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First Constraint on P-odd/T-odd Cross Section in Polarized Neutron Transmission through Transversely Polarized $^{139}$La

Rintaro Nakabe, Clayton J. Auton, Shunsuke Endo, Hiroyuki Fujioka, Vladimir Gudkov, Katsuya Hirota, Ikuo Ide, Takashi Ino, Motoyuki Ishikado, Wataru Kambara, Shiori Kawamura, Atsushi Kimura, Masaaki Kitaguchi, Ryuju Kobayashi, Takahiro Okamura, Takayuki Oku, Takuya Okudaira, Mao Okuizumi, J. G. Otero Munoz, Joseph D. Parker, Kenji Sakai, Tatsushi Shima, Hirohiko M. Shimizu, Takenao Shinohara, William M. Snow, Shusuke Takada, Ryuta Takahashi, Shingo Takahashi, Yusuke Tsuchikawa, Tamaki Yoshioka

Abstract

We report the first constraint on time-reversal invariance violating (TRIV) effects in polarized neutron transmission through a transversely polarized $^{139}$La target. We formulate the transmission asymmetry within the density matrix formalism, explicitly incorporating the forward scattering amplitude of $^{139}$La including tensor polarization terms up to third-rank. The formalism is applied to existing transmission data originally obtained to measure the spin-dependent cross section near the $0.75$~eV $p$-wave resonance. Since these data were not optimized for P-odd/T-odd observables, the attainable sensitivity is intrinsically limited; nevertheless, they provide a useful test of the formalism on real experimental data. No statistically significant TRIV signal is observed. By analyzing the global $χ^2$ structure in the parameter space, we obtain an upper limit of $|W_T|<15~\mathrm{eV}$ at the 90\% confidence level. This corresponds to an upper limit on the resonance-averaged TRIV cross section of $|Δσ_{\not{T}\not{P}}|<8.3\times10^2~\mathrm{b}$. These results validate the present theoretical framework and provide guidance for future dedicated TRIV searches in polarized neutron transmission experiments.

First Constraint on P-odd/T-odd Cross Section in Polarized Neutron Transmission through Transversely Polarized $^{139}$La

Abstract

We report the first constraint on time-reversal invariance violating (TRIV) effects in polarized neutron transmission through a transversely polarized La target. We formulate the transmission asymmetry within the density matrix formalism, explicitly incorporating the forward scattering amplitude of La including tensor polarization terms up to third-rank. The formalism is applied to existing transmission data originally obtained to measure the spin-dependent cross section near the ~eV -wave resonance. Since these data were not optimized for P-odd/T-odd observables, the attainable sensitivity is intrinsically limited; nevertheless, they provide a useful test of the formalism on real experimental data. No statistically significant TRIV signal is observed. By analyzing the global structure in the parameter space, we obtain an upper limit of at the 90\% confidence level. This corresponds to an upper limit on the resonance-averaged TRIV cross section of . These results validate the present theoretical framework and provide guidance for future dedicated TRIV searches in polarized neutron transmission experiments.

Paper Structure

This paper contains 12 sections, 33 equations, 5 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Spin observables in transmission through polarized $^{139}$La
  3. Observed asymmetry in neutron transmission
  4. Spin-correlation amplitudes for $^{139}$La
  5. Evaluation of the TRIV upper limit
  6. Physical interpretation of the previous experiment
  7. Experimental configuration
  8. Observable and dominant spin-correlation terms
  9. Evaluation of the TRIV upper limit
  10. Conclusion
  11. Density matrix formalism for neutron transmission
  12. Expectation value of transmission and observed asymmetry

Figures (5)

  • Figure 1: Schematic layout of the polarized-neutron transmission experiment through a transversely polarized $^{139}$La target. The incident pulsed neutron beam is polarized by a $^3$He spin filter under a longitudinal holding field ($B_0=15$ G). The neutron spin is transported downstream by a guide field ($\sim 20$ G), during which the spin direction gradually follows the local magnetic field. Upon entering the superconducting magnet, a strong transverse field of 6.8 T aligns the neutron spin along the $x$ axis, where the $^{139}$La target is polarized. The neutron momentum defines the $z$ axis.
  • Figure 2: Measured asymmetry $\left(A_I(\vartheta_{kI})\right)_{\rm exp}$ as a function of neutron time-of-flight (TOF). The red solid line represents the best-fit function consisting of the $p$-wave resonance asymmetry $\left(A_I(\vartheta_{kI})\right)_p$ and a quadratic background term describing the smoothly varying contribution from the $s$-wave resonances. The regions around the $s_1$ resonance at 72.3 eV and the $^{138}$La $s$-wave resonance at 2.99 eV were excluded from the fit. The 2.99 eV resonance originates from a 0.09% $^{138}$La impurity, for which $J=11/2$ was assigned in Ref. Alfimenkov1993.
  • Figure 3: $\chi^2$ contour maps in the two-parameter planes (a) $(\phi, W_T)$ and (b) $(W_T, E_p)$. For each point in the plane, the profile $\chi^2$ value is obtained by minimizing $\chi^2$ with respect to the remaining parameters. The inner and outer contours correspond to $\Delta\chi^2=2.30$ and $4.61$, representing the 68% and 90% confidence levels for two degrees of freedom. Four local minima appear in the $\phi$ direction, consistent with the four-fold solutions reported in Ref. Okudaira2024. In all local solutions, $W_T$ remains consistent with zero.
  • Figure 4: One-dimensional profile $\Delta\chi^2$ distributions for (a) $W_T$ and (b) $E_p$. For each value of the parameter of interest, the $\chi^2$ is minimized with respect to the remaining parameters. The horizontal lines correspond to $\Delta\chi^2=1.0$ and $2.71$, representing the 68% and 90% confidence levels for one degree of freedom. Panel (a) shows that the minimum occurs near $W_T \approx 0$, indicating no statistically significant TRIV signal. The intersections with $\Delta\chi^2=2.71$ give the upper limit $|W_T| < 15\,{\rm eV}$ at the 90% confidence level. Panel (b) exhibits two local minima around $E_p \approx 0.766\,{\rm eV}$ and $E_p \approx 0.792\,{\rm eV}$, reflecting a multimodal structure of the $\chi^2$ surface.
  • Figure A1: Experimental coordinate system defined by polar angle $\vartheta$ and azimuthal angle $\varphi$. The neutron momentum is fixed along the $z$-axis.