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Single atomic defects are prominent windows to look into host quantum states because collective responses from the host states emerge as localized states around the defects. Friedel oscillations and Kondo clouds in Fermi liquids are quintessential examples. However, the situation is quite different for quantum spin liquid (QSL), an exotic state of matter with fractionalized quasiparticles and topological order arising from a profound impact of quantum entanglement. Elucidating the underlying local electronic property has been challenging due to the charge neutrality of fractionalized quasiparticles and the insulating nature of QSLs. Here, using spectroscopic-imaging scanning tunneling microscopy, we report atomically resolved images of monolayer $\alpha-RuCl_3$, the most promising Kitaev QSL candidate, on metallic substrates. We find quantum interference in the insulator manifesting as incommensurate and decaying spatial oscillations of the local density of states around defects with a characteristic bias dependence. The oscillation differs from any known spatial structures in its nature and does not exist in other Mott insulators, implying it is an exotic oscillation involved with excitations unique to $\alpha-RuCl_3$. Numerical simulations suggest that the observed oscillation can be reproduced by assuming that itinerant Majorana fermions of Kitaev QSL are scattered across the Majorana Fermi surface. The oscillation provides a new approach to exploring Kitaev QSLs through the local response against defects like Friedel oscillations in metals., Comment: v2 to appear in PRX

The layered honeycomb magnet $\alpha$-RuCl$_3$ is the most promising candidate for a Kitaev quantum spin liquid (KQSL) that can host charge-neutral Majorana fermions. Recent studies have shown significant sample dependence of thermal transport properties, which are a key probe of Majorana quasiparticles in the KQSL state, highlighting the importance of preparing high-quality single crystals of $\alpha$-RuCl$_3$. Here, we present a relatively simple and reliable method to grow high-quality single crystals of $\alpha$-RuCl$_3$. We use a two-step crystal growth method consisting of a purification process by chemical vapor transport (CVT) and a main crystal growth process by sublimation. The obtained crystals exhibit a distinct first-order structural phase transition from the monoclinic ($C2/m$) to the rhombohedral ($R\bar{3}$) structure at $\sim150$ K, which is confirmed by the nuclear quadrupole resonance spectra with much sharper widths than previously reported. The Raman spectra show the absence of defect-induced modes, supporting the good crystallinity of our samples. The jumps in the thermal expansion coefficient and specific heat at the antiferromagnetic (AFM) transition at 7.6-7.7 K are larger and sharper than those of previous samples grown by the CVT and Bridgman methods and do not show any additional AFM transitions at 10-14 K due to stacking faults. The longitudinal thermal conductivity in the AFM phase is significantly larger than previously reported, indicating a very long mean free path of heat carriers. All the results indicate that our single crystals are of superior quality with good crystallinity and few stacking faults, which provides a suitable platform for studying the Kitaev physics., Comment: 9 pages, 7 figures

The quest for fascinating quantum states arising from the interplay between correlation, frustration, and topology is at the forefront of condensed-matter physics. Recently discovered nonmagnetic kagome metals $A$V${_3}$Sb${_5}$ ($A=$ K, Cs, Rb) with charge density wave (CDW) and superconducting instabilities may host such exotic states. Here we report that an odd electronic nematic state emerges above the CDW transition temperature ($T_{\rm CDW}=94$ K) in CsV${_3}$Sb${_5}$. High-resolution torque measurements reveal a distinct twofold in-plane magnetic anisotropy that breaks the crystal rotational symmetry below $T^*\approx130$ K. However, no relevant anomalies are detected in the elastoresistance data near $T^*$, which excludes the even-parity ferro-orbital nematicity often found in other superconductors. Moreover, in the temperature range between $T_{\rm CDW}$ and $T^*$, conical rotations of magnetic field yield a distinct first-order phase transition, indicative of time-reversal symmetry breaking. These results provide thermodynamic evidence for the emergence of an odd-parity nematic order, implying that an exotic loop-current state precedes the CDW in CsV$_3$Sb$_5$., Comment: A revised manuscript will appear in Nature Physics

