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${{\mathit p}}$ MAGNETIC POLARIZABILITY ${{\mathit \beta}_{{p}}}$

INSPIRE   PDGID:

S016MPL

The electric and magnetic polarizabilities are subject to a dispersion sum-rule constraint ${{\overline{\mathit \alpha}}}$ $+$ ${{\overline{\mathit \beta}}}$ = ($14.2$ $\pm0.5$) $ \times 10^{-4}$ fm${}^{3}$. Errors here are anticorrelated with those on ${{\overline{\mathit \alpha}}_{{p}}}$ due to this constraint.

See LI 2022D and therein for measurements of the mean square proton magnetic polarizability radius.

VALUE ($ 10^{-4} $ fm${}^{3}$) DOCUMENT ID TECN  COMMENT $\bf{ 2.5 \pm0.4}$ OUR AVERAGE  Error includes scale factor of 1.2. $3.15$ $\pm0.35$ $\pm0.36$ MCGOVERN 2013 RVUE ${{\mathit \chi}}$EFT + Compton scattering $3.4$ $\pm1.1$ $\pm0.1$ 1 BEANE 2003 EFT + ${{\mathit \gamma}}{{\mathit p}}$ $1.43$ $\pm0.98$ ${}^{+0.52}_{-0.98}$ 2 BLANPIED 2001 LEGS ${{\mathit p}}(\vec\gamma,{{\mathit \gamma}}$), ${{\mathit p}}(\vec\gamma,{{\mathit \pi}^{0}}$), ${{\mathit p}}(\vec\gamma,{{\mathit \pi}^{+}}$) $1.2$ $\pm0.7$ $\pm0.5$ 3 OLMOSDELEON 2001 CNTR ${{\mathit \gamma}}{{\mathit p}}$ Compton scattering $2.1$ $\pm0.8$ $\pm0.5$ 4 MACGIBBON 1995 RVUE global average • • We do not use the following data for averages, fits, limits, etc. • • $1.77$ ${}^{+0.52}_{-0.54}$ 5 PASQUINI 2019 fit of RCS data sets $2.3$ $\pm0.9$ $\pm0.7$ 6 BARANOV 2001 RVUE Global average $1.7$ $\pm0.6$ $\pm0.9$ MACGIBBON 1995 CNTR ${{\mathit \gamma}}{{\mathit p}}$ Compton scattering $4.4$ $\pm0.4$ $\pm1.1$ HALLIN 1993 CNTR ${{\mathit \gamma}}{{\mathit p}}$ Compton scattering $3.58$ ${}^{+1.19}_{-1.25}$ ${}^{+1.03}_{-1.07}$ ZIEGER 1992 CNTR ${{\mathit \gamma}}{{\mathit p}}$ Compton scattering $3.3$ $\pm2.2$ $\pm1.3$ FEDERSPIEL 1991 CNTR ${{\mathit \gamma}}{{\mathit p}}$ Compton scattering 1  BEANE 2003 uses effective field theory and low-energy ${{\mathit \gamma}}{{\mathit p}}$ and ${{\mathit \gamma}}{{\mathit d}}$ Compton-scattering data. It also gets for the isoscalar polarizabilities (see the erratum) $\alpha _{\mathit N}$= ($13.0$ $\pm1.9$ ${}^{+3.9}_{-1.5}$) $ \times 10^{-4}$ fm${}^{3}$ and $\beta _{\mathit N}$= ($-1.8$ $\pm1.9$ ${}^{+2.1}_{-0.9}$) $ \times 10^{-4}$ fm${}^{3}$. 2  BLANPIED 2001 gives ${{\mathit \alpha}_{{p}}}+{{\mathit \beta}_{{p}}}$ and ${{\mathit \alpha}_{{p}}}−{{\mathit \beta}_{{p}}}$. The separate ${{\mathit \alpha}_{{p}}}$ and ${{\mathit \beta}_{{p}}}$ are provided to us by A.$~$Sandorfi. The first error above is statistics plus systematics; the second is from the model. 3  This OLMOSDELEON 2001 result uses the TAPS data alone, and does not use the (re-evaluated) sum-rule constraint that ${{\mathit \alpha}}+{{\mathit \beta}}$= ($13.8$ $\pm0.4$) $ \times 10^{-4}~$fm${}^{3}$. See the paper for a discussion. 4  MACGIBBON 1995 combine the results of ZIEGER 1992 , FEDERSPIEL 1991 , and their own experiment to get a ``global average'' in which model errors and systematic errors are treated in a consistent way. See MACGIBBON 1995 for a discussion. 5  PASQUINI 2019 fit data sets for the unpolarized proton RCS cross section, using fixed-t subtracted dispersion relations and a bootstrap-based fitting technique. 6  BARANOV 2001 combines the results of 10 experiments from 1958 through 1995 to get a global average that takes into account both systematic and model errors and does not use the theoretical constraint on the sum $\alpha _{{{\mathit p}}}+\beta _{{{\mathit p}}}$.

References:

PASQUINI 2019 JP G46 104001 Proton scalar dipole polarizabilities from real Compton scattering data, using fixed-t subtracted dispersion relations and the bootstrap method MCGOVERN 2013 EPJ A49 12 Compton Scattering from the Proton in an Effective Field Theory with Explicit Delta Degrees of Freedom BEANE 2003 PL B567 200 Nucleon Polarizabilities from Low-Energy Compton Scattering Also PL B607 320 (errat.) Erratum to BEANE 2003 . Nucleon Polarizabilities from Low-Energy Compton Scattering'' BARANOV 2001 PPN 32 376 Experimental Status of the Electric and Magnetic Polarizabilities of a Proton BLANPIED 2001 PR C64 025203 ${{\mathit N}}$ $\rightarrow$ ${{\mathit \Delta}}$ Transition and Proton Polarizabilities from Measurements of ${{\mathit p}}$ (${{\mathit \gamma}}↑$, ${{\mathit \gamma}}$), ${{\mathit p}}$ (${{\mathit \gamma}}↑$, ${{\mathit \pi}^{0}}$), and ${{\mathit p}}$ (${{\mathit \gamma}}↑$, ${{\mathit \pi}^{+}}$) OLMOSDELEON 2001 EPJ A10 207 Low Energy Compton Scattering and the Polarizability of the Proton MACGIBBON 1995 PR C52 2097 Measurement of the Electric and Magnetic Polarizabilities of the Proton HALLIN 1993 PR C48 1497 Compton Scattering from the Proton ZIEGER 1992 PL B278 34 180$^\circ{}$ Compton Scattering by Proton below the Pion Threshold Also PL B281 417 (erratum) Erratum: ZIEGER 1992 180$^\circ{}$ Compton Scattering by Proton below the Pion Threshold FEDERSPIEL 1991 PRL 67 1511 Proton Compton Effect: a Measurement of the Electric and Magnetic Polarizabilities of the Proton