DMesonSemileptonicDecayFormFactorsatq2=0

RuiziLiIndianaUniversity

Fermilab/MILCcollabora>on

La?ce2018,MSU,MI,July27,2018

Outline

•  CurrentstatusofCKMmatrixelements,

•  usingHISQquarks– La?cesetup– Chiral-con>nuumextrapola>ons– Errorbudgets

•  Preliminaryresultsandoutlook

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Vcs

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Vcd

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f+

π / K

(q2 = 0)

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Currentstatusof,

•  TestofCKMmatrix– Morepreciseresultshelpprovideevidenceor/andconstraintonnewphysicsBSM.

– Needreducederrorsfromtheory

Semileptonic[1] 0.2140(29)(93) 0.967(7)(25)

Leptonic[2][10]* 0.2152(49)(5)(6) 1.001(16)(2)(3)

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Vcd

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Vcs

Errorinredisfromthetheore>caluncertaintyoftheformfactor• Errororderisexperiment,la?ce,structuredependentelectro-magne>c

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Vcs

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Vcd

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Dsemileptonicdecayformfactors

•  HadronicDsemileptonicdecay

with

•  Scalarcurrent

•  Kinema>cconstraint

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Hµ = P(p) l γµc D(p' )

= f+(q2) (p'+p)µ −

mD2 − mP

2

q2qµ

⎡

⎣ ⎢

⎤

⎦ ⎥ + f0(q

2) mD2 − mP

2

q2qµ ,

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f0(0) = f+(0)

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f0(q2) =

mc −ml

mD2 −mP

2 P(p) l c D(p')€

q = p' −p

4

MILCNf=2+1+1HISQensembles[3]

643*192 0.042 0.2 431x12 40 1.00

963*192 0.06 Phys. 866x6 31,39,40 1.01

483*144 0.06 0.2 942x8 34,41,48 1.11

643*96 0.09 Phys. 905x8 23,27,32 1.00

483*96 0.09 0.1 840x8 23,27,32 1.02

323*96 0.09 0.2 645x4 23,27,32 1.04

483*64 0.12 Phys. 942x4 15,18,20 0.98

323*64 0.12 0.1 992x4 15,18,20 1.02

243*64 0.12 0.2 1050x4 15,18,20 1.00

403*64 0.12 0.1 1018x8 15,18,20 1.02

243*64 0.12 0.1 1001x8 15,18,20 1.02

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a ( fm)

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V

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ml /ms

Textisthesource-sinkEuclidian>mesepara>onoftheDanddaughtermeson

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mcval /mc

tun

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Text

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Nconf × Nsrc

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Correlators&fitfunc>ons•  Correlators

–  Wallsourcesandpointsinks;twistedboundarycondi>onsfornonzeroquark-momentum

–  Blockeddatatoeliminateeffectsfromautoccorela>onsandstabilizefiterrorsizes

–  Simultaneous2pt&3ptfitsusingBayesiantechnique,includingvariousText’s–  Jackknifere-samplingonformfactors

•  Fitfunc>onsandparameters–  Usesamenumberofchannelsfornormal&oscilla>ngstates,exceptforzero-

momentumpionpropagator(nooscilla>ngstatesneeded)–  Includeuptosecondexcitedstatefitsonmostensembles,orthirdexcited

stateon(afew)others–  Alignedonvariousensemblestmin≈0.36fm(daughtermeson),0.45fm(D

meson)

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! p = pi(1,1,1)

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Correlators&fitfunc>ons

•  Mesonpropagators,3-ptcorrelators

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M (t) M(0) ≈ Rn+2(e−En

+ t + e−En+ (T − t )) + (−1)t Rn

−2(e−En− t + e−En

− (T − t ))[ ]n =0

N

∑

˙ = Rn+2e−En

+ t + (−1)t Rn−2e−En

− t + refl(T)[ ]n =0

N

∑

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, Rn−(M = π, ! p = 0) = 0

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P (0) l c(tc ) D(Text ) ≈ [Vn,mee Rn

+ ˜ R m+e−En

+ tc − ˜ E m+ (Text − tc )

m =0

ND

∑n =0

NP

∑ +Vn,moe (−1)tc Rn

− ˜ R m+e−En

− tc − ˜ E m+ (Text − tc )

+Vn,meo (−1)Text − tc Rn

+ ˜ R m−e−En

+ tc − ˜ E m− (Text − tc ) +Vn,m

oo (−1)Text Rn− ˜ R m

−e−En− tc − ˜ E m

− (Text − tc )

€

+ refl(T)]

f0 = 2V0,0ee mc −ml( ) E0

+ ˜ E 0+ ˜ E 0

+2− E0

+( ! p = 0)2( )7

Energydispersionrela>ons

•  Dispersionrela>onviola>ons– Combinedeffectsofla?cediscre>za>onsandsta>s>calerrors

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.atphysicalpoint.

