Glueballs and vector mesons at NICA

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by  Denis Parganlija

EPJ manuscript No.
(will be inserted by the editor)
Glueballs and vector mesons at NICA
Denis Parganlija
Technische Universit¨at Wien, Institut fu¨r Theoretische Physik, WiednerHauptstr. 8-10, 1040 Vienna,Austria
16.10.2015 / Revised version: 07.01.2016
6
Abstract. Two interconnected fields of interest are suggested for NICA. Firstly, existence of glueballs is
1
0 predicted bythe theory of strong interaction but – even after decades of research – glueball identification
2 in thephysicalspectrum is still unclear. NICAcan help to ascertain experimentalglueball candidates via
J/Ψ decays whose yield is expected to be large. Importance of glueballs is not limited to vacuum: since
p
theycoupletoothermesonstates,glueballscanalsobeexpectedtoinfluencesignaturesofchiral-symmetry
e
restoration inthehigh-energyphaseofstrongdynamics.Mass shiftingorin-mediumbroadeningofvector
S
andaxial-vectormesonsmayoccurtherebuttheextentofsuchphenomenaisstilluncertain.Additionally,

5 glueball properties could also be modified in medium. Exploration of these issues is the second suggested
1 field of interest that can be pursuedat NICA.

] PACS. 12.39.Mk Glueball and nonstandard multi-quark/gluon states – 14.40.Be Light mesons
h
p
-
p 1 Introduction current quark masses can contribute, their effects are
e
currently unclear. This is particularly the case in lat-
h
[ Quantum Chromodynamics (QCD), the established the- tice QCD where the inclusion of dynamical fermions
ory of the strong interaction, is per construction of non- leads to the emergence of states additional to those

2 Abeliannature.Asaconsequence,gaugebosonsofQCD– present in pure gluodynamics with consequencesthat,
v
thegluons–areself-interacting.Sincethestrongcoupling e.g., (i) states experience overlaps and (ii) the scalar
8
is large at sufficiently small energies [1,2], the expecta- glueball is no longer the lowest state of the spectrum.
2
tion is that the non-perturbativeregionof strong dynam- Thentheidentificationofstatesismorecomplicated–
3
5 ics enables gluons to build more complex objects denoted and conclusions from lattice QCD in the scalar chan-
0 as glueballs [3,4,5,6,7,8,9,10]. Theoretical studies have nel somewhat conflicting: Refs. [16,19,20] do not ob-
. shown lively interest in glueballs using various methods serve large unquenching effects in simulations relying
1
to approach the non-perturbative regime of QCD: onstaggeredfermionswhileadifferentopinion(inline
0
6 withthe expectationofRef.[15])isadvocatedbysim-
– Ab-initio numerical calculations in lattice QCD have
1 ulations with clover fermions [18].
resulted in predictions of glueball spectra in quenched
: Leading-order mass generation of glueballs is in con-
v as well as unquenched approximations [11,12,13,14,
trasttootherstronglyinteractingparticles(i.e.,hadrons)
i 15,16,17,18,19,20,21].
X whose masses are predominantly generated by quark
– TheAdS/CFTcorrespondencehasyieldedresultsboth
r dynamics and thus susceptible to, albeit very small,
a on glueball spectra [22,23,24,25,26] as well as decays contributionoftheBrout-Englert-Higgsmechanism(see
of glueballs [27,28,29,30]; an exemplary approach in
examples for pions [42]; kaons [43]; ω-ρ splitting [43,
this direction is briefly outlined in Sect. 2.
44]; nucleons [45]).
– Effective approaches to QCD have upon implementa-
Therefore glueballs representa very important tool to
tionofrelevantsymmetriesofstrongdynamicsconsid-
explore strong dynamics.
ered not only glueball decays but also various mixing
– The spin of glueballs is integer since gluons are vector
mechanisms between glueball and non-glueball states
particles. Consequently the spectrum of mesons (i.e.,
obtaining a satisfactoryoverallagreementwith exper-
hadrons of integer spin) would be incomplete if glue-
imental data [31,32,33,34,35,36,37,38]; see also Refs.
balls were omitted from experimental searches.
