Polarization for Prompt J/psi, psi(2s) production at the Tevatron and LHC

0.32 MB·English

by  Bin Gong

Polarization for Prompt J/ψ and ψ(2s) Production at the Tevatron and LHC
Bin Gong1,2,3, Lu-Ping Wan1,2, Jian-Xiong Wang1,2 and Hong-Fei Zhang1,2
Institute of High Energy Physics, Chinese Academy of Sciences, P.O. Box 918(4), Beijing, 100049, China.
Theoretical Physics Center for Science Facilities, CAS, Beijing, 100049, China.
Institute of Theoretical Physics, Chinese Academy of Sciences, P.O. Box 2735, Beijing, 100190, China.
WithnonrelativisticQCDfactorization, wepresentthefirstcompletenext-to-leadingorderstudy
on the polarization of prompt J/ψ hadroproduction by including feeddown from χc(3PJ1,3S18) and
ψ(2s) which turn out to be very important parts. By using the color-octet long-distance matrix
elementsobtainedfromacombinedfitofthemeasurementsattheTevatronandLHCforJ/ψ,ψ(2s)
and χc, the prompt J/ψ polarization predictions are presented, and the results are in agreement
withtheCDFRunIdata(excepttwopoints),butinconflictwiththeCDFrunIIdata,whilethey
areclosetotheALICEdata(inclusiveJ/ψ). ThemeasurementsattheLHCareexpectedtoclarify
3
thesituation.
1
0
PACSnumbers: 12.38.Bx,13.60.Le,13.88.+e,14.40.Pq
2

n
a Quantum chromodynamics (QCD) is a successful the- two groups[12, 13], and their predictions for pt distribu-
J ory to describe strong interaction, but its fundamen- tions agree with the experimental measurements at the

8 tal ingredients, the quarks and gluons, are not observed Tevatron and LHC. Similar progress is also achieved for
2 freely and must hadronize eventually. The fact makes it Υ hadroproduction[14] and J/ψ photoproduction [15].

impossible to calculate any processes involving detected Recently, the complete NLO calculation for polariza-
]
h hadronsinthe finalor initialstates directly. Thereforea tion of direct J/ψ (3P[8] included) hadroproduction are
J
p suitablefactorizationschemetodivideproblemsintoper- presented by two groups [16, 17]. One of them [16] find
- turbative calculable and nonperturbative parts is very that the CDF data (run II) [5] cannot be interpreted by
p
e important. In order to remedy the large discrepancy using a global fit of J/ψ yield data, while the other [17]
h between theoretical prediction and experimental data findsthatitcanbeinterpretedbyusingacombinedfitof
[ on the transverse momentum (pt) distribution of J/ψ J/ψyieldandpolarizationdatafromtheCDF.However,

