arXiv subjects

Ira Z. Rothstein

Publications and source records attributed to Ira Z. Rothstein.

At least 37 records · Page 2Linked to original sources

arXiv2020

Virtual Hawking Radiation

We consider the effects of off-shell Hawking radiation on scattering processes involving black holes coupled to quantum fields. The focus here is to the case of gravitational scattering of a scalar field mediated by the exchange of virtual Hawking gravitons from a four-dimensional Schwarzschild black hole. Our result is obtained in the context of a worldline effective field theory for the black hole, and is valid in the semi-classical limit where the Schwarzschild radius $r_s$ is larger than the Planck length $1/m_{Pl}$. In addition, we assume that four-momentum exchange $q$ is smaller than $r_s^{-1}$ and that the incoming particle has energy larger then the black hole's Hawking temperature. The inelastic cross section we obtain is a new, leading order quantum gravity effect, arising at the same order in $q^2/m_{Pl}^2$ as the well understood one-loop graviton vacuum polarization corrections to gravitational scattering between massive particles.

hep-th↗

arXiv2019

An Effective Field Theory of Quantum Mechanical Black Hole Horizons

We develop an effective theory which describes black holes with quantum mechanical horizons that is valid at scales long compared to the Schwarzschild radius but short compared to the lifetime of the black hole. Our formalism allows one to calculate the quantum mechanical effects in scattering processes involving black hole asymptotic states. We point out that the EFT Wightman functions which describe Hawking radiation in the Unruh vacuum are not Planck suppressed and are actually {\it enhanced} relative to those in the Boulware vacuum, for which such radiation is absent. We elaborate on this point showing how the non-Planck suppressed effects of Hawking radiation cancel in classical observables.

hep-th↗

arXiv2019

Second post-Newtonian order radiative dynamics of inspiralling compact binaries in the Effective Field Theory approach

We use the Effective Field Theory (EFT) framework to compute the mass quadrupole moment, the equation of motion, and the power loss of inspiralling compact binaries at the second order in the Post-Newtonian (PN) approximation. We present expressions for the stress-energy pseudo-tensor components of the binary system in higher PN orders. The 2PN correction to the mass quadrupole moment as well as to the acceleration computed in the linearized harmonic gauge presented here are the ingredients needed for the calculation of the next-to-next-to leading order radiation reaction force, which will be presented elsewhere. While this paper reproduces known results, it supplies the building blocks necessary for future higher order calculations in the EFT methodology.

gr-qc↗

arXiv2019

Breakdown of the naive parton model in super-weak scale collisions

In this letter we show that for observables which involve the measurement of weak charge in final states in hadronic collisions, the standard parton model picture breaks down at scales well above the weak scale due to nonfactorizable electroweak corrections at leading order in the power expansion. This implies that the resummation of these factorization-violating logarithms, which start at order $α_s^2\, α_W^2 \log^4(Q^2/M_W^2)$, cannot be accomplished solely by following standard DGLAP evolution equations; other techniques will be needed to systematically sum large logarithms.

hep-ph↗

arXiv2019

From Scattering Amplitudes to Classical Potentials in the Post-Minkowskian Expansion

We combine tools from effective field theory and generalized unitarity to construct a map between on-shell scattering amplitudes and the classical potential for interacting spinless particles. For general relativity, we obtain analytic expressions for the classical potential of a binary black hole system at second order in the gravitational constant and all orders in velocity. Our results exactly match all known results up to fourth post-Newtonian order, and offer a simple check of future higher order calculations. By design, these methods should extend to higher orders in perturbation theory.