[39,40,41].
In Sect. 3, some of the issues on the experimental side of
the glueball search are exemplified, together with sugges-
There are severalreasons for interest in glueballs:
tions for NICA in this regard.
– Glueballs are unique since their mass is, at the lead-
ingorder,generatedsolelyviaself-interactionofgluons Alreadyinvacuum,glueballscoupletonon-glueballstates
(puregluodynamics).AlthoughattheleveloffullQCD (possessingq¯q,q¯q¯qqandothervalencedegreesoffreedom).
2 Denis Parganlija: Glueballs and vector mesons at NICA
The expectation is that a coupling of modified strength
will remain at non-zero temperatures and densities. In However, irrespective of the lively theoretical interest in
that case, glueballs will influence q¯q states and the un- glueballs, the identification of these states in the physical
derlying phenomena of their in-medium behaviour, such spectrum is still outstanding.
asthechiral-symmetryrestoration.Itis,however,unclear
whatthisbehaviourexactlyentailssincevectorandaxial-
vector mesons may shift in mass or become broader in
3 Experimental ambiguities relevant for
medium but clear experimental evidence for this is still
glueballs: an example, and a suggestion for
outstanding. These issues together with further sugges-
tions for NICA are discussed in Sect. 4. Conclusions are NICA
presented in Sect. 5.
Reasonsforproblemsinexperimentalidentificationofglue-
balls are at least twofold:
2 Hallmarks of a glueball: an example
– Glueballs are expected to emerge starting at energies
A glueball state can be distinguished from other hadrons between approximately 1.5 GeV and 1.8 GeV where
byforexample(i)strongsuppressionintwo-photondecay thegroundstate,ascalar[51],ispredictedinnumerical
channels [46] and prominent presence in radiative decays simulationsofthespectrum[11].Historicallytherehas
[21]; (ii) decay patterns. Various approaches to glueball been a scarcity of precise experimental data exactly
dynamics (mentioned in the previous section) have been in the energy region where glueballs are expected to
applied in studies of glueball decays; in the following, a emerge[52].Althoughtherehasbeenanotablechange
recent approach based on the AdS/CFT correspondence in data availability [53,54,55], the amount of progress
is briefly discussed and its results for glueball identifica- is still not sufficient for an unambiguous identification
tion are presented. of these states.
– Glueball with a given set of quantum numbers will
The approach is based on the conjectured duality be- inevitablymix/interferewithnon-glueballstates(pos-
tween weakly coupled string theory (i.e., supergravity) sessing q¯q, q¯q¯qq and other valence degrees of freedom)
in an anti-de Sitter (AdS) space and a strongly coupled that have the same quantum numbers. The effects of
conformal field theory (CFT) in one dimension less [47].
The field theory possesses symmetries absent from QCD
(supersymmetry in addition to conformality); these are Table 1. Comparison of holographic scalar-glueball decays
removed by suitable compactifications in the full super- (theouterrightcolumn)obtainedinRef.[28]withexperimen-
gravity space [48] and the emerging U(Nc) gauge theory tal data for the two prime candidates for the scalar glueball,
(with Nc → ∞) may be used to explore the Yang-Mills the resonances f0(1500) and f0(1710). The ’t Hooft coupling
sectorofQCD.Then(holographic)glueballsareobtained (that is the only free quantity in the WSS Model, except for
as gravitonpolarisations in the supergravity background. theKaluza-Klein mass which sets theModel scale) was deter-
It was demonstrated in Ref. [22] that such an approach mined in two ways, by implementing the experimental value
leads to a glueballspectrum that is remarkablysimilar to of the pion decay constant or the lattice-QCD value of the
the one obtained in lattice-QCD simulations. string tension. This allows for theoretical uncertainties to be
estimatedandhenceholographicresultsarepresentedininter-
vals.AllexperimentaldataarefromPDG[52]exceptforthose
Studying glueball decays into q¯q states requires introduc-
tionofquarkdegreesoffreedom.Amethodtoincludechi- markedbyastarthatarefromRef.[63]wherethef0(1710)de-
caychannelswerecalculated assuminganegligible couplingof
ral quarks – the so-called Witten-Sakai-Sugimoto (WSS)
Model – was proposed in Refs. [49,50] by introducing N thatresonanceto4π.AllmassesareinMeV.Thef0(1710)res-
f onanceispreferredtohaveasignificantoverlapwiththescalar
(number offlavours)probe D8-andanti-D8-branesinthe
glueballbutaconclusivestatementinthisregardishampered
supergravityspacethatextendalongalldimensionsinthe
byexperimental uncertainties discussed in Sect. 3.
