The neutron and its role in cosmology and particle physics

Experiments with cold and ultracold neutrons have reached a level of precision such that problems far beyond the scale of the present standard model of particle physics become accessible to experimental investigation. Because of the close links between particle physics and cosmology, these studies also permit a deep look into the very first instances of our Universe. First addressed in this article, in both theory and experiment, is the problem of baryogenesis, the mechanism behind the evident dominance of matter over antimatter in the Universe. The question of how baryogenesis could have happened is open to experimental tests, and it turns out that this problem can be curbed by the very stringent limits on an electric dipole moment of the neutron, a quantity that also has deep implications for particle physics. Then the recent spectacular observation of neutron quantization in the Earth’s gravitational field and of resonance transitions between such gravitational energy states is discussed. These measurements, together with new evaluations of neutron scattering data, set new constraints on deviations from Newton’s gravitational law at the picometer scale. Such deviations are predicted in modern theories with extra dimensions that propose unification of the Planck scale with the scale of the standard model. These experiments start closing the remaining “axion window” on new spin-dependent forces in the submillimeter range. Another main topic is the weak-interaction parameters in various fields of physics and astrophysics that must all be derived from measured neutron-decay data. Up until now, about 10 different neutron-decay observables have been measured, much more than needed in the electroweak standard model. This allows various precise tests for new physics beyond the standard model, competing with or surpassing similar tests at high energy. The review ends with a discussion of neutron and nuclear data required in the synthesis of the elements during the “first three minutes” and later on in stellar nucleosynthesis.

Figure 1

The three Sakharov criteria, necessary for baryogenesis, and their possible realizations (SM is the standard model).

Figure 2

In the $\mathrm{SU}(2{)}_w$ gauge theory, there are degenerate ground states with nonzero topological winding number. Baryon-number violating transitions between two such SM vacua are possible, either by tunnelling (instanton transition at $T=0$) or by thermal excitation over the barrier (sphaleron transition).

Figure 3

The Higgs potential at $T<T_c$ (dashed line) has the usual “Mexican hat shape.” With additional $T^2$ and ${\Phi }^3$ terms, the Higgs potential resembles the free energy of a first-order phase transition.

Figure 4

Sketch of the Ramsey apparatus used at ILL to search for a neutron electric dipole moment ($n\mathrm{EDM}$). The block arrow shows the neutron polarization right after filling of the UCN trap (Port A and B open). The dashed line represents a UCN trajectory in the UCN bottle. The sources of the $\mathbf{E}$ and $\mathbf{B}$ fields are not shown.

Figure 5

Typical graphs in the standard model contributing to a neutron EDM. The vertical lines indicate hadronic intermediate states.

Figure 6

In supersymmetric extensions of the standard model, the EDMs of particles are naturally large. In the simplest version of a “minimal SUSY model” (MSSM), particle EDMs depend only on two phase angles ${\theta }_A$ and ${\theta }_{\mu }$. For a small SUSY-breaking scale, experimental atomic and neutron-EDM limits strongly constrain these phases to near the origin ${\theta }_A={\theta }_{\mu }=0$, where the three bands of the figure cross—much too small for electroweak baryogenesis. From 332.

Figure 7

Also in a careful reanalysis taking more freedom (see text) the EDMs strongly constrain baryogenesis. The $\tan \beta –m_A$ plane, with colored exclusion regions due to the Higgs mass, electroweak baryogenesis (EWB), and branching ratios for $b$ decays. The dark line at $d_n=2.9\times {10}^{-26}e\mathrm{cm}$ indicates the current experimental limit for the $n\mathrm{\text{−}}\mathrm{EDM}$: the viable parameter space lies below this curve. From 113.

Figure 8

Severe EDM constraints exist also when an additional scalar superfield is added to the MSSM, with more free parameters. The model is investigated by counting the (randomly chosen) points in parameter space that fulfil various constraints. The number of results is shown for the analysis of the baryon asymmetry of the Universe for large $M_2=1\mathrm{TeV}$, in dependence of the baryon-entropy abundance parameter ${\eta }_{10}^s=(n_B/s)\times {10}^{10}$. Approximately 50% of the parameter sets predict a value of the baryon asymmetry higher than the observed value ${\eta }_{10}^s=0.87$. The lower line corresponds to the small number of parameter sets (4.8%) that also fulfill current bounds on the electron EDM with 1 TeV sfermions. From 211.

