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PHYSICAL REVIEW D 103, 093002 (2021)

Tests of the Atomki in pair decays of heavy

† G. López Castro1,* and N´estor Quintero 2,3, 1Departamento de Física, Centro de Investigación y de Estudios Avanzados, Apartado Postal 14-740, 07000 M´exico D.F., M´exico 2Facultad de Ciencias Básicas, Universidad Santiago de Cali, Campus Pampalinda, Calle 5 No. 62-00, Código Postal 76001, Santiago de Cali, Colombia 3Departamento de Física, Universidad del Tolima, Código Postal 730006299, Ibagu´e, Colombia

(Received 14 January 2021; accepted 3 May 2021; published 27 May 2021)

The anomalies recently reported in lepton pair transitions of 8Be and 4He nuclei may be attributed to the existence of a feebly interacting light vector X17. We study the effects of this hypothetic in the semileptonic H → Heþe− decays (H a Qq¯ ) in the framework of the HQET þ VMD model. Using current bounds and the universality assumption of the X17 boson to , we find that decays of þ þ D and Ds mesons can be importantly enhanced relative to the dominant -mediated contributions. Dedicated experimental searches at current heavy meson factories may confirm the existence of this light boson or set stronger bounds of their couplings to ordinary .

DOI: 10.1103/PhysRevD.103.093002

I. INTRODUCTION [7]. Couplings to first-generation of Oð10−3Þ The existence of a light weakly coupled to (in units of the charge) required to explain Standard Model (SM) fermions has been suggested as a this ratio is not discarded by other data. More recently, the X17 solution to the observed discrepancy between the SM same group seems to confirm the particle in studies of 0− → 0þ 4 prediction and the experimental measurement of the the transitions of He [8]. Several new physics g − 2 magnetic moment anomaly (see for example [1,2]). It extensions of the SM have been proposed in the literature may be also a good candidate as a mediator of dark and with the required couplings to interpret the Atomki anomaly, ordinary matter interactions [1,2]. Several strategies aiming including enlarged Higgs and/or gauge sectors (see, for – their detection in different collider and fixed target experi- instance, Refs. [7,9 13]). Despite the excitement generated ments have not found any signal so far [3,4], but have by these anomalies, one must be warned that the addition of excluded different regions in the mass and coupling radiative corrections to the leading one photon exchange strengths of parameter space. Theoretically, different mod- amplitude may be responsible [14] for generating the bumps reported in the angle and mass spectrum of electron- els can accommodate a light vector boson and its required 8 interactions through dimension-four kinetic mixing with pairs in Be transitions. The almost isosinglet nature and the small mass differ- SM neutral gauge and their interactions with 8 fermionic currents of SM or [1–3]. ence of nuclei involved in Be decay provides an ideal The anomalies recently reported in the invariant-mass place to observe this light boson, in case it exists. Mixing of spectrum and angular distribution of lepton pairs produced in nuclear isospin states [7,8,15] and other nuclear interfer- 8Be transitions to its ground state [5] reinforces the interest ence effects [16] can only partially explain the observed in searches of light vector bosons. The observed anomalies anomaly. Further studies in analogous systems will be very 17 important in order to establish or discard this light boson. In seems to require the existence of a spin-1 boson named X þ − – ¼ð16 7 0 35 0 50Þ the present paper, we propose the study of H → He e [5 7] with mass mX . . . MeV and a 8 8 8 8 −6 HðH Þ Qq¯ relative ratio Bð Be → BeXÞ=Bð Be → BeγÞ¼5.8×10 decays, where is a heavy spin-0 (spin-1) meson. Previous related studies include (i) J=ψ → ηcX decays and associated production of J=ψ mesons at BESIII and Belle II *[email protected] experiments, recently reported in [17] and, (ii) a search † 0 0 0 0 þ − [email protected] proposal at LHCb of D → D A → D e e with dis- placed vertex or resonant production of the A0 Published by the American Physical Society under the terms of detailed in Ref. [18]. H → Heþe− decays seem to be the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to interesting to further test the Atomki anomaly: on the one the author(s) and the published article’s title, journal citation, hand, the mass splitting in heavy mesons is large enough and DOI. Funded by SCOAP3. (see Table I) to produce the X17 boson on shell; on the

2470-0010=2021=103(9)=093002(7) 093002-1 Published by the American Physical Society G. LÓPEZ CASTRO and NESTOR´ QUINTERO PHYS. REV. D 103, 093002 (2021)

TABLE I. Mass splittings of heavy mesons and electromagnetic couplings of H → Hγ transitions in the HQET þ VMD model. Within square brackets we show experimental values when available.

