Constraints on New Physics in the Electron g-2 from a Search for Invisible Decays of a Scalar, Pseudoscalar, Vector, and Axial Vector
Yu.M. Andreev, D. Banerjee, J. Bernhard, V.E. Burtsev, A.G. Chumakov, D. Cooke, P. Crivelli, E. Depero, A.V. Dermenev, S.V. Donskov, R.R. Dusaev, T. Enik, N. Charitonidis, A.Feshchenko, V.N. Frolov, A.Gardikiotis, S.G. Gerassimov, S.N. Gninenko, M. Hosgen, V.A. Kachanov, A.E. Karneyeu, G. Kekelidze, B. Ketzer, D.V.Kirpichnikov, M.M. Kirsanov, V.N. Kolosov, I.V. Konorov, S.G. Kovalenko, V.A. Kramarenko, L.V. Kravchuk, N.V. Krasnikov, S.V. Kuleshov, V.E. Lyubovitskij, V.Lysan, V.A. Matveev, Yu.V. Mikhailov, L. Molina Bueno, D.V. Peshekhonov, V.A. Polyakov, B. Radics, R. Rojas, A. Rubbia, V.D. Samoylenko, H. Sieber, D. Shchukin, V.O.Tikhomirov, I. Tlisova, A.N. Toropin, A.Yu. Trifonov, B.I. Vasilishin, P.V. Volkov, V.Yu. Volkov
EEUROPEAN LABORATORY FOR PARTICLE PHYSICS
CERN-EP-2021-017
Constraints on New Physics in the Electron g − from a Search for Invisible Decaysof a Scalar, Pseudoscalar, Vector, and Axial Vector Yu. M. Andreev, D. Banerjee, J. Bernhard, V. E. Burtsev, A. G. Chumakov,
12, 13
D. Cooke, P. Crivelli, E. Depero, A. V. Dermenev, S. V. Donskov, R. R. Dusaev, T. Enik, N. Charitonidis, A. Feshchenko, V. N. Frolov, A. Gardikiotis, S. G. Gerassimov,
3, 7
S. N. Gninenko ∗ , M. H¨osgen, V. A. Kachanov, A. E. Karneyeu, G. Kekelidze, B. Ketzer, D. V. Kirpichnikov, M. M. Kirsanov, V. N. Kolosov, I. V. Konorov,
3, 7
S. G. Kovalenko, V. A. Kramarenko,
2, 8
L. V. Kravchuk, N. V. Krasnikov,
2, 6
S. V. Kuleshov,
11, 16
V. E. Lyubovitskij,
12, 13, 14
V. Lysan, V. A. Matveev, Yu. V. Mikhailov, L. Molina Bueno, D. V. Peshekhonov, V. A. Polyakov, B. Radics, R. Rojas, A. Rubbia, V. D. Samoylenko, H. Sieber, D. Shchukin, V. O. Tikhomirov, I. Tlisova, A. N. Toropin, A. Yu. Trifonov,
12, 13
B. I. Vasilishin, P. V. Volkov,
2, 8 and V. Yu. Volkov (The NA64 Collaboration) Universit¨at Bonn, Helmholtz-Institut f¨ur Strahlen-und Kernphysik, 53115 Bonn, Germany Joint Institute for Nuclear Research, 141980 Dubna, Russia Technische Universit¨at M¨unchen, Physik Department, 85748 Garching, Germany CERN, European Organization for Nuclear Research, CH-1211 Geneva 23, Switzerland UCL Departement of Physics and Astronomy, University College London,Gower St. London WC1E 6BT, United Kingdom Institute for Nuclear Research, 117312 Moscow, Russia P.N. Lebedev Physical Institute, Moscow, Russia, 119 991 Moscow, Russia Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, 119991 Moscow, Russia Physics Department, University of Patras, 265 04 Patras, Greece State Scientific Center of the Russian Federation Institute for High Energy Physicsof National Research Center ’Kurchatov Institute’ (IHEP), 142281 Protvino, Russia Departamento de Ciencias F´ısicas, Universidad Andres Bello, Sazi´e 2212, Piso 7, Santiago, Chile Tomsk Polytechnic University, 634050 Tomsk, Russia Tomsk State Pedagogical University, 634061 Tomsk, Russia Universidad T´ecnica Federico Santa Mar´ıa, 2390123 Valpara´ıso, Chile ETH Z¨urich, Institute for Particle Physics and Astrophysics, CH-8093 Z¨urich, Switzerland SAPHIR Millennium Institute of ANID, Chile (Dated: February 4, 2021)We performed a search for a new generic X boson, which could be a scalar ( S ), pseudoscalar ( P ),vector ( V ) or an axial vector ( A ) particle produced in the 100 GeV electron scattering off nuclei, e − Z → e − ZX , followed by its invisible decay in the NA64 experiment at CERN. No evidence forsuch process was found in the full NA64 data set of 2 . × electrons on target. We place newbounds on the S, P, V, A coupling strengths to electrons, and set constraints on their contributions tothe electron anomalous magnetic moment a e , | ∆ a X | (cid:46) − − − for the X mass region m X (cid:46) a e from the electron g − PACS numbers: ∗ Corresponding author: [email protected] a r X i v : . [ h e p - e x ] F e b Searching for new physics (NP) with mass below theelectroweak scale ( (cid:28)
