The power spectrum of the circular noise

The circular noise is important in connection to Mach's principle, and also as a possible probe of the Unruh effect. In this letter the power spectrum of the detector following the Trocheries-Takeno motion in the Minkowski vacuum is analytically obtained in the form of an infinite series. A mean distribution function and corresponding energy density are obtained for this particular detected noise. The analogous of a non constant temperature distribution is obtained. And in the end, a brief discussion about the equilibrium configuration is given.Comment: accepted for publication in GR

Black Hole Evaporation in the Presence of a Short Distance Cutoff

A derivation of the Hawking effect is given which avoids reference to field modes above some cutoff frequency $\omega_c\gg M^{-1}$ in the free-fall frame of the black hole. To avoid reference to arbitrarily high frequencies, it is necessary to impose a boundary condition on the quantum field in a timelike region near the horizon, rather than on a (spacelike) Cauchy surface either outside the horizon or at early times before the horizon forms. Due to the nature of the horizon as an infinite redshift surface, the correct boundary condition at late times outside the horizon cannot be deduced, within the confines of a theory that applies only below the cutoff, from initial conditions prior to the formation of the hole. A boundary condition is formulated which leads to the Hawking effect in a cutoff theory. It is argued that it is possible the boundary condition is {\it not} satisfied, so that the spectrum of black hole radiation may be significantly different from that predicted by Hawking, even without the back-reaction near the horizon becoming of order unity relative to the curvature.Comment: 35 pages, plain LaTeX, UMDGR93-32, NSF-ITP-93-2

Motion of Inertial Observers Through Negative Energy

Recent research has indicated that negative energy fluxes due to quantum coherence effects obey uncertainty principle-type inequalities of the form |\Delta E|\,{\Delta \tau} \lprox 1\,. Here $|\Delta E|$ is the magnitude of the negative energy which is transmitted on a timescale $\Delta \tau$. Our main focus in this paper is on negative energy fluxes which are produced by the motion of observers through static negative energy regions. We find that although a quantum inequality appears to be satisfied for radially moving geodesic observers in two and four-dimensional black hole spacetimes, an observer orbiting close to a black hole will see a constant negative energy flux. In addition, we show that inertial observers moving slowly through the Casimir vacuum can achieve arbitrarily large violations of the inequality. It seems likely that, in general, these types of negative energy fluxes are not constrained by inequalities on the magnitude and duration of the flux. We construct a model of a non-gravitational stress-energy detector, which is rapidly switched on and off, and discuss the strengths and weaknesses of such a detector.Comment: 18pp + 1 figure(not included, available on request), in LATEX, TUPT-93-

Standard Model predictions for B → Kℓ+ℓ−, B → Kℓ−1ℓ+2 and B → Kv¯v using form factors from Nf = 2 + 1 + 1 lattice QCD

We use HPQCD’s recent lattice QCD determination of B → K scalar, vector and tensor form factors to determine Standard Model differential branching fractions for B → K ℓ + ℓ − , B → K ℓ + 1 ℓ − 2 and B → K ν ¯ ν . These form factors are calculated across the full q 2 range of the decay and have smaller uncertainties than previous work, particularly at low q 2 . For B → K ℓ + ℓ − we find the Standard Model branching fraction in the q 2 region below the squared J / ψ mass to exceed the LHCb results, with tensions as high as 4.7 σ for B + → K + μ + μ − . For the high q 2 region we see 3 σ tensions. The tensions are much reduced by applying shifts to Wilson coefficients C 9 and C 10 in the effective weak Hamiltonian, moving them away from their Standard Model values consistent with those indicated by other B phenomenology. We also update results for lepton-flavor ratios R μ e and R τ μ and the “flat term,” F ℓ H in the differential branching fraction for ℓ ∈ { e , μ , τ } . Our results for the form-factor dependent contributions needed for searches for lepton-flavor violating decays B → K ℓ − 1 ℓ + 2 achieve uncertainties of 7%. We also compute the branching fraction B ( B → K ν ¯ ν ) with an uncertainty below 10%, for comparison with future experimental results