We report the first result of a direct search for a Cosmic ${\it axion}$ Background (C$a$B) - a relativistic background of axions that is not dark matter - performed with the axion haloscope, the Axion Dark Matter eXperiment (ADMX). Conventional haloscope analyses search for a signal with a narrow bandwidth, as predicted for dark matter, whereas the C$a$B will be broad. We introduce a novel analysis strategy, which searches for a C$a$B induced daily modulation in the power measured by the haloscope. Using this, we repurpose data collected to search for dark matter to set a limit on the axion photon coupling of a C$a$B originating from dark matter cascade decay via a mediator in the 800-995 MHz frequency range. We find that the present sensitivity is limited by fluctuations in the cavity readout as the instrument scans across dark matter masses. Nevertheless, we suggest that these challenges can be surmounted using superconducting qubits as single photon counters, and allow ADMX to operate as a telescope searching for axions emerging from the decay of dark matter. The daily modulation analysis technique we introduce can be deployed for various broadband RF signals, such as other forms of a C$a$B or even high-frequency gravitational waves., Comment: 9 pages, 4 figures

This report summarizes the recent progress and promising future directions in theoretical high-energy physics (HEP) identified within the Theory Frontier of the 2021 Snowmass Process., Comment: Contribution to the US Community Study on the Future of Particle Physics (Snowmass 2021), v2: fixed typos

The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, characterized by Cooper pairs condensed at finite momentum, has been a long-sought state that remains unresolved in many classes of fermionic systems, including superconductors and ultracold atoms. A fascinating aspect of the FFLO state is the emergence of periodic nodal planes in real space, but its observation is still lacking. Here we investigate the superconducting order parameter at high magnetic fields $H$ applied perpendicular to the $ab$ plane in a high-purity single crystal of FeSe. The heat capacity and magnetic torque provide thermodynamic evidence for a distinct superconducting phase at the low-temperature/high-field corner of the phase diagram. Despite the bulk superconductivity, spectroscopic-imaging scanning tunneling microscopy performed on the same crystal demonstrates that the order parameter vanishes at the surface upon entering the high-field phase. These results provide the first demonstration of a pinned planar node perpendicular to $H$, which is consistent with a putative FFLO state., Comment: 11 pages, 9 figures, including Supplemental Material. Accepted for publication in Phys. Rev. Lett

Despite tremendous investigations, a quantum spin liquid state realized in spin-1/2 kagome Heisenberg antiferromagnet remains largely elusive. In herbertsmithite ZnCu$_3$(OH)$_6$Cl$_2$, a quantum spin liquid candidate on the perfect kagome lattice, precisely characterizing the intrinsic physics of the kagome layers is extremely challenging due to the presence of interlayer Cu/Zn antisite disorder within its crystal structure. Here we measured the specific heat and thermal conductivity of single crystal herbertsmithite in magnetic fields with high resolution. Our results are highlighted by the excellent scaling collapse of the intrinsic magnetic specific heat contribution arising from the kagome layers as a function of $T/H$ (temperature/magnetic field). In addition, no residual linear term in the thermal conductivity $\kappa/T(T\rightarrow 0)$ is observed in zero and applied magnetic fields, indicating the absence of itinerant gapless excitations. These results suggest a new picture for a quantum spin liquid state of the kagome layers of herbertsmithite, wherein localized orphan spins arise and interact with random exchanges in conjunction with a non-itinerant quantum spin liquid.

An anapole state that breaks inversion and time reversal symmetries with preserving translation symmetry of underlying lattice has aroused great interest as a new quantum state, but only a few candidate materials have been reported. Recently, in a spin-orbit coupled Mott insulator \SIR, the emergence of a possible hidden order phase with broken inversion symmetry has been suggested at $T_{\Omega}$ above the N\'{e}el temperature by optical second harmonic generation measurements. Moreover, polarized neutron diffraction measurements revealed the broken time reversal symmetry below $T_{\Omega}$, which was supported by subsequent muon spin relaxation experiments. However, the nature of this mysterious phase remains largely elusive. Here, we investigate the hidden order phase through the combined measurements of the in-plane magnetic anisotropy with exceptionally high-precision magnetic torque and the nematic susceptibility with elastoresistance. A distinct two-fold in-plane magnetic anisotropy along the [110] Ir-O-Ir bond direction sets in below $\sim T_{\Omega}$, providing thermodynamic evidence for a nematic phase transition with broken $C_4$ rotational symmetry. However, in contrast to the even-parity nematic transition reported in other correlated electron systems, the nematic susceptibility exhibits no divergent behavior towards $T_{\Omega}$. These results provide bulk evidence for an odd-parity order parameter with broken rotational symmetry in the hidden order state. We discuss the hidden order in terms of an anapole state, in which polar toroidal moment is induced by two current loops in each IrO$_6$ octahedron of opposite chirality. Contrary to the simplest loop-current pattern previously suggested, the present results are consistent with a pattern in which the intra-unit cell loop-current flows along only one of the diagonal directions in the IrO$_4$ square., Comment: 11 pages, 10 figures

