Search for Light New Physics at B Factories

Many extensions of the Standard Model include the possibility of light new particles, such as light Higgs bosons or dark matter candidates. These scenarios can be probed using the large datasets collected by B factories, complementing measurements performed at the LHC. This review summarizes recent searches for light New Physics conducted by the BABAR and Belle experiments.

Many extensions of the Standard Model include the possibility of light new particles, such as light Higgs bosons or dark matter candidates. These scenarios can be probed using the large datasets collected by B factories, complementing measurements performed at the LHC. This review summarizes recent searches for light New Physics conducted by the BABAR and Belle experiments.

I. INTRODUCTION
From supersymmetry to dark matter, many extensions of the Standard Model (SM) include the possibility of light New Physics. Thanks to their large luminosities, B factories offer an ideal environment to explore these theories. During the last decade, the BABAR Collaboration at PEP-II [1] and the Belle Collaboration at KEKB [2,3] have respectively collected about 550 fb −1 and more than 1 ab −1 of data at several Υ resonances, mostly the Υ (4S) resonance (see Table I). These datasets have been exploited to explore many aspects of precision physics, including searches for light new particles. In the following, we review searches for light Higgs bosons, dark matter candidates, hidden sectors, sgoldstinos and Majorana neutrinos.

II. SEARCH FOR LIGHT CP -ODD HIGGS BOSON IN Υ DECAYS
A light Higgs boson is predicted by several extensions of the Standard Model, such as the Next-to-Minimal Supersymmetric Standard Model (NMSSM). The NMSSM Higgs sector contains a total of seven states, three CP -even, two CP -odd, and two charged Higgs bosons. A CP -odd Higgs boson (A 0 ) lighter than 2m b can evade present experimental constraints [4], making it accessible through radiative Υ (nS) → γA 0 decays [5]. The corresponding branching fraction could be as large as a few×10 −4 , well above the sensitivity of B factories [4,6].
The Higgs boson decay pattern depends on its mass and couplings, as well as the NMSSM particle spectrum. In the absence of light neutralinos, the A 0 decays predominantly into a pair of muons below 2m τ , while τ + τ − and hadronic final states become significant above this threshold. The branching fraction A 0 → χ 0χ0 may be dominant if the neutralino (χ 0 ) is the lightest stable particle with m χ 0 < m A 0 /2 [7]. In this case, the neutralino is a natural dark matter candidate.
BABAR has performed searches for a light CP -odd Higgs boson in a variety of decay channels. These measurements are discussed in the next paragraphs, and the results are summarized in Table II. They place stringent constraints on light CP -odd Higgs models.
as a function of the A 0 mass derived by BABAR. The limits on the product B(A 0 → µ + µ − )f 2 Υ , are also shown (bottom). The J/ψ and ψ(2S) regions (solid bands) are excluded from the search. Right: Product of branching fraction Υ (3S) → γA 0 , A 0 → τ + τ − (top) and the corresponding 90% CL upper limit (bottom) as a function of the A 0 mass set by BABAR. The region corresponding to χ bJ (2P ) → γΥ (1S) transitions (shaded band) is excluded.
The two taus of the Υ (3S) → γA 0 , A 0 → τ + τ − decays are identified through their leptonic decays, τ + → e + ν eντ and τ + → µ + ν µντ . The signal signature consists of exactly two oppositely-charged tracks, identified as muons or electrons, and at least one photon with an energy greater than 100 MeV in the CM frame. A set of eight kinematic and angular variables are used to further suppress the background, which arises mainly from radiative τ production and two-photon processes. The signal yield is extracted as a function of m A 0 by a simultaneous fit to the photon energy distribution of the eeγ, µµγ and eµγ samples. No excess is seen; 90% CL limits on the branching fraction are set at the level of (1.5 − 16) × 10 −5 in the interval 4.03 < m A 0 < 10.1 GeV [11], as shown in  The hadronic final states are selected from fully reconstructed the A 0 → hadrons decays. The highest energy photon of the event is identified as the radiative photon from the Υ (nS) decay; the A 0 candidate is then constructed by adding the four-momenta of the remaining particles, constraining the A 0 decays products to originate from the interaction point to improve the resolution. The signal yield is obtained by fitting the candidate mass spectrum in the range 0.3 − 7.0 GeV in steps of 1 MeV. The results are compatible with the null hypothesis; limits on the branching fraction are therefore set in the range (0.1 − 8) × 10 −5 with 90% confidence level [12].