•  Chiral-con>nuumextrapola>on

– SU(3)hard-pion(kaon)HMrSChPT[4][5][6][7]

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f0P =

f p4 sC0

fπ1 + δfcl + Caχa 2 + Clχl + Cqχq 2 + Csχsea + Ceχe ...( )

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χa 2 = 8π 2 fπ2( )−1Δ (a)

χl = 4π 2 fπ2( )−1mu(d ),s

,val µ(a)

χq 2 = 8π 2 fπ2( )−1q2

χsea = 8π 2 fπ2( )−1 2mu(d ) + ms

sea( )µ(a)

χe = 2 4πfπ( )−1EP

Others:d:pion/kaonenergydiscre>za>onp:pion/kaonspa>almomentumn:strangevalence&seaquarkmassdifferencet:charmquarkmassmistuningNNLOterms

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f0π / K

(q2 = 0)

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•  Fioedf0pi/Koneachensembleandatthecon>nuumphysicallimit

- Dataoncoarseensembleswithsmallerandlargerthanaveragespa>alvolumesareaveragedaperFV(finitevolume)correc>onsforanes>mateofFVQCDeffects

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•  Chiral-con>nuumfitsstability

- IncludeuptoNNLOanaly>cterms(leoersincapital)forasystema>cerrores>mate- Beoerstabili>eswithq2terminfpithanfK

- Stabilityerrorsarees>matedfromcomparingcentralvaluesofvariousfitstocentralfits

Centralfitalsqχ2/dof=0.75 Centralfitalsqeχ2/dof=0.26

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Systema>cerrors•  1-looppar>alquenchingeffects

–  CalculateusingstaggeredChPT,comparebetween

•  La?cediscre>za>onsat–  Lightquarkmomentum,lightquarkmasses–  Excludecharmquarkmassdiscre>za>ons

•  Nonequilibratedtopologicalchargecorrec>ons[8]at– 

areseaquarkmasses;istheac>velightvalencequarkmass;isthetopologicalsuscep>bility;isthela?cespa>alvolume

•  Others

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ms = msval ,ms

sea

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O(α s2a2)

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f0 = f0(θ ) − f0'' (0) 2χTV( )−1 1− Q2 (χTV )

−1( )

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ml,s

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my

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f0'' (0) = −1/4 mlms /my( )

2ml + 2ms( )−2

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a ≈ 0.042 fm

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χT

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V

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Errorbudgets,results

•  La?ceresults

Systema(cerrors (pct.) (pct.)

Fitstab. 2.15 1.47

PQeffects N/A 0.12

La?cescale 0.05 0.03

FinitevolumeQCD[9] 0.04 <0.04

Nonequil.topologicalcharge 0.005 <0.005

Total 2.15 1.48

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f0π

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f0K

Thiswork 0.625(17)(13) 0.768(12)(11)

Average[2]* 0.637(20) 0.745(15)

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f+π (q2 = 0)

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f+K (q2 = 0)

*AveragedresultsfromrecentLQCDcalcula>ons 13

Es>mateof,,outlook

•  ,,withinputsfromrecentexperiments[1]

•  CKMmatrixsecondrowunitarity

•  Outlook–  Dsemileptonicvectorformfactorsatnonzero

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Vcs

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Vcd

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q2

|Vcd| |Vcs|

0.2280(31)(78) 0.941(7)(20)

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Vcs

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Vcd

Thiswork 0.939(44)

Semileptonic,Ave.[2] 1.005(53)

Leptonic,FNAL/MILC[2][10] 1.050(32)€

Vcd2

+ Vcs2

+ Vcb2

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References1  A.Ceccucciet.al.,PDGreview20182  S.Goolieb,talkat16thConferenceonFlavorPhysicsandCPViolaAon

(FPCP2018)3  A.Bazavovet.al.(MILCCollaboraAon),Phys.Rev.D87,054505(2013)4  C.AubinandC.Bernard,Phys.Rev.D76,014002(2007)5  J.BijnensandI.Jemos,Nucl.Phys.B840,54(2010)6  A.Bazavovet.al.(MILCCollaboraAon),Phys.Rev.D90,074509(2014)7  A.Bazavovet.al.(MILCCollaboraAon),PhysRev.D93,094510(2016)8  C.BernardandD.Toussaint,Phys.Rev.D97,074502(2018)9  Bernard,C.,Bijnens,J.,Gámiz,E.etal.,J.HighEnerg.Phys.(2017)2017:

120.hops://doi.org/10.1007/JHEP03(2017)1210  A.Bazavovet.al.(MILCCollaboraAon),arXiv:1712.09262[hep-lat]

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BackupSlides

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FitparametersEnsemblesa,ml/ms

BlocksizeD2pi,D2K

#P-pe-chnl/#D-pe-chnl

Fitstmin*pi/D,K/D

Thin2ptP/DD2pi,D2K

0.042,0.2 4,4 3/3,3/3 8/10,8/10 5/5,5/5

0.06,phys. 3,3 3/3,4/4 6/8,6/7 /

0.06,0.2 4,3 3/3,3/3 6/8,6/7 5/3,5/3

0.09,phys. 3,3 3/3,3/4 4/5,4/5 /

0.09,0.1 3,3 3/3,3/3 4/5,4/5 /

0.09,0.2 3,3 3/3,3/3 4/5,4/5 /

0.12,phys. 3,2 3/3,3/3 3/4,3/4 /

0.12,0.1 3,4 3/3,3/3 3/4,3/4 /

0.12,0.2 3,3 3/3,3/3 3/4,3/4 /

0.12,0.1,Vs 3,4 3/3,3/3 3/4,3/4 /

0.12,0.1,Vl 3,4 3/3,3/3 3/4,3/4 /

*3pttminadjustedtoalsoexcludedatawithlargesta>s>calerrors 17