# NEUTRINO CHARGE RADIUS SQUARED INSPIRE search

We report limits on the so-called neutrino charge radius squared. While the straight-forward definition of a neutrino charge radius has been proven to be gauge-dependent and, hence, unphysical (LEE 1977C), there have been recent attempts to define a physically observable neutrino charge radius (BERNABEU 2000 , BERNABEU 2002 ). The issue is still controversial (FUJIKAWA 2003 , BERNABEU 2003 ). A more general interpretation of the experimental results is that they are limits on certain nonstandard contributions to neutrino scattering.

VALUE ($10^{-32}$ cm${}^{2}$) CL% DOCUMENT ID TECN  COMMENT
$\bf{-2.1\text{ to }3.3 }$ 90 1
 2010
TEXO Reactor ${{\overline{\mathit \nu}}_{{e}}}{{\mathit e}}$
• • • We do not use the following data for averages, fits, limits, etc. • • •
$-4\text{ to }5.5$ 90 2
 2018
${{\mathit \nu}_{{\mu}}}$ coherent scat. on ${}^{}\mathrm {CsI}$
$-0.53\text{ to }0.68$ 90 3
 2003
${{\mathit \nu}_{{\mu}}}{{\mathit e}}$ scat.
$-8.2\text{ to }9.9$ 90 4
 2003
anomalous ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \nu}}{{\overline{\mathit \nu}}}{{\mathit \gamma}}$
$-2.97\text{ to }4.14$ 90 5
 2001
LSND ${{\mathit \nu}_{{e}}}$ ${{\mathit e}}$ $\rightarrow$ ${{\mathit \nu}_{{e}}}{{\mathit e}}$
$-0.6\text{ to }0.6$ 90
 1995 B
CHM2 ${{\mathit \nu}_{{\mu}}}{{\mathit e}}$ elastic scat.
$0.9$ $\pm2.7$
 1993
CNTR LAMPF ${{\mathit \nu}}$ ${{\mathit e}}$ $\rightarrow$ ${{\mathit \nu}}{{\mathit e}}$
$<2.3$ 95
 1992
ASTR HOME/KAM2 ${{\mathit \nu}}$ rates
$<7.3$ 90 6
 1992
CNTR Reactor ${{\overline{\mathit \nu}}}$ ${{\mathit e}}$ $\rightarrow$ ${{\overline{\mathit \nu}}}{{\mathit e}}$
$1.1$ $\pm2.3$
 1991
CNTR Repl. by ALLEN 1993
$-1.1$ $\pm1.0$ 7
 1990
CNTR ${{\mathit \nu}_{{\mu}}}{{\mathit e}}$ elastic scat.
$-0.3$ $\pm1.5$ 7
 1989
CHRM ${{\mathit \nu}_{{\mu}}}{{\mathit e}}$ elastic scat.
8
 1989 B
ASTR SN 1987A
1  DENIZ 2010 observe reactor ${{\overline{\mathit \nu}}_{{e}}}{{\mathit e}}$ scattering with recoil kinetic energies $3 - 8$ MeV using CsI(Tl) detectors. The observed rate and spectral shape are consistent with the Standard Model prediction, leading to the reported constraint on ${{\overline{\mathit \nu}}_{{e}}}$ charge radius.
2  CADEDDU 2018 use the data of the COHERENT experiment, AKIMOV 2018 . The limit is $\langle$r${}^{2}_{{{\mathit \nu}}}\rangle$ for ${{\mathit \nu}_{{\mu}}}$ obtained from the time-dependent data. Weaker limits were obtained for charge radii of ${{\mathit \nu}_{{e}}}$ and for transition charge radii. The published value was divided by 2 to conform to the convention of this table.
3  Based on analysis of CCFR 98 results. Limit is on $\langle$r${}^{2}_{V}\rangle$ + $\langle$r${}^{2}_{A}\rangle$. The CHARM II and E734 at BNL results are reanalyzed, and weaker bounds on the charge radius squared than previously published are obtained. The NuTeV result is discussed; when tentatively interpreted as ${{\mathit \nu}_{{\mu}}}$ charge radius it implies $\langle$r${}^{2}_{V}\rangle$ + $\langle$r${}^{2}_{A}\rangle$ = ($4.20$ $\pm1.64$) ${\times }$ 10 ${}^{-33}$ cm${}^{2}$.
4  Results of LEP-2 are interpreted as limits on the axial-vector charge radius squared of a Majorana ${{\mathit \nu}_{{\tau}}}$. Slightly weaker limits for both vector and axial-vector charge radius squared are obtained for the Dirac case, and somewhat weaker limits are obtained from the analysis of lower energy data (LEP-1.5 and TRISTAN).
5  AUERBACH 2001 measure ${{\mathit \nu}_{{e}}}{{\mathit e}}$ elastic scattering with LSND detector. The cross section agrees with the Standard Model expectation, including the charge and neutral current interference. The 90$\%$ CL applies to the range shown.
6  VIDYAKIN 1992 limit is from a ${{\mathit e}}{{\overline{\mathit \nu}}}$ elastic scattering experiment. No experimental details are given except for the cross section from which this limit is derived. Signal/noise was 1/10. The limit uses sin$^2\theta _{\mathit W}$ = $0.23$ as input.
7  Result is obtained from reanalysis given in ALLEN 1991 , followed by our reduction to obtain 1$~\sigma$ errors.
8  GRIFOLS 1989B sets a limit of $\langle \mathit r{}^{2}\rangle$ $<~0.2 \times 10^{-32}~$cm${}^{2}$ for right-handed neutrinos.
References:
PR D98 113010 Neutrino Charge Radii from COHERENT Elastic Neutrino-Nucleus Scattering
 DENIZ 2010
PR D81 072001 Measurement of ${{\overline{\mathit \nu}}_{{e}}}{{\mathit e}}$ Scattering Cross Section with a CsI(Ti) Scintillating Crystal Array at the Kuo-Sheng Nuclear Power Reactor
 HIRSCH 2003
PR D67 033005 Bounds on the ${{\mathit \nu}_{{\tau}}}$ and ${{\mathit \nu}_{{\mu}}}$ Vector and Axial Vector Charge Radius
 AUERBACH 2001
PR D63 112001 Measurement of ${{\mathit \nu}_{{e}}}{{\mathit e}^{-}}$ Elastic Scattering
 VILAIN 1995B
PL B345 115 Experimental Study of Electromagnetic Properties of the Muon Neutrino in Neutrino Electron Scattering
 ALLEN 1993
PR D47 11 Study of ${{\mathit \nu}_{{e}}}{{\mathit e}^{-}}$ Elastic Scattering at LAMPF
 MOURAO 1992
PL B285 364 The Neutrino Electromagnetic Moments and Charge Radius Confront Kamiokande-II and Homestake Experimental Results
 VIDYAKIN 1992
JETPL 55 206 Limitations on the Magnetic Moment and Charged Radius of the Electron Antineutrino
 ALLEN 1991
PR D43 1 Experimental Bound on the Charge Radius of the Electron Neutrino
 AHRENS 1990
PR D41 3297 Determination of Electroweak Parameters from the Elastic Scattering of Muon Neutrinos and Antineutrinos on Electrons
 DORENBOSCH 1989
ZPHY C41 567 Experimental Results on Neutrino Electron Scattering
 GRIFOLS 1989B
PR D40 3819 Charge Radius of the Neutrino: a Limit from SN1987a