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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

Violation of unitarity by Hawking radiation does not violate energy-momentum conservation

An argument by Banks, Susskind and Peskin (BSP), according to which violation of unitarity would violate either locality or energy-momentum conservation, is widely believed to be a strong argument against non-unitarity of Hawking radiation. We find that the whole BSP argument rests on the crucial assumption that the Hamiltonian is not highly degenerate, and point out that this assumption is not satisfied for systems with many degrees of freedom. Using Lindblad equation, we show that high degeneracy of the Hamiltonian allows local non-unitary evolution without violating energy-momentum conservation. Moreover, since energy-momentum is the source of gravity, we argue that energy-momentum is necessarily conserved for a large class of non-unitary systems with gravity. Finally, we explicitly calculate the Lindblad operators for non-unitary Hawking radiation and show that they conserve energy-momentum.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Simple and General Unitarity Conserving Numerical Real-Time Propagators of the Time-Dependent Schrödinger Equation Based on Magnus Expansion

Magnus expansion (ME) provides a general way to expand the real-time propagator of a time-dependent Hamiltonian within the exponential such that the unitarity is satisfied at any order. Here, we use this property and explicit integration of Lagrange interpolation formulas for the time-dependent Hamiltonian within each time interval and derive approximations that preserve unitarity for the differential time evolution operators of general time-dependent Hamiltonians. The resulting second-order approximation is the same as using the average of Hamiltonians for two end points of time. We identify three fourth-order approximations involving commutators of Hamiltonians at different times and also derive a sixth-order expression. A test of these approximations along with other available expressions for a two-state time-dependent Hamiltonian with sinusoidal time dependences provides information on the relative performance of these approximations and suggests that the derived expressions can serve as useful numerical tools for time evolution in time-resolved spectroscopy, quantum control, quantum sensing, real-time ab initio quantum dynamics, and open system quantum dynamics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Universal correlation between CP phase $\delta$ and the non-unitarity $\alpha$ parameter phases

The non-unitarity of the neutrino mixing matrix is a problem related with a more fundamental question about the origin of the neutrino mass. After a brief discussion on the questions ``why do we need model-independent framework for unitarity test?'', we show interesting properties present in the oscillation probabilities of neutrinos propagating in matter with non-unitarity. That is, (1) partial unitarity and (2) universal phase correlation. %To illuminate these points, we formulate a perturbative framework with the two expansion parameters $\epsilon \equiv \Delta m^2_{21} / \Delta m^2_{31}$ and $\alpha$ matrix elements. The complex triangular $\alpha$ matrix is introduced through the definition of $3 \times 3$ non-unitary flavor mixing matrix $N$ as %\begin{eqnarray} N &=& \left( \bf{1} - \alpha \right) U = \left\{ \bf{1} - \left[ \begin{array}{ccc}\alpha_{ee} & 0 & 0 \\\alpha_{\mu e} & \alpha_{\mu \mu} & 0 \\\alpha_{\tau e} & \alpha_{\tau \mu} & \alpha_{\tau \tau} \\\end{array}\right] \right\}U \label{alpha-matrix-def}\end{eqnarray}%where $U$ is the unitary MNS mixing matrix, and hence $\alpha$ characterizes the size and the flavor dependence of unitarity violation (UV)\footnote{%%%%%%%%%%%%%Despite that in the physics literature UV usually means ``ultraviolet'', we use UV in this manuscript as an abbreviation for ``unitarity violation'' or ``unitarity violating''.}~~caused by new physics (NP) at low- or high-scales.~~~~The point (1) above essentially means that despite non-unitary mixing, neutrino evolution must be unitary because the three active neutrinos span a complete state space of neutral leptons. The {\em phase correlation} mentioned in the point (2) refers an intriguing property that the complex $\alpha$ parameters and $\nu$Standard Model CP phase $\delta$ always come into the oscillation probabilities in a correlated way, $e^{- i \delta } \alpha_{\mu e}$, $\alpha_{\tau e}$, and $e^{i \delta} \alpha_{\tau \mu}$, universally in all the oscillation channels. The physical meaning of this result is briefly discussed. }