A quantum spin liquid (QSL) is an exotic state of matter characterized by quantum entanglement and the absence of any broken symmetry. A long-standing open problem, which is a key for fundamental understanding the mysterious QSL states, is how the quantum fluctuations respond to randomness due to quenched disorder. Transition metal dichalcogenide 1T-TaS$_2$ is a candidate material that hosts a QSL ground state with spin-1/2 on the two-dimensional perfect triangular lattice. Here, we performed systematic studies of low-temperature heat capacity and thermal conductivity on pure, Se-substituted and electron irradiated crystals of 1T-TaS$_2$. In pure 1T-TaS$_2$, the linear temperature term of the heat capacity $\gamma T$ and the finite residual linear term of the thermal conductivity in the zero-temperature limit $\kappa_{0}/T\equiv\kappa/T(T\rightarrow0)$ are clearly resolved, consistent with the presence of gapless spinons with a Fermi surface. Moreover, while the strong magnetic field slightly enhances $\kappa_0/T$, it strongly suppresses $\gamma$. These unusual contrasting responses to magnetic field imply the coexistence of two types of gapless excitations with itinerant and localized characters. Introduction of additional weak random exchange disorder in 1T-Ta(S$_{1-x}$Se$_x$)$_2$ leads to vanishing of $\kappa_0/T$, indicating that the itinerant gapless excitations are sensitive to the disorder. On the other hand, in both pure and Se-substituted systems, the magnetic contribution of the heat capacity obeys a universal scaling relation, which is consistent with a theory that assumes the presence of localized orphan spins forming random singlets. Electron irradiation in pure 1T-TaS$_2$ largely enhances $\gamma$ and changes the scaling function dramatically, suggesting a possible new state of spin liquid., Comment: 10 pages, 9 figures. arXiv admin note: text overlap with arXiv:1803.06100

We present measurements of cosmic shear two-point correlation functions (TPCFs) from Hyper Suprime-Cam Subaru Strategic Program (HSC SSP) first-year data, and derived cosmological constraints based on a blind analysis. The HSC first-year shape catalog is divided into four tomographic redshift bins ranging from $z=0.3$ to 1.5 with equal widths of $\Delta z =0.3$. The unweighted galaxy number densities in each tomographic bin are 5.9, 5.9, 4.3, and 2.4 arcmin$^{-2}$ from lower to higher redshifts, respectively. We adopt the standard TPCF estimators, $\xi_\pm$, for our cosmological analysis, given that we find no evidence of the significant B-mode shear. The TPCFs are detected at high significance for all ten combinations of auto- and cross-tomographic bins over a wide angular range, yielding a total signal-to-noise ratio of 19 in the angular ranges adopted in the cosmological analysis, $7'<\theta<56'$ for $\xi_+$ and $28'<\theta<178'$ for $\xi_-$. We perform the standard Bayesian likelihood analysis for cosmological inference from the measured cosmic shear TPCFs, including contributions from intrinsic alignment of galaxies as well as systematic effects from PSF model errors, shear calibration uncertainty, and source redshift distribution errors. We adopt a covariance matrix derived from realistic mock catalogs constructed from full-sky gravitational lensing simulations that fully account for survey geometry and measurement noise. For a flat $\Lambda$ cold dark matter model, we find $S_8 \equiv \sigma_8\sqrt{\Omega_m/0.3}=0.823_{-0.028}^{+0.032}$, and $\Omega_m=0.332_{-0.096}^{+0.050}$. We carefully check the robustness of the cosmological results against astrophysical modeling uncertainties and systematic uncertainties in measurements, and find that none of them has a significant impact on the cosmological constraints., Comment: Replaced with the bug-fixed version. The results presented in the original publication were found to be affected by bugs in the software used for the numerical computation. The erratum will be published in PASJ. In this version, revised results obtained from corrected computations are presented. Revised chains are available from http://th.nao.ac.jp/MEMBER/hamanatk/HSC16aCSTPCFbugfix/index.html

