# Search for ${{\boldsymbol A}^{0}}$ (Axion) Resonance in Bhabha Scattering INSPIRE search

The limit is for $\Gamma\mathrm {({{\mathit A}^{0}})}$[B( ${{\mathit A}^{0}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$ )]${}^{2}$.
VALUE ($10^{-3}$ eV) CL% DOCUMENT ID TECN  COMMENT
• • • We do not use the following data for averages, fits, limits, etc. • • •
$<1.3$ 97 1
 1992
CNTR ${\mathit m}_{{{\mathit A}^{0}}}$ = $1.75 - 1.88$ MeV
$\text{none 0.0016 - 0.47}$ 90 2
 1992 C
CNTR ${\mathit m}_{{{\mathit A}^{0}}}$= $1.5 - 1.86$ MeV
$<2.0$ 90 3
 1992
CNTR ${\mathit m}_{{{\mathit A}^{0}}}$= $1.56 - 1.86$ MeV
$<0.013$ 95
 1991
CNTR ${\mathit m}_{{{\mathit A}^{0}}}$ = $1.832$ MeV
$\text{none 0.19 - 3.3}$ 95 4
 1991
CNTR ${\mathit m}_{{{\mathit A}^{0}}}$= $1.78 - 1.92$ MeV
$<5$ 97
 1990
CNTR ${\mathit m}_{{{\mathit A}^{0}}}$ = $1.832$ MeV
$\text{none 0.09 - 1.5}$ 95 5
 1990
CNTR ${\mathit m}_{{{\mathit A}^{0}}}$ = $1.832$ MeV, elastic
$<1.9$ 97 6
 1989
CNTR ${\mathit m}_{{{\mathit A}^{0}}}$ = $1.82$ MeV
$\text{<(10 - 40)}$ 97 6
 1989
CNTR ${\mathit m}_{{{\mathit A}^{0}}}$ = $1.51-1.65$ MeV
$\text{<(1 - 2.5)}$ 97 6
 1989
CNTR ${\mathit m}_{{{\mathit A}^{0}}}$ = $1.80-1.86$ MeV
$<31$ 95
 1988
CNTR ${\mathit m}_{{{\mathit A}^{0}}}$ = $1.646$ MeV
$<94$ 95
 1988
CNTR ${\mathit m}_{{{\mathit A}^{0}}}$ = $1.726$ MeV
$<23$ 95
 1988
CNTR ${\mathit m}_{{{\mathit A}^{0}}}$ = $1.782$ MeV
$<19$ 95
 1988
CNTR ${\mathit m}_{{{\mathit A}^{0}}}$ = $1.837$ MeV
$<3.8$ 97 7
 1988
CNTR ${\mathit m}_{{{\mathit A}^{0}}}$ = $1.832$ MeV
8
 1988
CNTR
9
 1987
CNTR
$<2500$ 90
 1987
CNTR ${\mathit m}_{{{\mathit A}^{0}}}$ = $1.8$ MeV
10
 1987
CNTR
1  HALLIN 1992 quote limits on lifetime, $8 \times 10^{-14}~--~5 \times 10^{-13}$ sec depending on mass, assuming B( ${{\mathit A}^{0}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$ ) = 100$\%$. They say that TSERTOS 1991 overstated their sensitivity by a factor of 3.
2  HENDERSON 1992C exclude axion with lifetime ${\mathit \tau}_{{{\mathit A}^{0}}}=1.4 \times 10^{-12}~--~4.0 \times 10^{-10}~$s, assuming B( ${{\mathit A}^{0}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$ )=100$\%$. HENDERSON 1992C also exclude a vector boson with =$1.4 \times 10^{-12}~--~6.0 \times 10^{-10}~$s.
3  WU 1992 quote limits on lifetime $>3.3 \times 10^{-13}~$s assuming B( ${{\mathit A}^{0}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$ )=100$\%$. They say that TSERTOS 1989 overestimate the limit by a factor of ${{\mathit \pi}}$/2. WU 1992 also quote a bound for vector boson, $>8.2 \times 10^{-13}~$s.
4  WIDMANN 1991 bound applies exclusively to the case B( ${{\mathit A}^{0}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$ )=1, since the detection efficiency varies substantially as $\Gamma\mathrm {({{\mathit A}^{0}})}_{{\mathrm {total}}}$ changes. See their Fig.$~$6.