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2014

Constraining astrophysical neutrino flavor composition from leptonic unitarity

The recent IceCube observation of ultra-high-energy astrophysical neutrinos has begun the era of neutrino astronomy. In this work, using the unitarity of leptonic mixing matrix, we derive nontrivial unitarity constraints on the flavor composition of astrophysical neutrinos detected by IceCube. Applying leptonic unitarity triangles, we deduce these unitarity bounds from geometrical conditions, such as triangular inequalities. These new bounds generally hold for three flavor neutrinos, and are independent of any experimental input or the pattern of lepton mixing. We apply our unitarity bounds to derive general constraints on the flavor compositions for three types of astrophysical neutrino sources (and their general mixture), and compare them with the IceCube measurements. Furthermore, we prove that for any sources without ν{sub τ} neutrinos, a detected ν{sub μ} flux ratio < 1/4 will require the initial flavor composition with more ν{sub e} neutrinos than ν{sub μ} neutrinos.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Leptonic unitarity triangles

We present a comprehensive analysis of leptonic unitarity triangles, using both current neutrino oscillation data and projections of next-generation oscillation measurements. Future experiments, sensitive to the degree of CP violation in the lepton sector, will enable the construction of precise triangles. We show how unitarity violation could manifest in the triangles and discuss how they serve as unitarity tests. We also propose the use of Jarlskog factors as a complementary means of probing unitarity. This analysis highlights the importance of testing the unitarity of the leptonic mixing matrix, an understanding of which is crucial for deciphering the nature of the neutrino sector.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2016

Unitarity and the three flavor neutrino mixing matrix

Unitarity is a fundamental property of any theory required to ensure we work in a theoretically consistent framework. In comparison with the quark sector, experimental tests of unitarity for the 3x3 neutrino mixing matrix are considerably weaker. It must be remembered that the vast majority of our information on the neutrino mixing angles originates from v - e and v μ disappearance experiments, with the assumption of unitarity being invoked to constrain the remaining elements. New physics can invalidate this assumption for the 3x3 subset and thus modify our precision measurements. We also perform a reanalysis to see how global knowledge is altered when one refits oscillation results without assuming unitarity, and present 3σ ranges for allowed U PMNS elements consistent with all observed phenomena. We calculate the bounds on the closure of the six neutrino unitarity triangles, with the closure of the v - e and v μ triangle being constrained to be ≤0.03, while the remaining triangles are significantly less constrained to be ≤ 0.1 - 0.2. Similarly for the row and column normalization, we find their deviation from unity is constrained to be ≤ 0.2 - 0.4, for four out of six such normalizations, while for the v μ and v e row normalization the deviations are constrained to be ≤0.07, all at the 3σCL. Additionally, we emphasize that there is significant room for new low energy physics, especially in the v τ sector which very few current experiments constrain directly.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

The Unitarity-Limit Expansion for Two Nucleons with Perturbative Pions: Digest and Ideas

Theorists love nontrivial fixed points. In the Unitarity Limit, the NN 𝑆-wave binding energies are zero, the scattering lengths infinite, Physics is universal, i.e. insensitive to details of the interactions, and observables display richer symmetries, namely invariance under both scaling and Wigner’s combined SU(4) transformation of spin and isospin. In “Pionless” EFT, both are explicitly but weakly broken and hence perturbative in the Unitarity Window (phase shifts 45° ≲ δ(k) ≲ 135°, i.e. momenta k≈mπ). This Unitarity Expansion provides strong hints that Nuclear Physics resides indeed in a sweet spot: bound weakly enough to be insensitive to the details of the nuclear interaction; and therefore interacting strongly enough that the NN scattering lengths are perturbatively close to the Unitarity Limit. In this paradigm change, NN details are less important than NNN interactions to explain the complexity and patterns of the nuclear chart. This presentation is a digest of the first quantitative exploration of corrections to this picture when pions are included [1] (see there for a more comprehensive list of references). Since the pion mass and decay constant introduce dimensionful scales in the NN system, they explicitly break the symmetries of the Unitarity fixed point. In χEFT, these symmetries must therefore be hidden and instead be classified as emergent.

