Precision tests of the J/psi from full lattice QCD: mass, leptonic width and radiative decay rate to eta_c

0.38 MB·English

by  C. T. H. Davies

Precision tests of the J/ψ from full lattice QCD:
mass, leptonic width and radiative decay rate to η
c
C. T. H. Davies , G. C. Donald, R. J. Dowdall, J. Koponen
∗
3
1
UniversityofGlasgow
0
2 E-mail: [email protected]

n E. Follana
a
J
UniversidaddeZaragoza

0
3 K. Hornbostel

] SouthernMethodistUniversity
t
a
l G. P. Lepage
-
p
e CornellUniversity
h
[ C. McNeile

1
UniversitätWuppertal
v
3
HPQCD collaboration
0
2
7
We show results from calculations in full lattice QCD of the mass, leptonic width and radiative
.
1 decayratetoη oftheJ/ψmeson.Theseprovidefew%testsofQCD.Another(1.5%)testcomes
c
0
3 fromcomparisonoftime-momentsofthevectorcharmoniumcorrelatorwithresultsderivedfrom
1 theexperimentalvaluesofR(e+e hadrons)inthecharmregion.
−
: →
v
i
X
r
a
XthQuarkConfinementandtheHadronSpectrum,
October8-12,2012
TUMCampusGarching,Munich,Germany
∗Speaker.
(cid:13)c Copyrightownedbytheauthor(s)underthetermsoftheCreativeCommonsAttribution-NonCommercial-ShareAlikeLicence. http://pos.sissa.it/
J/ψ fromfulllatticeQCD C.T.H.Davies
0.50
V) 0.48
Ge 0.120 V) 0.46
( e
Mηc 0.115 (G 0.44
− /ψ 0.42
ψ fJ
M/J 0.110 0.40
0.38
0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.1 0.2 0.3 0.4 0.5
(amc)2 (amc)2
Figure 1: The charmonium hyperfinesplitting on theleft and decay constantof the J/ψ on the rightas a
functionoflatticespacing. Thegreybandisourfittothecalculatedbluepoints. Ata=0itagreeswellwith
theexperimentalvaluegivenbytheblackpoint.
1. Introduction
Precision tests of lattice QCD against experiment are critical to provide benchmarks against
which to calibrate the reliability of predictions from lattice QCD [1]. Many of these tests are
also important tests of QCD itself because frequently lattice QCD provides the only method for
precisioncalculation. Mosttestscarriedoutsofarhavebeenbasedonthespectrumofgold-plated
hadron masses. It is important to have tests that also involve decay matrix elements but, for weak
decays, uncertainties in CKM elements are a limiting factor (indeed, the lattice calculations are
usedtodeterminetheCKMelements). Electromagneticdecayratesthereforehavethepotentialto
providegoodtestsbecausetheirnormalisation,relatedtoα ,iswell-known.
QED
Here we provide such tests for the J/ψ including the full effect of u, d and s quarks in the
sea for the first time. We are able to do this because we have developed a particularly accurate
formalismfordiscretisingthequarkpieceoftheQCDLagrangianontoalattice,knownasHighly
ImprovedStaggeredQuarks(HISQ)[2]. Theworkdescribedherehasnowbeenpublished[3]and
werefertothatpaperforalldetails. Herewesimplygivehighlightsfromtheresults. Forasimilar
calculationusingtwistedmassquarksandincludinguandd quarksinthesea,see[4]. Forearlier
workinthequenchedapproximationsee[5].
2. Results
Figure1showsresultsontheleftforthehyperfinesplitting(M M )andontherightfor
J/ψ− ηc
theJ/ψ decayconstant, f ,asafunctionoflatticespacing,a(giveninunitsofthecquarkmass,
J/ψ
m ). Thebluepointsshowourresultsatfourdifferentwidelyspacedvaluesofaandthegreyband
c
showsourfit,includingthe1σ errorbar,whichallowsextrapolationtotherealworldata=0. The
blackpointata=0.0istheexperimentalvalue. For f thisisderivedfromΓ(J/ψ e+e ).
J/ψ −
→
Our value for the hyperfine splitting is 116.5(2.1)(2.4) MeV where the first error is from our
calculationandfitandthesecondisfromuncertaintiesintheη massfromelectromagneticeffects
c
and η annihilation, neither of which are included in our lattice QCD calculation. The current
c
2
J/ψ fromfulllatticeQCD C.T.H.Davies
1.4
2.2 n=10
1.2
)
1
−
V
2 Ge 1.0 n=8
(
)2
1.8 /(n−0.8
1
V(0) )ent 0.6 n=6
m
1.6 o
m
thn 0.4
(
1.4 n=4
0.2
1.2 0.0
0 0.1 0.2 0.3 0.4 0.5 0.0 0.1 0.2 0.3 0.4 0.5
(mca)2 (amc)2
Figure 2: On the left is the value of the vector form factor between J/ψ and η at squared 4-momentum
c
transferequaltozero,andontherightthenthtime-momentsofthevectorcharmoniumcorrelatorforn=4,
6,8,and10. SymbolsareasinFigure1.
experimentalaverageis115.9(1.1)MeV[6]. Ourvaluefor f is405(6)(2)MeVtobecompared
J/ψ
to407(5)MeVfromexperiment[6].
Figure2showsontheleftresultsforV(0), thevectorformfactoratq2 =0betweentheJ/ψ
and η , which is related the decay rate for J/ψ γη . Our final result for V(0) is 1.90(7)(1)
c c
→
givingΓ(J/ψ e+e γη )=2.49(18)(7)keV.Thisistobecomparedtotheexperimentalvalueof
− c
→
1.84(30) keV [6]. Agreement is acceptable, but an improvement in the experimental error would
allowamuchmorestringenttestofQCD.
The righthand plot of Figure 2 shows results for the 4th, 6th, 8th and 10th time-moments of
the charmonium vector correlator. These moments test the short time behaviour of the correlator,
wherethelargetimebehaviourgivesthepropertiesoftheground-statecharmoniumvectormeson,
the J/ψ, discussed above. The continuum limit of the time-moments can be compared to q2-
derivative moments of the charm quark vacuum polarisation function derived from experimental
resultsforR [7]. Goodagreementwiththeexperimentalresultsisseenwitherrorsat1.5%.
e+e
−
References
[1] C.Daviesetal(HPQCD,UKQCD,MILC,FermilabLatticeCollaborations),Phys.Rev.Lett.
92:022001(2004),hep-lat/0304004.
[2] E.Follanaetal(HPQCDCollaboration),Phys.Rev.D75:054502(2007),hep-lat/0610092.
[3] G.C.Donaldetal(HPQCDCollaboration),Phys.Rev.D86:094501(2012),arXiv:1208.2855.
[4] D.BecirevicandF.Sanfilipo,arXiv: 1206.1445;F.Sanfilippo,theseProceedings.
[5] J.J.Dudek,R.G.EdwardsandD.G.Richards,Phys.Rev.D73:074507(2006),hep-ph/0601137.
[6] J.Beringeretal(ParticleDataGroup),Phys.Rev.D86:010001(2012).
[7] J.H.Kuhn,M.SteinhauserandC.Sturm,Nucl.Phys.B778:192(2007),hep-ph/0702103.
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