Gravitational Waves David A Kosower Institut de Physique Th é orique CEA Saclay partly work with Ben Maybee and Donal OConnell Edinburgh Breakthoughs in QFT and Gravity ID: 814687
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Slide1
Amplitudes in Search of Gravitational Waves
David A. KosowerInstitut de Physique Théorique, CEA–Saclaypartly work with Ben Maybee and Donal O’Connell (Edinburgh)Breakthoughs in QFT and Gravity @ QMUL— November 7, 2019A SAGEX Meeting EventThis project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 764850 (SAGEX)
Slide2The Universe had a very violent origin
It remains a violent place
Slide3Much of that violence is associated with black holes
Imagine a small black hole — 3 — eating the Earth It’s about 8.9 km in size, a bit smaller than ParisWould release about JSun’s luminosity is about W, J over its lifetimeSupernova releases J in a few seconds, mostly in neutrinosPeak visible luminosity W
a galaxyLuminosity of the local Supercluster
W
Peak luminosity of
black hole merger
W
according to omnicalculator.com/physics/black-hole
Slide4Until very recently, this violence was
invisibleIt’s all in gravitational radiation
Slide5Fittingly, that changed during the
centennial year of the modern theoryof gravity, Einstein’s General RelativityIn September 2015, LIGO saw their first event: a merger of two black holesEach tens of solar masses
Slide6Gravitational Waves
A new window on the universeA synthetic view
Slide7Gravitational Wave Events
LIGO & VIRGO11 confirmed events since Sept 2015, 27 strong candidates in 2019 (to Nov 5) gracedb.ligo.org/latest/3 neutron-star pair mergers, 2 mixed, 2 unknown (“mass gap”), 31 black hole pair mergers
Slide8Gravitational Wave Observatories
LIGO: 4km armsHanford, WashingtonLivingston, LousianaVirgo: 3km armsPisa, ItalyTo be joined by KAGRA (3km) inside Kamioka (2019?) IndiGO, Aundha Nagnath, Maharashtra, India (?)
Slide9Future Gravitational Wave Observatories
Next-generation Terrestrial (underground):Einstein Telescope (Europe) and Cosmic Explorer (US)Space-based (solar system):Laser Interferometer Space Antenna (LISA), ~2034?Supermassive Black HolesSpace-based (galactic):International Pulsar Timing Array, decade-long observationsSupermassive Black HolesCold Atom InterferometryIdea stage
Slide10Science Goals
Presence and distribution of heavy compact objectsNeutron starsDetermine equation of state —GW170817Contribution to transferric element productionMeasure Hubble constant?Limits on exotic compact objectsPrecision strong-field tests of Einstein gravityInsight into quantum gravity?
Slide11Laser Interferometers
Measure displacements of ~ times smaller than protonExtreme sensitivity to noiseLaser stabilityMirror qualityWorld’s third-largest vacuum chambersCorrelate different detectorsHigh Noise level Rehman [1711.07421]400 times larger than signal!Need theoretical templates for waveforms
Slide12Theorists’ Role
Waveform templatesFor detectionFor measurements Three Phases:Inspiral: a weak-field perturbative approach worksMerge: strong-field, numerics neededRingdown: normal modes
Slide13Gravitational Waves
Theoretical waveformsHigher-order terms in the Post-Newtonian/Newton’s coupling expansion still awaitGeneral relativists have worked hard for many resultsUsing an Effective One-Body formalismBuonanno & Damour; Buonanno, Pan, Taracchini, Barausse, Bohé, Cotesta, Shao, Hinderer, Steinhoff, Vines; Damour, Nagar, Bernuzzi, Bini, Balmelli, Messina; Iyer, Sathyaprakash; Jaranowski, SchaeferNumerical Relativity Pretorius; Campanelli et al.; Baker et al.Joined by Effective Field TheoristsGoldberger, Rothstein; Goldberger, Li, Prabhu, Thompson; Chester; Porto,… Kol; Levi,…
Slide14Approaches
Traditional: solve General Relativity perturbativelyEffective Field Theory: use separation of scales to compute better in General Relativity
Slide15Buonano
@ Amplitudes 2018
Slide16Approaches
Traditional: solve General Relativity perturbativelyEffective Field Theory: use separation of scales to compute better in General RelativityAn idea: use scattering amplitudes
Slide17Scattering Amplitudes
It’s a bound-state classical problemWhy might quantum scattering amplitudes help?Calculate only what’s needed for physical quantitiesNo auxiliary Hamiltonians or potentialsDouble copy: amplitude calculations in gravity are vastly simplified by the observation thatGravity (Yang–Mills)2Kawai, Lewellen, Tye; Bern, Carrasco, Johansson
Slide18Feynman Vertices
De Witt October 1967: Three-point Four-point
Slide19The Double Copy
Yang–Mills three-point amplitudeGravity three-point amplitudeField-theory equivalent of Kawai–Lewellen–Tye expression for closed-string amplitudes in terms of open-string ones
Slide20Direct Route to Predictions
Compute PotentialCompute effective-field theory scattering amplitude from parametrized & match amplitude to EFT Cheung, Rothstein, Solon; Bern, Cheung, Roiban, Shen, Solon, Zeng Extract potential from form of terms in scattering amplitudeBjerrum-Bohr, Damgaard, Festuccia, Planté, Vanhove; Foffa, Mastrolia, Sturani, SturmChung, Huang, Kim, LeeGuevara, Ochirov, VinesFeed potential into Effective-One-Body formalismCompute Effective ActionPlefka, Shi, Steinhoff, WangOther connections to classical scatteringGoldberger, Ridgway; Goldberger, Ridgway, Li, Prabhu; Shen