−1 −1 −1 Transition mH − mH (MeV) eQ=mH ½GeV eq=mqð0Þ½GeV FHHγð0Þ½GeV Dþ → Dþγ 140.603(15) 0.33 −0.85 −0.54 0.05 [−0.47 0.06 [19] ] D0 → D0γ 142.014(30) 0.33 1.70 2.11 0.10 [<10.8 [19] ] þ þ −0 48 −0 17 0 03 −16 4 Ds → Ds γ 143.8(4) 0.32 . ( . . )[> . [19] ] Bþ → Bþγ 45.37(21) −0.063 1.70 1.64 0.09 B0 → B0γ 45.37(21) −0.063 −0.85 −0.92 0.12 0 → 0γ 48 6ðþ1.8Þ −0 062 −0 48 ð−0 42 0 02Þ Bs Bs . −1.5 . . . .

L ð Þ¼ λhH σμν ðρÞ H¯ i other hand, strong decays of H are either very suppressed 2 H HV i b Fμν ba a ; of forbidden by kinematics, leaving electromagnetic decays as dominant. Furthermore, the large amount of data where h i denotes the trace in flavor space, FμνðρÞ¼ produced at heavy meson factories would allow one to μ ∂μρν − ∂νρμ þ½ρμ; ρν is the field strength tensor and ρ ¼ test the proposed channels in the near future. pffiffiffi ig ρˆ μ= 2 where ρˆμ is the 3 × 3 matrix of the nonet of light The Lagrangian describing the interaction of and V vector mesons. The heavy meson field H is defined in lepton flavorsPf with the photon and the X boson is L ¼ − ð þ ε Þ¯γμ terms of the pseudoscalar (Pa) and vector (Paμ) mesons ðγ;XÞff e f efAμ fXμ f f, with couplings 1 μ ¯ 0 † 0 fields as Ha ¼ 2 ð1 þ =vÞ½Paμγ − Paγ5, and Ha ¼ γ Haγ . strengths ef and εf given in units of the electron charge e. The photon and X boson couplings to are On the other hand, the coupling of light vector mesons to described each by a single vector form factor which takes the vector currents are described in terms of a single into account their structure in the momentum transfer constant fV in the SU(3) flavor symmetry [20,21]: 2 2 2 region 4m ≤ q ≤ ðm − m Þ , with q ¼ p þ þ p − . e H H e e h0j¯ iγμ j ð ηÞi ¼ ημ ð iÞ The form factors describing the couplings of the off-shell qT q V q; fVTr VT ; vector particles ðV ¼ γ;XÞ in H ðpH ; ϵH Þ → HðpHÞVðqÞ ð iÞ ¼ δ δ ¼ 1 2 3 ¼ are defined from the hadronic amplitude where T mn im in and i ; ; for q u; d; s quarks, respectively. The values of coupling constant are 2 ν α β given below. Mμ ¼ ieFHHVðq Þϵμναβϵ p p : ð1Þ H H H The vector H and pseudoscalar H heavy mesons are For on-shell vector particles V, this Lorentz-vector ampli- composed of a Qq¯ pair, with Q ¼ b; c and q ¼ u; d; s. The ϵμ ð Þ hadronic matrix element of the electromagnetic current is tude must be contracted with its vector polarization V q . The case of lepton pair production is discussed in Sec. III. given by [20]