space except for a (Kaluza-Klein) circle. D-branes intro-
duceaU(Nf)×U(Nf)symmetryinthetheory;sinceD8- Decay Mexp. Γ/M (exp.) Γ/M (holography)
and anti-D8-branes merge at a certain point in the bulk
space,theoriginalU(N )×U(N )symmetryisreducedto f0(1500) (total) 1505 0.072(5) 0.027...0.037
its diagonal subgroup.fThis is infterpreted as a geometric f0(1500)→4π 1505 0.036(3) 0.003...0.005
f0(1500)→2π 1505 0.025(2) 0.009...0.012
realisation of chiral-symmetry breaking.
f0(1500)→2K 1505 0.006(1) 0.012...0.016
f0(1500)→2η 1505 0.004(1) 0.003...0.004
ItwasdemonstratedalreadyinRefs.[49,50]thattheWSS
Modelcandescribephenomenologyofq¯q statesatleastin f0(1710) (total) 1723 0.078(4) 0.059...0.076
a semiquantitatively correct way. Decays of dilaton glue- f0(1710)→2K 1723 0.047(17)* 0.012...0.016
balls were in turn explored in Refs. [28,29] where predic- f0(1710)→2η 1723 0.022(11)* 0.003...0.004
tions for decays of the scalar and tensor glueballs in the f0(1710)→2π 1723 0.009(2)* 0.009...0.012
f0(1710)→4π 1723 ? 0.024...0.030
2π, 4π, 6π, 2K and 2η channels have been made, as pre-
f0(1710)→2ω→6π 1723 seen 0.011...0.014
sented in Tables 1 and 2.
Denis Parganlija: Glueballs and vector mesons at NICA 3
Table 2. Decays of the holographic tensor glueball predicted Reactions(i)and(iii)allowforreconstructionoff0(1710)
by the WSS Model for two different masses, MT =2000 MeV –seeRef.[64]–whereasf0(1790)isreconstructedfromre-
and MT = 2400 MeV [28]. The former mass is chosen to ap- actions(ii) and(iv). Importantly,assumingf0(1710)and
proximately correspond to that of the f2(1950) resonance, a f0(1790) to be the same resonance leads to a contradic-
possible candidate for the tensor glueball due to its mostly tion: such a resonance would have to possess a pion-to-
flavour-blinddecaymodes;forthisstate,Γ/M =0.24(1)where kaon-decay ratio of 1.82±0.33 according to reactions (i)
Γ is the total decay width [52]. The value MT =2400 MeV is and (ii) and a pion-to-kaon-decay ratio < 0.11 according
chosenexemplaryasanelementoftheintervallforthetensor- to reactions (iii) and (iv) [61,62]. Decay ratios must be
glueball mass predictedbylattice QCD[11,14,15,17,20]. Just
independentoftheproductionmechanismforasingleres-
as for results presented in Table 1, the ’t Hooft coupling was
onance. The assumption that f0(1710) and f0(1790) rep-
determined in two ways: by implementing the experimental
resent a single resonance clearly leads to a contradiction
value of the pion decay constant or the lattice-QCD value of
in the value of the mentioned decay ratio; consequently,
the string tension. Holographic results are thus presented in
the employed data – obtained by the BES Collaboration
intervals in order to estimate theoretical uncertainties.
– prefer f0(1790) as a resonance distinct from f0(1710).
Decay MT (MeV) Γ/MT (holography) Nonetheless, additional inspection of this claim is by all
means needed in further experiments.
