The FAMU experiment will measure the hyperfine splitting in the
ground state of muonic hydrogen \u394Ehfs(\u3bc
 12
p)1s with a precision \u3b4\u3bb/\u3bb < 10
 125
providing rZ, the Zemach radius of the proton with higher precision, than what was
previously possible, disentangling discordant theoretical values. The aim is to set
a cornerstone result about not yet explained anomalies on the charge radius rch of
the proton. The Zemach radius rZ and the charge radius rch are the only proton
shape-related values that can be directly extracted from experimental data, and rZ
is the only one that gives information about the proton\u2019s magnetic dipole moment
distribution. The status of the experiment is presented

the FAMU Collaboration, For

Vacchi, A.

English

The FAMU experiment will measure the hyperfine splitting in the
ground state of muonic hydrogen ΔEhfs(μ
−
p)1s with a precision δλ/λ < 10
−5
providing rZ, the Zemach radius of the proton with higher precision, than what was
previously possible, disentangling discordant theoretical values. The aim is to set
a cornerstone result about not yet explained anomalies on the charge radius rch of
the proton. The Zemach radius rZ and the charge radius rch are the only proton
shape-related values that can be directly extracted from experimental data, and rZ
is the only one that gives information about the proton’s magnetic dipole moment
distribution. The status of the experiment is presented