5  JUDGE 1990 excludes an elastic pseudoscalar ${{\mathit e}^{+}}{{\mathit e}^{-}}$ resonance for $4.5 \times 10^{-13}~$s $<$ $\tau\mathrm {({{\mathit A}^{0}})}$ $<$ $7.5 \times 10^{-12}~$s (95$\%$ CL) at ${\mathit m}_{{{\mathit A}^{0}}}$ = $1.832$ MeV. Comparable limits can be set for ${\mathit m}_{{{\mathit A}^{0}}}$ = $1.776-1.856$ MeV.
7  The upper limit listed in TSERTOS 1988 is too large by a factor of 4. See TSERTOS 1988B, footnote 3.
8  VANKLINKEN 1988 looked for relatively long-lived resonance ($\tau$ = $10^{-10}-10^{-12}~$s). The sensitivity is not sufficient to exclude such a narrow resonance.
9  MAIER 1987 obtained limits $\mathit R\Gamma$ ${ {}\lesssim{} }$ 60 eV (100 eV) at ${\mathit m}_{{{\mathit A}^{0}}}$ $\simeq{}$ $1.64$ MeV ($1.83$ MeV) for energy resolution $\Delta \mathit E_{{\mathrm {cm}}}$ $\simeq{}$ 3 keV, where $\mathit R$ is the resonance cross section normalized to that of Bhabha scattering, and $\Gamma$ = $\Gamma {}^{2}_{ {{\mathit e}} {{\mathit e}} }/\Gamma _{{\mathrm {total}}}$. For a discussion implying that $\Delta \mathit E_{{\mathrm {cm}}}$ $\simeq{}$ 10$~$keV, see TSERTOS 1989 .
10  VONWIMMERSPERG 1987 measured Bhabha scattering for $\mathit E_{{\mathrm {cm}}}$ = $1.37-1.86$ MeV and found a possible peak at $1.73$ with $\int{\sigma \mathit d\mathit E_{{\mathrm {cm}}}}$ = $14.5$ $\pm6.8$ keV$\cdot{}$b. For a comment and a reply, see VANKLINKEN 1988B and VONWIMMERSPERG 1988 . Also see CONNELL 1988 .
References:
 HALLIN 1992
PR D45 3955 Sensitive Search for Resonances in Low Energy ${{\mathit e}^{+}}{{\mathit e}^{-}}$ Scattering
 HENDERSON 1992C
PRL 69 1733 Search in s Channel for Production of 1 $−$ 2 ${\mathrm {MeV}}/\mathit c{}^{2}$ Longlived ${{\mathit e}^{+}}{{\mathit e}^{-}}$ Resonances
 WU 1992
PRL 69 1729 Search for Low Mass States in Elastic ${{\mathit e}^{+}}{{\mathit e}^{-}}$ Scattering
 TSERTOS 1991
PL B266 259 Experimental Exclusion of Neutral Resonances in Bhabha Scattering at MeV Energies
 WIDMANN 1991
ZPHY A340 209 Limits for Two-Photon and ${{\mathit e}^{+}}{{\mathit e}^{-}}$ Decay Widths of Positron Electron Scattering Resonances for $\sqrt {s }$=1.78 to 1.92 MeV
 BAUER 1990
NIM B50 300 The Stuttgart Positron Beam, its Performance and Recent Experiments
 JUDGE 1990
PRL 65 972 Search for Longlived Neutral Resonances in Bhabha Scattering around 1.8 ${\mathrm {MeV}}/\mathit c{}^{2}$
 TSERTOS 1989
PR D40 1397 High Sensitivity Measurements of the Excitation Function for Bhabha Scattering at MeV Energies
 LORENZ 1988
PL B214 10 Search for Narrow Resonance Production in Bhabha Scattering at Centre-of-Mass Energies near 1.8 MeV
 TSERTOS 1988
PL B207 273 Sensitive Search for Neutral Resonances in Bhabha Scattering around 1.8 ${\mathrm {MeV}}/\mathit c{}^{2}$
ZPHY A326 527 Experimental Limits for Narrow Lines in the Excitation Function of Positron-Electron Scattering around $\mathit E{}^{*}$ = 620 keV and $\mathit E{}^{*}$ = 810 keV
PR D36 707 Search for a Bhabha Scattering Resonance near 1.8 ${\mathrm {MeV}}/\mathit c{}^{2}$
ZPHY A331 103 New Limits for Resonant Bhabha Scattering around the Invariant Mass of 1.8 ${\mathrm {MeV}}/\mathit c{}^{2}$