h ð Þj emj ð ϵ Þi II. HH-VECTOR VERTICES H PH Jμ H PH ; H ¯ ¼ ehHðPHÞjeQQγμQ þ eqq¯γμqjH ðPH ; ϵH Þi; The form factors FHHVðqÞ are evaluated in the frame- Q q work of the heavy quark effective theory supplemented ¼ eðeQJμ þ eqJμÞ; ð2Þ with a dominance model (HQET þ VDM) [20,21], which has shown to give a good description of where eQðeqÞ is the of the heavy quark (light H → Hγ decays. Since we will normalize results for our quark) in units of the positron charge, and similarly, observables to this radiative decay, we use the ratio of X Q q hHðPHÞjJμ jH ðPH ; ϵH Þi ¼ eðεQJμ þ εqJμÞ for the X decay rates because they are rather insensitive to the 2 boson current. specific q dependency of the form factor. This is due to A straightforward evaluation of the form factors in the − the smallness of the H H mass splitting (see Table I) HQET þ VMD model [20] leads to compared to typical hadronic scales (∼1 GeV2). Also, 1 rffiffiffiffiffiffiffiffiffi  since the contributions of heavy quarks are =mQ sup- 2 mH eQ eq ð Þ¼ þ ð Þ pressed, we expect that such ratios are relatively indepen- FH Hγ q 2 ; 3 m m m ðq Þ dent of constants involved in light-quark contributions H H q through the vector meson dominance model. rffiffiffiffiffiffiffiffiffi  ε ε 2 mH Q q For self-containedness purposes, we reproduce here the ð Þ¼ þ ð Þ FH HX q 2 ; 4 term of the Lagrangian density relevant for our calculations mH mH mqðq Þ and definitions of couplings constants [20,21]. The strong interaction of heavy mesons are described by with the effective light “quark mass” parameter