A. Vacchi

for the FAMU Collaboration

Archivio istituzionale della ricerca - Università degli Studi di Udine

DOI 10.1393/ncc/i2019-19126-6Colloquia: EuNPC 2018IL NUOVO CIMENTO 42 C (2019) 126Measuring the muonic H ground state hyperfine splitting withFAMUA. Vacchi(1)(2)(3) for the FAMU Collaboration(1) Sezione INFN di Trieste - Trieste, Italy(2) Dipartimento di Scienze Matematiche, Informatiche e Fisiche, Università di UdineUdine, Italy(3) RIKEN Nishina Center - Wako, Japanreceived 5 February 2019Summary. — The FAMU experiment will measure the hyperfine splitting in theground state of muonic hydrogen ΔEhfs(μ−p)1s with a precision δλ/λ < 10−5providing rZ , the Zemach radius of the proton with higher precision, than what waspreviously possible, disentangling discordant theoretical values. The aim is to seta cornerstone result about not yet explained anomalies on the charge radius rch ofthe proton. The Zemach radius rZ and the charge radius rch are the only protonshape-related values that can be directly extracted from experimental data, and rZis the only one that gives information about the proton’s magnetic dipole momentdistribution. The status of the experiment is presented.1. – IntroductionMuonic hydrogen allows high-precision spectroscopy studies of the fundamental in-teractions and of the structure of the proton. The typical binding energies and dis-tances in the muonic hydrogen atom are rescaled with the muon-to-electron mass ratioρ = mμ/me ≈ 200. Physical phenomena at a range of distances of the order of 250fmcan be observed, relativistic and higher order QED effects on the energy spectrum areenhanced by the factor ρ ≈ 200; the overlap of muon and proton densities is enhanced ρ3times, this makes accessible the spatial distribution of the proton charge and magneticmoment. The rescaled transition energies between levels in muonic hydrogen are shiftedto spectral ranges that allow high precision laser spectroscopy. This, together with theevolution in precision of the theoretical calculations, allows to experimentally explore thefundamental interactions from the low-momentum transfer front [1] [2] [3]. The avail-ability of pulsed, intense, low-energy negative muon beams and IR laser sources unlocksthe possibility to realise the measurement of the hyperfine splitting (hfs) in the groundstate of muonic hydrogen ΔEhfs(μ−p)1s [4] [5] [6].Creative Commons Attribution 4.0 License (http://creativecommons.org/licenses/by/4.0) 12 A. VACCHI for the FAMU COLLABORATIONThe FAMU (Fisica Atomi MUonici, Muonic Atom Physics) measurement ofΔEhfs(μ−p)1s, with a relative accuracy 10−5, will contribute to the determination ofrZ , the first moment of the convolution of proton’s electric charge and magnetic mo-ment distributions with an accuracy of 1% or better. This will boost the resolution ofthe ambiguities about the electromagnetic structure of proton and explore the limits ofthe theoretical predictions becoming sensitive to new phenomena and potentially probephysics beyond the Standard Model connecting the fields of precision atomic and high en-ergy physics. The exceptional precision of the experimental value of ΔEhfs in hydrogenmakes this measurement sensitive, in addition to QED corrections, to the contributionfrom proton finite size and polarizability. Both cannot be extracted from a single ex-perimental value. A measurement of ΔEhfs(μ−p)1s with an accuracy better than 10−4provides another independent combination of the non QED part and would therefore be asignificant step forward in the study of the proton structure. It also allows to investigatethe stubborn discrepancy among measurements of the proton charge radius rch with anew independent high precision measurement on muonic hydrogen [7] [8].A recent evaluation of the 1S-hfs in μp leads to:ΔEhfsth(μ−p)1s = 182.819(1)[meV ] − 1.301[meV/fm]rZ + 0.064(21)[meV ](1)where the first term includes the Fermi energy, QED corrections, hadronic vacuumpolarization, recoil corrections and weak interactions, the second term, proportionalto rZ , is the finite size contribution containing also higher order mixed radiative fi-nite size corrections, and the third term is given by the proton polarizability contribu-tion [1] [10] [11] [12] [13] [14]. Each of these terms is subject to constantly improvedcalculations, and the specific numerical values and their uncertainty may vary in thefuture. FAMU [15] realises a new method to obtain the first measurement of (μ-p)1Shfs. It will become possible to deduce rZ with a relative accuracy better than 5 × 10−3limited by the relative accuracy on the polarizability contribution. By now the value ofrZ has been extracted from the hyperfine splitting in ordinary hydrogen by 4 independentgroups and the results of 3 of them converge to the value rZ=1.03 fm [12].2. – The progressionThe steps leading to the original idea are summarized in the following articles [16] [17][4] [5] [6] [18]. An experimental proposal was presented in 2013 at the Program AdvisoryCommittee of the RIKEN laboratory where it received the first approval. Subsequentlytwo proposals with the same physics target have been approved [19] [14]. Since 2013the FAMU team at the RIKEN-RAL muon facility has demonstrated that the proposedmethod, the beam, and the detection systems are all optimal for the task [20] [21].3. – The methodFAMU measures the weak magnetic M1 transition between the hyperfine para-statewith spin F=0 and ortho-state F=1 of the (μ-p)1S . The muonic hydrogen atoms areformed and propagate in a gas container with a mixture of hydrogen and a high Z gasat low concentration. The observable is the time distribution of the characteristic X-rayevents of the muonic atoms formed by muon transfer from hydrogen to the atom of theadmixture gas and its response to variations of the laser wavelength. The efficiency ofthe method is bound to the collisional energy dependence of the muon transfer rate.MEASURING THE MUONIC H GROUND STATE HYPERFINE SPLITTING WITH FAMU 3There are experimental evidences, confirmed by FAMU recent experimental results, thatoxygen has a sharp energy dependence [21] [22] [23].The chain of physical processes is the following: a muonic hydrogen atom in theground F=0 