arXiv:hep-ph/9704379v1 23 Apr 1997
SLA C {PU B{7463
TA U P 2417-97
hep-ph/9704379
A pril1997
Intrinsic C harm of V ector M esons:
A P ossible Solution of the \
P uzzle"
Stanley J.B rodsky
Stanford Linear Accelerator C enter
Stanford U niversity,Stanford,C alifornia 94309
e-m ail: sjbth@ slac.stanford.edu
and
M arek K arliner
SchoolofPhysics and A stronom y
Raym ond and Beverly Sackler Faculty ofExactSciences
Tel-A viv U niversity,69978 Tel-A viv,Israel
e-m ail: m arek@ vm .tau.ac.il
A BST R A C T
A n outstanding m ystery of charm onium physics is w hy the J= decays prom inently to pseudoscalar plus vector m eson channels,such as J= !
and J= !
0
K K , w hereas the (2S) does not. W e show that such decays of J= and their
suppression for 0(2S) follow naturally from the existence ofintrinsic charm jqqcci
Fock com ponents ofthe light vector m esons.
Subm itted to PhysicalR eview Letters.
W ork supported in part by the D epartm ent ofEnergy,contract D E{A C 03{76SF00515.
O ne ofthe basic tenets ofquantum chrom odynam ics is that heavy quarkonium
states such as the J= ; 0;and
m ust decay into light hadrons via the annihilation
ofthe heavy quark constituents into gluons,as show n in Fig.1(a). T his assum ption
is m otivated by the O ZI rule w hich postulates suppression of transitions between
hadrons w ithoutvalence quarks in com m on. A centralfeature ofthe PQ C D analysis
is the fact that the annihilation am plitude for quarkonium decay into gluons occurs
at relatively short distances r ’ 1=m Q ,thus allow ing a perturbative expansion in a
sm allQ C D coupling
s(m Q
).
In thisletterwe shallchallengetheassum ption thatquarkonium statesnecessarily
decay via interm ediate gluon states. W e shallargue,in analogy w ith the analysis[1,2]
ofthe nucleon strangeness content,that the wavefunctions ofthe light hadrons,particularly vector m esons such as the
and K ,have a non-negligible probability to
have higherFock state com ponentscontaining heavy quark pairs[3]. T he presence of
intrinsic charm and bottom in the lighthadron wavefunctions then allow stransitions
between heavy quarkonium and light hadrons by rearrangem ent of the underlying
quark lines,rather than by annihilation.
O ne ofthe m ost dram atic problem s confronting the standard picture ofquarkonium decaysisthe J= !
puzzle [4]. T hisdecay occursw ith a branching ratio of
(1:28 0:10)% [5],and itisthe largesttwo-body hadronic branching ratio ofthe J= .
T he J= isassum ed to be a ccbound state pairin the (1S)state. O ne then expects
the
0
= (2S)to decay to
w ith a com parable branching ratio,scaled by a factor
0:15,due to the ratio ofthe (2S) to (1S) wavefunctions squared at the origin.
In fact,B (
0
!
) < 3:6
10 5 [6],m ore than a factor of50 below the expected
rate. M ost ofthe branching ratios for exclusive hadronic channels allowed in both
J= and
0
decays indeed scale w ith their lepton pair branching ratios,as would be
expected from decay am plitudescontrolled by the quarkonium wavefunction nearthe
origin,
B ( 0 ! h)
B ( 0 ! e+ e )
’
= 0:147
B (J= ! h) B (J= ! e+ e )
w here h denotes a given hadronic channel. T he J= !
0:023 [5;6]
and J= ! K K
(1)
de-
cays also con ict dram atically w ith PQ C D hadron helicity conservation: all such
pseudoscalar/vector two-body hadronic nalstates are forbidden at leading tw ist if
helicity is conserved at each vertex [7,8].
2
T he O ZI rule states that hadronic am plitudes w ith disconnected quark lines are
suppressed;in Q C D thiscorrespondsto the assum ption thatthere isa num ericalsuppression ofam plitudes in w hich m ultiple-gluon interm ediate states occur. A lthough
the O ZI rule has provided a useful guide to the general pattern of hadronic reactionsinvolving strange particle production,there are glaring exceptions: forexam ple,
experim ents at LEA R have found [9] that in the pp annihilation at rest the O ZIviolating ratio B (pp !
=pp ! ! )isenhanced by alm osttwo ordersofm agnitude
com pared to the na ve O ZI expectations, and that the process pp !
occurs at
roughly the sam e rate as pp ! !!.