093002-2 TESTS OF THE ATOMKI ANOMALY IN LEPTON PAIR DECAYS … PHYS. REV. D 103, 093002 (2021)    X pffiffiffi 2 −1 2 f q nuclear transitions [6]. First, since m ≫ m ðq Þ we have a m ðq2Þ−1 ¼ − 2 2g λ V 1 − : ð5Þ H q q V 2 2 suppression of the heavy quark relative to the light quarks V mV mV contributions in Eqs. (3) and (4), which is stronger for The expressions for the form factors of heavy mesons are bottom meson transition amplitudes. In order to be more explicitly separated in Eqs. (3) and (4) into its heavy and explicit, and for the easy reference of the interested reader, in light quark components. In the model under consideration, Table II we display the values of the two contributions that the couplings of heavy quarks to the photon and X boson appear within square brackets in Eq. (4), by assuming 2 ¼ 2 are fixed by HQET, while the couplings to the light q mX for the square of the momentum transfer of the ð Þ antiquarks are modeled by the dominance of light vector X boson. This has the advantage that the ratio RX=γ H is mesons [20]. For the latter, the sum extends over light more sensitive to the Xqq¯ couplings, which are relatively vector-meson resonances (V ¼ ρ0; ω; ϕ) according to well bounded from other processes [6]. On the other hand, the light-quark content of heavy mesons [20]. Under the given the larger phase space in heavy meson decays, this assumption of the ideal mixing for vector mesons, the cou- ratio is not suppressed by kinematics, as it happens for decay 8 plings of light u and d quarks are dominated by the of the Be nucleus. exchange of ρ and ω mesons, while the coupling of the Predictions for the H → HX decay fractions require an ε 17 s quark corresponds to the exchange of the ϕ meson. estimate of the Q;q couplings. For the couplings of the X Numerical inputs for couplings constants can be found in boson to the quarks of the first generation we use εu ≃ ¼ 5 8 −3 −3 Ref. [20] and are reproduced here for reference: gV . , 3.7 × 10 and εd≃ ∓ 7.4 × 10 [22]. They are λ ¼ −0 289 0 016 −1 −3 . . GeV (updated from new experi- obtained by combining jεu þ εdj ≈ 3.7 × 10 , obtained 8 mental inputs [19]) and fV (mV) the decay constant (mass) in Refs. [6,7] from the Be anomaly, with the null results of vector meson V. Using current experimental data for on searches of the π0 → Xγ by the NA48/2 experiment − þ lepton-pair decays of vector mesons V → e e [19], one [23], which translates into the constraint j2ε þ ϵ j ≤ 8 × 2 u d gets ðfρ;fω;fϕÞ¼ð0.171; 0.155; 0.232Þ GeV , with very 10−4 [22] for the X17 boson couplings. By assuming the small uncertainties. In Table I we list values for the NA48/2 constraint to be exactly zero, namely the “proto- electromagnetic form factor predicted in the HQET þ phobic” assumption (see however [24]), one gets the results 2 VMD model at q ¼ 0. The quoted uncertainty is domi- used in this paper. On the other hand, the limits on the λ −3 nated by the input on the H HV strong coupling ( ) in this coupling to can be obtained 0.2 × 10 ≲ jεej ≲ model (in all the predictions from this model quoted below, 1.4 × 10−3 from beam dump experiments at SLAC and all the other uncertainties are very small). A comparison measurements of the g − 2 anomalous magnetic moment of with the magnitude of the measured form factor (within the electron according to Ref. [22]. Our study requires the square brackets), obtained from the measurement of the knowledge of second- and third-generation couplings, þ → þγ radiative decay D D branching fraction [19],give namely strange εs, charm εc, and bottom εb. A priori these confidence on this model. parameters are independent [7], and need not be related to Let us define the following ratio of two-body decay the first-generation couplings. Our simplest starting rates: assumption is universality of down- and up-type quark ε couplings, thus, we will take ε ¼ ε and ε ¼ ε ¼ ε ; 2 2 3 f c u b s d Γð → Þ ð Þ j⃗ j ð Þ¼ H HX ¼ FH HX mX pX ð Þ henceforth, our results will be obtained under this RX=γ H · 3 ; 6 ΓðH → HγÞ FHHγð0Þ jp⃗γj assumption [6,7]. Values of the H HX couplings and RX=γðH Þ ratios for these transitions are given in where p⃗V is the momentum of the final state boson in the rest Table II. The ratios are larger than the ones in the nuclear frame of H. This ratio exhibits two important differences case mainly due to the unsuppressed phase space for X17 with respect to the similar ratio defined in 8Be → 8Be production.

2 ¼ 2 TABLE II. The H HX form factors evaluated at q mX and ratio RX=γ defined in Eq. (6).

−1 2 −1 2 −1 ε ½ ε ð Þ½ ð Þ½ ð Þ Transition Q=mH GeV q=mq mX GeV FH HX mX GeV RX=γ H Dþ → DþX 1.84 × 10−3 −1.89 × 10−2 ð−1.76 0.11Þ × 10−2 1.1 × 10−3 D0 → D0X 1.84 × 10−3 9.43 × 10−3 ð1.17 0.05Þ × 10−2 3.0 × 10−5 þ þ −3 −7 83 10−3 −2 −3 Ds → Ds X 1.75 × 10 . × ð−0.91 0.06Þ × 10 3.1 × 10 Bþ → BþX −1.39 × 10−3 9.43 × 10−3 ð0.81 0.05Þ × 10−2 1.9 × 10−5 B0 → B0X −1.39 × 10−3 −1.88 × 10−2 ð−2.03 0.10Þ × 10−2 4.0 × 10−4 0 0 −1 37 10−3 −7 83 10−3 −2 −4 Bs → Bs X . × . × ð−0.92 0.04Þ × 10 4.1 × 10