T →2ρ→4π 2000 0.135...0.178
T →K∗K∗ →2(Kπ) 2000 0.119...0.177
T →2ω→6π 2000 0.045...0.059 If the existence of the f0(1790) resonance is confirmed,
T →2π 2000 0.014...0.018 itwillmostcertainlyhaveimplicationsforglueballsearch
T →2K 2000 0.010...0.013 since its mass is within the interval in which the scalar
T →2η 2000 0.0018...0.0024 glueball is expected to appear according to lattice QCD.
T (total) 2000 ≈ 0.32...0.45
T →K∗K∗ →2(Kπ) 2400 0.173...0.250 NICA [65] program focused on the Spin Physics Detec-
T →2ρ→4π 2400 0.159...0.211 tor (SPD) [66,67] appears to be relevant for the issue of
T →2ω→6π 2400 0.053...0.070 f0(1790)butcouldalsodiscoverfurtherresonances.Ifthe
T →2φ 2400 0.032...0.051 Monte Carlo simulations of J/Ψ production rates at SPD
T →2π 2400 0.014...0.019 prove correct, then the yearly yield of these resonances
T →2K 2400 0.012...0.016 should amount to ∼ 107 events [66,67]. It would thus be
T →2η 2400 0.0025...0.0034 of the same magnitude as that of BES II [61,62], where
T (total) 2400 ≈ 0.45...0.62 the best available evidence for the existence of f0(1790)
has been presented – and then a careful reconstruction
ofresonancesin2π finalstatesemergingfromJ/Ψ decays
couldclarifywhetherf0(1790)exists.Newresonanceseven
suchinterferenceinexperimentaldatarendertheiden-
higherinenergymayalsobediscoveredorthoseforwhich
tification of resonances in general, and thus glueballs
thereis alreadyindication– f0(2020),f0(2100),f0(2200),
in particular, highly non-trivial [56].
f0(2330) [52] – could be confirmed.
Comparison of SPD with other running or planned pro-
Existingissuesinexperimentalglueballsearchescanbeil- grams is in order. Given the above data on f0(1790), two
lustrated by the following example relevant for the scalar sorts of production mechanisms are particularly relevant:
glueball. This state possesses quantum numbers IJPC = (i) e+e− (as at BES) and (ii) pp (since planned at SPD).
00++ whereI,J,P andC respectivelydenotetheisospin,
total spin, parity and charge conjugation. Particle Data Firstly, e+e− collisions at the VEPP-4M Collider have
Group (PDG) cites the existence of five IJPC = 00++ produced ∼ 7 million J/Ψ events, as reported by the
resonancesintheenergyregionupto∼1.8GeV:f0(500), KEDR Collaboration [68]. This could in principle enable
f0(980),f0(1370),f0(1500)andf0(1710).Theyareknown the reconstruction of f0(1790) but an even larger J/Ψ
as scalar isoscalar resonances [52]; for a brief review, see yield is expected at SPD.
Refs.[57,58].Claimshavebeenmade[59,60,61,62]thata Additionally, CMD-3 and SND Collaborations at VEPP-
sixthsuchstateexists,namelyf0(1790)–astateveryclose 2000canusee+e− collisionsforscansoftheenergyregion
tof0(1710)butwithadifferentdecaybehaviour:f0(1790) from hadron-production threshold up to 2 GeV but their
decays predominantlyinto pions whereas f0(1710)decays focus is currently on vector mesons only [69], and SPD
predominantly into kaons. could fill this gap.
Note further that, although the primary focus of Belle-II
There are four basic production mechanisms for f0(1710) [70] is on precision measurements beyond the Standard
and f0(1790) via J/ψ decays: Model, discoveries in non-perturbative QCD can be ex-
pected also from that source given the large expected lu-
– (i) J/ψ →φK+K−, minosity (larger than at SPD). Belle-II will rely on re-
– (ii) J/ψ →φπ+π−, construction of resonances from Υ(4S) rather than J/Ψ
– (iii) J/ψ →ωK+K−, decays; particles below 2 GeV may be nonetheless recon-
– (iv) J/ψ →ωπ+π−.
