Matrix elements of heavy-light mesons from a fine lattice

0.06 MB·English

by  A. Ali Khan

Matrix elements of heavy-light mesons from a fine
lattice
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0 A. AliKhan∗,A.Al-Haydaria, V.M.Braunb, S.Collinsb,M.Göckelerb,
2
G. N.Lacagninac, M.Panerob,d, A.Schäferb,andG. Schierholzb,e
n
a
a DepartmentofPhysics,FacultyofScience,TaizUniversity,Taiz,YemenRepublic
J
7 b InstituteforTheoreticalPhysics,UniversityofRegensburg,93040Regensburg,Germany
c INFN,SezionediMilano,20133Milano,Italy

] d InstituteforTheoreticalPhysics,ETHZürich,8093Zürich,Switzerland
t
a e DeutschesElektronen-SynchrotronDESY,22603Hamburg,Germany
l
-
p
e Weperformedacalculationofmatrixelementsofheavymesonsonaquenchedlattice,generated
h withWilsongaugefieldsatb =6.6withalatticesizeof403×80andalatticespacinga−1≃5
[
GeV determined from the Sommer parameter r =0.5 fm. We use a non-perturbativelyO(a)
0
1
improvedWilsonfermionactionandimprovedcurrents.
v
2 We havecalculatedthecharmoniumspectrumaswellasformfactorsofsemileptonicdecaysof
2 pseudoscalarheavy-lightmesonscontainingacorabquarktopseudoscalarlightmesonsthrough
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avectorcurrent:
0
1. hP(p)|Vm |H(p )i= m2H−m2Pqm f (q2)+ pm +pm −m2H−m2Pqm f (q2),
0 H q2 0 (cid:18) H q2 (cid:19) +
9
0 where p and m are the momentum and the mass of the light meson respectively, and p and
P H
:
v m themomentumandthemassoftheheavymesonrespectively. q=p −pisthemomentum
H H
i m
X transfer. V denotesalocalvectorcurrent. Acomparisonwithotherlatticecalculationsforthe
decayB→p ln isshowninFigure1.
r
a ForthedecayconstantoftheJ/y mesonwefindapreliminaryvalueof f =341(10)MeV,using
V
thedefinition
h0|Vj|J/y i= fVmJy e j(l ),
where e (l ) is the polarization vector of the J/y . We obtain the following values for mass
j
splittings of charmoniumstates: D M(J/y −h )=74(2) MeV and D M(c −J/y )=394(15)
c c1
MeV,wheretheerrorsareonlystatistical.
8thConferenceQuarkConfinementandtheHadronSpectrum
September1-62008
Mainz,Germany
∗Speaker.
(cid:13)c Copyrightownedbytheauthor(s)underthetermsoftheCreativeCommonsAttribution-NonCommercial-ShareAlikeLicence. http://pos.sissa.it/
Heavy-lightmesonsfromafinelattice A.AliKhan
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0
0 5 10 15 20 25 30
2 2
q [GeV ]
Figure1: Thesolidlinesdenoteourresultsfortheformfactors(f :upperline, f :lowerline)ofthedecay
+ 0
B→p ln . Thedashedlinesdenoteourerrorbounds. Thesquaresdenote f , circlesdenote f fromother
+ 0
recentlatticecalculations(red:quenched,[2],green:N =2+1,[3],magenta:N =2+1,[4])
f f
.
The details of our calculation of the matrix elements and the results for the form factors at
q2=0aregiveninRef.[1]. Weobservearelativelygoodagreementofourformfactorswithother
latticecalculations.
Ourresultsforthecharmoniumspectrumareinverygoodagreementwithapreviousquenched
calculationatthesamelatticespacing[5]andinagreementwitharecentcalculationwithtwoheavy
flavors [6]. Since we work on fine lattices where discretization effects are under good control for
charmonia it is also of interest to calculate the charmonium decay constants. Our result for the
decay constant of the J/y is lower than the result of 399(4) MeV from quenched anisotropic
lattices of [7] and of 413(40) MeV from lattices with N =2 of [8]. The experimental value is
f
411(7) MeV.
Acknowledgement: WethankJ.Simoneforusefuldiscussions.
References
[1] QCDSFcollaboration,A.Al-Haydarietal.,inpreparation.
[2] A.Abadaetal.,Nucl.Phys.B619,565(2001)[arXiv:hep-lat/0011065].
[3] J.Baileyetal.,arXiv:0811.3640[hep-lat].
[4] E.Dalgicetal.,Phys.Rev.D73(2006)074502[Erratum-ibid.D75(2007)119906]
[arXiv:hep-lat/0601021].
[5] S.Choeetal.[QCD-TAROCollaboration],JHEP0308,022(2003)[arXiv:hep-lat/0307004].
[6] C.EhmannandG.Bali,PoSLAT2007,094(2007)[arXiv:0710.0256[hep-lat]].
[7] J.J.Dudek,R.G.EdwardsandD.G.Richards,Phys.Rev.D73,074507(2006)
[arXiv:hep-ph/0601137].
[8] P.Dimopoulos,C.McNeile,C.Michael,S.SimulaandC.Urbach[ETMCollaboration],
arXiv:0810.1220[hep-lat].
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