Figure 9

When the standard model is augmented not by SUSY, but by a higher-dimensional term in the effective Higgs sector, strong EDM constraints exist as well. Shown are the Higgs masses $m_h$ and scales $\Lambda$ of new physics excluded (shaded areas) by the present EDM limits for neutron $d_n$, thallium $d_{\mathrm{Tl}}$, and mercury $d_{\mathrm{Hg}}$. (a) In the minimal scenario, the observed baryon asymmetry ${\eta }_1=6\times {10}^{-10}$ is excluded by the present limit on the neutron EDM $d_n$ (and so is one-tenth and 10 times ${\eta }_1$). (b) Therefore additional $CP$-odd sources must be introduced to lower the exclusion limits. From 210.

Figure 10

The ADD model has $n$ extra dimensions, compactified to distances $r<R$, and only one single energy scale. In this model, gravitation is diluted in $3+n$ dimensions, while the other interactions are active only in three dimensions. At the electroweak scale ${\lambda }_w\approx {10}^{-3}\mathrm{fm}$, the Coulomb potential $V_{\mathrm{el}}\propto 1/r$ equals the gravitational potential $V_{\mathrm{grav}}\propto 1/r^{n+1}$. At large distances, $r\gg R$, both have the usual $1/r$ potential, but with coupling strengths differing by a factor $\sim {10}^{34}$.

Figure 11

Scheme of the experiment on UCN gravitational quantum levels. UCN plane waves enter from the left, and form standing waves in the triangular potential formed by the mirror potential $V\approx \infty$ and the gravitational potential $V=mgz$. For the absorber height $h=20\mu \mathrm{m}$ shown, only neutrons in the first eigenstate ${\psi }_1$ with energy $E_1=1.4\mathrm{peV}$ pass the device and are detected, while the higher eigenstates ${\psi }_{n>1}$ are removed from the beam. Adapted from 273.

Figure 12

Ultracold neutron transmission of the device in Fig. 11, measured in dependence of the height $h$ of the absorber. Dotted line: classical expectation; solid line: quantum calculation. From 403.

Figure 13

Position sensitive detection of the transmitted UCN after their “fall” over a step of $30\mu \mathrm{m}$ height at the exit of the slit system, measured at two different distances from the slit exit, $x=0$ and $6\mathrm{cm}$. This differential phase sensitive measurement of neutron transmission in principle is much more sensitive to fifth forces than is the integral transmission curve, Fig. 12. Adapted from 224.

Figure 14

Exclusion plot on new short-range interactions. Shown are the strength $g^2$ of the interaction vs its range $\lambda$. The upper scale gives the corresponding mass $m=h/\lambda c$ of the exchanged boson. Values above the curves shown are excluded by experiment. The constraints from neutron scattering in the subatomic range are combined from several different neutron measurements, see 298. Most other curves are adapted from 229.

Figure 15

Exclusion plot on new short-range spin-dependent interactions. The neutron measurements constrain axion interactions with nucleons in the axion window, left open by the astrophysical constraints (dashed vertical lines). The methods have room for improvement by several orders of magnitude. Black lines: coupling to nucleon spins; gray lines: coupling to electron spins. Most of the curves are adapted from 45.

Figure 16

Expected effect of a spin-dependent extra interaction on the UCN transmission curve from the gravitational level experiment. One neutron spin component would be attracted, the other repelled at short distances (dashed lines). Even unpolarized neutrons are sensitive to such spin-dependent interactions (solid line). From 46.

Figure 17

Twofold correlations between momenta ${\mathbf{p}}_e$, ${\mathbf{p}}_{\nu }$ and spins ${\mathit{\sigma }}_n$, ${\mathit{\sigma }}_e$ in the $\beta$ decay of slow neutrons, with the correlation coefficients: $\beta$ asymmetry $A$, neutrino asymmetry $B$, electron-antineutrino correlation $a$, electron helicity $G$, and spin-spin and spin-momentum coefficients $N$ and $H$.

Figure 18

The mean neutron lifetime, horizontal gray bar, as derived from cold neutron decay “in beam” (◊), and from the decay of ultracold neutrons trapped in “bottles” (▪). The width of the gray bar gives the upscaled error. For the UCN measurements, the vertical arrows show the extrapolation from the measured storage times (□) to the derived neutron lifetimes (▪); see Eq. (6.27). For details, see text.