production at the Tevatron, a color-octet (CO) mech- there only exist polarization measurements for prompt
2
v anism [1] was proposed based on nonrelativistic QCD (or even inclusive) J/ψ production until now [5, 18]. It
2 (NRQCD) factorization [2], which is proven in next-to- is known that among all the feeddown contributions to
8 next-to-leading order analysis [3]. It allows consistent promptJ/ψ production from higher charmoniumstates,
6 theoretical prediction to be made and improved pertur- χ contributes more than 20 30% of prompt experi-
cJ
6 batively. However, the leading-order calculation based mentalmeasurements[19,20],a−ndψ(2s)alsocontributes
.
5 onNRQCD predicts a sizable transversepolarizationfor a small fraction, while others are negligible. The feed-
0 J/ψ hadroproduction at high pt [4] while the measure- down contribution is so large that it can drastically
2 ment at the Tevatron [5] gives almost an unpolarizedre- change the polarization results and must be considered.
1 sult. Many efforts have been made to clarify the situa- Therefore, to test NRQCD factorization and solve (or
:
v tion thereafter (see Ref. [6] and references therein). It is clarify) the long-standing J/ψ polarization puzzle, it is
i expected that the long-standing J/ψ polarizationpuzzle a veryimportantstepto achievethe polarizationpredic-
X
couldbesolvedorclarifiedbytheexperimentalmeasure- tions for prompt J/ψ hadroproduction.
r
a mentsattheLHCandprogressintheoreticalcalculation. In this Letter, we present the calculation of the polar-
In the last five years, there was some very important ization for prompt J/ψ hadroproduction at NLO QCD.
progress made in the next-to-leading order (NLO) QCD In addition to calculating the polarization of J/ψ from
correction calculation. The NLO corrections to color- the same intermediate states (3S[1], 1S[8], 3S[8], 3P[8]) as
singlet J/ψ hadroproduction have been investigated in 1 0 1 J
in previous works [8, 10, 16, 17], we have also calculated
Refs.[7,8]anditsp distributionisfoundtobeenhanced
t that from χ (3P[1], 3S[8]) feeddown, in which the cal-
by 2 3 order of magnitude at the high p region. And cJ J 1
it is −found that J/ψ polarization changets from trans- culation of the 3P[1] part is even more complicated than
J
verse into longitudinal at NLO [8]. The results are re- thatofthe3P[8] partofJ/ψ. Inthepresentedresults,the
J
produced at leading-order in a new factorization scheme polarizationfor ψ(2s),χ and prompt J/ψ are obtained
cJ
forlargept quarkoniumproduction[9]. TheNLOcorrec- for the first time.
tionstoJ/ψproductionviaS-waveCOstates(1S[8],3S[8]) InNRQCDformalism,thecrosssectionofhhadropro-
0 1
are studied in Ref. [10] and the corrections to p distri- duction is
t
butions of both J/ψ yield and polarization are small.
In Refs. [11], NLO corrections for χ hadroproduction σ[pp hx]= dx dx GiGjσˆ[ij (cc¯) x] h ,(1)
cJ → Z 1 2 p p → n hOni
are studied. The complete NLO calculation for prompt X
J/ψ hadroproduction (with 3P[8] included) is given by where p is either a proton or antiproton, the indices i,j
J
2
run over all the partonic species and n represents the cc¯ (χ J/ψ) = 0.0116,0.344,0.195 for J = 0,1,2, re-
cJ
intermediate states (3S[1], 3S[8], 1S[8], 3P[8]) for J/ψ and Bspectiv→ely [26]. The factorization, renormalization and
1 1 0 J
ψ(2s), or (3PJ[1], 3S1[8]) for χcJ. The short-distance contri- µNRQ=CmD,scraelsepseacrteivcehlyo.seTnhaescµern=terµ-off-=mpass4men2ce+rgpie2tsaanrde
bution σˆ can be perturbatively calculated and the long- Λ c
distancematrixelements(LDMEs) h aregovernedby 1.96 and 7 TeV for the Tevatron and LHC, respectively.
hOni Itiswellknownthatthe uncertaintiesforp distribution
nonperturbative QCD effects. t
of charmonium hadroproductionfrom m ,µ ,µ and µ
The polarization of J/ψ is described in Ref. [21] as c Λ r f
arelargeatsmallp region. Arecentworkonrelativistic
t
dσ dσ √2Redσ 2dσ corrections to J/ψ hadroproduction [27] also shows that
11 00 10 1,−1
λ= − ,µ= ,ν = . the correction is negative and large when p < 10 GeV.
dσ +dσ dσ +dσ dσ +dσ t
11 00 11 00 11 00 It is also very clearlyshownin Refs. [10, 12] that the ex-
wheredσSzSz′ isthespindensitymatrixofJ/ψhadropro- perimentaldatainsmallpt regioncannotbeinterpreted
duction. For experimental measurement, a simultaneous well. In Ref. [13], the data in small pt region are also
study of the polarization variables in different reference included in their fit, but the experimental data in large