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III. LEPTON PAIR PRODUCTION interference in the dilepton spectrum vanishes at the position of the X17 and it is suppressed by more than 6 The decay amplitude for lepton pair production þ − orders of magnitude relative to the one-photon contribution H ðP Þ → HðP Þe ðpþÞe ðp−Þ is the coherent sum H H outside the resonance. of the photon and X-boson mediated amplitudes þ − The lepton-pair distributions due to MðH → He e Þ¼Mγ þ M , where ðV ¼ γ;XÞ: X photon (solid red plot) and X17 boson (dashed blue curve) 2 2 μ ν α δ exchange are shown separately in Fig. 1 for the six different M ¼ −e G ðq Þϵμναδl ϵ P P ; ð Þ V H HV H H H 7 decay channels under consideration. The shaded bands around each curve represent the theoretical error, which are where lμ ¼ u¯ðp−ÞγμvðpþÞ is the leptonic current and 2 2 2 2 2 difficult to visualize in the log scale. The peak due to the ð Þ¼− ð Þ ð Þ¼ε ð Þ GH Hγ q FH Hγ q =q , GH HX q eFH HX q = production of the X17 boson in each channel is not located ð 2 − 2 þ Γ Þ q mX imX X . In numerical evaluations throughout very close to the end of the lepton-pair spectrum as it α ¼ αð0Þ this paper we use em , the fine-structure con- happens in the nuclear case, avoiding in this way possible stant, because according to Table I the maximum value end-point kinematical effects. In contradistinction to the 2 ¼ of the squared photon momentum is not large [qmax on-shell X17 production, the effect of this boson is 2 þ þ þ þ þ − ð − Þ mH mH ]. On the other hand, running effects between the largest for the D ðDs Þ → D ðDs Þe e decay. 2 ¼ 0 2 q and qmax are very small compared with the present The corresponding peaks of this boson contribution are and forthcoming experimental accuracies which, in the suppressed by 1 or 2 orders of magnitude in all other cases, absence of real estimates, we will assume to be not better relative to the photon contribution. Note that we are than 5% for the branching fractions. assuming universality bounds on heavier quark εc;s;b As in Refs. [6,7], we assume negligible decays of the couplings; since this is a conservative assumption, the X17 boson into channels, such that its full width is experimental study of heavy mesons transitions involving given by lepton pairs may serve to set bounds on these unknown couplings of the hypothetical X17 boson. þ − ΓX ≡ ΓðX → e e Þ Table III displays the values of the decay rates for the α ε2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi lepton-pair production in H → H transitions normalized ¼ em emX ð1 þ 2 Þ 1 − 4 3 re re to the corresponding rates of the radiative decays H → Hγ, namely ¼ 8.0 × 10−8 MeV ð8Þ ΓðH → Heþe−Þ 2 2 ¼ ReeðH Þ ≡ ð10Þ with re me=mX. The total width quoted above corre- ΓðH → HγÞ sponds to a maximum value of εe, discussed in the previous section. Decays of a light vector boson into neutrino- where the radiative rate is given by ΓðH → HγÞ¼ Γ 2 3 antineutrino pairs that may increase width are also ðα 3Þj ð0Þj j⃗j X em= FH Hγ pγ . We expect that the remaining allowed by kinematics and are included in some extensions model-dependent terms in the form factors are cancelled of the SM involving enlarged Higgs and/or gauge sectors in this ratio (all other lepton-pair and angular distributions – ε [7,9 13]. The relevant coupling ν can be constrained from in the following are normalized to this radiative width). As neutrino-electron scattering in the case of the first gen- in the case of the lepton-pair spectra, the largest contribu- eration like was done in the TEXONO experiment [25] tion of the X17 boson is observed for the Dþ and Dþ jε ε j1=2 ≲ 7 10−5 νν¯ s yielding to e ν × [7]. The addition of the decays, making these channels the most sensitive for the channels will modify the total width of the X boson by less observation of these light boson effects. Our calculation of that 0.1%, and our results will remain unchanged. the electromagnetic contribution in the case of Ds decays γ The lepton pair invariant mass distribution, normalized yields R ðDþÞ¼6.8 × 10−3 is in good agreement with → γ ee s to the radiative decay width of H H , becomes the sum the experimental value ð7.2þ1.8Þ × 10−3 reported in [26]. X −1.6 of the photon and -boson mediated distributions, namely X17 λð Þ¼ 2 þ 2 þ 2 − 2 − 2 − 2 When we add the contribution of the boson exchange, [we use x; y; z x y z xy xz yz]: γþXð Þ¼ð9 80 6Þ 10−3 our prediction increases to Ree Ds . . × , Γð → þ −Þ α2 which exceeds the experimental value but it is still con- d H He e em 2 ¼ G γðq Þ 1 4σ dq2 72πΓðH → HγÞ H H sistent with it within . . Let us notice that a previous   prediction of this ratio R ðDÞ¼6.5 × 10−3 was esti- λð 2 2 2Þ1=2 3 ee s 2 2 2 mH ;mH;q mated in Ref. [26] based on the model proposed in [27] þGHHXðq Þj q : mH which includes only the electromagnetic contribution. ð9Þ The sensitivity of Ds decays into lepton pairs to the effects of X17 boson exchange observed in the previous Given the very narrow width of the X17 boson, the paragraph suggests this channel can be useful to constrain interference of the amplitudes is negligible. Indeed, the the parameter space of the hypothetical vector boson.