hep-th↗

arXiv2018

Manifestly Soft Gauge Invariant Formulation of vNRQCD

Homogeneous power counting in Non-Relativistic QCD (NRQCD) implies the simultaneous existence of both soft and ultrasoft gluons. In the velocity renormalization group (vNRQCD) formalism we show that operators involving soft fields interacting with heavy potential quarks can be put in a manifestly gauge invariant form by utilizing gluon and quark building blocks which contain Wilson lines, and are analogous to those used in the soft collinear effective theory. This leads to several simplifications, in particular significantly reducing the size of the operator basis, which stream-lines matching and anomalous dimension calculations at subleading order in the velocity expansion. Also, soft ghosts no longer couple via potential like interactions to the heavy quark fields, and hence do not appear until two loops. Furthermore the the color structures that appear at each order in $α_s$ in the static potential are only those which should arise according to non-Abelian exponentiation. We also discuss how zero-bin subtractions clarify the role of $i\varepsilon$ terms in the heavy quark propagator poles carrying soft momenta. Even though the choice of the direction of the soft Wilson lines in our building blocks does not matter, there is still a limited set of consistent choices, and the predicted form of the eikonal poles does influence results at two-loops and beyond.

hep-ph↗

arXiv2018

Symmetry Obstruction to Fermi Liquid Behavior in the Unitary Limit

We show that a Fermi gas, in three dimensions, at temperatures above the superconducting phase transition but below the Fermi temperature, can not be described by Fermi Liquid Theory (FLT) in the unitary limit where the scattering length diverges. The result follows by showing that the there are no effective field theory descriptions that both behave like a Fermi liquid and properly non-linearly realize the spontaneously broken boost and conformal invariance of the system.

cond-mat.str-el↗

arXiv2018

Symmetry Realization via a Dynamical Inverse Higgs Mechanism

The Ward identities associated with spontaneously broken symmetries can be saturated by Goldstone bosons. However, when space-time symmetries are broken, the number of Goldstone bosons necessary to non-linearly realize the symmetry can be less than the number of broken generators. The loss of Goldstones may be due to a redundancy or the generation of a gap. This phenomena is called an Inverse Higgs Mechanism (IHM). However, there are cases when a Goldstone boson associated with a broken generator does not appear in the low energy theory despite the lack of the existence of an associated IHM. In this paper we will show that in such cases the relevant broken symmetry can be realized, without the aid of an associated Goldstone, if there exists a proper set of operator constraints, which we call a Dynamical Inverse Higgs Mechanism (DIHM). We consider the spontaneous breaking of boosts, rotations and conformal transformations in the context of Fermi liquids, finding three possible paths to symmetry realization: pure Goldstones, no Goldstones and DIHM, or some mixture thereof. We show that in the two dimensional degenerate electron system the DIHM route is the only consistent way to realize spontaneously broken boosts and dilatations, while in three dimensions these symmetries could just as well be realized via the inclusion of non-derivatively coupled Goldstone bosons. We have present the action, including the leading order non-linearities, for the rotational Goldstone (angulon), and discuss the constraint associated with the possible DIHM that would need to be imposed to remove it from the spectrum. Finally we discuss the conditions under which Goldstone bosons are non-derivatively coupled, a necessary condition for the existence of a Dynamical Inverse Higgs Constraint (DIHC), generalizaing the results for Vishwanath and Wantanabe.

hep-th↗

arXiv2018

Effective Field Theory of 2D van Hove Singularities

We study the effective field theory of 2D fermions with a short-range interaction in the presence of a van Hove singularity. We find that there are additional divergences associated with the singularity that necessitate regularization beyond the usual Wilsonian cut-off. In the full theory these divergences are cut off by the finite size of the Brillouin zone. This leads to a UV/IR mixing and causes the RG equation for the coupling constant to have an explicit dependence on the ratio of the Wilsonian cut-off to the bandwidth. We discuss the properties of the superconducting ground state and the transport properties of the normal state and show that the latter are approximately described by the marginal Fermi liquid scenario. To leading order, our results are universal in the sense that they do not depend upon the nature of the non-van Hove portion of the Fermi surface. We also comment on the van Hove scenario of high-Tc superconductivity.