T he absence ofO ZIsuppression can be understood [1,2]ifone takes into account
the presence ofintrinsic strangeness in the proton,i.e.,one allow s for juudssi Fock
com ponents in the proton wavefunction.y T he intrinsic strange quarks are part of
the hadronic com position ofthe proton in distinction to extrinsic strangeness arising
from sim ple gluon splitting. T he pp !
and pp !
am plitudes can then occur
sim ply by rearrangem ent diagram s in w hich the strange quarks initially present in
the incom ing p and p appearasthe valence com ponentsof m esonsin the nalstate.
T he O ZIrule isevaded,since the annihilation ofthe p and p into interm ediate gluons
is in fact not required.
It is clearly interesting to extend these considerations to the charm and bottom
sector. In general,the probability to nd heavy quarks or high m ass uctuations in
the lighthadron wavefunctions w hich are m ulti-connected to the valence constituents
issuppressed by inverse powersofthe relevantm ass. Forexam ple one can use PQ C D
E
to show that the probability for intrinsic charm or bottom Fock states uudQ Q
in the proton wavefunction scales as 1=m 2Q [11]. T he light cone wavefunctions for
such states,
p
uud Q Q
(xi;k? i; i),peak at the sm allest invariant m ass ofthe partons;
i.e.,at equalrapidity for the constituents. T hus the heavy quarks tend to have the
1
largest m om entum fractions xi = ki+ =p+ / m ? i = (m 2i + k?2 i)2 :In fact the EM C
experim ent w hich m easured the charm structure function of the nucleon found an
excess ofevents atlarge Q 2 and xbj wellbeyond w hatisexpected from photon gluon
fusion. A nalysis show s that the EM C data are consistent w ith an intrinsic charm
probability of0:6
0:3% [12]. T here is also a recent interesting proposalto apply
T he Fock stateexpansion m ay be rigorously de ned in a fram e-independentway using light-cone
y
H am iltonian m ethods [10].
3
these ideasin orderto reconcile the recentH ER A data w ith the Standard M odel[13].
A n interesting test ofintrinsic charm in the proton would be a search for pp !
J= J= ,pp !
J= ,pp ! !J= above the charm threshold,processes w hich can
occur w ithout annihilation into gluons and thus w ithout O ZIsuppression because of
the presence ofcharm and strangeness in the initialstate. Sim ilarly,exclusive open
charm reactions such as pp !
c c
can occur through rearrangem ent ofthe initial
charm quark lines.
T he discussion and the experim entalevidence for the intrinsic charm is usually
phrased in term s of the charm content of the nucleon. O n the other hand, there
is a wellknow n and highly successfulphenom enologicalconstituent quark m odelin
w hich thenucleon containsjustthreeconstituentquarks.In orderto reconcilethetwo
physicalpictures,one is inevitably led to the conclusion that the constituent quarks
are them selves com plicated com posite objects, containing a sea of gluons, light qq
pairs and a sm all, but non-negligible cc intrinsic charm com ponent. In addition,
intrinsic contributions are produced from diagram s w hich are m ulticonnected to two
orm ore valence quarksin the nucleon. T histhen im m ediately im pliesthatthe vector
m esons,such as ,K ,etc.,also contain an intrinsic charm com ponent,for they are
built from the sam e constituent quarks as the baryons.
T he presence ofintrinsic charm in light hadrons can also have im portant consequences[14]forthe exclusive hadronic decaysofD -and B -m esons,w hich are usually
analyzed by assum ing only valence quarksin hadronic states. A ny hadron containing
a lightquark would also beexpected to havehigherFock statescontaining heavy quark
pairs by the sam e type ofquantum
uctuations w hich produce intrinsic strangeness
and charm in thenucleon.T hesurprisingly largebranching ratiosD !
K ispossibly
due to this e ect [14].
Let us now re-exam ine the J=
!
decay, allow ing for intrinsic charm in
the wavefunctions of the nal state hadron. For exam ple, consider the light-cone
Fock representation ofthe :
+
E
=
ud
ud +
E
ud cc
udcc +
:T heudcc
wavefunction w illbe m axim ized at m inim alinvariant m ass;i.e.at equalrapidity for
the constituents and in the spin con guration w here the ud are in a pseudoscalar
E
state,thus m inim izing the Q C D spin-spin interaction. T he cc in the udcc Fock
state carries the spin projection ofthe :W e also expect the wavefunction ofthe cc
quarks to be in an S-wave con guration w ith no nodes in its radialdependence,in
4
orderto m inim ize the kinetic energy ofthe charm quarks and thus also m inim ize the
totalinvariant m ass.
E
T he presence ofthe udcc Fock state in the
w illallow the J= !
decay
to occur sim ply through rearrangem ent ofthe incom ing and outgoing quark lines;in
E
fact,the udcc Fock state wavefunction hasa good overlap w ith the radialand spin
E
jcciand ud wavefunctionsofthe J= and pion.M oreover,there isno con ictw ith
hadron helicity conservation, since the cc pair in the
otherhand,the overlap w ith the
0
is in the 1 state. O n the
w illbe suppressed,since the radialwavefunction
E
ofthe n = 2 quarkonium state is orthogonalto the node-less cc in the udcc state
ofthe . T his sim ple argum ent provides a com pelling explanation ofthe absence of
0
!
and other vector pseudoscalar-scalar states.z
W e can attem ptto m ake a rough estim ate ofthedecay rateJ= !
ing itw ith the m easured rate ofthe analogousdecay
!
