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Decoding the genome confers the capability to predict characteristics of the organism(phenotype) from DNA (genotype). We describe the present status and future prospects of genomic prediction of complex traits in humans. Some highly heritable complex phenotypes such as height and other quantitative traits can already be predicted with reasonable accuracy from DNA alone. For many diseases, including important common conditions such as coronary artery disease, breast cancer, type I and II diabetes, individuals with outlier polygenic scores (e.g., top few percent) have been shown to have 5 or even 10 times higher risk than average. Several psychiatric conditions such as schizophrenia and autism also fall into this category. We discuss related topics such as the genetic architecture of complex traits, sibling validation of polygenic scores, and applications to adult health, in vitro fertilization (embryo selection), and genetic engineering., Comment: 33 pages, 7 figures, 1 table, A version of this article was prepared for "Genomic Prediction of Complex Traits", Springer Nature book series "Methods in Molecular Biology"

We construct genomic predictors for heritable and extremely complex human quantitative traits (height, heel bone density, and educational attainment) using modern methods in high dimensional statistics (i.e., machine learning). Replication tests show that these predictors capture, respectively, $\sim$40, 20, and 9 percent of total variance for the three traits. For example, predicted heights correlate $\sim$0.65 with actual height; actual heights of most individuals in validation samples are within a few cm of the prediction. The variance captured for height is comparable to the estimated SNP heritability from GCTA (GREML) analysis, and seems to be close to its asymptotic value (i.e., as sample size goes to infinity), suggesting that we have captured most of the heritability for the SNPs used. Thus, our results resolve the common SNP portion of the "missing heritability" problem -- i.e., the gap between prediction R-squared and SNP heritability. The $\sim$20k activated SNPs in our height predictor reveal the genetic architecture of human height, at least for common SNPs. Our primary dataset is the UK Biobank cohort, comprised of almost 500k individual genotypes with multiple phenotypes. We also use other datasets and SNPs found in earlier GWAS for out-of-sample validation of our results., Comment: 17 pages, 10 figures

In the standard model extended with a seesaw mass matrix, we study the production of sterile neutrinos from the decay of vector bosons at $T\simeq M_{W,Z}$. We derive a general quantum kinetic equation for the production of sterile neutrinos and their effective mixing angles valid in a wide range of temperature, to all orders in interactions of the standard model, and to leading order mixing angle $\theta \ll 1$. Production rates and effective mixing angles depend sensitively on helicity. Positive helicity states interact more weakly with the medium and their effective mixing angle is not modified significantly whereas the mixing angle for negative helicity is strongly suppressed by the medium. If $M_s \lesssim 8.35\,\mathrm{MeV}$, there are fewer states with negative helicity produced than those with positive helicity. There is an MSW resonance in the absence of lepton asymmetry, but is screened by the damping rate, without production enhancement. Negative helicity states freeze-out at $T^-_f\simeq 5\,\mathrm{GeV}$ and positive helicity states freeze-out at $T^+_f \simeq 8\,\mathrm{GeV}$, both distributions are far from thermal. Negative helicity states feature a broader momentum distribution than that for those with positive helicity. Sterile neutrinos produced via vector boson decay do not satisfy the abundance, lifetime and cosmological constraints to be the sole dark matter component in the universe but might solve the $^{7}Li$ problem, albeit at the very edge of the possible parameter space. A heavy sterile neutrino with a mass of a few MeV could decay into light sterile neutrinos, of a few keV in mass, that contribute to warm dark matter. We argue that heavy sterile neutrinos with lifetime $\leq 1/H_0$ reach local thermodynamic equilibrium., Comment: published version