093002-4 TESTS OF THE ATOMKI ANOMALY IN LEPTON PAIR DECAYS … PHYS. REV. D 103, 093002 (2021)

(a) (b)

(c) (d)

(e) (f)

FIG. 1. Lepton pair invariant mass distributions of H → Heþe− transitions normalized to the radiative H → Hγ decay width: þ þ þ − 0 0 þ − þ þ þ − þ þ þ − 0 0 þ − 0 0 þ − (a) D → D e e , (b) D → D e e , (c) Ds → Ds e e , (d) B → B e e , (e) B → B e e , and (f) Bs → Bs e e . The red solid plot denotes the virtual photon contribution, while the X17 boson contribution is represented by the blue dashed curve. The (almost invisible) shaded bands account for the theoretical uncertainties in form factors.

TABLE III. Photon and X17 boson exchange contributions to the ratio of decay rates defined in Eq. (10). We assume universal −3 couplings of the hypothetical X17 boson to down-type quarks [εb ¼ εs ¼ εd ¼ ∓7.4 × 10 ] and up-type quarks −3 [εc ¼ εu ¼3.7 × 10 ] (see end of Sec. II). Unless explicitly indicated, theoretical uncertainties are at least 3 orders of magnitude smaller than the corresponding central values.

γ X Channel ReeðH Þ ReeðH Þ Total Experiment Dþ → Dþeþe− 6.67 × 10−3 ð1.05 0.07Þ × 10−3 ð7.72 0.07Þ × 10−3 D0 → D0eþe− 6.67 × 10−3 3.02 × 10−5 6.70 × 10−3 þ → þ þ − 6 72 10−3 ð3 10 0 60Þ 10−3 ð9 82 0 60Þ 10−3 ð7 2þ1.8Þ 10−3 Ds Ds e e . × . . × . . × . −1.6 × [26] Bþ → Bþeþe− 4.88 × 10−3 ð1.91 0.03Þ × 10−5 4.90 × 10−3 B0 → B0eþe− 4.88 × 10−3 3.96 × 10−4 5.28 × 10−3 0 0 þ − −3 −4 −3 Bs → Bs e e 4.99 × 10 4.08 × 10 5.40 × 10

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Finally, let us comment that the angular distribution of the eþe− pair, in the rest frame of the decaying particle, will be peaked closer to the collinear configuration compared to the nuclear case of 8Be transitions, where θðeþe−Þ ∼ 1400. This happens because the X17 boson is produced with a larger velocity, while in nuclear transitions this boson is produced almost at rest.

