Searching for a new force at VEPP-3

The idea here is worth your attention: put a positron beam on the internal hydrogen target at VEPP-3 and reconstruct the missing mass in e+e- -> gamma A'. Because you only detect the recoil photon, the search is independent of the A' decay mode and lifetime, which is the thing that limits the beam-dump and collider searches. The 5-20 MeV window is genuinely under-covered, and the kinematics and cross sections in Section III are textbook QED with the right citations (Heitler, Tsai). The arithmetic in Section V is internally consistent: 30 kHz over six months at 75% uptime gives 3.5e11 annihilation events, 0.08% residual background gives 2.8e8, sqrt gives 1.7e4, and that lands at 1.1e-8 at five-to-one. The detector plan is concrete and sensible, reusing the PRIMEX PbWO4 and CLEO-II CsI calorimeters, and the electron-beam calibration run to get a smooth white spectrum is a nice touch. This is a repurposing of existing hardware, partly sketched in the authors' own earlier note (ref. 27), but the quantitative reach estimate is new and that is the contribution. The soft spot is exactly where the stress test says it is. The 0.08% residual and the factor-50 positron-veto suppression are estimates, not simulation or data. The 98% veto efficiency is a design number for a 15X0 sandwich; the factor 50 folds in geometric acceptance, which the 2 cm vertical gap degrades. The paper says the gap lets median-plane positrons through and compensates by discarding a horizontal band in the photon detector, losing about 20% phi acceptance, but the residual leakage is never quantified. Since the reach scales as 1/sqrt(B), a factor-5 underestimate of B weakens the limit to about 2.5e-8 and a factor-25 to about 5.5e-8. The paper also quantifies only statistical uncertainty; with 2.8e8 background events, a 0.1% systematic in the normalization is 17 times the statistical fluctuation, so the 5-sigma reach needs the background shape controlled to roughly 6e-5, which is not discussed. The detector resolution at 200 MeV is extrapolated from 1-5 GeV measurements, which the authors acknowledge. The facility work (RF cavity removal, wall and quadrupole machining, a new D2 magnet) has no cost or schedule, normal for a proposal but worth noting. None of this is fatal; it is the normal state of a design study, and the fix is a GEANT simulation plus a test-beam measurement of the veto. Who should read it: anyone working on light dark photons below 100 MeV, and anyone thinking about storage-ring internal-target experiments. It deserves a serious referee, mainly to press on the background model.

The central claim (abstract:s3; Section V; Summary) is a projected |f_eA'|² = 1.1e-8 at 5:1 S/N. The arithmetic is internally consistent: 30 kHz × 6 months × 0.75 = 3.5e11 annihilation events; 0.08% residual = 2.8e8 background; √B = 1.7e4; 1.7e4/3.5e11 = 4.8e-8 per 1σ; ×5 gives 5 × 2.2e-9 = 1.1e-8. The chain holds. The load-bearing step is the 0.08%. It is the product of (a) the raw bremsstrahlung being 30–100× below the annihilation band in the 2D signal region, and (b) a factor-50 positron-veto suppression. Neither is derived from a simulation or from the existing VEPP-3 data (ref 32, a 4-month run at 1e32). The 98% veto efficiency is a design number for a 15X0 W/scintillator sandwich; the factor 50 is that efficiency times the geometric acceptance of the veto, which is degraded by the 2 cm vertical gap introduced to keep the 6 MHz veto rate manageable. The paper notes the gap lets through positrons near the median plane and compensates by discarding a horizontal band in the photon detector, losing ~20% φ acceptance, but the residual leakage is not quantified. Because the reach scales as 1/√B, a factor-5 underestimate of B weakens the coupling limit by √5 ≈ 2.2 (1.1e-8 → 2.5e-8), and a factor-25 underestimate by 5 (→ 5.5e-8). The paper quantifies only statistical uncertainty; with 2.8e8 background events, a 0.1% systematic in the background normalization is 2.8e5 events, 17× the statistical fluctuation, so the 5σ reach also requires the background shape to be controlled to ~6e-5, which is not discussed. The concern lands.

This is a 2012 design proposal, not a measurement. The QED inputs are standard (Heitler, ref 29; Tsai, ref 30), the kinematics in Section III are textbook, and the arithmetic chain in Section V is internally consistent. The cross-section normalization from event fraction to |f_eA'|² (4.8e-8 → 2.2e-9) is not shown explicitly, but it is consistent with the standard e+e-→γA' result (the massless ratio is 2ε² from the identical-particle factor, reduced by the (1-M²/s) phase space at M²/s = 0.44), so it is within a factor of ~2 and not the load-bearing gap. The mass resolution (~4% at 15 MeV from 5% energy and 0.1° angular resolution) is adequate to resolve the peak. The detector-resolution extrapolation from PRIMEX/CLEO-II is acknowledged by the authors ('the accuracy of such an estimation is questionable'), so it is not a new finding. The load-bearing gap is the background model. The 0.08% residual and the factor-50 veto suppression are the two numbers that set the statistical fluctuation, and the entire 5:1 reach scales as 1/√B. Neither number is backed by a simulation or by the existing VEPP-3 data. The paper's own language is 'estimated.' A factor-5 error in B moves the headline from 1.1e-8 to 2.5e-8; a factor-25 error moves it to 5.5e-8. The qualitative claim of a large improvement over the g-2 limit survives, but the specific abstract number does not. The reader's weakest-assumption call is correct, and the verdict CONDITIONAL is appropriate: the proposal is sound in principle, but the projected reach should be demonstrated by a simulation or a test-beam/data-driven background measurement before the headline number is believed.