Sterile neutrinos are SU(2) singlets that mix with active neutrinos via a mass matrix, its diagonalization leads to mass eigenstates that couple via standard model vertices. We study the cosmological production of heavy neutrinos via standard model charged and neutral current vertices under a minimal set of assumptions: i) the mass basis contains a hierarchy of heavy neutrinos, ii) these have very small mixing angles with the active (flavor) neutrinos, iii) standard model particles, including light (active-like) neutrinos are in thermal equilibrium. The same weak interaction processes that produce active-like neutrinos also produce the heavier species. We introduce the kinetic equations that describe their production, freeze out and decay and discuss the various processes that lead to their production in a wide range of temperatures assessing their feasibility as dark matter candidates. We identify processes in which finite temperature collective excitations lead to the production of the heavy species. As a specific example, we consider the production of heavy neutrinos from pion decay shortly after the QCD crossover including finite temperature corrections to the pion form factors and mass. We consider the different decay channels that allow for the production of heavy neutrinos showing that their frozen distribution functions exhibit effects from "kinematic entanglement" and argue for their viability as mixed dark matter candidates. We discuss abundance, phase space density and stability constraints and argue that heavy neutrinos with lifetime $\tau> 1/H_0$ freeze out of local thermal equilibrium, and \emph{conjecture} that those with lifetimes $\tau \ll 1/H_0$ may undergo cascade decay into lighter DM candidates and/or inject non-LTE neutrinos into the cosmic neutrino background. We provide a comparison with non-resonant production via active-sterile mixing., Comment: 62 pages, 17 figs, expanded discussions, matches published version

We study the production of sterile neutrinos in the early universe from $\pi \rightarrow l \nu_s$ shortly after the QCD phase transition in the absence of a lepton asymmetry while including finite temperature corrections to the $\pi$ mass and decay constant $f_{\pi}$. Sterile neutrinos with masses $\lesssim 1 MeV$ produced via this mechanism freeze-out at $T_f \simeq 10 MeV$ with a distribution function that is highly non-thermal and features a sharp enhancement at low momentum thereby making this species \emph{cold} even for very light masses. Dark matter abundance constraints from the CMB and phase space density constraints from the most dark matter dominated dwarf spheroidal galaxies provide upper and lower bounds respectively on combinations of mass and mixing angles. For $\pi \rightarrow \mu \nu_s$, the bounds lead to a narrow region of compatibility with the latest results from the $3.55 \mathrm{KeV}$ line. The non-thermal distribution function leads to free-streaming lengths (today) in the range of $\sim \mbox{few kpc}$ consistent with the observation of cores in dwarf galaxies. For sterile neutrinos with mass $\lesssim 1 eV$ that are produced by this reaction, the most recent accelerator and astrophysical bounds on $U_{ls}$ combined with the non-thermal distribution function suggests a substantial contribution from these sterile neutrinos to $N_{eff}$., Comment: 32 pages, 8 figures, new references and corrected typos

We study non-perturbatively the time evolution of cascade decay for generic fields $\pi \rightarrow \phi_1\phi_2\rightarrow \phi_2\chi_1\chi_2$ and obtain the time dependence of amplitudes and populations for the resonant and final states. We analyze in detail the different time scales and the manifestation of unitary time evolution in the dynamics of production and decay of resonant intermediate and final states. The probability of occupation (population) "flows" as a function of time from the initial to the final states. When the decay width of the parent particle $\Gamma_\pi$ is much larger than that of the intermediate resonant state $\Gamma_{\phi_1}$ there is a "bottleneck" in the flow, the population of resonant states builds up to a maximum at $t^* = \ln[\Gamma_\pi/\Gamma_{\phi_1}]/(\Gamma_\pi-\Gamma_{\phi_1})$ nearly saturating unitarity and decays to the final state on the longer time scale $1/\Gamma_{\phi_1}$. As a consequence of the wide separation of time scales in this case the cascade decay can be interpreted as evolving sequentially $\pi \rightarrow \phi_1\phi_2; ~ \phi_1\phi_2\rightarrow \phi_2\chi_1\chi_2$. In the opposite limit the population of resonances ($\phi_1$) does not build up substantially and the cascade decay proceeds almost directly from the initial parent to the final state without resulting in a large amplitude of the resonant state. An alternative but equivalent non-perturbative method useful in cosmology is presented. Possible phenomenological implications for heavy sterile neutrinos as resonant states and consequences of quantum entanglement and correlations in the final state are discussed., Comment: typos corrected, references updated