IV. CONCLUSIONS The hypothetical light vector boson X17, proposed as a solution for the anomaly observed in lepton-pair production of 8Be and 4He transitions, can be studied in the clean environment provided by vector to pseudoscalar heavy mesons transitions in Belle, Belle II [28], and BESIII factories. These HðQq¯Þ → HðQq¯Þeþe− decays are free from theoretical uncertainties associated with nuclear effects. We have used the HQET þ VMD framework to model the hadronic form factors of 1− → 0− meson 1σ FIG. 2. The confidence level allowed regions in the parameter transitions; however, our results are little dependent on space of up-type (εU ¼ εc) and down-type (εD ¼ εs) X-quark þ → þ þ − hadronic uncertainties because the rates are normalized to couplings from Ds Ds e e (light red shaded band). The → γ region within dashed lines corresponds to the assumption of a the dominant H H electromagnetic decays and the fivefold improvement in the experimental uncertainty. The corre- dominant contributions in most channels are dominated by photon emission off the light quarks in this model. sponding constraints on (εU ¼ εu; εD ¼ εd) from the experimental results from 8Be [5–7] and NA48/2 [7,23] are represented by the Although all the branching fractions of the heavy meson two parallel thin black lines and the wider steepest blue band, channels considered in this paper exhibit some sensitivity þ þ respectively. to the effects of the X17 boson, decays of D and Ds mesons turn out to be the most sensitive ones. This happens because (i) the radiative charged charmed vector meson In Fig. 2 we show the 1σ confidence level allowed for the decay rates used as a normalization factor in ReeðDs Þ and parameter space in the ðε ; ε Þ plane, obtained from the þ c s R ðD Þ are suppressed in the HQET þ VMD owing to a comparison of the experimental branching fraction reported ee partial cancellation of the heavy and light quarks contri- by CLEO [26] and the result of integrating Eq. (9) for Ds → þ − butions and, (ii) the large contribution of the light quark D e e (light red shaded band). The current experimental þ þ s coupling to X17 for D → D transition. Also, improved uncertainty in RðDÞ is close to 25%, and current experi- s measurements of these leptonic decay channels can set ments producing a large dataset of charmed mesons have additional and complementary constraints on the X17 not planned new measurements. Therefore, we will assume boson couplings to ordinary fermions, as shown in that a dedicated measurement of this observable may reach Fig. 2 for the case of D → D eþe− decays or, eventually, an improvement of the current uncertainty by a factor of 5. s s confirm the existence of this light boson. Under this assumption we get the region enclosed by the red dashed contour in Fig. 2. For comparison, we also show ACKNOWLEDGMENTS the two thin parallel black lines corresponding to the 8 allowed values of (εu, εd) obtained from Be results G. L. C. acknowledges support from Ciencia de Frontera [6,7] and the region allowed from the so-called “proto- project No. 428218 (Conacyt) and PRODEP project phobic condition” obtained from the nonobservation of No. 162336. The work of N. Q. has been financially π0 → γX by the NA48/2 experiment [7,23] (single steepest supported by MINCIENCIAS and Universidad del blue band). The different sensitivities observed from these Tolima through Convocatoria Estancias Postdoctorales measurements to the up-type and down-type quark cou- No. 848-2019 (Contract No. 834-2020), and Dirección plings makes worth an improved measurement of the heavy General de Investigaciones–Universidad Santiago de Cali mesons decays discussed in this paper. under Project No. 935-621120-G01.