Quantum oscillations (QOs) in transport and thermodynamic parameters at high magnetic fields are an unambiguous signature of the Fermi surface, the defining characteristic of a metal. Therefore, recent observations of QOs in insulating SmB$_6$ and YbB$_{12}$, in particular the QOs of the resistivity $\rho_{xx}$ in YbB$_{12}$, have been a big surprise, pointing to the formation of a novel state of quantum matter. Despite the large charge gap inferred from the insulating behaviour of $\rho_{xx}$, these compounds seemingly host a Fermi surface at high magnetic fields. However, the nature of the ground state in zero field has been little explored. Here we report the use of low-temperature heat-transport measurements to discover gapless, itinerant, charge-neutral excitations in the ground state of YbB$_{12}$. At zero field, despite $\rho_{xx}$ being far larger than that of conventional metals, a sizable linear temperature dependent term in the thermal conductivity is clearly resolved in the zero-temperature limit ($\kappa_{xx}/T(T\rightarrow0)=\kappa_{xx}^0/T\neq0$). Such a residual $\kappa_{xx}^0/T$ term at zero field, which is absent in SmB$_6$, leads to a spectacular violation of the Wiedemann-Franz law: the Lorenz ratio $L=\kappa_{xx}\rho_{xx}/T$ is $10^{4}$-$10^{5}$ times larger than that expected in conventional metals. These data indicate that YbB$_{12}$ is a charge insulator but a thermal metal, suggesting the presence of itinerant neutral fermions. Remarkably, more insulating crystals with larger activation energies exhibit a larger amplitude of the resistive QOs as well as a larger $\kappa_{xx}^0/T$, in stark contrast to conventional metals. Moreover, we find that these fermions couple to magnetic field, despite their charge neutrality. Our findings expose novel gapless and highly itinerant, charge-neutral quasiparticles in this unconventional quantum state., Comment: 7 pages, 4 figures. This is the original submitted version. Final version is accepted for publication in Nature Physics

The pseudogap phenomenon in cuprates is the most mysterious puzzle in the research of high-temperature superconductivity. In particular, whether the pseudogap is associated with a crossover or phase transition has been a long-standing controversial issue. The tetragonal cuprate HgBa$_2$CuO$_{4+\delta}$, with only one CuO$_2$ layer per primitive cell, is an ideal system to tackle this puzzle. Here, we measure the anisotropy of magnetic susceptibility within the CuO$_2$ plane with exceptionally high-precision magnetic torque experiments. Our key finding is that a distinct two-fold in-plane anisotropy sets in below the pseudogap temperature $T^*$, which provides thermodynamic evidence for a nematic phase transition with broken four-fold symmetry. Most surprisingly, the nematic director orients along the diagonal direction of the CuO$_2$ square lattice, in sharp contrast to the bond nematicity reported in various iron-based superconductors and double-layer YBa$_2$Cu$_3$O$_{6+\delta}$, where the anisotropy axis is along the Fe-Fe and Cu-O-Cu directions, respectively. Another remarkable feature is that the enhancement of the diagonal nematicity with decreasing temperature is suppressed around the temperature at which short-range charge-density-wave (CDW) formation occurs. This is in stark contrast to YBa$_2$Cu$_3$O$_{6+\delta}$, where the bond nematicity is not influenced by the CDW. Our result suggests a competing relationship between diagonal nematic and CDW order in HgBa$_2$CuO$_{4+\delta}$., Comment: 7 pages, 8 figures

To reveal the nature of elementary excitations in a quantum spin liquid (QSL), we measured low temperature thermal conductivity and specific heat of 1T-TaS$_2$, a QSL candidate material with frustrated triangular lattice of spin-1/2. The nonzero temperature linear specific heat coefficient $\gamma$ and the finite residual linear term of the thermal conductivity in the zero temperature limit $\kappa_0/T=\kappa/T(T\rightarrow 0)$ are clearly resolved. This demonstrates the presence of highly mobile gapless excitations, which is consistent with fractionalized spinon excitations that form a Fermi surface. Remarkably, an external magnetic field strongly suppresses $\gamma$, whereas it enhances $\kappa_0/T$. This unusual contrasting behavior in the field dependence of specific heat and thermal conductivity can be accounted for by the presence of two types of gapless excitations with itinerant and localized characters, as recently predicted theoretically (I. Kimchi et al., arXiv:1803.00013 (2018)). This unique feature of 1T-TaS$_2$ provides new insights into the influence of quenched disorder on the QSL., Comment: 6 pages, 4 figures