Mode
Mass range ( GeV) BF upper limit (90% CL) This final state is characterized by a pair of low-momentum tracks, a single energetic photon, and large missing energy and momentum. Additional criteria on the photon and the extra neutral energy in the event are applied to further suppress contributions from electron bremsstrahlung, radiative hadronic Υ (1S) decays and two-photon processes in which particles escape undetected. The signal is extracted by a series of bidimensional unbinned likelihood fits to the dipion recoil mass and the missing mass squared for both two-body decays, Υ (1S) → γA 0 , A 0 → invisible, and non-resonant three-body processes, Υ (1S) → γA 0 , A 0 → χχ. Values of m A 0 and m χ0 are probed over 0 < m A < 9.2 GeV and 0 ≤ m χ0 ≤ 4.5 GeV, respectively. No significant signal is found; [13]. These limits are displayed in Fig. 2 as a function of the A 0 and χ 0 masses.
The Υ (3S) → γA 0 , A 0 → invisible decays are also selected from events containing a single energetic photon with no additional activity in the detector. The background arises mainly from e + e − → γγ, radiative Bhabha, and two-photon fusion events. The A 0 yield is extracted by a series of unbinned likelihood fits to the photon energy distribution for 0 < m A 0 < 7.8 GeV. No excess is seen, and limits on the branching fraction at the level of (0.7 − 31) × 10 −6 are derived with 90% confidence level [14].

III. SEARCH FOR DARK MATTER IN INVISIBLE Υ (1S) DECAYS
In a minimal model, a single dark matter particle (χ) is added to the SM content, together with a new boson mediating SM-dark matter interactions [15][16][17]. A light mediator could be produced in bb annihilation and decay into a χχ pair, contributing to the invisible width of Υ mesons. In the SM, invisible Υ (1S) decays proceed via the production of a νν pair with a branching fraction B(Υ (1S) → νν) ∼ (1 × 10 −5 ) [18], well below the current experimental sensitivity. The rate Υ (1S) → χχ is predicted to be larger by one or two orders of magnitude than that of Υ (1S) → νν, assuming no flavor changing currents [19].
The event topology consists of exactly two oppositely-charged tracks without any additional activity. The selection is performed using a multivariate classifier based on variables describing the pions, the neutral energy deposited in the calorimeters and the multiplicity of K 0 L candidates. The distribution of the resulting dipion recoil mass (Fig. 3) shows a clear peak corresponding to Υ (1S) mesons on top of a non-resonant component. In addition to signal events, a background from Υ (1S) decays in which the decay products escape undetected, is also present. This component, kinematically indistinguishable from the signal, is evaluated using Monte Carlo simulations.
The sum of signal and peaking background yields is first extracted by an extended maximum likelihood fit to the dipion recoil mass. After subtracting the peaking background, a signal yield of −118 ± 105 ± 124 is measured, where the first uncertainty is statistical and the second systematic. No evidence for Υ (1S) → invisible decays is observed and a 90% confidence level Bayesian upper limit on its branching fraction is set at 3.0 × 10 −4 using a prior flat in branching fraction. This result improves the best previous measurement [21] by nearly an order of magnitude, and sets stringent constraints on minimal light dark matter models.

IV. SEARCH FOR DARK MATTER AND HIDDEN SECTORS
A new class of dark matter model has recently been proposed, following observation from satellite and groundbased experiments. These models introduce a new hidden sector with WIMP-like fermionic dark matter particles charged under a new Abelian gauge group [22][23][24]. The corresponding gauge boson, dubbed a hidden photon (A ′ ), is constrained to have a mass at the GeV scale to explain the electron/positron excess observed by PAMELA [25] and FERMI [26], without a comparable anti-proton signal. The hidden photon couples to the SM photon through kinetic mixing with a mixing strength ǫ, connecting the hidden sector to SM particles [27].
The Higgs mechanism generates the hidden boson masses, adding hidden Higgs bosons (h ′ ) to the theory. A minimal model includes a single hidden photon and a Higgs boson [28]. Additional gauge and Higgs bosons are considered in more complex variations [29,30].

