SnowMass2021 Workshop on Opportuni es in Hadron Spectroscopy
Quakonium and related observables from proton-proton to heavy-ion collisions
Elena G. Ferreiro IGFAE, Universidade de San ago de Compostela, Spain
E. G. Ferreiro USC Quarkonium & related observables from pp to AA SnowMass2021 16/12/2020 Old paradigm: the three systems (understanding before 2012)
Hot QCD ma er: This is where we expect the QGP to be created in central collisions
QCD baseline: This is the baseline for “standard” QCD phenomena
Cold QCD ma er: This is to isolate nuclear effects in absence of QGP, e.g. nuclear pdfs
E. G. Ferreiro USC Quarkonium & related observables from pp to AA 1 SnowMass2021 16/12/2020 New paradigm: small systems Totally unexpected: the discovery of correla ons –ridge, flow- in small systems pA & pp • Smooth con nua on of heavy ion phenomena to small systems and low density • Small systems as pA and pp show QGP-like features
Two serious contenders remain today: • ini al state: quantum correla ons as calculated by CGC • final state: with (hydrodynamics) or without equilibra on The old paradigm that • we study hot & dense ma er proper es in heavy ion AA collisions • cold nuclear ma er modifica ons in pA • and we use pp primarily as comparison data appears no longer sensible
We should examine a new paradigm, where the physics underlying collec ve signals can be the same in all high energy reac ons, from pp to central AA
E. G. Ferreiro USC Quarkonium & related observables from pp to AA 2 SnowMass2021 16/12/2020
Why quarkonia? A li le bit of history
Poten al between q-an -q pair 4 α V(r) = − s + kr V(r) grows linearly at large distances 3 r
Screening of long range confining poten al r at high enough temperature or density.
Debye screening radius λD(T) depends on temperature
What happens when the range of the binding force becomes smaller than the radius of the V(r) state? r > λD
different states “mel ng” at different temperatures due to different binding energies: Debye screening
Quarkonia as a QGP thermometer
E. G. Ferreiro USC Quarkonium & related observables from pp to AA 3 SnowMass2021 16/12/2020
5.2 Nuclear modification factor RAA 9 where the relevant initial conditions are changed by varying the viscosity to entropy ratio, h/s, and the initial momentum-spaceMeasuring nuclear anisotropy.effects The initial: the temperature nuclear is determinedmodifica on by requir- factor AA ing agreement with charged particle multiplicity and elliptic flow measurements. The model of Du, He, and Rapp usesNuclear a kinetic-ratemodifica on equation factor R to simulateAA the time evolution of bottomo- • RAA<1: suppression nium abundances in ultra-relativistic heavy2 p� ion collisions. It considers medium effects with temperature-dependent binding energies,� � and/�� a� lattice-QCD-based�� equation• R ofAA=1: no nuclear state for the effects fireball evolution. Within� the current = theoretical and experimental uncertainties, both models AA 2 pp • RAA>1: enhancement are in agreement with the results. Ncoll � � /�����
PbPb 368/464 µ b -1, pp 28.0 pb -1 (5.02 TeV) p < 30 GeV Original mo va on to measure quarkonium 1.2 T CMS |y| < 2.4 Υ Cent. in nuclear collisions (AA): Signal of QGP 1 68% CL 95% CL 0-100%Observable: RAA vs energy density ϒ (1S) ϒ (2S) ϒ (2S) 0.8 ϒ (2S) ϒ (3S) ϒ (3S)
AA • The 3 upsilon states are suppressed R 0.6 Υ with increasing centrality 0.4
0.2 RAA[Υ(1S)] > RAA[Υ(2S)] > RAA[Υ(3S)]
0 0 50 100 150 200 250 300 350 400 => Sequen al mel ng
Figure 5: Nuclear modificationE. G. Ferreiro USC factors for the U( 1S ), UQuarkonium & related observables from pp to AA (2S) and U(3S) mesons as a function 4 of SnowMass2021 16/12/2020 N . The boxes at the dashed line at unity represent global uncertainties: the open box for h parti the integrated luminosity in pp collisions and NMB in PbPb collisions, while the full boxes show the uncertainties of pp yields for U(1S) and U(2S) states (with the larger box corresponding to the excited state). For the U(3S) meson, the upper limits at 68% (green box) and 95% (green arrow) CL are shown.