We report discovery of 41 new high-z quasars and luminous galaxies, which were spectroscopically identified at 5.7 < z < 6.9. This is the fourth in a series of papers from the Subaru High-z Exploration of Low-Luminosity Quasars (SHELLQs) project, based on the deep multi-band imaging data collected by the Hyper Suprime-Cam (HSC) Subaru Strategic Program survey. We selected the photometric candidates by a Bayesian probabilistic algorithm, and then carried out follow-up spectroscopy with the Gran Telescopio Canarias and the Subaru Telescope. Combined with the sample presented in the previous papers, we have now spectroscopically identified 137 extremely-red HSC sources over about 650 deg2, which include 64 high-z quasars, 24 high-z luminous galaxies, 6 [O III] emitters at z ~ 0.8, and 43 Galactic cool dwarfs (low-mass stars and brown dwarfs). The new quasars span the luminosity range from M1450 ~ -26 to -22 mag, and continue to populate a few magnitude lower luminosities than have been probed by previous wide-field surveys. In a companion paper, we derive the quasar luminosity function at z ~ 6 over an unprecedentedly wide range of M1450 ~ -28 to -21 mag, exploiting the SHELLQs and other survey outcomes., Comment: ApJS in press. arXiv admin note: substantial text overlap with arXiv:1704.05854

A central issue in the quest to understand the superconductivity in cuprates is the nature and origin of the pseudogap state, which harbours anomalous electronic states such as Fermi arc, charge density wave (CDW), and $d$-wave superconductivity. A fundamentally important, but long-standing controversial problem has been whether the pseudogap state is a distinct thermodynamic phase characterized by broken symmetries below the onset temperature $T^*$. Electronic nematicity, a fourfold ($C_4$) rotational symmetry breaking, has emerged as a key feature inside the pseudogap regime, but the presence or absence of a nematic phase transition and its relationship to the pseudogap remain unresolved. Here we report thermodynamic measurements of magnetic torque in the underdoped regime of orthorhombic YBa$_2$Cu$_3$O$_y$ with a field rotating in the CuO$_2$ plane, which allow us to quantify magnetic anisotropy with exceptionally high precision. Upon entering the pseudogap regime, the in-plane anisotropy of magnetic susceptibility increases after exhibiting a distinct kink at $T^*$. Our doping dependence analysis reveals that this anisotropy is preserved below $T^*$ even in the limit where the effect of orthorhombicity is eliminated. In addition, the excess in-plane anisotropy data show a remarkable scaling behaviour with respect to $T/T^*$ in a wide doping range. These results provide thermodynamic evidence that the pseudogap onset is associated with a second-order nematic phase transition, which is distinct from the CDW transition that accompanies translational symmetry breaking. This suggests that nematic fluctuations near the pseudogap phase boundary have a potential link to the strange metallic behaviour in the normal state, out of which high-$T_c$ superconductivity emerges., Comment: 6 pages, 4 figures. An updated manuscript with SI will appear in Nature Physics

Hyper Suprime-Cam (HSC) is a wide-field imaging camera on the prime focus of the 8.2m Subaru telescope on the summit of Maunakea in Hawaii. A team of scientists from Japan, Taiwan and Princeton University is using HSC to carry out a 300-night multi-band imaging survey of the high-latitude sky. The survey includes three layers: the Wide layer will cover 1400 deg$^2$ in five broad bands ($grizy$), with a $5\,\sigma$ point-source depth of $r \approx 26$. The Deep layer covers a total of 26~deg$^2$ in four fields, going roughly a magnitude fainter, while the UltraDeep layer goes almost a magnitude fainter still in two pointings of HSC (a total of 3.5 deg$^2$). Here we describe the instrument, the science goals of the survey, and the survey strategy and data processing. This paper serves as an introduction to a special issue of the Publications of the Astronomical Society of Japan, which includes a large number of technical and scientific papers describing results from the early phases of this survey., Comment: 14 pages, 7 figures, 5 tables. Corrected for a typo in the coordinates of HSC-Wide spring equatorial field in Table 5

We describe a compact, ultra-clean device used to deploy radioactive sources along the vertical axis of the KamLAND liquid-scintillator neutrino detector for purposes of calibration. The device worked by paying out and reeling in precise lengths of a hanging, small-gauge wire rope (cable); an assortment of interchangeable radioactive sources could be attached to a weight at the end of the cable. All components exposed to the radiopure liquid scintillator were made of chemically compatible UHV-cleaned materials, primarily stainless steel, in order to avoid contaminating or degrading the scintillator. To prevent radon intrusion, the apparatus was enclosed in a hermetically sealed housing inside a glove box, and both volumes were regularly flushed with purified nitrogen gas. An infrared camera attached to the side of the housing permitted real-time visual monitoring of the cable's motion, and the system was controlled via a graphical user interface., Comment: Revised author affiliations, corrected typos, made minor improvements to text, and revised references