framesisparticularlyinterestingsinceconsistencychecks pt region are sacrificed. Therefore, data in pt < 7 GeV
on the results can be performed, and it provides a much region are excluded in our fit.
better control of the systematic effects due to detector InRef.[17],acombinedfitofthepromptJ/ψyieldand
limitations and analysis biases. Therefore, both the he- polarizationmeasurementsofCDF(runII)isperformed.
licity andCollins-Soper(CS)framesareemployedinour Without the feeddown contribution, we can repeat their
polarizationcalculation. ToobtaindσSzSz′,similartreat- results by an exactly same fit. With the feeddown con-
ment as in Ref. [15] is taken for direct J/ψ and ψ(2s) tribution, we perform a similar fit and find that the pt
production. The feeddown from ψ(2s) is obtained from distribution of transverse polarized production rate for
dσJ/ψ = dσψ(2s) (ψ(2s) J/ψ). χ , χ , and directJ/ψ partbecomes negativewhenpt >24 GeV,by
SzSz′|ψ(2s) SzSz′ B → c0 c1 varying the values of fitted CO LDMEs within the un-
χ have different masses and decay branching ratios to
c2
J/ψ, thus are treated differently from J/ψ(3P[8]). The certainty range, the negative behavior of direct part can
J be delayed as p increases,but cannotbe avoided,which
t
feeddown can be expressed as
meansthatnophysicalsolutioninthe LDME parameter
J/ψ(S )γ(L )χ (J,J ) a CSz,Lz. (2) space can be achieved. It clearly shows that the feed-
h z z | c z i≡ J J,Jz down contribution is so important that the conclusions
forthe polarizationarecompletely differentforthe cases
Here, CSz,Lz is the Clebsch-Gordan coefficient, and a
J,Jz J withorwithoutthefeeddownpart. Therefore,wechoose
is supposed to be independent of S , L , and J as an
z z z tofittheCDFandLHCbexperimentaldatafortheyield
approximation. Then the branching ratio of χ to J/ψ
cJ onlyandgivepredictionsforpolarizationinthiswork. In
is approximately expressed as
addition,pJ/ψ ph(M /M )isusedasanapproxima-
t ≈ t J/ψ h
2 tionto countforthekinematics effectinthe feeddownof
(χ J/ψ)= a CSz,Lz = a 2, (3)
B cJ → X (cid:12) J J,Jz (cid:12) | J| h=ψ(2s),χcJ.
Jz,Lz,Sz(cid:12) (cid:12) For χ production, the CO LDME is obtained
(cid:12) (cid:12) cJ
from which we obtain aJ 2. Thus, the spin density ma- as hOχc0(3S1[8])i = (0.221 ± 0.012) × 10−2 GeV3 with
trix of J/ψ from χ fe|edd|own is obtained as χ2/d.o.f. = 2.57/10 by fitting the CDF and LHCb
cJ
data [19, 20, 29].
dσSJz/Sψz′|χcJ = B(χcJ →J/ψ)JXz,Jz′δJz−Sz,Jz′−Sz′ binTehdefiCtOofLthDeMCEDsFofanψd(2Ls)HCarbeeoxbptearinimedenftraolmdaataco[3m0-]
as
CSz,Jz−SzC∗Sz′,Jz′−Sz′dσχcJ . (4)
× J,Jz J,Jz′ Jz,Jz′ ( (1S[8]) , (3S[8]) ,hO(3P0[8])i) O GeV3, (5)
The newly upgraded FDC package [22] is used in our hO 0 i hO 1 i m2c ≡ 100
calculation,inwhichthe reductionmethodforloopinte- =( 0.012 0.869,0.34 0.12,0.42 0.24)
O − ± ± ±
grals proposed in Ref. [23] is implemented.
In our numerical calculation, The parton distribution with χ2/d.o.f. = 17.8/17. The large uncertainty arises
function CTEQ6M [24] and the corresponding two-loop from approximately linear dependence of three short-
QCD coupling constant α are used. The charm-quark distanceparts. Toclarifythesituation,arotationmatrix
s
mass is chosen as m = 1.5 GeV and an approximation V asdiscussedinRef.[12]isusedtomakefittingvariables
c
M = 2m is made to fix the masses of quarkonia. The independent by introducing Λ V, and Λ is obtained
h c ≡ O
color-singlet LDMEs are estimated by using a potential with only independent error for each Λi in the fit. Then
model result [25], which gives R (0)2 = 0.810 GeV3, differential cross section dσ is obtained with
J/ψ
| |
R (0)2 =0.529 GeV3, and R′ (0)2 =0.075 GeV5,
r|esψp(e2cs)tivel|y. Branching ratios| aχrce |(J/ψ[ψ(2s)] dσ = Oidσˆi = OVV−1dσˆ = ΛV−1dσˆ.
B → X X X
µµ) = 0.0593(0.0077), [ψ(2s) J/ψ] = 0.595 and Λ=(0.16 0.91,0.47 0.05, 0.21 0.01), (6)
B → ± ± − ±
3
FIG. 1: pt distribution of prompt J/ψ and ψ(2s) hadroproduction. CDF and LHCb data are taken from Refs. [28–30].
FIG. 2: Polarization parameter λ of ψ(2s) in helicity(up) and CS(down) frames. The CDF data are taken from Ref. [5, 18]
where Λ is obtained with same χ2/d.o.f. but much from transverse to slight longitudinal in CS frame. As
smalleruncertainty. WiththevaluesofΛandrelationin is shown in Fig. 3, the polarizations of J/ψ from χ
cJ
Eq. (6), theoretical predictions with proper uncertainty feeddown result in small transverse polarization ( 0.2)