, ( !
by com par)
6
10 4
G eV [5],assum ing that the latter also occurs via coupling to the intrinsic ss com ponentin the . C onsiderthe Feynm an graph w here an Q Q isconnected to two valence
quarks in the wavefunction ofthe hadron through two hard gluons. T his gives a factorof
2
2
s(M Q )in
the am plitude and thus
4
2
s(M Q )in
the probability. T he sam e factor
occurs in the rearrangem ent decay rate show n in gure 1(b),since there is im plicitly
a hard gluon connecting the c w ith the u and the c w ith the d in the
wavefunction.
T hus,qualitatively,we can estim ate thatthe ratio ofprobabilitiesforintrinsic charm
to intrinsic strangeness in a light hadron is oforder
R (cc=ss) ’
m 2s
m 2c
4
s(M
4
s(M
2
c)
;
2
s)
(2)
w hich is ofthe order of10 3 . T his is also consistent in order ofm agnitude w ith the
estim ates ofthe ratio ofintrinsic charm to strangeness obtained from deep inelastic
scattering on the nucleon. T he actualnum ericalvalue is uncertain due to the uncertainties in the values ofthe m ass param eters and the running ofthe coupling at
low scales. T here m ay be other suppression factors from the evolution ofthe light
hadron wavefunctions,higher order corrections,etc. In the case ofin scattering reT he possibility that the radialcon gurations ofthe initialand nalstates could be playing a
z
role in the J= !
puzzle was rst suggested by S.Pinsky [15],w ho however had in m ind the
radialwavefunctions ofthe light quarks in the ,rather than the wavefunction ofthe cc intrinsic
charm com ponents ofthe nalstate m esons.
5
actions w ith probes oflow resolution,there is an additionalscreening ofthe intrinsic
sea[16,11],butthistype ofsuppression doesnotapply to decay am plitudescom puted
from the overlap ofwavefunctions.
T he ratio of decay rates for J= !
to
!
from quark rearrangem ent
should roughly scale w ith R (cc=ss) tim es phase space,assum ing that the integration
over the quarkonium wavefunctions give sim ilar probabilities.x
)
10 6 G eV ,w hich isconsistent w ith
O ur analysis utilizes the fact that quantum
uctuations in a Q C D bound state
T his rough estim ates im plies (J= !
the m easured rate of10 6 G eV .
wavefunction w illinevitably produce Fock states containing heavy quark pairs. T he
heavy quark pairs arising from perturbative gluon splitting are the extrinsic contributions associated w ith the substructure ofthe gluons;the probability forsuch pairs
dependslogarithm ically on theultravioletresolution scale.In thecaseofcharm onium
decay to light hadrons,the extrinsic heavy quark uctuations provide hard radiative
corrections to the usualcc annihilation am plitude.
O n the other hand,the intrinsic heavy quarks arise from quantum
uctuations
w hich are m ulticonnected to the valence quarks ofthe light hadrons,and the wavefunctions describing these con gurations w ill have m axim al am plitude at m inim al
E
o -shellness and m inim al invariant m ass. In the case of the
m eson the du cc
wavefunction w illthus be m axim ized w hen the con guration ofthe quarks resem bles
E
that ofa j J= i interm ediate state,rather than a higher m ass D D
state. T his
preference for the lowest invariant m ass induces a relatively strong coupling gJ=
i.e. there isa naturaloverlap between a
,
and J= w hich facilitatesthe J= !
decay, as schem atically illustrated in Fig. 1(b). T he decay of the
0
is naturally
suppressed due to the node in its radialwavefunction, also show n schem atically in
Fig.1(c).Sim ilarly,the juscciFock com ponentofthe K w illhave a favored J= K
con guration,allow ing the J= ! K K decay to also occurby quark line rearrangem ent,rather than cc annihilation.
Intrinsic charm in the pion w illalso allow the decay J= (1S) !
to proceed
In the case ofthe intrinsic charm or intrinsic strangeness rearrangem ent contribution,we only
x
need to com pute the overlap ofthe light-cone wavefunctions. T hus there is no extra
form factor
suppression beyond the penalty to nd intrinsic charm w ith large invariantm assoforderofthe J=
m ass in the
wavefunction.
6
through quark rearrangem ent diagram s. In this case the decay can utilize con guE
rations ofthe pion’s ducc Fock state w hich resem ble J= ,w here the
have opposite helicity. A gain, (2S) !
and J=
decay w illbe suppressed because ofthe
suppressed overlap ofthe radialcc wavefunctions.