A. Search for a hidden photon
Hidden photons can be readily formed in e + e − → γA ′ interactions, and be reconstructed via their leptonic decays as resonances in the e + e − → γl + l − (l = e, µ) spectrum. This signature is similar to that of light CP -odd Higgs production in e + e − → Υ (2S, 3S) → γµ + µ − [8], and searches for this channel have therefore been reinterpreted as constraints on hidden photon production [31]. The limits are shown in Fig. 4, together with bounds derived from measurements of φ → ηA ′ , A ′ → e + e − decays at KLOE [32], and searches for direct production in fixed-target experiments [31,33,34]. A hidden photon could also contribute to the muon anomalous magnetic moment, and constraints from this measurement are also shown. Values of the mixing strength down to 10 −3 − 10 −2 are probed for 0.212 < m A ′ < 9.3 GeV.
Other measurements could be reinterpreted as bounds on hidden photon production, such as searches for peaks in e + e − → γτ + τ − events [11] or inclusive e + e − → γ hadrons production [12]. Invisible decays, occurring if hidden bosons decay to long-lived states, could also be detected as a mono-energetic photon peaks in e + e − → γ + invisible events [14].

B. Search for hidden sector bosons
Non-Abelian extensions of hidden sectors introduce additional hidden gauge bosons, generically denoted W ′ , W ′′ , .... The phenomenology depends on the precise structure of the model, but heavy hidden bosons decay to lighter states if kinematically accessible, while the lightest bosons are metastable and decay to SM fermions via their mixing with the hidden photon [29,30]. Non-Abelian hidden sectors could also accommodate inelastic dark matter [36] if the mass spectrum contains nearly degenerated states.
BABAR has performed a search for di-boson production in e + e − → A ′ * → W ′ W ′′ , W ′ → l + l − , W ′′ → l + l − (l = e, u) events, where the bosons are reconstructed via their decays into lepton pairs [37]. The study has been performed in the context of inelastic dark matter models, searching for two bosons with similar masses.
The signal signature consists of two narrow dileptonic resonances with similar masses carrying the full beam energy. This topology is quite unique; the only backgrounds arise from QED processes. The signal is extracted as a function of the average dileptonic mass in the range 0.24 − 5.3 GeV. No significant signal is found; limits on the e + e − → A ′ * → W ′ W ′′ cross-section are derived. The results are translated into limits on the product α D ǫ 2 , where α D = g 2 D /4π and g D is the hidden sector gauge coupling constant. Values down to 10 −10 are probed, assuming nearly degenerate bosons.

C. Search for a hidden Higgs boson
The Higgsstrahlung process, e + e − → A ′ h ′ , h ′ → A ′ A ′ , offers another gateway to hidden sectors. This process is one of the few suppressed by only a single power of the mixing strength, and the background is expected to be almost negligible. The event topology is driven by the boson masses. While Higgs bosons heavier than two hidden photons decay promptly, they become metastable below this threshold and either produce displaced decays or escape undetected.
A search for hidden Higgs boson in Higgsstrahlung production in the prompt decay regime has been conducted at BABAR, based on a data sample of 521 fb −1 [38]. The measurement is performed in the range 0.8 < m h ′ < 10.0 GeV and 0.25 < m A ′ < 3.0 GeV, with the constraint m h ′ > 2m A ′ . The signal is either fully reconstructed into lepton or pion pairs (exclusive mode), or partially reconstructed (inclusive mode). The exclusive modes contain of six tracks, forming three hidden photon candidates with equal masses and a total invariant mass close to the e + e − CM energy. The six pion final state has a significantly larger background than the other exclusive modes and is excluded from the search. Only two of the three hidden photons are reconstructed as dileptonic resonances for the inclusive modes. The remaining hidden photon, assigned to the recoiling system, must have a mass compatible with the Higgsstrahlung hypothesis.
No significant signal is observed, and upper limits on the e + e − → A ′ h ′ , h ′ → A ′ A ′ cross section are set as a function of the hidden Higgs and hidden photon masses. These bounds are finally converted into limits on the product α D ǫ 2 . The results are displayed in Fig. 5. Values down to 10 −10 − 10 −8 are excluded for a substantial fraction of the parameter space probed. These limits are translated into constraints on the mixing strength in the range 10 −4 − 10 −3 , assuming α D = α ≃ 1/137.

