN-RAL impinging on a cryogenic hydrogen target with an high-Z gas admixture and a tunable mid-IR high power laser, to measure the hyperfine (HFS) splitting of the 1S state of the muonic hydrogen. From the value of the exciting laser frequency, the energy of the HFS transition may be derived with high precision and thus, via QED calculations, the Zemach radius of the proton. The experimental apparatus includes a precise fiber-SiPMT beam hodoscope and a crown of eight LaBr3 crystals and a few HPGe detectors for detection of the emitted characteristic X-rays. Preliminary runs to optimize the gas target filling and its operating conditions have been taken in 2014 and 2015-2016. The final run, with the pump laser to drive the HFS transition, is expected in 2018.


The FAMU experimental method
The experimental method to be used by the FAMU Collaboration [7] is shown schematically in figure 1. It makes use of a high intensity pulsed low-energy muon beam, stopping in a hydrogen target, to produce muonic hydrogen (in a mixture of singlet F=0 and triplet F=1 states) and a tunable mid-IR high power laser to excite the hyperfine splitting (HFS) transition of the 1S muonic hydrogen (from F=0 to F=1 states). Exploiting the muon transfer from muonic hydrogen to another higher-Z gas in the target (such as O 2 or Ar), the µ − p 1S HFS transition will be recognized by an increase of the number of X-rays from the (µZ * ) cascade, while tuning the laser frequency ν 0 (∆E HFS = hν res 0 ).   After the initial phase of thermalization, a laser pulse will induce the singlet to triplet transitions in the muonic hidrogen atoms. Further collisions with H 2 molecules will convert back F=1 states to F=0 states with ∼ 0.2 keV kinetic energy (∼ ∆E HFS ). Finally, the muon is transferred from (µ − p) to the higher Z admixture gas and the characteristic X-ray K-lines from (µZ * ) cascade are observed.
One can thus measure ∆E HFS with a relative accuracy ∼ 10 −5 and determine, via QED calculations, the proton Zemach radius with high precision.
The FAMU experiment will be performed in steps, starting from the study of the transfer rate from muonic hydrogen to another higher-Z gas (2014-2016) and ending with a full working setup (2018 → ... ) with the pump laser and a cavity to determine the proton Zemach radius. The preliminary steps will allow determining the best mixture to be used inside the cryogenic target and optimize the operating conditions.

The experimental setup
The RIKEN-RAL muon facility is located at the Rutherford Appleton laboratory at Didcot (UK) and provides high intensity pulsed muon beams at four experimental ports. Its schematic layout is shown in the left panel of figure 2. The ISIS primary proton beam at 800 MeV/c, with a 50 Hz repetition rate, impinges from the left on a secondary carbon target producing a high-intensity pulsed muon beam, ICNFP 2016 that reflects the primary beam structure: a double pulse structure with 70 ns pulse width (FWHM) and 320 ns peak to peak distance. The FAMU experiment makes use of the decay muon beam (muons produced outside the target from pion decay and collected by a decay solenoid) at ∼ 60 MeV/c. The intensity is around 8 × 10 4 µ − /s, as shown in figure 2, with an energy spread ∼ 10% and an angular divergence ∼ 60 mrad.