state, after absorbing a photon at the hyperfine splitting resonance energyΔEhfs ≈ 0.183 eV, and being excited to F=1, is very quickly de-excited to F=0 in sub-sequent collisions with the surrounding H2 molecules (the de-excitation (F=1)⇒(F=0)cross section exceeds the elastic (F=1)⇒(F=1) cross section by a factor ∼20) [24]. Be-cause of energy and momentum conservation, at the exit of the collision the muonic atomis accelerated by ∼2/3 of the excitation energy ΔEhfs, which takes away as kinetic en-ergy. Since the muon is transferred from μ−p to μ−O at a rate λo(E) that increases withenergy, by varying the emission wavelength of the tunable excitation-laser, it is possibleto experimentally observe the number of muonic atoms that have undergone the abovesequence of processes and identify the resonance wavelength as the value for which thenumber of spin-excited atoms is maximal. The thermalization of μ−p has to be slowerthan the epithermic μ− transfer, this dictates the physical conditions of the gas mixtureand target. Within the FAMU preliminary experiment we have reached a confirmationof the method for oxygen [21] [6].The experiment needs an intense pulsed low momentum negative muons beam anda pulsed tunable narrow-band mid-infrared laser in the 6.78 micron wavelength rangewith energy output of more than 1 mJ coupled to a multi-pass highly reflective cavity.Requires also fast high energy resolution X-ray detectors with best efficiency for themuonic oxygen characteristic X-rays (100–200 KeV).The beam structure, of the RIKEN-RAL pulsed muon facility at the ISIS acceleratorof the Rutherford-Appleton Laboratory (UK), has two subsequent pulses 320 ns aparteach with 70 ns FWHM delivering about 104 (depending on the momentum) negativemuons per second, with 30-80 MeV/c, with a pulse repetition rate 50 Hz, σp/p= 4% anda beam transversal section of σx,σy = 1.5 cm [25].The pulsed laser, tunable around 6785± 3 nm, with energy output of ∼4 mJ with line-width less than 0.07 nm, tunability steps 0.007nm, 20 ns pulses at repetition rate 25 Hz,is based on direct difference frequency generation (DFG) in lithium thioindate (LiInS2)non-oxide crystals, cut for type II difference frequency generation, with pump and signalcoming from one narrow band fixed wavelength and one tunable laser emitting at wave-lengths below 2 μm. This scheme is based on mixing single frequency single longitudinalmode Nd:YAG laser (1.064 μm) and a tunable narrow bandwidth Cr:forsterite laser (∼1.262 μm), pumped by a second Nd:YAG synchronised to the first one. It is an attractivescheme due to its compactness, energy scalability and ability to fulfil the required laserparameters. The results obtained by a test system showed that the LiInS2 is among themost appropriate crystals [26]. To maximize the spin-flip probability, the target volumehas to be efficiently irradiated by the laser light pulse by means of a multi-pass opticalcavity.FAMU is a time resolved X-ray spectroscopy experiment, the detector of choice isthe scintillator LaBr3(Ce). It offers the appropriate energy resolution, fast emission andexcellent linearity. High purity germanium HpGe detectors are used as cross referencecomplementing the LaBr based detectors [15]. The detector’s output is recorded for5μs after the trigger using a 500MHz 14-bit digitizer. The waveform is then processedto extract the energy spectrum of the detected X-rays, their time distribution and anddisentangle pile-up events [6] [27]. The optimization of all the aspects of the FAMUexperimental lay-out is obtained through an experimentally validated simulation [28][18] [23].4 A. VACCHI for the FAMU COLLABORATION4. – ConclusionsA set of tests on the RIKEN RAL muon beam using a high pressure, cryogenic,hydrogen gas target confirms the FAMU experimental method - pulsed muon beam andthe muon transfer technique -. The results of the study on muon transfer rate to oxygenat different temperatures indicates the working conditions needed to optimise the twocomplementary effects of μp thermalization and μ transfer to oxygen. This data are ofcrucial importance for the detailed planning of the subsequent spectroscopy experiment.REFERENCES[1] Carlson C. E. et al., Phys. Rev. A, 83 (2011) 042509.[2] Karshenboim, S. G., Phys. Rev. A, 91 (2015) 012515.[3] Krauth, J. J. et al., ArXiv170600696 Phys, (2017) .[4] Bakalov, D. et al., Phys. Lett. A, 172 (1993) , pp. 277-280.[5] Adamczak, A. et al., Nucl. Instrum. Methods Phys. Res. Sect. B, 281 (2012) , pp.72-76.[6] Adamczak, A. et al., J. Instrum., 11 (2016) P05007.[7] Pohl, R. et al., Science, 353 (2016) , pp. 669-673.[8] Pohl, R. et al., Nature, 466 (2010) , pp. 213-216.[9] Antognini, A. et al., Science, 339 (2013) , pp. 417-420.[10] Eides, I. et al., Phys. Rep., 342 (2001) 63–261.[11] Volotka, A. V. et al., Eur. Phys. J. D, 33 (2005) , pp. 23-27.[12] Dupays, A. et al., Phys. Rev. A, 68 (2003) 052503.[13] Faustov, R. N. et al., Phys. Lett. B, 733 (2014) , pp. 354-358.[14] Antognini, A., ArXiv151201765 Phys., (2015) .[15] Adamczak, A. et al., JINST, 13 (2018) .[16] Ruckstuhl, W. et al., Nucl. Phys. A, 433 (1985) , pp. 634-648.[17] Beltrami, I. et al., Nucl. Phys. A, 451 (1986) , pp. 679-700.[18] Bakalov, D. et al., Phys. Lett. A, 379 (2015) , pp. 151-156.[19] Sato, M. et al., doi:10.3204/DESY-PROC-2014-04/67, (2014) , pp. 460-463.[20] Vacchi A. et al., RIKEN Accel Prog Rep, 49 (2016) .[21] Vacchi A. et al., RIKEN Accel Prog Rep, 50 (2017) .[22] Werthmüller, A. et al., Hyperfine Interact., 116 (1998) , pp. 1-16.[23] Bakalov, D. et al., Hyperfine Interact., 233 (2015) , pp. 97-101.[24] Adamczak, A. et al., At. Data Nucl. Data Tables, 62 (1996) , pp. 255-344.[25] Matsuzaki, T. et al., Nucl. Instrum. Methods Phys. Res., 465 (2001) , pp. 365-383.[26] Stoychev L.I. et al., 2015 Fotonica AEIT Ital. Conf. Photonics Technol., (2015) .[27] Mocchiutti E. et al., ArXiv170803172 Phys., (2017) .[28] Danev, P. et al., J. Instrum., 11 (2016) P03019.

Measuring the muonic H ground state hyperfine splitting with FAMU

for the FAMU Collaboration,

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Measuring the muonic H ground state hyperfine splitting with FAMU

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