4 Denis Parganlija: Glueballs and vector mesons at NICA
structable but, given the large difference in mass and the Theconstant-rhoscenariois basedonanobervation,e.g.,
well-known issues of overlapping scalar states, great care from Linear Sigma Model with vector and axial-vector
willhavetobegiventoproperdataanalysis.Lowerstatis- mesons that the ρ meson – although consistent with a
tics should be sufficient for SPD to reach the same goal q¯q state [82] – actually has two contributions to its mass,
since the J/Ψ production is expected to be abundant. one from the chiral and another from the gluon conden-
sate;anoverallmesonstudy[37,78,79]thensuggeststhat
Proton-protoncollisions are nowadaysmost prominent at m is dominated by the gluon condensate rather than by
ρ
the LHC. It is clear that the LHCb [55], TOTEM [71] the chiral one. 1
and ALICE [72] Collaborations can draw on huge cross-
sections obtained at very large energies. Nonetheless, a Two questions are crucial: (i) the behaviour of the gluon
comparative advantage of the SPD program is the use of condensateinmedium;(ii)thebehaviourofvectormesons
polarised proton and deuteron beams that were of enor- in medium.
mous importance for meson discoveries in the past [56].
Generalconclusionfromarangeofapproachesisthatthe
Historically, proton-proton collisions have always repre- gluon condensate is virtually unchanged below a critical
sented a method of meson research with a large discov- temperature T whose value in lattice QCD is strongly
c
ery potential even at moderate beam energies [63] that dependent on whether pure gluodynamics is considered
has proven complementary to antiproton-proton [73] and or, in addition, effects of massive quarks. For pure Yang-
pion-nucleon[74]collisionsortophotoproduction[75,76]. Mills QCD, there is a sharpdrop of the gluon condensate
atT ≃260MeV;however,iflightquarksarepresentthen
c
My suggestion is thus that NICA Collaboration measure the condensate exhibits a more gradual decrease between
at SPD the number of events as a function of centre-of- temperatures of ≃ 130 MeV and ≃ 190 MeV [83,84,85,
mass energy for 2π, 2K and 4π final states at energies 86]. Effective models of QCD have found the gluon con-
above ∼ 1.5 GeV and carefully analyse the data for new densate to remain stable up to T ≃ 200 MeV [87,88,89];
resonances. Further final states can be analysed as the see also Refs. [90,91]. A similar result has been obtained
data become available. Glueball production may be co- from finite-T renormalisationgroup equations [92].
pious in any of these channels, with results presented in
Tables 1 and 2 suggesting a very prominent 4π coupling Measurements of in-medium vector mesons have so far
both forscalarandtensor glueballs.The potentialfor the obtained conflicting results on the issue of mass shift but
discoveryofnewresonancesthusappearstobelarge,with also on the related question of whether these resonances
consequences even for non-glueball states. experience an in-medium broadening [93,94,95,96,97,98,
99].
High-energy limit of QCD is dominated by a gluon-rich
4 Vector mesons and NICA
environment [100,101,102]. It is therefore quite possible
thatglueballsinfluencephenomenaemerginginthisphase
There are four established resonances in the JPC = 1−− ofQCD, particularly scalarand tensor ones [103]. Lattice
(i.e.,vector)mesonchannelintheenergyregionuptoap- simulationsinpureYang-MillsQCDhavefoundthescalar
proximately1 GeV: ρ(770),ω(782), K∗(892)andφ(1020) state to exhibit a mass decrease starting atT ≥200MeV
[52].IntheJPC =1++ (i.e.,axial-vector)channel,thees- withamassdropofapproximately300MeVandathermal
tablishedresonancesupto1.5GeVarea1(1260),f1(1285), decay width of ∼ 300 MeV at T = Tc [104]. The tensor
K1(1270),K1(1400)andf1(1420)withtheK1 statespos- massisclaimedtodecreaseonlyslightlybelow∼200MeV
sibly having noticeable admixture from the JPC = 1+− but, once T is reached,the mass drops by approximately
c
(pseudovector)channel[77].Phenomenologyofallofthese 500 MeV and a thermal width of ≃400 MeV is obtained.
resonances has been extensively studied in vacuum – see Similar results were obtained in lattice simulations pre-
Refs.[78,79]andrefs.therein;chiralpartnersamongthese sented in Ref. [105].
