Charmonium spectrum and diffractive production in a light-front Hamiltonian approach

0.46 MB·

by  Guangyao Chen

Nuclearand
ParticlePhysics
Proceedings
NuclearandParticlePhysicsProceedings00(2017)1–5
ff
Charmonium spectrum and di ractive production in a light-front Hamiltonian
approach
GuangyaoChen∗,YangLi,PieterMaris,KirillTuchin,JamesP.Vary
DepartmentofPhysicsandAstronomy,IowaStateUniversity,Ames,IA50011,USA
7 Abstract
1
0 Westudyexclusivecharmoniumproductionindiffractivedeepinelasticscatteringandultra-peripheralheavy-
2 ioncollisionswithinthedipolepicture. Themassspectrumandlight-frontwavefunctionsofcharmoniumareob-

n tainedfromthebasislight-frontquantizationapproach,usingtheone-gluonexchangeinteractionplusaconfining
a potentialinspiredbylight-frontholography. Weapplytheselight-frontwavefunctionstoexclusivecharmonium
J
production. Theresultingcrosssectionsareinreasonableagreementwithelectron-protoncollisiondataatHERA

9 andultra-peripheralnucleuscollisionmeasurementsatRHICandLHC.Thecharmoniumcross-sectionhasmodel

dependence on the dipole model. We observe that the cross-section ratio of excited states to the ground state
]
h hasaweakerdependencethanthecross-sectionitself. Wesuggestthatmeasurementsofexcitedstatesofheavy
t quarkonium production in future electron-ion collision experiments will impose rigorous constraints on heavy
-
l quarkonium light-front wavefunctions, thus improving our understanding of meson structure, which eventually
c
u willhelpusdevelopaprecisedescriptionofthegluondistributionfunctioninthesmall-xregime.
n
[ Keywords:

charmonium,lightfront,mesonproduction,dipolemodel
1
v
9
7 1. Introduction front wavefunction (LFWF) [7, 11]. Such phe-
2 nomenological models contain free parameters that
2 Exclusive vector meson production processes are weaken the predictive power of the diffractive heavy
0 valuable probes of hadron structures [1] and provide quarkoniumproductionprocess.
.
1 insights to QuantumChromodynamics (QCD) in the
0 high energy limit, where saturation dominates the Recently, a new description of heavy quarkonium
7
gluondynamics[1–3].Modelsincorporatingthesatu- system has emerged [13, 14] within the basis light-
1
rationphysicshavebeenverysuccessfulindescribing front quantization (BLFQ) approach [15–17]. The
:
v highprecisionelectron-protoncollisiondatacollected mass spectra for charmonium and bottomonium are
i
X attheHadron-ElectronRingAccelerator(HERA)[4– obtained by diagonalizing a Hamiltonian within the
8]. BLFQ framework, with the one-gluon exchange in-
r
a The diffractive DIS process can be effectively ap- teraction and a confining potential inspired by light-
proximated by the scattering of a color dipole, a frontholography[13]. Thesuccessfulapplicationsof
quark-antiquark pair, from the proton [9, 10]. The theBLFQformalismtotheelectronanomalousmag-
so called dipole picture has been very successful in neticmoment[16,18],andtothepositroniumsystem
explainingbothexclusiveanddiffractiveHERAmea- [19,20]havepavedthewayforthestudyoftheheavy
surements in the high-energy limit [11, 12], by em- quarkoniumsystem. TheLFWFsfromtheBLFQap-
ploying some phenomenological vector meson light- proach, which arise from successful fits to the heavy
quarkonia mass spectroscopy, show success in appli-
cations to decay constants and to additional observ-
∗Correspondingauthor ablessuchaschargeformfactors.Herewereportpre-
Emailaddresses:[email protected](GuangyaoChen), dictions of the LFWFs obtained from the BLFQ ap-
[email protected](YangLi),[email protected]
proachandcomparewithselectedexperimentdataon
(PieterMaris),[email protected](KirillTuchin),
[email protected](JamesP.Vary) diffractive charmonium production, which were dis-
γ*�→�/ψ�
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0 100 200 300
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Figure 1: Predictions of the BLFQ LFWF (solid Figure 2: Predictions of the BLFQ LFWF (solid
curves) and the boosted Gaussian LFWF (dashed curves) and the boosted Gaussian LFWF (dashed
curves) compared with the HERA experimental data curves) compared with the HERA experimental data
of total J/Ψ cross section for different values of Q2 fortheσΨ(2s)/σJ/Ψcross-sectionratioasafunctionof
and W [26, 27]. The inner bars indicate the statisti- Q2 inelectron-protonscattering[28]. Errorbarsindi-
caluncertainties;theouterbarsarethestatisticaland catethestatisticaluncertainties.
systematicuncertaintiesaddedinquadrature.
Weemploytheimpactparameterdependentsatura-
cussedindetailinRef.[21]. tion(bSat)model[7]andtheimpactparameterdepen-
dent Color Glass Condensate (bCGC) model [8] for
this study. We use five sets of parameters (bSat I-V)
2. Theoreticalframework
in the bSat model[11, 22] and three sets of parame-
ters (bCGC I-III) in the bCGC model [23, 24]. The
The amplitude for producing an exclusive vector
meson in diffractive DIS is calculated as follows in parametersforthesedipolecrosssectionparametriza-
tionsaresummarizedinTables1and2inRef.[21].
thedipolepicture[11],
TheheavyquarkoniummassspectrumandLFWFs
AγT∗,Lp→Ep =i (cid:90) d2r(cid:90) 14dπz (cid:90) d2b(Ψ∗EΨ)T,L(r,z,Q) aeffreeoctbivtaeinliegdhtb-yfrsoonltvHinagmtihletoeniigaenn,vwahluiceheqcoumatiboinneosftahne
0 holographicQCDHamiltonian[25]andtheone-gluon
dσ
e−i[b−(1−z)r]·∆ qq¯(x,r), (1) exchangedynamics[13],
d2b
where Q2 is the virtuality of photon, T and L denote Heff|ψh(cid:105)= Mh2|ψh(cid:105), (Heff ≡ P+Pˆ−eff−P(cid:126)2). (3)
thetransverseandlongitudinalpolarizationofthepro-
with
duced vector meson, and the momentum transfer be-
itnhge qtu=ark−∆(cid:126)an2d. (cid:126)arnitsiqtuhaerktraannsdvezrsisetsheepaLrFatiloonngbietutwdieneanl Heff =kz(2⊥1+−mz)2q +κc4onζ⊥2 − 4κcm4on2∂z(cid:0)z(1−z)∂z(cid:1)
momentumfractioncarriedbythequarkrespectively. q
4πC α
(cid:126)bistheimpactparameterofthedipolerelativetothe − F su¯ (k)γ u (k(cid:48))v¯ (k¯(cid:48))γµv (k¯), (4)
proton and x is the Bjorken variable. Ψ and Ψ∗ are Q2 s µ s(cid:48) s¯(cid:48) s¯
E
LFWFsofthevirtualphotonandtheexclusivelypro-
whereC = 4, Q2 = −1(k(cid:48) −k)2 − 1(k¯ −k¯(cid:48))2. The
ducedvectormesonrespectively. Thecrosssectionis F 3 2 2
strong coupling constant α is fixed, α (M ) (cid:39) 0.36
relatedtotheamplitudeas s s cc¯
andα (M )(cid:39)0.25. Theeffectivequarkmassm and
s bb¯ q
dσγT∗,Lp→Ep = 1 |Aγ∗p→Ep(x,Q,∆)|2 . (2) tthhee hcoeanvfiyniqnugasrktroennigutmh κmcoanssarsepedcettreurmmintoedthbeyefixptteinrig-
dt 16π T,L
mental measurements. The calculated spectra agree
Moreover,contributionsfromtherealpartofthescat- with the experimental values within a root-mean-