The proposal addresses a genuine gap: the 5–20 MeV mass range is poorly covered by existing fixed-target and colliding-beam searches, and the missing-mass technique is genuinely decay-mode independent, which distinguishes it from beam-dump and e+e− invariant-mass searches. The kinematic treatment in §III and the cross sections in Eqs. (1)–(2) are standard QED with appropriate citations (Heitler, Tsai), and the detector discussion is concrete, naming existing calorimeters with measured resolutions. The projection is falsifiable and, if the background model holds, would represent a substantial improvement over the electron g−2 bound in this mass window. These are real strengths and are the reason the proposal merits serious consideration.

The authors propose to search for a hypothetical light gauge boson, the $A'$ or dark photon, by colliding the 500 MeV positron beam of the VEPP-3 storage ring with a hydrogen gas target inside the ring. The signature is the reaction $e^+e^-$ → $A'$ + $γ$: detect the single photon, measure its energy and angle, and reconstruct the missing mass. Because only the photon is observed, the method works regardless of whether the $A'$ decays visibly, invisibly, or lives long enough to escape the detector — a property most competing searches lack. The projected reach after a six-month run at a luminosity of $10^{32}$ cm$^{-2}$s$^{-1}$ is an upper limit on the square of the electron coupling of about $1.1×10^{-8}$ at $m_{A'}=15$ MeV with a five-to-one signal-to-noise ratio, which the authors present as roughly a thousand-fold improvement over the bound inferred from the electron anomalous magnetic moment in a mass window of 5–20 MeV that other proposed experiments do not cover.

What carries the argument. The load-bearing mechanism is missing-mass reconstruction with single-arm photon detection. A chicane of three dipole magnets bends the positron beam into the target, sweeps scattered positrons away from the photon line, and returns the beam to the ring, letting photons reach a calorimeter through a thin beryllium window at 1.5°–4.5° in the lab. Two kinematic handles do the work: the lab photon energy varies strongly with angle, which controls systematics, and the $A'$ photon is shifted below the annihilation peak by the factor $(1 - M_{A'}^2/s)$, which is what makes the missing-mass peak identifiable. Background rejection relies on a tungsten–scintillator sandwich veto downstream of the second dipole, which tags the degraded positron from bremsstrahlung with above 98% efficiency, combined with a vertical gap in the veto and a matching excluded horizontal band in the photon detector that together cost only about 20% of the azimuthal acceptance.

Core claim. The paper's claim is a projected sensitivity, not a measurement. It argues that a modest-luminosity positron beam striking an internal hydrogen target constitutes a low-energy $e^+e^-$ collider in which the two-body kinematics of $e^+e^-$ → $A'γ$ cleanly separates the signal photon from the two-photon annihilation peak: the $A'$ photon sits at $E_γ(A'γ) = E_γ(γγ)(1 - M_{A'}^2/s)$, displaced into the continuum below the annihilation line. With photon energy resolution near 5%, a 15% wide search window, and background suppressed by a factor of 50 or more through a positron veto counter and a multi-photon rejection, the residual background in that window is estimated at 0.08% of the annihilation photon rate. In a six-month run at $10^{32}$ cm$^{-2}$s$^{-1}$ that yields about $3.5×10^{11}$ annihilation events and a statistical background uncertainty of $1.7×10^4$ events, so a signal equal to that fluctuation corresponds to $4.8×10^{-8}$ of the annihilation rate, or $|f_{eA'}|^2 = 2.2×10^{-9}$; the quoted five-to-one result of $1.1×10^{-8}$ follows from the same accounting.

The premise it rests on. The projected limit rests entirely on the estimated background suppression: that the positron veto removes bremsstrahlung by at least a factor of 50 and that the leftover background in a 15% energy window is only 0.08% of the annihilation photon rate, numbers given as estimates rather than as the output of a documented simulation or existing data.

A null result would set a direct limit on the electron coupling of the $A'$ in the 5–20 MeV mass range, a window the authors argue is inaccessible to most other fixed-target and colliding-beam proposals.

Because the method needs no assumption about the $A'$ decay mode or lifetime, it covers invisible and long-lived dark photon scenarios that beam-dump and decay-product searches cannot exclude.

A positive signal would appear as a peak in the missing-mass spectrum whose position fixes $m_{A'}$ and whose height fixes $|f_{eA'}|^2$, with the angular dependence of the photon energy providing an independent cross-check.

Running with an electron beam instead of a positron beam gives a smooth photon spectrum with no annihilation peak and no $A'$ signal, providing a data-driven calibration of the detector response and line shape.

The same internal-target and chicane infrastructure is shared with an existing photon-tagging setup, so the incremental hardware cost is limited mainly to a large-aperture dipole and a new calorimeter.

The projected reach scales as the square root of the residual background, so a documented simulation of the veto and multi-photon rejection, rather than an estimate, is what would decide whether the thousand-fold improvement survives contact with reality.

If the technique works at $10^{32}$ cm$^{-2}$s$^{-1}$, the same apparatus with the planned factor of 5–10 luminosity upgrade would push the coupling reach down by a further factor of roughly 2–3 without new detector concepts.

The mass reach is set by $m_{A'} \lesssim \sqrt{E_+[\text{MeV}]}$ MeV, so a higher-energy positron beam at the same facility would extend the search upward in mass at the cost of a $1/E_{cm}^2$ cross-section penalty.

A confirmed light vector boson in this mass range would be a natural mediator for MeV-scale dark matter annihilation, tying this search to the astrophysical positron excess that motivates the mass window in the first place.

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