The 2014 and 2015-2016 preliminary runs
The setup for the 2014 (R484) and 2015-2016 (R582) FAMU data taking are schematically shown in figures 3 and 4. A fiber-SiPMT beam hodoscope is the most upstream detector of the setup and had a 3 mm pitch in the first 2014 run and a 1 mm pitch in the following ones. It was used to optimize beam steering inside the target. Both beam hodoscopes (with 1 mm and 3 mm pitch) have a similar structure based on BCF12 Bicron square single-clad scintillating fibers along X/Y directions (32+32 channels) read at one end by Advansid SiPMT. Difficulties encountered in developing the mechanics of the two beam hodoscopes (especially the one with 1 mm pitch) were solved via 3D printing. Details of the construction and preliminary performances of the first beam hodoscope were reported in references [8] and [9].
The 1 mm pitch beam hodoscope (active area ∼ 3.2 × 3.2 cm 2 ) was developed to be put in front of the thin Beryllium window of the cryogenic target, used in the 2015-2016 run. An effort was done to minimize materials present in the beamline. Thus Bicron BCF12 square 1 mm 2 scintillating fibers, with white EMA coating to avoid light cross-talk, were used. Scintillating fibers were cut at Cern with a Fiberfin4 machine, that produced ready-to-use fibers of the right length with polished ends. The main mechanics components and a picture of the detector after the beam collimator are shown in figure 5. to the one of the previous 3 mm pitch beam hodoscope, derived from the INFN TPS project 1 . All channels of the same plane (x,y) of the 1mm pitch beam hodoscope were instead powered by a single HV channel and the output signals were directly fed into a fast FADC 2 . Signals were routed from the PCB's, where the SiPMTs were mounted, to the external MCX cables, going to the FADC, via a short flat cable. The impedance mismatch of this cable was tested and found negligible. Figure 6 shows the FADC waveform for a typical channel, where the two pulses beam structure is evident (left panel) and the reconstructed x,y beam profiles from the integrated charge information. As expected, the beam profile is dominated by the size of the collimator and has an RMS ∼ 7 − 8 mm. The target, used in the 2014 run, was an Al cylindrical vessel 3 filled with a high-pressure gas. In the following runs, it was replaced by a cryogenic one. The layout of the cryogenic target is shown in the left panel of figure 7, where the percentage of stopped muons as a function of the beam momentum is shown nearby. Emitted X-rays are detected with high precision Germanium detectors (HpGe) and fast LaBr3:Ce detectors. Two HPGe detectors (one small area ORTEC GLP detector and one ORTEC GMX detector) were used in the 2014 run, while in the following runs two additional HPGe detectors from RIKEN-RAL were also used. In the 2014 run a mosaic of four 0.5-inch diameter, 0.5-inch length LaBr 3 (5%Ce) read by Hamamatsu R11265-200 UBA photomultipliers and a single 1-inch diameter, 1-inch length Brillance 380 LaBr 3 crystal read by a Phillips XP2060 photomultiplier were used. In the following runs, the LaBr 3 mosaic was replaced by a crown of eight 1-inch LaBr 3 detectors read by Hamamatsu R11265-200 UBA photomultipliers, with an active divider, as shown in figure 7. The LaBr 3 detectors were read through 500 Mhz, 14-bit digitizer (CAEN V1730) with a 5µs window after the trigger, provided by the RF of the beamline, while for the HPGe detectors a slower 100 MHz, 14-bit digitizer (CAEN V1724) was used. In addition, during the 2016 data new X-rays detectors, developed for PET, based on PrLuAG and CeCAAG crystals and read out by Hamamatsu TSV SiPMT arrays, were introduced to instrument the volume under the cryogenic target [10].

The setup for the final step of the FAMU experiment.
To excite the HFS transition, a laser tunable at a wavelength around λ 0 ∼ 2πhc ∆E HFS ∼ 6.785 µm will be used. In reference [11], the main requirements on the laser system, such as energy (≥ 0.25 mJ) and linewidth precision (λ 0 ≤ 0.07 nm ) are discussed. The layout of the proposed laser system, under development at the Electra laboratory (Ts), is schematically shown in figure 8. A scheme based on direct difference frequency generation in nonlinear crystals, using a Q-switched Nd-Yag laser and a tunable Cr:forsterite laser will be used and is presently under test [12]. To increase the probability of the spin-flip (F=0 to F=1) process either the target temperature may be lowered or a multipass cavity may be used: see reference [13] for an example. With a multipass cavity that provides ∼ 2 × 10 3 reflections, the spin-flip probability would reach a reasonable ∼ 12% value, that makes the experiment feasible. Studies of a suitable multipass cavity, that may accomodate the available cryogenic target, are under way inside the FAMU collaboration.

Detector performances and preliminary results
The aim of the 2014 run (R482) was to test the suitability of the proposed setup for the foreseen measurement: in particular the detection of the characteristic X-rays in a large background environment. The detection of characteristic X-rays from LaBr 3 detectors was cross-checked with two high precision HpGe detectors. As an example, for an H 2 + 2%Ar filled target, figure 9 shows the spectra detected by the HPGe detectors and the LaBr 3 crystals. All characteristic X-ray lines from the Ar Regarding the time distribution of the events, figure 10 shows an example of the time evolution of the X-ray spectrum for the H 2 − CO 2 target. The prompt peaks, corresponding to the two beam spills, are followed by a tail populated by the products of muon decay. From the events in the tails, the lifetime of muonic atoms may be estimated. Results are reported in table 2 and are compatible with previous ones, as reported in reference [14]. Studies are under way to determine the transfer rate from hydrogen to the gas mixture contaminants (Argon or Oxygen), using the time evolution of the X-rays events inside the Argon (Oxygen) peak. EPJ Web of Conferences Figure 10. A snapshot of the detected X-ray spectrum (energy vs time). The two peaks are due to the two pulses structure in the incoming muon beam.

Conclusions
The feasibility of the method proposed by the FAMU Collaboration to determine the proton Zemach radius has been demonstrated with preliminary measurements at RIKEN-RAL: in particular the possibility to use a high-rate X-rays detection system based on LaBr 3 crystals.
The mid-IR pulsed laser and the multipass cavity are under development, showing that a final data taking in 2018 is feasible.