teringamplitudeandskewednesscorrectionshouldbe squaredeviationofaround50MeVforthestatesbe-
takenintoaccount,seeRef.[21]fordetails. lowtheopenflavorthresholds.
2
Pb+Pb→Pb+Pb+J/Ψ sNN=2.76TeV The BLFQ LFWFs provide a better fit to the data at
6.
bSatI+BLFQΨV bCGCI+BLFQΨV largerQ2region.
bSatI+bGΨV bCGCI+bGΨV Using the BLFQ LFWF, the bSat I dipole
ALICE parametrization and the bCGC I dipole parametriza-
4. CMS tion yield a prediction of dσ/dy = 59.9 µb and
]mb dσ/dy = 52.6 µb respectively for the coherent J/Ψ
[
σ/ddy2. plirdoidnugcattio√nsaNtNm=id2-r0a0piGdietVy watitRhHtwICo.gBooldthnruecsulelitscaorle-
consistentwithlatestdatadσ/dy = 45.6±13.3(stat)
±5.9(sys)µb[29].
In Fig. 3, solid curves show the prediction of the
0.
-4. -2. y0. 2. 4. BLFQ J/Ψ LFWF using bSat I (red) and bCGC
I (blue) dipole model parametrizations for coherent
Figure3: ThepredictionsoftheBLFQLFWF(solid
production of J/Ψ at mid-rapidity in ultra-peripheral
curves) and the boosted Gaussian LFWF (dashed √
Pb-Pb collisions at s = 2.76 TeV [30, 31]. We
curves) for the coherent production of J/Ψ produc- NN
√ find both of these results are within the statistical
tioninultra-peripheralcollisionat s =2.76TeV,
NN uncertainty of the experimental data. In contrast,
comparedtothemeasurementsbytheALICEcollabo-
dashedcurvesarethepredictionsoftheboostedGaus-
ration[30]andCMScollaboration[31]atLHC.Error
sian LFWF of J/Ψ using bSat I (red) and bCGC I
barsshowstatisticaluncertaintiesonly.
(blue) dipole model parametrizations. We find both
of these overshoot the data. Both the BLFQ LFWF
and boosted Gaussian LFWF underestimate the pro-
TheheavyquarkoniumLFWFfromtheBLFQap-
duction of Ψ(2s) in ultra-peripheral Pb-Pb collisions
proachhasseveraladvantagesoverLFWFsfromphe- √
at s =2.76TeV[32].
nomenological models. First, it is constrained by a NN
variety of observables. Second, it provides access to
higher excited states without introducing additional 4. Dipolemodeldependence
assumptions. Moreover, it can be improved by in-
cludinghigherFocksectors,e.g.,thequark-antiquark- Theuncertaintiesassociatedwiththeheavyquarko-
gluonsector. nium LFWFs and the dipole cross section both con-
tributetouncertaintiesintheresultsforheavyquarko-
nium production in the dipole picture. On the other
3. Charmonium production at HERA, RHIC and
hand, the uncertainties from the dipole cross section
LHC
parametrizationmaybecorrelatedforthecalculation
We study the diffractive charmonium production ofdifferentstatesofthesamequarkoniumsystem,for
example, J/Ψ and Ψ(2s) states of charmonium. It
using the heavy quarkonium LFWF from the BLFQ
couldleadtoweakerdependenceonthedipolemodel
approach.Theresultingcrosssectionsasafunctionof
forthecalculationofthecross-sectionratioofhigher
various kinematic variables are in reasonable agree-
excited states over the ground state than the calcula-
ment with electron-proton collision data at HERA
tionofthecrosssectionitself. Wecalculatetheratio
and ultra-peripheral nucleus collision measurements
of the Ψ(2s) cross section to the J/Ψ cross section
at RHIC and LHC. We present some representative
as a function of Q2 predicted by the BLFQ LFWF
resultsusingtheBLFQLFWFsofheavyquarkonium
and various dipole cross section parametrizations in
and compare our predictions with the predictions of
Tables 1 and 2 in Ref. [21] for electron-proton colli-
boostedGaussianLFWFs.
sions and electron-ion collision as well. We observe
To make comparison with HERA measurements
that the cross-section ratio exhibits insignificant de-
[26, 27], we employ the bSat II dipole model in Ta-
pendenceondipolemodels,especiallyinthelargeQ2
ble1inRef.[21]. InFig.1, solidanddashedcurves
arepredictionsofthetotalJ/Ψcrosssectionasafunc- regime. Thecaseforelectron-leadcollisionsisshown
tionofvariousvaluesof Q2 andW bytheBLFQand inFig.4.
the boosted Gaussian LFWFs respectively. Except
when Q2 is very small, the predictions of the BLFQ 5. Conclusions
LFWF are slightly lower than the experimental mea-
surements. Note that the theoretical uncertainty in We study diffractive charmonium production with
the dipole model is large at small Q2. Fig. 2 shows BLFQ light-front wavefunctions within the dipole
thepredictionsoftheBLFQLFWFs(solidcurve)and model. It has been shown that the effective Hamil-
the boosted Gaussian LFWFs (dashed curve) for the tonian incorporating one-gluon exchange dynamics
σΨ(2s)/σJ/Ψ cross-sectionratioasafunctionof Q2 in fromQCDLagrangianandeffectiveconfiningpoten-
electron-proton scattering measured at HERA [28]. tialinspiredbysoft-walllight-frontholographicQCD
3
1. ingustheexperimentaldataforΨ(2s)measurement.
σψ(��)/σ�/ψ�����(��) ThisworkwassupportedinpartbytheDepartmentof
EnergyunderGrantNos. DE-FG02-87ER40371and
0.8 ���� � ���� � DESC0008485 (SciDAC-3/NUCLEI). We acknowl-
���� �� ���� � edge computational resources provided by the Na-
���� ��� ���� ��
ψ ���� �� ���� ��� tional Energy Research Scientific Computing Center
σ/�0.6 (NERSC)underContractNo.DE-AC02-05CH11231.
/
)�
�
ψ(0.4 References
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5