100 GeV) at the high-intensity andhigh-precision frontiers has received significant attentionin recent years [1–8]. Motivations for searches of feebly-coupled particles in the low-mass range come from theevidence for NP in the neutrino and dark matter sectors,and are well supported by theoretical arguments, see, e.g.Refs.[1, 7–13]. Existing anomalies observed in particleexperiments also contribute to the field. Well-known ex-amples are the current muon g − (cid:39) . σ discrepancy between the predicted and observed valueof the muon anomalous magnetic moment [14], or theX17 anomaly - an excess of e + e − events in the Be and He nuclei transitions [15, 16], which might be explainedby NP models at low-mass scale, see, e.g. Refs.[17, 18].These anomalies are being scrutinized in the upcomingexperiments at Fermilab and JPARC [19, 20], and withNA64 at CERN [21–23], respectively.Recently, a new puzzle indicating the possible presenceof NP in the electron g − Rb rubidium atoms report a new valuefor the fine-structure constant α − = 137.035999206(11)with a relative accuracy of 81 parts per trillion [24]. Thisresult improves the accuracy on α by 2.5 over the pre-vious measurements performed at Berkeley with Csatoms [25] but, surprisingly, it reveals a 5 . σ differencefrom this latest result. Using these measurements of thefine-structure constant, the Standard Model (SM) predic-tion of the anomalous magnetic moment of the electron, a e = ( g − e / . σ lower and − . σ higherthan the direct experimental measurement of a expe [28]:∆ a e = a expe − a LKBe = (4 . ± . × − (1)∆ a e = a expe − a Be = ( − . ± . × − (2)for the LKB and Berkeley measurements, respectively.The errors on ∆ a e are dominated mostly by the uncer-tainty in a expe . As the SM predicts a certain value ofthe a e [26, 27] the measurements of this parameter indifferent processes should be consistent with each other.With new measurements and improved SM calculations,one hopes to clarify whether the deviations of Eqs.(1,2)are a result of yet unknown experimental errors, or it isa sign of new physics in the electron g − X boson could contribute to the electron g − X in sub-GeV massrange, which could be a scalar ( S ), pseudoscalar ( P ),vector ( V ), or an axial vector ( A ) particle feebly coupledto electrons. It is assumed that the X decays predom-inantly invisibly, Γ( X → invisible ) / Γ tot (cid:39)
1, e.g. intodark sector particles, thus escaping stringent constraintsplaced today on the visible decay modes of the X intoSM particles from collider, fixed-target, and atomic ex-periments [46]. The most stringent limits on the invisible X in the sub-GeV mass range are obtained, so far, forthe V case of dark photons coupled to electrons throughthe mixing with the ordinary photons by the NA64 [47]and BABAR [48] experiments, leaving a large area of theparameter space for the generic X still unexplored. Vari-ous aspects of such invisible X weakly coupled to leptonsincluding possible phenomenological implications can befound in Refs.[1–8, 45, 49, 50].The e − X -interaction with the coupling strength g X defined as g X = ε X e (here ε X is a parameter and e is thecharge of the electron) is given for the S, P, V, A cases byphenomenological Lagrangians: L S = g S eeS L P = ig P eγ eP L V = g V eγ µ eV µ L A = g A eγ µ γ eA µ (3)The corresponding one-loop contributions to the ( g − e FIG. 1: One-loop contribution of the S and P (left panel) andthe V and A (right panel) to ∆ a e . factor induced by diagrams shown in Fig. 1 are given by:∆ a S = g S π (cid:0) m e m X (cid:1) (cid:2) ln m X m e − (cid:3) (4)∆ a P = g P π (cid:0) m e m X (cid:1) (cid:2) − ln m X m e + 1112 (cid:3) (5)∆ a V = g V π (cid:0) m e m X (cid:1)