Griesshammer, Harald W. [The George Washington Uni↗
DOE OSTI2025

On two nucleons near unitarity with perturbative pions

We explore the impact of perturbative pions on the Unitarity Expansion in the two-nucleon S-waves of Chiral Effective Field Theory at next-to-next-to leading order (N 2 LO). Pion exchange explicitly breaks the nontrivial fixed point’s universality, i.e. invariance of S waves under both conformal and Wigner’s combined SU(4) spin–isospin transformations. On the other hand, Unitarity explicitly breaks chiral symmetry. The two seem incompatible in their respective exact-symmetry limits. χEFT with Perturbative Pions in the Unitarity Expansion resolves the apparent conflict in the Unitarity Window (phase shifts 45° ≲ δ(k) ≲ 135°), i.e. around momenta most relevant for low-energy nuclear systems. Its only LO scale is the scattering momentum; NLO adds only scattering length, effective range and non-iterated one-pion exchange (OPE); and N 2 LO only once-iterated OPE. Agreement in the 1 S 0 channel is very good.

Chiral symmetry↗
DOE OSTI2020

Current and future neutrino oscillation constraints on leptonic unitarity

The unitarity of the lepton mixing matrix is a critical assumption underlying the standard neutrino-mixing paradigm. However, many models seeking to explain the as-yet-unknown origin of neutrino masses predict deviations from unitarity in the mixing of the active neutrino states. Motivated by the prospect that future experiments may provide a precise measurement of the lepton mixing matrix, we revisit current constraints on unitarity violation from oscillation measurements and project how next-generation experiments will improve our current knowledge. With the next-generation data, the normalizations of all rows and columns of the lepton mixing matrix will be constrained to ≲10% precision, with the e-row best measured at ≲1% and the τ-row worst measured at ~10% precision. The measurements of the mixing matrix elements themselves will be improved on average by a factor of 3. We highlight the complementarity of DUNE, T2HK, JUNO, and IceCube Upgrade for these improvements, as well as the importance of ντ appearance measurements and sterile neutrino searches for tests of leptonic unitarity.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Unitarity methods in AdS/CFT

We develop a systematic unitarity method for loop-level AdS scattering amplitudes, dual to non-planar CFT correlators, from both bulk and boundary perspectives. We identify cut operators acting on bulk amplitudes that put virtual lines on shell, and show how the conformal partial wave decomposition of the amplitudes may be efficiently computed by gluing lower-loop amplitudes. A central role is played by the double discontinuity of the amplitude, which has a direct relation to these cuts. We then exhibit a precise, intuitive map between the diagrammatic approach in the bulk using cutting and gluing, and the algebraic, holographic unitarity method of [1] that constructs the non-planar correlator from planar CFT data. Our analysis focuses mostly on four-point, one-loop diagrams — we compute cuts of the scalar bubble, triangle and box, as well as some one-particle reducible diagrams — in addition to the five-point tree and four-point double-ladder. Analogies with S-matrix unitarity methods are drawn throughout.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Non-unitarity, sterile neutrinos, and non-standard neutrino interactions

The simplest Standard Model extension to explain neutrino masses involves the addition of right-handed neutrinos. At some level, this extension will impact neutrino oscillation searches. In this work we explore the differences and similarities between the case in which these neutrinos are kinematically accessible (sterile neutrinos) or not (mixing matrix non-unitarity). We clarify apparent inconsistencies in the present literature when using different parametrizations to describe these effects and recast both limits in the popular neutrino non-standard interaction (NSI) formalism. We find that, in the limit in which sterile oscillations are averaged out at the near detector, their effects at the far detector coincide with non-unitarity at leading order, even in presence of a matter potential. We also summarize the present bounds existing in both limits and compare them with the expected sensitivities of near future facilities taking the DUNE proposal as a benchmark. We conclude that non-unitarity effects are too constrained to impact present or near future neutrino oscillation facilities but that sterile neutrinos can play an important role at long baseline experiments. As a result, the role of the near detector is also discussed in detail.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Unitarity bounds on effective field theories at the LHC