Slide21Related Work
Double copying classical solutionsExamples: Yang–Mills solutions to Kerr–Schild metricsPoint charges map to black holesMonteiro, O’Connell, White (2015)Double copy for Taub–NUT spacetimeLuna, Monteiro, O’Connell, White (2015)
Slide22A New Result
Potential to 3rd post-Minkowski orderBern, Cheung, Roiban, Shen, Solon, Zeng (2019)
Slide23Our Strategy: Take the Scenic Route
Pick well-defined observables in the quantum theory That are also relevant classicallyExpress them in terms of scattering amplitudes in the quantum theoryUnderstand how to take the classical limit efficiently
Slide24Set-up
Scatter two massive particlesLook at three observables:Change in momentum (‘impulse’) of one of themMomentum radiated during the scatteringSpin kickWe all love scattering amplitudesBut they aren’t the final goal or physically meaningful on their own
Slide25Classical Limit
Classical limit requires Need to restore Dimensional analysis; keep [Ampln] in couplings:
;
Distinguish wavenumber from momentum:
Slide26Classical Limit
Net: n-point, L-loop amplitude in scalar QED scalesThis isn’t the end of the story: compensating factors of from scaling of momenta
Slide27Wave Packets
Point particles: localized positions and momentaWavefunction Incoming pair plane waves Initial state
Absorb factors of
Impact parameter
Slide28Momentum
Insert a complete set of states and rewrite,
Think of
as final-state momenta: connection to scattering amplitudes
Slide29Impulse
aka time integral of change in momentumWrite
and use unitarity
Expression holds to all orders in perturbation theory
Slide30Impulse
Diagrammatically (
is momentum mismatch, momentum transfer)
First term is linear in amplitude
+
Slide31Radiated Momentum
Expectation of messenger (photon or graviton) momentum
Insert complete set of states
Expressible as scattering amplitude squared or cut of amplitude
Valid to all orders
Slide32Radiated Momentum
Diagrammatically
Slide33Classical Limit, part 2
Minimum-uncertainty non-relativistic wavefunction: Compton wavelength: Wavefunction spreadTake relativistic wavefunction to be controlled by
as well
Needs four-momentum parameter
: four-velocity
Simplest dependence
Slide34Classical Limit, part 2
Three scales: Compton wavelength: wavefunction spread: impact parameterParticles localized: Well-separated wave packets: More careful analysis confirms this ‘Goldilocks’ condition
Slide35Classical Limit, part 2
In-state wavefunctions and both represent particleShould be sharply peakedOverlap should be Angular-averaged on-shell functions transmit constraint to will be smeared out to sharply peaked functions
and will turn back into delta functions as gets smaller
Slide36Classical Limit, part 2
Shrinking on : Fixed on : Natural integration variables for messenger (massless) momenta are wavenumbers, not momenta:mismatch
, transfer
(from analysis of outgoing states),
loop
(from unitarity)
More factors of
to extract
Slide37Impulse at LO
O()Only first term contributes, with tree-level amplitude
Slide38Scalar QED Impulse at LO
2 2 amplitudeImpulse (use )Evaluate the integral
Slide39(Dilaton) Gravity Impulse at LO
Squaring pure Yang–Mills gives gravity + dilatonImpulseEvaluate integral (same as QED)
Slide40Gravity Impulse at LO
One can remove the dilaton to obtain the classic GR resultPortilla; Westpfahl, Goller; Ledvinka, Schäfer, Bičák; DamourAt this order, the impulse is connected to the scattering angle straightforwardly
Slide41Impulse at NLO
O(): both terms contributeFirst term, with one-loop amplitude
Slide42Impulse at NLO
Second term, with tree amplitudes
Slide43Impulse at NLO
Massless loops are purely quantumas are vertex, wavefn, propagator corrections—after renormalizationLoops with masses are not purely quantumLeft with triangles, boxes, and cut boxesTechnical note: summing over gives functionsExample: triangle contributionBoxes and cut boxes individually singular as Cancel between contributionsNeed to Laurent expandTechnical note: need to retain terms in s until after expansionGeneral proof of cancellation lacking
Slide44Impulse at NLO
Assemble result in scalar QEDAgrees with direct classical calculation
Slide45Radiation at LO
Leading contribution is O()Five-point tree amplitude
Slide46Scalar QED Radiation at LO
Evaluating the five-point tree, one finds for the kernelMatches classical resultMomentum conservation follows automatically, without addition of the Abraham–Lorentz–Dirac force as in the classical theory
Slide47Spin kick
Maybee, O’Connell, VinesSpin using Pauli–Lubanski vector
A few subtleties
Slide48Summary
Dawn of gravitational astronomy: new impetus to theoretical calculations in classical general relativityAmplitudes and the double copy offer a simpler avenue to such calculationsFormulate observables valid in both quantum and classical theoriesOrganize formalism to take limit in a simple wayCount sMomenta for massive particles, wavenumbers for masslessLots of interesting things for Amplitudes researchers to do