Figure 19

Neutron lifetime from the latest UCN storage experiment. Shown is the UCN disappearance rate $1/{\tau }_{\mathrm{storage}}$ vs the (normalized) loss rate $\gamma \propto 1/{\tau }_{\mathrm{loss}}$; see Eq. (6.27). For $\gamma =0$, the linear fit gives ${\tau }_{\mathrm{storage}}={\tau }_n=878.5\pm 0.8\mathrm{s}$. Open dots are for the larger trap, full dots for the smaller trap, each for five different UCN energy bands. The extrapolation is over $\Delta \tau =5\mathrm{s}$. Shown is also the PDG 2010 average. From 360 and 365.

Figure 20

The negative of the experimental proton asymmetry $-C$ as a function of electron energy $E_e$. The bold line indicates the fit region. From 358.

Figure 21

The ratio of axial vector to vector coupling constants $\lambda =g_A/g_V$ (horizontal gray bar) as derived from various sources: from the neutron $\beta$ asymmetry $A$, neutrino asymmetry $B$, proton asymmetry $C$, from the electron-neutrino correlation $a$, the hyperon correlations $F+D$, and indirectly with Eq. (6.9), from the neutron lifetime ${\tau }_n$ combined with nuclear $|V_{ud}{|}^2$. The width of the horizontal gray bar gives the upscaled error.

Figure 22

Measured $\mathcal{F}t$ values both from nuclear superallowed $0^{+}\to 0^{+}$ $\beta$ transitions ($Z\ge 5$) and from the measured vector part of neutron decay ($Z=1$). The superallowed data are shown before (◊) and after (⧫) corrections for nuclear and radiative effects, as well as their mean value after correction (horizontal gray bar). For comparison, the neutron $\mathcal{F}{t}_{n\mathrm{\text{−}}\mathrm{Vector}}$ value is inserted as derived from Eq. (6.50) using only the latest two results for the neutron lifetime ${\tau }_n$ and the latest two results for $\lambda =g_A/g_V$.

Figure 23

Exclusion plot for the SM-forbidden Fierz interference terms $b$, derived from electron-energy dependence of the neutron $\beta$ asymmetry $A(E_e)$ with $1\sigma$ (dark gray), $2\sigma$ (gray), and $3\sigma$ contours (light gray) contours. The standard model prediction is $b=0$. The vertical line indicates $\lambda$ from Eq. (6.41).

Figure 24

Exclusion plot for the SM-forbidden Fierz interference terms $b$ and $b^{\prime }$ derived from the PDG 2010 values of the parameters $A$, $B$, $C$, and $\mathcal{F}{t}_n/\mathcal{F}{t}_{0\to 0}$. The standard model prediction is $b=b^{\prime }=0$.

Figure 25

Exclusion plot for the parameters of the manifest left-right symmetric model (beyond the SM), namely, the mass ratio squared $\delta =(m_R/m_L{)}^2$ of left-handed and right-handed $W$ bosons, and their relative phase $\zeta$. The exclusion contours, defined as in Fig. 23, are based on the neutron-decay correlation coefficients $A$, $B$, and $C$. The standard model prediction is $\delta =\zeta =0$.

Figure 26

Exclusion plot as in Fig. 25, but based on the coefficients $A$, $B$, $C$, and $\mathcal{F}{t}_n/\mathcal{F}{t}_{0\to 0}$.

Figure 27

Neutron mass fraction $n/(n+p)$ in the early Universe, as a function of temperature $T$ and time $t$ (upper scale) after the big bang. For the dashed line, it is assumed that neutrons and protons are permanently in thermal equilibrium, with $n/p$ following Boltzmann’s law $n/p=\exp (-\Delta m/kT)$. For the dash-dotted line, it is assumed that neutrons decouple from the protons near arrow A and decay freely. Nucleosynthesis sets in near arrow B as soon as deuteron break up by photons ceases. The solid line is from a full network calculation with all relevant nuclear reactions. From 116.

Figure 28

Pathways of nucleosynthesis in the nuclear chart $Z$ vs $N$. The slow or $s$ process proceeds near the valley of stability via neutron captures (horizontal lines) and subsequent ${\beta }^{-}$ decays (diagonal lines). The rapid or $r$ process takes place far-off stability after multiple neutron captures (hatched area). $s$-only stable isotopes are marked $s$, $r$-only isotopes are marked $r$. The isolated open squares are proton-rich stable isotopes reached only by the so-called $rp$ or $p$ processes. The inset shows relative element abundances in the solar system, for the small peaks marked $r$ and $s$, see text. Adapted from 230.