We study corrections to the power spectra of curvature and tensor perturbations and the tensor-to-scalar ratio in single field slow roll inflation due to initial conditions imprinted by a fast-roll stage prior to slow roll. For a wide range of initial inflaton kinetic energy, this stage lasts only a few e-folds and merges smoothly with slow-roll leading to non-Bunch-Davies initial conditions for modes that exit the Hubble radius during slow roll. We describe a program that yields the dynamics in the fast-roll stage while matching to the slow roll stage independent of the inflationary potentials. Corrections to the power spectra are encoded in a transfer function $\mathcal{T}_\alpha(k)$. We obtain $\mathcal{T}_\alpha(k)$ to leading order in a Born approximation valid for modes of observational relevance today. A fit yields $\mathcal{T}_\alpha(k) =1+ A_{\alpha}k^{-p}\cos[2\pi \omega k/H_{sr}+\varphi_\alpha]$, with $1.5 \lesssim p \lesssim 2$, $\omega \simeq 1$ and $H_{sr}$ the Hubble scale during slow roll inflation, where curvature and tensor perturbations feature the same $p,\omega$ for a wide range of initial conditions. These corrections lead to both a suppression of the quadrupole and oscillatory features in both $P_R(k)$ and $r(k_0)$ with a period of the order of the Hubble scale during slow roll inflation. The results are independent of the specific inflationary potentials, depending solely on the ratio of kinetic to potential energy $\kappa$ and the slow roll parameters to leading order. For a wide range of $\kappa$ and the values of $\epsilon_V;\eta_V$ corresponding to the upper bounds from Planck, we find that the low quadrupole is consistent with the results from Planck, and the oscillations in $r(k_0)$ could be observable if the modes corresponding to the quadrupole and the pivot scale crossed the Hubble radius a few e-folds after the onset of slow roll., Comment: Updated references, comments on BICEP result 31 pages, 9 figs

If the large scale anomalies in the temperature power spectrum of the cosmic microwave background are of primordial origin, they may herald modifications to the slow roll inflationary paradigm on the largest scales. We study the possibility that the origin of the large scale power suppression is a modification of initial conditions during slow roll as a result of a pre-slow roll phase during which the inflaton evolves rapidly. This stage is manifest in a potential in the equations for the Gaussian fluctuations during slow roll and modify the power spectra of scalar perturbations via an initial condition transfer function $\mathcal{T}(k)$. We provide a general analytical study of its large and small scale properties and analyze the impact of these initial conditions on the infrared aspects of typical test scalar fields. The infrared behavior of massless minimally coupled test scalar field theories leads to the dynamical generation of mass and anomalous dimensions, both depend non-analytically on $\mathcal{T}(0)$. During inflation all quanta decay into many quanta even of the same field because of the lack of kinematic thresholds. The decay leads to a quantum entangled state of sub and superhorizon quanta with correlations across the horizon. We find the modifications of the decay width and the entanglement entropy from the initial conditions. In all cases, initial conditions from a ``fast-roll'' stage that lead to a suppression in the scalar power spectrum at large scales also result in a suppression of the dynamically generated masses, anomalous dimensions and decay widths., Comment: expanded discussion on fast-slow roll stage. version to appear in PRD

In inflationary cosmology all particle states decay as a consequence of the lack of kinematic thresholds. The decay of an initial single particle state yields an \emph{entangled quantum state of the product particles}. We generalize and extend a manifestly unitary field theoretical method to obtain the time evolution of the quantum state. We consider the decay of a light scalar field with mass $M\ll H$ with a cubic coupling in de Sitter space-time. Radiative corrections feature an infrared enhancement manifest as poles in $\Delta=M^2/3H^2$ and we obtain the quantum state in an expansion in $\Delta$. To leading order in $\Delta$ the pure state density matrix describing the decay of a particle with sub-horizon wavevector is dominated by the emission of superhorizon quanta, describing \emph{entanglement between superhorizon and subhorizon fluctuations and correlations across the horizon}. Tracing over the superhorizon degrees of freedom yields a mixed state density matrix from which we obtain the entanglement entropy. Asymptotically this entropy grows with the \emph{physical} volume as a consequence of more modes of the decay products crossing the Hubble radius. A generalization to localized wave packets is provided. The cascade decay of single particle states into many particle states is discussed. We conjecture on \emph{possible} impact of these results on non-gaussianity and on the ``low multipole anomalies'' of the CMB., Comment: discussion on wave packets and cascade decay, 18 pages, 3 figs