T hebranching ratiosfortheJ= (1S)and (2S)form any hadronicchannelstrack
fairly wellw ith theirleptonic branching ratios,aswould beexpected ifccannihilation
into gluonsand/orphotonsisdom inant and unsuppressed by helicity selection rules.
For exam ple,the vector m eson -scalar m eson two-body decay channels J= (1S)!
V S can proceed through ccannihilation.N otethattheccrearrangem entcontribution
to J= (1S)! V S isdisfavored: the J= -scalarintrinsic charm excitation in a vector
m eson wavefunction is fairly m assive,and it is thus relatively suppressed com pared
to the J= -pseudoscalar excitations. O n the other hand,tensor m esons could have
an appreciable intrinsic charm content. In general,a fullanalysis ofeach exclusive
decay channelw illrequiretaking into accountboth ccannihilation and rearrangem ent
diagram s as wellas their interference.
A t rst sight, the decay of J= to pseudovector{scalar should be helicity suppressed in PQ C D for the sam e reason J= to pseudoscalar{vector is suppressed [7].
T he argum ent is that there is only one Lorentz invariant,parity-conserving am plitude,and this requires that the pseudovector have helicity
1. H owever, the light
quark and antiquarks em erging from the cc annihilation into gluons have opposite
helicity.
It is im portant to note that the pseudovector and scalar states are dom inantly
P -wave bound statesoflightquarks. T he nonzero helicity ofthe pseudovectorm eson
can arise from the orbital angular m om entum , and thus unlike the pseudoscalarvector channels,there is no strong PQ C D suppression ofthe annihilation am plitude
due to helicity conservation. H owever,the form factor suppression com paring (1S)
and (2S)pseudovector-scalar decaysisstrongerthan norm albecause P -wave wavefunctions vanish at the origin. T hus it is possible that both the cc annihilation and
intrinsic charm rearrangem entm echanism s w illcontribute signi cantly to such decay
am plitudes.
Itwould also beinteresting to com parebranching ratiosforthe
ascluesto the im portance of
C (1S)intrinsic charm
C
(1S)and
C
(2S)
excitationsin the wavefunctions
oflighthadrons. In principle,sim ilaranalysescan be carried outforexclusive (1S)
7
and (2S) decays as clues to the intrinsic bb content oflight hadrons.
T hus a system atic com parison ofthe various hadronic channels ofheavy quarkonium could provide im portantconstraintson the quantum num bers,m agnitudes,and
con gurationsofthe intrinsic heavy quark excitationsin lighthadron wavefunctions.
T he existence of non-O ZI rearrangem ent m echanism s for exclusive J=
w ill inevitably also e ect the total inclusive rate for J=
the value of
s
decay
decay, and thus m odify
obtained by assum ing that the decay am plitude is due solely to cc
annihilation [17].
A cknow ledgm ents
T he authorsw ish to thank C ER N and the organizersofthe W orkshop on Strange
Structure ofthe N ucleon fortheirhospitality and forproviding a stim ulating environm ent w hich catalyzed this work. T his research was supported in part by the Israel
Science Foundation adm inistered by the IsraelA cadem y ofSciences and H um anities,
and by a G rantfrom theG .I.F.,theG erm an-IsraeliFoundation forScienti cR esearch
and D evelopm ent.
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8
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9
[16] S.J.Brodsky,J.C .C ollins,S.D .Ellis,J.F.G union,and A .H .M ueller,in Proc.
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10
(a)
ρ
π
(b)
c
c
ρ u
d
+
+
c
J/ ψ
+
–
|udcc>
c
J/ ψ
+
+
+
J/ ψ
ρ
g ψρπ
J/
–
π
π
(c)
c
c
ρ
u
d
4-97
8298A1
+
+
+
ψ' = Ψ (2s)
ψ'
ρ
gψ'ρπ
–
π
π
Figure 1:
(a) T he decay J= (Jz = 1) !
via the standard PQ C D cc annihilation m echanism .
A light quark helicity- ip is required,since the m ust be produced w ith helicity 1:
(b) A connected quark rearrangem ent diagram w hich induces the gJ=
coupling,via the
higher Fock state ofthe ,judcci. T he + = signs on the quark lines denote the helicities
ofthe corresponding quarks. In the dom inant intrinsic charm Fock state ofthe ,the ud
and cc com ponents ofthe are in 0 and 1 states,respectively,thus generating m axim al
overlap w ith the and J= spin wavefunctions.
(c) A \tw isted" connected diagram ,schem atically indicating the suppression of 0 coupling due to the m ism atch between the nodeless wavefunction ofthe cc in the judcci Fock
state ofthe and the one-node 2S cc wavefunction ofthe 0.
11