Fifth Force and Hyperfine Splitting in Bound Systems

Abstract

Two recent experimental observations at the ATOMKI Institute of the Hungarian Academy of Sciences (regarding the angular emission pattern of electron-positron pairs from nuclear transitions from excited states in 8 Be and 4 He) indicate the possible existence of a particle of a rest mass energy of roughly 17 MeV. The so-called X17 particle constitutes a virtual state in the process, preceding the emission of the electron-positron pair. Based on the symmetry of the nuclear transitions (1 + → 0 + and 0 − → 0 + ), the X17 could either be a vector, or a pseudoscalar particle. Here, we calculate the effective potentials generated by the X17, for hyperfine interactions in simple atomic systems, for both the pseudoscalar as well as the vector X17 hypotheses. The effective Hamiltonians are obtained in a general form which is applicable to both electronic as well as muonic bound systems. Because of the short range of the X17-generated potentials, the most promising pathway for the observation of the X17-mediated effects in bound systems concerns hyperfine interactions, which, for S states, are given by modifications of short-range (Dirac-δ) potentials in coordinate space. For the pseudoscalar hypothesis, the exchange of one virtual X17 quantum between the bound lepton and the nucleus exclusively leads to hyperfine effects, but does not affect the Lamb shift. Effects due to the X17 are shown to be drastically enhanced for muonic bound systems. Prospects for the detection of hyperfine effects mediated by X17 exchange are analyzed for muonic deuterium, muonic hydrogen, true muonium (µ + µ − bound system), and positronium. I. INTRODUCTIONFor decades, atomic physicists have tried to push the accuracy of experiments and theoretical predictions of transitions in simple atomic systems higher [1]. The accurate measurements have led to stringent limits on the time variation of fundamental constants [2-4], and enabled us to determine a number of important fundamental physical constants [5] with unprecedented accuracy. Yet, a third motivation, hitherto not crowned with success, has been the quest to find signs of a possible low-energy extension of the Standard Model, based on a deviation of experimental results and theoretical predictions.Recently, the possible existence of a fifth-force particle, commonly referred to as the "X17" particle because of the observed rest mass of 16.7 MeV, has been investigated in Refs. [6,7], based on a peak in the emission spectrum of electron-positron pairs in nuclear transitions of excited helium and beryllium nuclei. Two conceivable theoretical explanations have been put forward, both being based on low-energy additions to the Standard Model. The first of these involves a vector particle (a "massive, dark photon", see Refs. [8,9]), and the second offers a pseudoscalar particle (see Ref. [10]), which couples to light fermions as well as hadrons.Somewhat unfortunately, the rest mass range of 16.7 MeV makes the X17 particle hard to detect in atomic physics experiments. The observed X17 rest mass energy...

Anomalies in $^8$Be nuclear transitions and $(g-2)_{e,μ}$: towards a minimal combined explanation

“…In [54] the possibility of a light pseudoscalar particle with j π = 0 − was examined, while a potential explanation based on an axial vector particle (including an ab-initio computation for the relevant form factors) was carried in [56]. Further ideas were put forward and discussed (see, for instance, [57][58][59][60][61][62][63][64][65][66][67][68]).…”

Is the $X17$ composed of four bare quarks?

“…Since the above two mass values are both about 17 MeV, this structure is called the "X17". Its observations quickly attracted lots of interests from theorists, and various explanations were proposed, such as a fifth force [5][6][7][8][9][10][11][12][13], new and/or dark matter [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28], and axions [29][30][31][32], etc. More discussions can be found in Refs.…”