V. SEARCH FOR DIMUON DECAYS OF PSEUDOSCALAR SGOLDSTINOS
The observation of three Σ + → pµ + µ − events with a dimuon invariant mass clustered around 214 MeV by the HyperCP Collaboration [39] triggered much discussion about the possibility of a new light state X produced in Σ + → X, X → µ + µ − decays. Speculations about the nature of this state included a pseudoscalar sgoldstino [40], a hidden sector photon [35,41] or a light Higgs boson [42]. Subsequent measurements in e + e − collisions [8,33] and pp interactions [43] excluded the light Higgs boson and hidden photon hypotheses.
The Belle Collaboration performed a search for this state in B → K * 0 X, K * 0 → K + π − , X → µ + µ − (B K * 0 X ) and B → ρ 0 X, ρ 0 → π + π − , X → µ + µ − (B ρ 0 X ) decays using a sample of 675 millions B 0B0 pairs [44]. The B mesons are reconstructed by combining two well-identified muons with a K + π − or π + π − pair. The signal candidates are identified using the beam-energy constrained mass M bc = E 2 beam − p B and the energy difference ∆E = E beam − E B , where E beam denotes the beam energy and p B (E b ) the momentum (energy) of the B candidate in the e + e − center-of-mass frame. Signal B K * 0 X (B ρ 0 X ) events are selected in the region 5.27 < M bc < 5.29 GeV and −0.03 < ∆E < 0.04 GeV (−0.04 < ∆E < 0.04 GeV). The corresponding dimuon mass distributions are shown in Fig. 6. No events are observed in the signal region.
Lacking evidence for a pseudoscalar dimuon resonance at 214.3 MeV, 90% C.L. upper limits on the branching fraction B → K * 0 X and B → ρ 0 X are set at the level of 2.26 × 10 −8 and 1.73 × 10 −8 , respectively. They rule out models II and III of the sgoldstino interpretation of the HyperCP observation [45].

VI. SEARCH FOR LEPTON NUMBER VIOLATION AND A MAJORANA NEUTRINO
Lepton number is conserved in low-energy processes in the SM model, but can be violated in a number of New Physics scenarios, such as models containing Majorana neutrinos. In this case, the neutrino is its own antiparticle, and reactions changing the lepton number by two units become possible. The most sensitive searches have so far been based on neutrinoless nuclear double beta decays 0νββ [46], but the nuclear environment complicates the extraction of the neutrino mass scale. Processes involving meson decays, such as B → h − l + l + (h = π, K, D and l = e, µ), have been proposed as a possible alternative. The presence of a Majorana neutrino could mediate such a reaction, and would appear as an enhanced peak in the mass spectrum of the hadron and one of the leptons [47,48].
BABAR has performed a search for the lepton number violating B + → h − l + l + decays with h = π, K and l = e, µ, based on a sample of 471 ± 3 millions BB pairs [49]. The B meson candidates are reconstructed by combining a hadron with a pair of tracks identified as leptons from particle identification algorithms. The background is suppressed through boosted decision trees (BDTs) using variables describing the event shape and the B meson candidate. The number of B → h − l + l − events is extracted by a multidimensional likelihood fit of the BDTs response and the beamenergy constrained mass m ES = s/4 − p * 2 B , where p * B is the momentum of the e + e − CM frame. No evidence for such decays is observed, and limits on the corresponding branching fractions are set.
A similar analysis has been conducted by Belle in B + → D − e + e + , B + → D − e + µ + and B + → D − µ + µ + decays, followed by a subsequent D − → K + π − π − decay [50]. The analysis is based on a data sample of 772 million BB pairs collected at the Υ (4S) resonance. The B candidates are identified using the energy difference, ∆E = E B − E beam and m ES . The signal region is defined as 5.27 < m ES < 5.29 GeV and −0.055(−0.035) < ∆E < 0.035 GeV for the e + e + and e + µ + (µ + µ + ) final states. No signal events are observed and 90% CL limits on the branching fractions are set, assuming uniform three-body phase space distributions for B + → D − l + l ′+ decays.
The results are reported in Table III, and the limits on B + → h − l + l + decays as a function of the Majorana neutrino mass m ν = m l + h − are also displayed in Fig. 7. The sensitivities of the B → h − µ + µ + channels is similar to that of recent measurements from LHCb in the same channel [51,52], and are an order of magnitude more stringent than the previous results for B + → h − e + e + decays [53].

VII. CONCLUSION
B factories have proved to be versatile machines, ideally suited to search for light New Physics over a wide range of processes. The next generation of flavor factories are expected to improve the sensitivity of these searches by one to Mode BF UL (10 −8 ) mode BF UL (10 −6 ) B + → π − e + e + 3.0 B + → D − e + e + 2.6 B + → K − e + e + 2.3 B + → D − e + µ + 1.8 B + → π − µ + µ + 10.7 B + → D − µ + µ + 1.0 B + → K − µ + µ + 6.7  two orders of magnitude, further constraining the parameter space of these theories. Many more results are to come in the near future, and will hopefully contribute to elucidate the nature of physics beyond the Standard Model.