Effective Field Theory (EFT) extensions of the Standard Model are tools to compute observables (e.g. cross sections with partonic center-of-mass energy √s^) as a systematically improvable expansion suppressed by a new physics scale M. If one is interested in EFT predictions in the parameter space where M < √s^, concerns of self-consistency emerge, which can manifest as a violation of perturbative partial-wave unitarity. However, when we search for the effects of an EFT at a hadron collider with center-of-mass energy √s using an inclusive strategy, we typically do not have access to the event-by-event value of √s^. This motivates the need for a formalism that incorporates parton distribution functions into the perturbative partial-wave unitarity analysis. Developing such a framework and initiating an exploration of its implications is the goal of this work. Our approach opens up a potentially valid region of the EFT parameter space where M << √s. We provide evidence that there exist valid EFTs in this parameter space. The perturbative unitarity bounds are sensitive to the details of a given search, an effect we investigate by varying kinematic cuts.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2017

Nonviolent unitarization: basic postulates to soft quantum structure of black holes

A first-principles approach to the unitarity problem for black holes is systematically explored, based on the postulates of 1) quantum mechanics 2) the ability to approximately locally divide quantum gravitational systems into subsystems 3) correspondence with quantum field theory predictions for appropriate observers and (optionally) 4) universality of new gravitational effects. Unitarity requires interactions between the internal state of a black hole and its surroundings that have not been identified in the field theory description; correspondence with field theory indicates that these are soft. A conjectured information-theoretic result for information transfer between subsystems, partly motivated by a perturbative argument, then constrains the minimum coupling size of these interactions of the quantum atmosphere of a black hole. While large couplings are potentially astronomically observable, given this conjecture one finds that the new couplings can be exponentially small in the black hole entropy, yet achieve the information transfer rate needed for unitarization, due to the large number of black hole internal states. This provides a new possible alternative to arguments for large effects near the horizon. If universality is assumed, these couplings can be described as small, soft, state-dependent fluctuations of the metric near the black hole. As a result, open questions include that of the more fundamental basis for such an effective picture.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Unitarity violation and the geometry of Higgs EFTs

We derive the scale of unitarity violation from the geometry of Effective Field Theory (EFT) extensions of the Standard Model Higgs sector. The high-energy behavior of amplitudes with more than four scalar legs depends on derivatives of geometric invariants with respect to the physical Higgs field h, such that higher-point amplitudes begin to reconstruct the scalar manifold away from our vacuum. In theories whose low-energy limit can be described by the Higgs EFT (HEFT) but not the Standard Model EFT (SMEFT), non-analyticities in the vicinity of our vacuum limit the radius of convergence of geometric invariants, leading to unitarity violation at energies below 4πv. Our results unify approaches to the HEFT/SMEFT dichotomy based on unitarity, analyticity, and geometry, and more broadly illustrate the sense in which observables probe the geometry of an EFT. Along the way, we provide novel basis-independent results for Goldstone/Higgs boson scattering amplitudes expressed in terms of geometric covariant quantities.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Physics of parameter correlations around the solar-scale enhancement in neutrino theory with unitarity violation

We discuss the physics of the three neutrino flavor transformation with non-unitary mixing matrix, with particular attention to the correlation between the $\nu$SM- and the $\alpha$ parameters which represent the effect of unitarity-violating (UV) new physics. Towards this goal, a new perturbative framework is created to illuminate the effect of non-unitarity in the region of the solar-scale enhanced oscillations. We refute the skepticism about the physical reality of the $\nu$Standard Model CP phase $\delta$–$\alpha$ parameter phase correlation by analysis with the SOL convention of $U_{{\tiny MNS}}$, in which $e^{\pm i \delta}$ is attached to $s_{12}$. Then, a comparative study between the solar- and atmospheric-scale oscillation regions allowed by the framework reveals a dynamical $\delta$–(blobs of the $\alpha$ parameters) correlation in the solar oscillation region, in sharp contrast to the “chiral”-type phase correlation $[e^{- i \delta} \bar{\alpha}_{\mu e},\ e^{- i \delta} \bar{\alpha}_{\tau e},\ \bar{\alpha}_{\tau \mu}]$ in the Particle Data Group convention seen in the atmospheric oscillation region. An explicit perturbative calculation to the first order in the $\nu_{\mu} \rightarrow \nu_{e}$ channel allows us to decompose the UV related part of the probability into the unitary evolution part and the genuine non-unitary part. We observe that the effect of non-unitarity tends to cancel between these two parts, as well as between the different $\alpha_{\beta \gamma}$ parameters.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Even-point multi-loop unitarity and its applications: exponentiation, anomalies and evanescence

