Post on 26-Jun-2020
transcript
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
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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 )
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+ 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