The decay of a parent particle into two or more daughter particles results in an entangled quantum state as a consequence of conservation laws in the decay process. Recent experiments at Belle and BaBar take advantage of quantum entanglement and the correlations in the time evolution of the product particles to study CP and T violations. If one (or more) of the product particles are not observed, their degrees of freedom are traced out of the pure state density matrix resulting from the decay, leading to a mixed state density matrix and an entanglement entropy. This entropy is a measure of the loss of information present in the original quantum correlations of the entangled state. We use the Wigner-Weisskopf method to construct an approximation to this state that evolves in time in a {\em manifestly unitary} way. We then obtain the entanglement entropy from the reduced density matrix of one of the daughter particles obtained by tracing out the unobserved states, and follow its time evolution. We find that it grows over a time scale determined by the lifetime of the parent particle to a maximum, which when the width of the parent particle is narrow, describes the phase space distribution of maximally entangled Bell-like states. The method is generalized to the case in which the parent particle is described by a wave packet localized in space. Possible experimental avenues to measure the entanglement entropy in the decay of mesons at rest are discussed., Comment: Discussion on wavepackets and experimental measurement. 20 pages, 2 figs

Pseudoscalar meson decay leads to an entangled state of charged leptons ($\mu,e$) and massive neutrinos. Tracing out the neutrino degrees of freedom leads to a reduced density matrix for the charged leptons whose off-diagonal elements reveal \emph{charged lepton oscillations}. Although these decohere on unobservably small time scales $ \lesssim 10^{-23} s $ they indicate charged lepton \emph{mixing} as a result of common intermediate states. The charged lepton self energy up to one loop features flavor off-diagonal terms responsible for charged lepton mixing: a dominant ``short distance'' contribution with $W$ bosons and massive neutrinos in the intermediate state, and a subdominant ``large distance'' contribution with pseudoscalar mesons and massive neutrinos in the intermediate state. Mixing angle(s) are GIM suppressed, and are \emph{momentum and chirality dependent}. The difference of negative chirality mixing angles near the muon and electron mass shells is $\theta_L(M^2_\mu) -\theta_L(M^2_e)\propto G_F \sum U_{\mu j} m^2_j U^*_{j e}$ with $m_j$ the mass of the neutrino in the intermediate state. Recent results from TRIUMF, suggest an upper bound $\theta_L(p^2\simeq M^2_\mu)-\theta_L(p^2 \simeq M^2_e) < 10^{-14}\,\Big(M_S/\mathrm{100}\,MeV\Big)^2$ for one generation of a heavy sterile neutrino with mass $M_S$. We obtain the wavefunctions for the propagating modes, and discuss the relation between the lepton flavor violating process $\mu \rightarrow e\gamma$ and charged lepton mixing, highlighting that a measurement of such process implies a mixed propagator $\mu, e$. Furthermore writing flavor diagonal vertices in terms of mass eigenstates yields novel interactions suggesting further contributions to lepton flavor violating process as a consequence of momentum and chirality dependent mixing angles., Comment: 26 pages, 5 figs

The production of heavy sterile neutrinos from $\pi^-,K^-$ decay at rest yields charged leptons with negative helicity (positive for $\pi^+,K^+$). We obtain the branching ratio for this process and argue that a Stern-Gerlach filter leads to spatially separated domains of both helicity components with abundances determined by the branching ratio. Complemented with a search of monochromatic peaks, this setup can yield both the mass and mixing angles for sterile neutrinos with masses in the range $3 MeV \lesssim m_s \lesssim 414 MeV$ in next generation high intensity experiments. We also study oscillations of light Dirac and Majorana sterile neutrinos with $m_s \simeq eV$ produced in meson decays including decoherence aspects arising from lifetime effects of the decaying mesons and the stopping distance of the charged lepton in short baseline experiments. We obtain the transition probability from production to detection via charged current interactions including these decoherence effects for 3+1 and 3+2 scenarios, also studying $|\Delta L|=2$ transitions from $\bar{\nu} \leftrightarrow \nu$ oscillations for Majorana neutrinos and the impact of these effects on the determination of CP-violating amplitudes. We argue that decoherence effects are important in current short baseline accelerator experiments, leading to an underestimate of masses, mixing and CP-violating angles. At MiniBooNE/SciBooNE we estimate that these effects lead to an $\sim 15%$ underestimate for sterile neutrino masses $m_s \gtrsim 3 \,\mathrm{eV}$. We argue that reactor and current short baseline accelerator experiments are fundamentally different and suggest that in future high intensity experiments with neutrinos produced from $\pi,K$ decay at rest, stopping the charged leptons on distances much smaller than the decay length of the parent meson suppresses considerably these decoherence effects., Comment: 42 pages, 16 figures. To appear in Phys. Rev. D