13 (6)∆ a A = g A π (cid:0) m e m X (cid:1) (cid:0) − (cid:1) (7)assuming that m X (cid:29) m e . One can see that presumablya scalar and a vector can explain the positive deviationof Eq.((1)), while only a pseudoscalar and an axial vec-tor could explain the negative value of Eq.((2)). Therequired couplings g X to explain deviations of Eqs.(1,2)are in the range 10 − (cid:46) | g X | (cid:46) − which is accessibleto the NA64 search, thus making it interesting.The method of the search, discussed in this work andproposed in Refs. [51, 52], is based on the detection of themissing energy, carried away by the hard bremsstrahlung X produced in the process e − Z → e − ZX ; X → invisible of high-energy electrons scattering in an ac-tive beam dump. The NA64 experiment employed a100 GeV pure electron beam, using the H4 beam-lineof the CERN’s North Area. The beam was slowly ex-tracted towards NA64 in 4.8 s spills, and had an inten-sity up to (cid:39) electrons per spill. The e − beam wasdefined by the scintillator ( S ) and veto ( V ) counters. Amagnetic spectrometer consisting of two successive dipolemagnets with the integral magnetic strength of (cid:39) · mand a low-material-budget tracker consisting of a set ofMicromegas (MM), Straw-Tube (ST) and Gaseous Elec-tron Multiplier (GEM) chambers allowed to measure theincoming e − momenta with the precision δp/p (cid:39)
1% [53].The synchrotron radiation (SR) emitted in the magnetswas used for the electron identification and their efficienttagging with a SR detector (SRD)[54], which was an ar-ray of a Pb-Sc sandwich calorimeter of a fine segmen-tation. By using the SRD the intrinsic hadron contam-ination of the beam of the order of ∼
1% was furthersuppressed to a negligible level. The downstream partof the detector was equipped with an electromagnetic( e-m ) calorimeter (ECAL), a matrix of 6 × E ECAL . Each ECAL module has (cid:39) X ) with the first 4 X serving as apreshower detector (PS). Further downstream the detec-tor was equipped with a high-efficiency veto counter ( V ),and a hermetic hadronic calorimeter (HCAL) of (cid:39)
30 nu-clear interaction lengths in total. The HCAL was used asan efficient veto against hadronic secondaries and also todetect muons produced in e − interactions in the target.The search described in this paper uses the data sam-ples of n EOT = 2 . × electrons on target (EOT),collected in the years 2016, 2017 and 2018 (runs I,II, andIII, respectively) at the beam intensities mostly in therange (cid:39) (5 − × e − per spill with the hardwaretrigger [47, 55, 56] T r ( X ) = Π S i · V · PS( > E th PS ) · ECAL( < E th ECAL ) , (8)accepting events with in-time hits in beam-defining coun-ters S i and clusters in the PS and ECAL with theenergy exceeding the thresholds E th PS (cid:39) . E th ECAL (cid:46)
80 GeV, respectively. The missing energyevents have the signature S ( X ) = T r ( X ) · Track( P e ) · V ( < E th V ) · HCAL( < E th HCAL )(9)with the incoming track momentum P e (cid:39) ± V and HCAL zero-energy deposition, defined as en-ergy below the thresholds E th V (cid:39) E th HCAL (cid:39) X in the process e − Z → e − ZX ; X → invisible has been simulated foreach type of interactions listed in Eq.(3) with cross-sections obtained from exact tree-level (ETL) calcula-tions, see, e.g., Refs. [60–62]. The produced signal sam-ples were processed by the same reconstruction programas the real data and passed through the same selectioncriteria. The total number n X of the produced X persingle electron on target (EOT) was calculated as n X ( g X , m X , E ) = ρN A A Pb (cid:88) i n ( E , E e , s ) σ X ( E e )∆ s i (10)where ρ is density of the target, N A is the Avogadro’snumber, A Pb is the Pb atomic mass, n ( E , E e , s ) is thenumber of e ± in the e-m shower at the depth s (in ra-diation lengths) with the energy E e within the targetof total thickness T , and σ ( E e ) is the cross section ofthe X production in the kinematically allowed regionup to E X (cid:39) E e by an electron with the energy E e in the reaction e − Z → e − ZX ; X → invisible . Thelatter depends in particular on the coupling and mass g X , m X , and the beam energy E . The X energy dis-tribution dn X dE X was calculated for each case by takinginto account the corresponding differential cross-section dσ ( E e ,E X ) dE X , as described in Ref.