∼
can be made. inthe helicityframe,andslightlongitudinalpolarization
After the treatment of feeddown, the CO LDMEs for ( 0.1) in the CS frame at large p . Finally our the-
t
∼ −
J/ψ are obtained from a combined fit of the CDF and oretical predictions for prompt J/ψ polarization in both
LHCb experimental data [28, 29]. By using the same helicityandCSframesareshowninFig.4,incomparison
definition in Eq. (5) for J/ψ, the fit gives with current existing measurements from the CDF and
ALICE Collaborations. In the forward rapidity region,
= (9.7 0.9, 0.46 0.13, 0.95 0.25), our predictions are close to the ALICE measurement for
O ± − ± − ±
Λ = ( 9.6 1.0,1.7 0.1, 0.37 0.01), (7) inclusiveJ/ψ productioninbothhelicityandCSframes.
− ± ± − ±
In the central rapidity region, our results are in agree-
with χ2/d.o.f. = 5.32/10. Thereafter, we use the error ment with the CDF run I data (except two points), but
of eachindependent variable in Λ to generate all the un- in conflict with the CDF run II data. However, we still
certainty bands in theoretical predictions. It is clearly cannotdrawadefiniteconclusionsincethereisnowayto
shown in the following figures that the uncertainty band judge these two measurements. From this point of view,
isnottoowideevenwithlargeuncertaintyinΛinEq.(6). thisisanotherreasonforustoexcludeCDFdataonJ/ψ
In Fig. 1, we find that the feeddown part contributes polarization in our fitting. With the optimized analysis
almost the same as the direct part in prompt J/ψ yield method to measure more J/ψ polarization information
when pt > 25 GeV at the Tevatron, so as for y < 2.4 with two different frames (helicity and CS) as used in
| |
when pt > 30 GeV at the LHC, but is less important in the ALICE measurement, it is expected that J/ψ and
the forward range 4.5>y >2. The ψ(2s) polarizations, ψ(2s)polarizationmeasurementsattheLHCwouldhelp
shown in Fig. 2, go from longitudinal to transverse as to solve the polarization puzzle or clarify the situation.
p increases in the helicity frame, which has totally op-
t
posite trend with current CDF measurement [5], and go The polarization predictions in Ref. [16] and [17] are
4
FIG. 3: Polarization parameter λ of J/ψ from χcJ feeddown in helicity(up) and CS(down) frames.
for direct J/ψ production. Comparing them with the can be reproduced. It means that the polarization con-
CDF(ALICE)measurementsforprompt(inclusive)J/ψ tributed from χ and ψ(2s) feeddown is a very impor-
c
productionandmaking a definite conclusioncanbe con- tant part and must be included to solve or clarify the
sidered as reasonable when and only when the feeddown J/ψ polarizationpuzzle. Therefore,wechoosetousethe
contributionisnegligible. Ourcalculationshowsthatthe new CO LDMEs from a combined fit of J/ψ yield mea-
feeddown contribution is very important and cannot be surements at the Tevatron and LHC with p > 7 GeV.
t
neglected. Our predictions are in better agreement with And the NLO theoretical predictions on polarization for
the ALICE measurement than theirs in Ref [16]. By ex- promptJ/ψarepresentedattheTevatronandLHC.The
cluding the feeddown contribution, our polarization pre- resultsareinagreementwiththeCDFrunIdata(except
dictionsfordirectJ/ψproductionareconsistentwiththe twopoints), but inconflict withthe CDF runII data. It
results inRef. [16]and[17] by usingtheir fitted LDMEs. isclosetotheALICEmeasurementattheLHCalthough
In summary, we presented the first complete NLO the measurement is for inclusive J/ψ. Finally, it is clear
study on polarization for prompt J/ψ and ψ(2s) thatthe polarizationmeasurementsat the LHC arevery
hadroproduction in both the helicity and CS frames by important to clarify the long-standing J/ψ polarization
including feeddowncontributionsfromhighercharmonia puzzle.
χ andψ(2s)basedontheNRQCDfactorizationscheme. We are thankful for help from the Deepcomp7000
c
It is found that there is no physical solution for a com- projectoftheSupercomputingCenter,CNIC,CAS.This
bined fit of both J/ψ yield and polarization measure- workissupportedbytheNationalNaturalScienceFoun-
ments by CDF at the Tevatron (run II) for prompt J/ψ dation of China (No. 10979056, No. 10935012, and No.
hadroproduction,whilethe previousfit[17]withoutcon- 11005137), and by CAS under Project No. INFO-115-
sidering the polarization from feeddown of χ and ψ(2s) B01.
c
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