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[1] P. Fayet, U-boson production in eþe− annihilations, ψ and [15] J. L. Feng, T. M. P. Tait, and C. B. Verhaaren, Dynamical ϒ decays, and , Phys. Rev. D 75, 115017 evidence for a explanation of the ATOMKI (2007). nuclear anomalies, Phys. Rev. D 102, 036016 (2020). [2] M. Pospelov, Secluded U(1) below the weak scale, Phys. [16] X. Zhang and G. A. Miller, Can explain the Rev. D 80, 095002 (2009). anomaly observed in the internal pair production in the [3] R. Essig et al., Working Group Report: New light weakly Beryllium-8 nucleus? Phys. Lett. B 773, 159 (2017). coupled particles, arXiv:1311.0029. [17] K. Ban, Y. Jho, Y. Kwon, S. C. Park, S. Park, and P. Y. [4] See talks at the Workshop on Feeble Interacting Particles Tseng, Search for new light vector boson using J=Ψ at 2020, https://indico.cern.ch/event/864648/timetable/ (2020). BESIII and Belle II, J. High Energy Phys. 04 (2021) [5] A. J. Krasznahorkay et al., Observation of Anomalous 091. Internal Pair Creation in Be8: A Possible Indication of a [18] P. Ilten, J. Thaler, M. Williams, and W. Xue, Dark Light, Neutral Boson, Phys. Rev. Lett. 116, 042501 (2016). from charm mesons at LHCb, Phys. Rev. D 92, 115017 [6] J. L. Feng, B. Fornal, I. Galon, S. Gardner, J. Smolinsky, (2015). T. M. P. Tait, and P. Tanedo, Protophobic Fifth-Force [19] P. A. Zyla et al. (Particle Data Group), Review of particle Interpretation of the Observed Anomaly in 8Be Nuclear physics, Prog. Theor. Exp. Phys. (2020), 083C01. Transitions, Phys. Rev. Lett. 117, 071803 (2016). [20] P. Colangelo, F. De Fazio, and G. Nardulli, Radiative heavy [7] J. L. Feng, B. Fornal, I. Galon, S. Gardner, J. Smolinsky, meson transitions, Phys. Lett. B 316, 555 (1993). T. M. P. Tait, and P. Tanedo, models for the [21] R. Casalbuoni, A. Deandrea, N. Di Bartolomeo, R. Gatto, F. 17 MeV anomaly in beryllium nuclear decays, Phys. Rev. D Feruglio, and G. Nardulli, Effective Lagrangian for heavy 95, 035017 (2017). and light mesons: Semileptonic decays, Phys. Lett. B 299, [8] A. J. Krasznahorkay et al., New evidence supporting the 139 (1993). existence of the hypothetic , arXiv:1910.10459. [22] B. Fornal, Is there a sign of new physics in beryllium [9] L. Delle Rose, S. Khalil, and S. Moretti, Explanation of the transitions? Int. J. Mod. Phys. A 32, 1730020 (2017). 17 MeV Atomki anomaly in a Uð1Þ0-extended two Higgs [23] J. R. Batley et al. (NA48/2 Collaboration), Search for the doublet model, Phys. Rev. D 96, 115024 (2017). dark photon in π0 decays, Phys. Lett. B 746, 178 (2015). [10] L. Delle Rose, S. Khalil, S. J. D. King, S. Moretti, and A. M. [24] X. Zhang and G. A. Miller, Can a protophobic vector boson Thabt, Atomki anomaly in family-dependent Uð1Þ0 exten- explain the ATOMKI anomaly? Phys. Lett. B 813, 136061 sion of the standard model, Phys. Rev. D 99, 055022 (2019). (2021). [11] L. Delle Rose, S. Khalil, S. J. D. King, and S. Moretti, New [25] M. Deniz et al. (TEXONO Collaboration), Measurement of ¯ physics suggested by Atomki anomaly, Front. Phys. 7,73 νe -electron scattering cross section with a CsI(Tl) scintillat- (2019). ing crystal array at the Kuo-Sheng nuclear power reactor, [12] O. Seto and T. Shimomura, Atomki anomaly in gauged Phys. Rev. D 81, 072001 (2010). ð1Þ U R symmetric model, J. High Energy Phys. 04 (2021) [26] D. Cronin-Hennessy et al. (CLEO Collaboration), Obser- þ þ þ − 025. vation of the Dalitz decay Ds → Ds e e , Phys. Rev. D [13] T. Nomura and P. Sanyal, Explaining Atomki anomaly and 86, 072005 (2012). − 2 ð1Þ muon g in U X extended flavour violating two Higgs [27] L. G. Landsberg, Electromagnetic decays of light mesons, doublet model, arXiv:2010.04266. Phys. Rep. 128, 301 (1985). [14] A. Aleksejevs, S. Barkanova, Y. G. Kolomensky, and B. [28] E. Kou et al. (Belle-II Collaboration), The Belle II physics Sheff, A standard model explanation for the “ATOMKI book, Prog. Theor. Exp. Phys. (2019), 123C01; Erratum, anomaly”, arXiv:2102.01127. (2020), 029201.

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