[61]. An example of thesimulated X (or missing) energy spectrum in the targetcalculated by using the detailed simulation of e-m showerdevelopment by Geant4 is shown for the P and V casesin Fig. 2 for the mass m X = 20 MeV. The expected E v en t s / G e V FIG. 2: The emission spectra of the 20 MeV P (solid line)and V (dashed line) particles produced from the interactionsof the 100 GeV electron beam in the ECAL target obtainedfrom the ETL calculations. The spectra are normalized tothe same number of EOT. . number of X events in our detector from the reaction e − Z → e − ZX ; X → invisible was determined for each X interaction type also by comparison to the rare pro-cess of dimuon production, e − Z → e − Zγ ; γ → µ + µ − ,which has a well-known reaction rate. These eventsoriginate from the QED reaction in the ECAL, dom-inated by the hard bremsstrahlung photon conversioninto dimuon pairs on a target nucleus and accompaniedby small energy deposition in the HCAL, thus mimick-ing the X → invisible decay events below the two-MIPthreshold. The reaction was also used as a benchmarkprocess allowing us to verify the reliability of the MCsimulation, correct the signal acceptance, cross-check sys-tematic uncertainties and background estimate [47, 56].Good agreement was found between the observations andsimulations. Using rare dimuon events as a crosscheckfor normalization to the signal modes cancels many sys-tematic uncertainties by keeping selection cuts identicalwhenever possible.In order to avoid biases in the determination of theselection criteria for signal events, a blind analysis simi-lar to the one described in Ref.[47] was performed. Thesignal box ( E ECAL <
50 G eV ; E HCAL < eV ) was de-fined based on the energy spectrum calculations for X semitted by e ± from the e-m shower generated by theprimary e − s in the ECAL [60, 61] and the HCAL zero-energy threshold determined mostly by the noise of theread-out electronics. Finally, to maximize the acceptancefor signal events and to minimize backgrounds we usedthe following selection criteria: (i) The incoming electrontrack momentum should be within 100 ± e − s in the magnets and in time with thetrigger; (iii) The shower shape in the ECAL should beconsistent with the one expected for the signal shower[60]; (iv) There should be only a single track activityin the tracker chambers upstream of the dump in orderto reject interactions in the beam line materials, and noactivity in V .The dominant background for e − Z → e − ZX ; X → invisible arises from the interactions of the e − beam inthe downstream part of the detector resulting in hadronelectro-production in the beam line materials. In rarecases, these reactions are accompanied by the emissionof large-angle (high p T ) hadronic secondaries faking thesignal due to the insufficient downstream detector cover-age. Charged secondaries were rejected by requiring noadditional tracks or hits in the downstream ST chambers,which have the largest transverse acceptance in our setup.We also requested no extra in-time hits upstream of themagnets and at most one extra in-time hit downstream ofthe magnets in the MM chambers. The remaining back-ground from the large-angle neutral hadronic secondarieswas evaluated mainly from data by the extrapolation ofevents from the sideband ( E ECAL >
50 G eV ; E HCAL < eV ) into the signal region and assessing the system-atic errors by varying the fit functions selected as de-scribed in Ref. [56]. The shape of the extrapolation func-tions was evaluated from the study of a larger data sam-ple of events from hadronic e − interactions in the dump,which was also cross-checked with simulations. Anotherbackground from punch-through of leading (with energy (cid:38) . E ) neutral hadrons ( n, K L ) produced in the e − interactions in the target, was studied by using events from the region ( E ECAL <
50 G eV ; E HCAL > eV ),which were pure neutral hadronic secondaries producedin the ECAL. Its level was estimated from the data byusing the longitudinal segmentation of the HCAL andthe punch-through probability estimated conservativelyand was found to be negligible. Several other backgroundsources that may fake the signal, such as loss of dimuonsdue to statistical fluctuations of the signal or muon de-cays, and decays in flight of mistakenly SRD tagged beam π , K were simulated with the full statistics of the dataand also were found to be negligible. After determiningall the selection criteria and background levels, we un-blinded the signal region and found 0 events consistentwith 0 . ± .