cond-mat.str-el↗

arXiv2017

On the Apparent Ambiguities in the Post-Newtonian Expansion for Binary Systems

We discuss the source of the apparent ambiguities arising in the calculation of the dynamics of binary black holes within the Post-Newtonian framework. Divergences appear in both the near and far zone calculations, and may be of either ultraviolet (UV) or infrared (IR) nature. The effective field theory (EFT) formalism elucidates the origin of the singularities which may introduce apparent ambiguities. In particular, the only (physical) 'ambiguity parameters' that necessitate a matching calculation correspond to unknown finite size effects, which first appear at fifth Post-Newtonian (5PN) order for non-spinning bodies. We demonstrate that the ambiguities linked to IR divergences in the near zone, that plague the recent derivations of the binding energy at 4PN order, both in the ADM and 'Fokker-action' approach, can be resolved by implementing the so-called 'zero-bin' subtraction in the EFT framework. The procedure yields ambiguity-free results without the need of additional information beyond the PN expansion.

gr-qc↗

arXiv2016

Deriving analytic solutions for compact binary inspirals without recourse to adiabatic approximations

We utilize the dynamical renormalization group formalism to calculate the real space trajectory of a compact binary inspiral for long times via a systematic resummation of secularly growing terms. This method generates closed form solutions without orbit averaging, and the accuracy can be systematically improved. The expansion parameter is $v^5 νΩ(t-t_0)$ where $t_0$ is the initial time, $t$ is the time elapsed, and $Ω$ and $v$ are the angular orbital frequency and initial speed, respectively, and $ν$ is the binary's symmetric mass ratio. We demonstrate how to apply the renormalization group method to resum solutions beyond leading order in two ways. First, we calculate the second order corrections of the leading radiation reaction force, which involves highly non-trivial checks of the formalism (i.e. its renormalizability). Second, we show how to systematically include post-Newtonian corrections to the radiation reaction force. By avoiding orbit averaging we gain predictive power and eliminate ambiguities in the initial conditions. Finally, we discuss how this methodology can be used to find analytic solutions to the spin equations of motion that are valid over long times.

gr-qc↗

arXiv2015

Constraints on Galactic Wino Densities from Gamma Ray Lines

We systematically compute the annihilation rate for neutral winos into the final state gamma + X, including all leading radiative corrections. This includes both the Sommerfeld enhancement (in the decoupling limit for the Higgsino) and the resummation of the leading electroweak double logarithms. Adopting an analysis of the HESS experiment, we place constraints on the mass as a function of the wino fraction of the dark matter and the shape of the dark matter profile. We also determine how much coring is needed in the dark matter halo to make the wino a viable candidate as a function of its mass. Additionally, as part of our effective field theory formalism, we show that in the pure-Standard Model sector of our theory, emissions of soft Higgses are power-suppressed and that collinear Higgs emission does not contribute to leading double logs.

hep-ph↗

arXiv2015

On the Annihilation Rate of WIMPs

We develop a formalism that allows one to systematically calculate the WIMP annihilation rate into gamma rays whose energy far exceeds the weak scale. A factorization theorem is presented which separates the radiative corrections stemming from initial state potential interactions from loops involving the final state. This separation allows us to go beyond the fixed order calculation, which is polluted by large infrared logarithms. For the case of Majorana WIMPs transforming in the adjoint representation of SU(2), we present the result for the resummed rate at leading double log accuracy in terms of two initial state partial wave matrix elements and one hard matching coefficient. For a given model, one may calculate the cross section by calculating the tree level matching coefficient and determining the value of a local four fermion operator. We find that the effects of resummation can be as large as 100% for a 20 TeV WIMP. The generalization of the formalism to other types of WIMPs is discussed.

hep-ph↗

arXiv2015

The Higgs Transverse Momentum Distribution at NNLL and its Theoretical Errors

In this letter, we present the NNLL-NNLO transverse momentum Higgs distribution arising from gluon fusion. In the regime $p_\perp\ll m_H$ we include the resummation of the large logs at next to next-to leading order and then match on to the $α_s^2$ fixed order result near $p_\perp \sim m_h$. By utilizing the rapidity renormalization group (RRG) we are able to smoothly match between the resummed, small $p_\perp$ regime and the fixed order regime. We give a detailed discussion of the scale dependence of the result including an analysis of the rapidity scale dependence. Our central value differs from previous results, in the transition region as well as the tail, by an amount which is outside the error band. This difference is due to the fact that the RRG profile allows us to smoothly turn off the resummation.