We report a measurement of the neutrino-electron elastic scattering rate of 862 keV 7Be solar neutrinos based on a 165.4 kton-day exposure of KamLAND. The observed rate is 582 +/- 90 (kton-day)^-1, which corresponds to a 862 keV 7Be solar neutrino flux of (3.26 +/- 0.50) x 10^9 cm^-2s^-1, assuming a pure electron flavor flux. Comparing this flux with the standard solar model prediction and further assuming three flavor mixing, a nu_e survival probability of 0.66 +/- 0.14 is determined from the KamLAND data. Utilizing a global three flavor oscillation analysis, we obtain a total 7Be solar neutrino flux of (5.82 +/- 0.98) x 10^9 cm^-2s^-1, which is consistent with the standard solar model predictions., Comment: 8 pages, 6 figures, submitted to Phys. Rev. C

The Proceedings of the 2011 workshop on Fundamental Physics at the Intensity Frontier. Science opportunities at the intensity frontier are identified and described in the areas of heavy quarks, charged leptons, neutrinos, proton decay, new light weakly-coupled particles, and nucleons, nuclei, and atoms., Comment: 229 pages

We report a measurement of the neutrino-electron elastic scattering rate from 8B solar neutrinos based on a 123 kton-day exposure of KamLAND. The background-subtracted electron recoil rate, above a 5.5 MeV analysis threshold is 1.49+/-0.14(stat)+/-0.17(syst) events per kton-day. Interpreted as due to a pure electron flavor flux with a 8B neutrino spectrum, this corresponds to a spectrum integrated flux of 2.77+/-0.26(stat)+/-0.32(syst) x 10^6 cm^-2s^-1. The analysis threshold is driven by 208Tl present in the liquid scintillator, and the main source of systematic uncertainty is due to background from cosmogenic 11Be. The measured rate is consistent with existing measurements and with Standard Solar Model predictions which include matter enhanced neutrino oscillation., Comment: 6 pages, 3 figures

The difference between the CP asymmetries of the $B^0 \to K^+ \pi^-$ and $B^+ \to K^+ \pi^0$ decays has been recently confirmed with an evidence larger than $5\sigma$'s. We discuss it as a possible signal of new physics associated with new (large) CP violation in the electroweak penguin contributions. We propose a supersymmetry breaking scheme where such new sources of CP violation occur in the flavor non-universal trilinear scalar couplings., Comment: 4 pages, 2 figures

The Kaplan-Manohar ambiguity in light quark masses allows for a larger uncertainty in the ratio of up to down quark masses than naive estimates from the chiral Lagrangian would indicate. We show that it allows for a relaxation of experimental bounds on the QCD axion, specifically KSVZ axions in the $2-3 \mu$eV mass range composing 100% of the galactic dark matter halo can evade the experimental limits placed by the ADMX collaboration., Comment: 9 pages, 5 figures

The seesaw mechanism for the small neutrino mass has been a popular paradigm, yet it has been believed that there is no way to test it experimentally. We present a conceivable outcome from future experiments that would convince us of the seesaw mechanism. It would involve a variety of data from LHC, ILC, cosmology, underground, and low-energy flavor violation experiments to establish the case., Comment: 5 pages, 4 figures

During 2004, four divisions of the American Physical Society commissioned a study of neutrino physics to take stock of where the field is at the moment and where it is going in the near and far future. Several working groups looked at various aspects of this vast field. The summary was published as a main report entitled ``The Neutrino Matrix'' accompanied by short 50 page versions of the report of each working group. Theoretical research in this field has been quite extensive and touches many areas and the short 50 page report provided only a brief summary and overview of few of the important points. The theory discussion group felt that it may be of value to the community to publish the entire study as a white paper and the result is the current article. After a brief overview of the present knowledge of neutrino masses and mixing and some popular ways to probe the new physics implied by recent data, the white paper summarizes what can be learned about physics beyond the Standard Model from the various proposed neutrino experiments. It also comments on the impact of the experiments on our understanding of the origin of the matter-antimatter asymmetry of the Universe and the basic nature of neutrino interactions as well as the existence of possible additional neutrinos. Extensive references to original literature are provided., Comment: 143 pages, many figures, v2 references corrected, very minor modifications to the text