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Universalityintheclassicallimitofgravita3onalsca4ering

JulioParra-Mar,nez

ManiL.BhaumikIns,tuteforTheore,calPhysics,UCLA

@QCDmeetsGravity,UCLA,December2019

w/Z.Bern,H.Ita,M.Ruf.(massless)

inparalleltoS.Caron-Huot,Z.Zahraee.(massive)

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Focusofthistalk:

Deflec,onangleinGeneralRela,vityfromscaXeringamplitude

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Recent puzzle

•Twoconcretepredic,ons

• MasslessscaXeringangle

• MassivescaXeringangle

Tobecomparedwith:

vs.

[Amati, Ciafaloni, Veneziano (ACV)]

[Bern, Cheung, Shen, Solon, Roiban, Zeng (BCSSRZ)]

•Re-examinegravita,onaldeflec,onangleofmasslesspar,clesinGeneralRela,vity-WeconfirmtheresultofACV

•Provideevidenceforuniversalityinthedeflec,onangleuptotwo-loops

•Commentonuniversalityinthemassivecaseanditsconsequences

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Goalsofthistalk:

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•EFT-Hamiltonian-ClassicalEoM

•Impulsefrom

•Eikonalresuma,on

Routes from to

[Cheung, Solon, Rothstein; BCRSSZ]

[ACV; Bjerrum-Bohr, Damgaard, Festuccia, Planté, Vanhove; Koemans Collado, di Vecchia, Russo; Luna, Naculich, White…]

SeeMikhail’stalk!

SeeDavid,Gregor’stalks!

SeeChia-Hsien,Emil,Gabriele,Paolo,PoulHenrik’stalks!

[Maybee, Kosower, O’Connell]

Newandexci,ngtools

Tradi,onaland,metestedmethod-willuseinthistalk

Deflec3onanglefromtheeikonalphase

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(Quickreview)

Eikonal in impact parameter space

• Fouriertransform-factoriza,on

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• Leadingphaseexponen,ates(resumsladders)

• ScaXeringangle-sta,onaryphase

• Exponen,a,onnotguaranteed [Akhoury, Saotome, Sterman]

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•Sphericalpar,alwaves

Alternative approach

•Unitarityguaranteesexponen,a,on

• Sta,onaryphases,llgivesangle

PreferredbyDamour.

i

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i

7

it7

ri ww

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•Iden,fiedtheleadingcorrec,onfromthe“H”-diagram

• CleverlyextractedbuildingblocksfromstringamplitudesintheReggelimittocalculateitsimaginarypart

ACV calculation 1990

•Usedcrossingsymmetryandanaly,citytoreconstructrealpart!

• UsedbyDamourinfirstaXempttoderive3PMEOBHamiltonian

it7

ri ww

Credit:ACVPaper

•Stateoftheart:three-loop•Two-loop

Gravity amplitudes

[Dixon, Boucher-Veronneau]

[Henn, Mistleberger]

•Newresultsattwo-loops:

•ClassicalGRmassive

•Classicalmassive

•FullGRmassless

[JPM; Caron-Huot, Zahree]

[Bern, Cheung, Roiban, Shen, Solon, Zeng]

[Abreu, Jaquier, Febres Cordero, Ita, Page, Ruf, Sotnikov]

(fourpoints)

•Forwardto2010s

Graviton four-point amplitude[Abreu, Jaquier, Febres Cordero, Ita, Page, Ruf, Sotnikov]

•Fullquantumamplitudecalcula,on

•Manychecks:

•Knowninfraredandultravioletdivergences•Comparisonwithknown“all-plus”result

•Reggelimit

•Nospurioussingulari,es•DonebytheQCDprofessionals,usingwelltestedtechnologyinQCD(numericalunitarity,finitefields,IBP)

Ifyouhaveques3onsgotoMichael!

2.0

[Dunbar, Norridge; Bern, Cheung, Chi, Davies, Dixon, Nohle; Bern, Chi, Dixon, Edison]

[Weinberg]

•Large/(&small)

•Massive

•Massless

(Regge)

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Classical limit - massive vs massless

Masslessclassicallimit=Reggelimit

Forreference:

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Amplitude and its Regge limit•Amplitudehastheform

•IntheReggelimit,relevantcontribu,on

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Result of eikonal calculation

Oneloopanglequantum,asexpected

TwoloopangleagreeswithACV

[Bern, JPM, Ita, Ruf]

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Some comments

•Fullquantumamplitudecalculatedfromfirstprinciplesusedestablishedon-shellmethods

•Phasecalculatedusingbothimpactparameterandpar,alwaves.Standard/textbookmethods.

•Angleprovides:

•Yetanothernontrivialcheckandamplitudescalcula,on

•Conclusiveconfirma,onofACVresult

Universalityintheclassicallimit

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Supergravity amplitudes

•Whystopthere?Useavailablesupergravityresults[Dixon, Boucher-Veronneau]

•One-loopremainder

•Two-loopremainder

•Relevantpiecesareuniversal!

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Classical angle is universal through

Oneloopangle,quantum,non-universal

Twoloopangleuniversal

[Bern, JPM, Ita, Ruf]

SeePaolo’stalk,forN=8

PreliminaryunderstandingfromRegge

Universalityforthemassiveangle?

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•One-loop

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•EasilyobtainedbyKKreducingknownintegrand

Tree, one-loop amplitude

[Green, Schwarz, Brink]

•Treelevel

(ignoringBPSangles)

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[Caron-Huot, Zahraee]Notriangles=Noprecession!

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•Integrandknownsince90s•Extremelysimpleform

Two-loop amplitude

[Bern, Dixon, Perelstein, Rozowsky]

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Iterations

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•Notriangles≠nopreccessionstar,ngbeyondone-loop?

Features of result

•Onlynewkindofcontribu,onattwoloopsfromH-typediagrams

SeeMao’stalk!

•Allintegralsknownintheclassicallimitwithfullvelocitydependence

SeeGregor’stalk!

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Graviton seems to dominate also in massive case

[JPM; Caron-Huot, Zahraee]

Fulleikonalcalcula,onunderway-willbeabletoobtainanglebyindependentmethod(noEFT,Hamiltonian)

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Summary

•Fruimulcombina,onofeikonalandamplitudes

methods

•Providedaconclusiveconfirma,onofACVresultfor

masslessscaXeringangle

•Universalityofhighenergybehavior-requiresdetailedexplana,on

•Supersymmetriccalcula,onusefulplayground,

providespreliminarysupportforBCRSSZamplitude

Thanks for your attention!

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