hep-ph↗

arXiv2014

Probing Quarkonium Production Mechanisms with Jet Substructure

We use fragmenting jet functions (FJFs) in the context of quarkonia to study the production channels predicted by NRQCD (3S_1^(1), 3S_1^(8), 1S_0^(8), 3P_J^(8)). We choose a set of FJFs that give the probability to find a quarkonium with a given momentum fraction inside a cone-algorithm jet with fixed cone size and energy. This observable gives several lever arms that allow one to distinguish different production channels. In particular, we show that at fixed momentum fraction the individual production mechanisms have distinct behaviors as a function of the the jet energy. As a consequence of this fact, we arrive at the robust prediction that if the depolarizing 1S_0^(8) matrix element dominates, then the gluon FJF will diminish with increasing energy for fixed momentum fraction, z, and z > 0.5.

hep-ph↗

arXiv2013

A Formalism for the Systematic Treatment of Rapidity Logarithms in Quantum Field Theory

Many observables in QCD rely upon the resummation of perturbation theory to retain predictive power. Resummation follows after one factorizes the cross section into the rele- vant modes. The class of observables which are sensitive to soft recoil effects are particularly challenging to factorize and resum since they involve rapidity logarithms. In this paper we will present a formalism which allows one to factorize and resum the perturbative series for such observables in a systematic fashion through the notion of a "rapidity renormalization group". That is, a Collin-Soper like equation is realized as a renormalization group equation, but has a more universal applicability to observables beyond the traditional transverse momentum dependent parton distribution functions (TMDPDFs) and the Sudakov form factor. This formalism has the feature that it allows one to track the (non-standard) scheme dependence which is inherent in any scenario where one performs a resummation of rapidity divergences. We present a pedagogical introduction to the formalism by applying it to the well-known massive Sudakov form factor. The formalism is then used to study observables of current interest. A factorization theorem for the transverse momentum distribution of Higgs production is presented along with the result for the resummed cross section at NLL. Our formalism allows one to define gauge invariant TMDPDFs which are independent of both the hard scattering amplitude and the soft function, i.e. they are uni- versal. We present details of the factorization and resummation of the jet broadening cross section including a renormalization in pT space. We furthermore show how to regulate and renormalize exclusive processes which are plagued by endpoint singularities in such a way as to allow for a consistent resummation.

hep-ph↗

arXiv2013

Classical Space-Times from the S Matrix

We show that classical space-times can be derived directly from the S-matrix for a theory of massive particles coupled to a massless spin two particle. As an explicit example we derive the Schwarzchild space-time as a series in $G_N$. At no point of the derivation is any use made of the Einstein-Hilbert action or the Einstein equations. The intermediate steps involve only on-shell S-matrix elements which are generated via BCFW recursion relations and unitarity sewing techniques. The notion of a space-time metric is only introduced at the end of the calculation where it is extracted by matching the potential determined by the S-matrix to the geodesic motion of a test particle. Other static space-times such as Kerr follow in a similar manner. Furthermore, given that the procedure is action independent and depends only upon the choice of the representation of the little group, solutions to Yang-Mills (YM) theory can be generated in the same fashion. Moreover, the squaring relation between the YM and gravity three point functions shows that the seeds that generate solutions in the two theories are algebraically related. From a technical standpoint our methodology can also be utilized to calculate quantities relevant for the binary inspiral problem more efficiently than the more traditional Feynman diagram approach.

hep-th↗

arXiv2013

Anomalous dimensions of the double parton fragmentation functions

Double parton fragmentation is a process in which a pair of partons produced in the short-distance process hadronize into the final state hadron. This process is important for quarkonium production when the transverse momentum is much greater than the quark mass. Resummation of logarithms of the ratio of these two scales requires the evolution equations for double parton fragmentation functions (DPFF). In this paper we complete the one-loop evaluation of the anomalous dimensions for the DPFF. We also consider possible mixing between the DPFF and single parton power suppressed gluon fragmentation and show that such effects are sub-leading.

hep-ph↗