Abstract We identify novel structure in newly computed multi-loop amplitudes and quantum actions for even-point effective field theories, including both the nonlinear sigma model (NLSM) and double-copy gauge theories such as Born-Infeld and its supersymmetric generalizations. We exploit special properties of all even-point theories towards establishing an efficient unitarity based amplitude construction. In doing so, we find evidence that the leading IR divergence of NLSM amplitudes exponentiates when the target space is$$ \mathbbm{CP} $$ CP 1 ≅ SU(2)/U(1). We then systematically compute the two-loop anomalous behavior of Born-Infeld, and find that the counterterms needed to restore U(1) invariant behavior at loop-level can be constructed via a symmetric-structure double-copy. We also demonstrate that the divergent part of the one-minus (−+++) two-loop anomaly vanishes upon introducing an evanescent operator. In addition to these purely photonic counterterms, we verify through explicit calculation that the anomalous matrix elements that violate U(1) duality invariance can be alternatively cancelled by summing over internal$$ \mathcal{N} $$ N = 4 DBIVA superfields. Finally we find that$$ \mathcal{N} $$ N = 4 Dirac-Born-Infeld-Volkov-Akulov (DBIVA) amplitudes admit double-copy construction through two-loop order by reproducing our unitarity based result with a double copy between color-dual$$ \mathcal{N} $$ N = 4 super-Yang-Mills and our two-loop NLSM amplitudes. This result supports the possibility of color-dual representations for NLSM beyond one-loop. We conclude with an overview of howD-dimensional four-photon counterterms can be constructed in generality with the symmetric-structure double-copy, and outline a convenient way of counting evanescent operators using Hilbert series as generating functions.

Physics↗
DOE OSTI2022

On unitarity of tree-level string amplitudes

Four-particle tree-level scattering amplitudes in string theory are magically consistent with unitarity, reflected in the non-trivial fact that beneath the critical dimension, the residues of the amplitudes on massive poles can be expanded in partial waves with all positive coefficients. While this follows (rather indirectly) from the no-ghost theorem, the simplicity of the statement and its fundamental importance for the physical consistency of string theory begs for a more direct and elementary understanding. In this note we take a step in this direction by presenting a new expression for the partial wave coefficients of string amplitudes, given by surprisingly simple double/triple contour integrals for open/closed strings. This representation allows us to directly prove unitarity of all superstring theories in D ≤ 6 spacetime dimensions, and can also be used to determine various asymptotics of the partial waves at large mass levels.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Complementarity and the unitarity of the black hole S -matrix

Recently, Akers et al. proposed a non-isometric holographic map from the interior of a black hole to its exterior. Within this model, we study properties of the black hole S-matrix, which are in principle accessible to observers who stay outside the black hole. Specifically, we investigate a scenario in which an infalling agent interacts with radiation both outside and inside the black hole. Because the holographic map involves postselection, the unitarity of the S-matrix is not guaranteed in this scenario, but we find that unitarity is satisfied to very high precision if suitable conditions are met. If the internal black hole dynamics is described by a pseudorandom unitary transformation, and if the operations performed by the infaller have computational complexity scaling polynomially with the black hole entropy, then the S-matrix is unitary up to corrections that are superpolynomially small in the black hole entropy. Furthermore, while in principle quantum computation assisted by postselection can be very powerful, we find under similar assumptions that the S-matrix of an evaporating black hole has polynomial computational complexity.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