B → K and D → K form factors from fully relativistic lattice QCD

We present the result of lattice QCD calculation of the scalar, vector and tensor form factors for the B → K ℓ + ℓ − decay, across the full physical range of momentum transfer. We use the highly improved staggered quark (HISQ) formalism for all valence quarks on eight ensembles of gluon-field configurations generated by the MILC collaboration. These include four flavors of HISQ quarks in the sea, with three ensembles having the light u / d quarks at physical masses. In the first fully relativistic calculation of these form factors, we use the heavy-HISQ method. This allows us to determine the form factors as a function of heavy-quark mass from the c to the b , and so we also obtain new results for the D → K tensor form factor. The advantage of the relativistic formalism is that we can match the lattice weak currents to their continuum counterparts much more accurately than in previous calculations; our scalar and vector currents are renormalized fully nonperturbatively and we use a well-matched intermediate momentum-subtraction scheme for our tensor current. Our scalar and vector B → K form factors have uncertainties of less than 4% across the entire physical q 2 range and the uncertainty in our tensor form factor is less than 7%. Our heavy-HISQ method allows us to map out the dependence on heavy-quark mass of the form factors and we can also see the impact of changing spectator quark mass by comparing to earlier HPQCD results for the same quark weak transition but for heavier mesons

Acceleration and Classical Electromagnetic Radiation

Classical radiation from an accelerated charge is reviewed along with the reciprocal topic of accelerated observers detecting radiation from a static charge. This review commemerates Bahram Mashhoon's 60th birthday.Comment: To appear in Gen. Rel. Gra

Stochastic Theory of Accelerated Detectors in a Quantum Field

We analyze the statistical mechanical properties of n-detectors in arbitrary states of motion interacting with each other via a quantum field. We use the open system concept and the influence functional method to calculate the influence of quantum fields on detectors in motion, and the mutual influence of detectors via fields. We discuss the difference between self and mutual impedance and advanced and retarded noise. The mutual effects of detectors on each other can be studied from the Langevin equations derived from the influence functional, as it contains the backreaction of the field on the system self-consistently. We show the existence of general fluctuation- dissipation relations, and for trajectories without event horizons, correlation-propagation relations, which succinctly encapsulate these quantum statistical phenomena. These findings serve to clarify some existing confusions in the accelerated detector problem. The general methodology presented here could also serve as a platform to explore the quantum statistical properties of particles and fields, with practical applications in atomic and optical physics problems.Comment: 32 pages, Late

Toward accurate form factors for B-to-light meson decay from lattice QCD

We present the results of a lattice QCD calculation of the scalar and vector form factors for the unphysical B s → η s decay, over the full physical range of q 2 . This is a useful testing ground both for lattice QCD and for our wider understanding of the behavior of form factors. Calculations were performed using the highly improved staggered quark (HISQ) action on N f = 2 + 1 + 1 gluon ensembles generated by the MILC Collaboration with an improved gluon action and HISQ sea quarks. We use three lattice spacings and a range of heavy quark masses from that of charm to bottom, all in the HISQ formalism. This permits an extrapolation in the heavy quark mass and lattice spacing to the physical point and nonperturbative renormalization of the vector matrix element on the lattice. We find results in good agreement with previous work using nonrelativistic QCD b quarks and with reduced errors at low q 2 , supporting the effectiveness of our heavy HISQ technique as a method for calculating form factors involving heavy quarks. A comparison with results for other decays related by SU(3) flavor symmetry shows that the impact of changing the light daughter quark is substantial but changing the spectator quark has very little effect. We also map out form factor shape parameters as a function of heavy quark mass and compare to heavy quark effective theory expectations for mass scaling at low and high recoil. This work represents an important step in the progression from previous work on heavy-to-heavy decays ( b → c ) to the numerically more challenging heavy-to-light decays

Quantum Vacuum Instability Near Rotating Stars

We discuss the Starobinskii-Unruh process for the Kerr black hole. We show how this effect is related to the theory of squeezed states. We then consider a simple model for a highly relativistic rotating star and show that the Starobinskii-Unruh effect is absent.Comment: 17 Pages, (accepted by PRD), (previously incorrect header files have been corrected

Quantum Stability of Accelerated Black Holes

We study quantum aspects of the accelerated black holes in some detail. Explicitly shown is the fact that a uniform acceleration stabilizes certain charged black holes against the well-known thermal evaporation. Furthermore, a close inspection of the geometry reveals that this is possible only for near-extremal black holes and that most nonextremal varieties continue to evaporate with a modified spectrum under the acceleration. We also introduce a two-dimensional toy model where the energy-momentum flow is easily obtained for general accelerations, and find the behavior to be in accordance with the four-dimensional results. After a brief comparison to the classical system of a uniformly accelerated charge, we close by pointing out the importance of this result in the WKB expansion of the black hole pair-creation rate.Comment: LaTeX, 22 pages, 5 uuencoded figures (minor errors corrected, more discussions on the case with black holes formed by gravitational collapse.