17 events from the conservative backgroundestimations [47] allowing us to obtain the m X -dependentupper limits on the e − X coupling strengths. FIG. 3: The 90% C.L. upper limits on the coupling parameter ε X in the ( m X , ε X ) plane obtained by NA64 and presented incomparison with the bounds derived from the results of theLKB [24] and Berkeley (B) [25] experiments. The limits areshown by lines labeled with the X type of the same color. The overall signal efficiency (cid:15) X defined as the prod-uct of signal efficiencies accounting for the geometricalacceptance, the track, SRD, V and HCAL reconstruc-tion, and the DAQ dead time was found to be slightlydependent on m X , E X values [47]. The signal-event re-construction efficiency (cid:15) ECAL was estimated as a functionof energy deposited in the ECAL for different X masses.Compared to the ordinary e-m shower, the (cid:15) ECAL valuefor a shower from X event has to be corrected due todifference in the e-m showers development at the earlystage in the ECAL PS [60]. Depending on the energythreshold in the PS ( E th PS ) used in trigger (8) this cor-rection was (cid:46) (5 ± E th PS variation during the run. The V and HCALefficiency defined by the leak of the signal shower energyfrom the ECAL to these detectors, was studied for differ-ent X masses with simulations that were validated withmeasurements at the e − beam. The uncertainty in theefficiencies dominated mostly by the pileup effect was es-timated to be (cid:46) . ± .
02. The X signal-event acceptance wasestimated by taking into account the efficiency of selec-tion cuts for the signal shower shape in the ECAL [60].The dominant uncertainty in the signal yield (cid:39)
10% wasconservatively accounted for the difference between thepredicted and measured dimuon yield [56]. The total sig-nal efficiency (cid:15) X was in the range 0.5 - 0.7 depending onthe beam intensity and the X mass.To set the limits we analysed runs I-III simultane-ously using the technique based on the RooStats pack-age [63] allowing multibin limit setting [56]. For each of X = S, P, V, A cases, we tried to optimize the size of thesignal box by comparing sensitivities defined as an aver-age expected limit calculated using the profile likelihoodmethod. The calculations were done by taking into ac-count the background estimate, efficiencies, and their cor-rections with uncertainties used as nuisance parameters[64]. For this optimization, the most important inputscame from the background extrapolation into the sig-nal region from the data samples of runs I-III with theirerrors estimated from the extrapolation procedure. Theoptimal signal box size was found to be weakly dependenton the e − X type of interaction and X mass varying witha few GeV, and was finally set to E ECAL (cid:46)
50 GeV forall four cases of Eq.(3) and the whole mass range. The
FIG. 4: Shown are the NA64 90% C.L. exclusion region in the( m X , | ∆ a X | ) plane for the S, P, V and A contributions to a e together with the bands of Eqs.(1,2), representing the resultsof the LKB [24] (black dashed) and Berkeley [25] (blue solid)experiments. The legend is the same as for Fig. 3. total number of signal events was the sum of expected events from the all three runs in the signal box: N X = (cid:88) i =1 N iX = (cid:88) i =1 n iEOT (cid:15) iX n iX ( g X , m X , ∆ E e ) (11)where (cid:15) iX and n iX ( (cid:15), m X , ∆ E X ) is the signal efficiencyand the signal yield per EOT in the energy range ∆ E e ,respectively. These values were calculated from simu-lations and processing of signal events through the re-construction program with the same selection cuts andefficiency corrections as for the data sample from run i .The combined 90% C.L. exclusion limits on the cou-pling parameter ε X as a function of the X mass, calcu-lated by using the modified frequentist approach [47, 65–67] are shown in Fig. 3. By using Eqs.(1), (2) and (4) -(7), it is also possible to translate the measurements ofRefs.[24, 25] into constraints on the coupling ε X whichare shown in Fig. 3 for comparison. The limits werecalculated by taking into account the sign of the contri-butions ∆ a X in Eqs.(4) - (7) assuming that the S and V contribute to the deviation of Eq.(1) , while only the P and A can resolve the discrepancy of Eq.(2). Our boundsare more stringent than those derived from the resultsof high-precision measurements of Refs.[24, 25, 28]. Us-ing Eqs.(4) - (7) and obtained limits on the X couplingstrength we can derive constraints on the X contribu-tion ∆ a X to a e . This results in stringent bounds in therange | ∆ a X | (cid:46) − − − for S, P, V and A withsub-GeV masses, which are shown in the ( m X ; | ∆ a X | )plane in Fig. 4 together with the experimental bands ofthe ∆ a X values defined by Eqs.(1, 2). For the low massregion m X (cid:46)
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