resonancescan offer insight into important phenomena of Additionally, T-matrix formalism of Ref. [106] finds the
high-energy QCD [80]. scalar glueball to start dissolving at T ∼ (1.3 − 1.5)T
c
whilethedissolutiononsetforthetensorisatT ∼1.15T .
c
CurrentexperimentalambiguitiesregardingmesonsinmediumAsthe temperatureincreases,the scalarglueballbecomes
canbe illustratedby the followingexample:fromthe side masslessatT ∼900MeVaccordingto Ref.[107];see also
of theory, general expectation is that the (axial-)vector Refs. [108,109].
masses will follow one of the following two scenarios:
Hence there are many theoretical predictions, and new
– The mass decreases to zero as the chiral condensate
vanishes (i.e., the chiral symmetry of QCD becomes 1 It has to be noted here that the mentioned expectation is
restored) – the ”Brown-Rho scenario” [81]. basedonexperimentaldatainvacuumthatsufferfrom uncer-
– The mass remains essentially constant or decreases taintiesdiscussedinSect.3.Forthisreason,improvedmeasure-
marginally as the chiral condensate vanishes – the so- mentsinvacuumphysicswouldenablemoreprecisetheoretical
called ”constant-rho scenario” [80]. predictions of in-medium meson properties.
Denis Parganlija: Glueballs and vector mesons at NICA 5
experimental measurements are needed. Glueballs, although theoretically expected to emerge as
bound states of gluons in the low-energy region of QCD,
Two of the planned experiments at NICA appear to be haveremainedelusive evenafter decades ofresearch.One
relevanthere:(i)MultiPurposeDetector(MPD)program ofthe mainreasonsis alackofpreciseexperimentaldata.
intendedtostudyhotanddensebaryonicmatterinheavy- Glueball search would be aided greatly if SPD @ NICA
ioncollisionsatacentre-of-massenergyupto11GeV[110, were to measure 2π, 2K and 4π (and other) final states
111] and (ii) Baryonic Matter at Nuclotron (BM@N), fo- in the energy regionwhere glueballs areexpected to start
cused on production of strange matter in heavy-ion col- emerging, i.e., above ∼1.5 GeV.
lisions at beam energies between 2 AGeV and 6 AGeV These measurements regarding vacuum strong dynamics
[112,113].MysuggestionisthatNICACollaborationper- wouldhavewiderimplications:sinceglueballscoupletoq¯q
form a careful study of in-medium spectral functions for states already in vacuum they can be expected to influ-
vector and axial-vector mesons listed at the beginning of enceq¯qin-mediumdynamicsaswell.Consequently,clearer
this section – in this way information can be obtained on dataonglueballsinvacuumwillpermitamoreprecisepre-
the mass shifts, decay properties and other phenomena diction of dynamics at non-zero temperatures and densi-
that can improve theoretical studies of chiral-symmetry ties–includingchiral-symmetryrestoration–whereaddi-
restoration. tional ambiguities are present, particularly regarding the
behaviourof vectorand axial-vectormesons suchas mass
A range of measurements has already been performed at shifts and in-medium broadening. Currently the possible
RHIC [114] and LHC [115] exploring high temperatures in-mediummodificationsofglueballsarealsounclear.Res-
and low baryon densities and at HADES [116] exploring olutionofthesequestionscanbeaidedbyprecisemeasure-
lower temperatures and moderate densities. The main in- [email protected]
terestofNICA/MPDandBM@Nisinthe regionofQCD appearstohavealargepotentialtodecisivelyincreaseour
phase diagram intermediate to the mentioned two, build- understanding of strong dynamics.
ing on the results obtained at SPS [117]. Hence future
measurements at NICA appear to open a unique possi- Acknowledgments.IamgratefultoF.Bru¨nner,D.Bugg,
bility to study in particular (axial-)vectormesons at high F. Giacosa and A. Rebhan for extensive discussions. This
densities and moderate temperatures. The Collaboration work is supported by the Austrian Science Fund FWF,
alsoestimatesthatcolliderexperimentsatMPDwillhave project no. P26366.
anearlyconstantacceptanceandoccupancy,unlikethefu-
tureFAIR/CBMexperiment[118]thatwillrelyonafixed
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