Figure 7 compares centrality-integrated RAA values at psNN = 2.76 TeV to those at 5.02 TeV. The centrality-integrated R for U(1S) is measured to be 0.376 0.013 (stat) 0.035 (syst), to AA ± ± be compared with the result at 2.76 TeV, 0.453 0.014 (stat) 0.046 (syst) [21]. The suppression ± ± at 5.02 TeV is larger by a factor of 1.20 0.15 (in which only the T uncertainty was consid- ⇠ ± AA ered correlated and therefore removed), although the two RAA values are compatible within the uncertainties. The centrality-integrated results for the U(2S) and U(3S) states at 5.02 TeV are R (U(2S)) = 0.117 0.022 (stat) 0.019 (syst) and R (U(3S)) = 0.022 0.038 (stat) AA ± ± AA ± ± 0.016 (syst) (<0.096 at 95% CL). Despite having a bigger binding energy than the already mea- sured y(2S) meson [18, 19, 27], no U(3S) meson signal is found in the PbPb data, in any of the studied kinematic regions. This suggests a pT- and binding-energy-dependent interplay of different phenomena affecting quarkonium states that is yet to be fully understood [49].
Since the suppression is expected to be larger for higher temperatures in the medium, the RAA results for the U(1S) meson at the two different collision energies can provide information on the medium temperature. The temperatures reported in the model of Krouppa and Strickland shown in Fig. 6 are T = 641, 631, and 629 MeV corresponding to 4ph/s = 1, 2, and 3, respec- tively. For the model of Du, He, and Rapp, the temperatures are in the range T = 550–800 MeV. The models, which are also in agreement with the results at 2.76 TeV [12, 50], predict increases ...but the situa on is by far much more complicate pA 1.4
pPb p-Pb sNN = 8.16 TeV
R • There are other effects, not related to 1.2 ALICE inclusive J/ψ LHCb prompt J/ψ (PLB 774 (2017) 159 ) colour screening, that induce suppression 1 of quarkonium states 0.8 • These effects are not all mutually 0.6 EPS09NLO + CEM (R. Vogt) nCTEQ15 (J. Lansberg et al.) exclusive EPPS16 (J. Lansberg et al.) 0.4 CGC + NRQCD (R. Venugopalan et al.) CGC + CEM (B. Ducloue et al.) • They should be also taken into account in 0.2 Energy loss (F. Arleo et al.) Transport (P. Zhuang et al.) AA collisions Comovers (E. Ferreiro) 0 −5 −4 −3 −2 −1 0 1 2 3 4 5 y cms Figure 30: Comparison of the• ALICEModifica on [598] and LHCb of [599the] measurements gluon flux of the ini al-state nuclear modification effect factor ofw J/ Nuclearproduction PDF in in nuclei: nPDF shadowing pPb collisions at psnn = 8.16 TeV with several model calculations [25, 75, 600–604]. Note that the curves labelled nCTEQ15 and EPPS16 are obtained after reweighting the corresponding nuclear PDF sets using LHC heavy-flavour data. Figurew fromGluon Ref. satura on [598]. at low x: CGC Warning (by JPL): The J.Lansberg et al curves are reweighted nPDF;this should be state; and in fact I am not the first author ... Warning (by MW): point taken. However,• I lookedParton up and propaga on the reference is arxiv: in medium 1610.05382, where ini al you/final are firsteffect author w Coherent energy loss Warning (by JPL): Well the reference is incorrect. Just look : nCTEQ and EPPS16 have the same uncertainties; it’s only possible after •reweighting. Quarkonium- I will try to updatehadron the plot interac on with Acrobat. The final- correctstate ref is [effect26]. w Comover interac on w Nuclear break-up 1700 It is worth making remarks on some essential issues in the model calculations. Firstly, the fundamental 1701 mechanisms of the heavy-quark• QGP- pairlike production effects? in pA collisions could be quite di↵erent from that in pp 1702 collisions. In particular, when PT (mQ) or less and when one specifically addressed PT dependent E. G. Ferreiro USC ⇡O Quarkonium & related observables from pp to AA 5 SnowMass2021 16/12/2020 1703 quantities as oppose to integrated ones, the perturbative QCD collinear factorisation approach for quarko- 1704 nium production is no longer the most reliable theoretical approach [51, 52]. Remark (by JPL): Please verify 1705 the relevance of [51]. To simplify I would cite review. Maybe [35].As discussed in Secs. 2.2 and 4, the trans- 1706 verse momentum dependent (TMD) factorisation framework should take over the collinear factorisation for 1707 heavy-quark pair production when P m , which makes the nPDFs e↵ect unclear. T ⌧ Q 1708 For evaluating nuclear e↵ects in the TMD factorisation approach, we must clarify how to include 1/3 1709 nuclear size or A enhanced power corrections [605–607] into the leading-twist TMD factorisation ap- 1710 proach [608], although the power corrections in hadronic collisions cannot be factorised beyond the sub- 1711 leading power [67, 609], in general. Besides, we must understand how nuclear dependence comes into 1712 non-perturbative TMD distributions [610]. Interestingly, it has been clarified that the leading-twist TMD 1713 factorisation framework can be recovered by getting rid of higher body scattering corrections in the CGC 1714 framework [542, 611, 612]. Therefore, precautions are required to compare nPDFs with parton saturation 1715 e↵ects. We can study higher twist e↵ects by considering “clean” processes, such as Drell-Yan process in 1716 pA collisions, and semi-inclusive nuclear DIS at the Electron-Ion Collider. See Sec. 5.2.5 for experimental 1717 prospects. 1718 It has been argued that if the quarkonium is produced at a very forward rapidity the hadronisation of the 1719 pair takes place outside of the colliding heavy ion (see e.g. [613] and references therein). Multiple scattering 1720 of the produced pair in the nuclear medium could enhance its invariant mass so much (beyond the DD¯ or 1721 BB¯ mass threshold) to prevent the pair from binding leading to a threshold sensitive suppression [614].
61 20 CHAPTER 1. FROM QUANTUM CHROMODYNAMICS TO THIS THESIS 1.2. J/y PRODUCTION IN HEAVY-ION AND PP COLLISIONS 19
393 culations, one can compare to leading-order calculations like the ones implemented in 394 PYTHIA. As explained in the previous section, In LO and NLO order NRQCD models, 395 the cc¯ pair is a short distance perturbative process via color-singlet or color-octet chan- 396 nels. In the color singlet channel no gluon radiation is emitted. On the other hand, the
p = 397 color-octet quark-antiquark emits a soft gluon radiation. in pp collisions at s 7 TeV. The measurements are shown as a function of pT and in several bins of rapidity. Cal- 4 4 4 culations from POWHEG [152] (matched398 In to NLL’ PYTHIA calculations, [151]) and MC@NLO a [ hard47, 153] gluons (matched to is HERWIG first produced[46]), in the short-distance process with are found to reproduce the data. Measurements from both lifetime- and lepton-based tagging methods are shown. 0.30 0.300.30a z(J/ ) distribution for each of the five mechanisms.0.300.300.30a z(J/ ) distribution for each of the five mechanisms.0.300.30a z(J/ ) distribution for each of the five mechanisms.0.30 399 virtualityB&K of order of a jet energyFrom scaleB&K the GFIP (EJ). calculations, The gluon we know is as a allowed functionFrom of B&K the to GFIP shower calculations, until we know one as a of functionFrom of the GFIP calculations, we know as a function of 2.2.4. Prompt charmonium 0.25 0.250.25z the fraction of J/ that survive the muon cut and0.250.250.25z wethe fraction of J/ that survive the muon cut and0.250.25z wethe fraction of J/ that survive the muon cut and0.25 we 400 In this section, we show and discuss athe selection gluons of experimental in the measurements shower reaches of prompt charmoniumapply a virtuality this correction production to comparable our analytic calculations. to two Theapply times this correction the to mass our analytic of calculations.the c Theapply this correction to our analytic calculations. The 0.20 0.200.20z(J/ ) distributions from each mechanism are weighted0.200.200.20z(J/ ) distributions from each mechanism are weighted0.200.20z(J/ ) distributions from each mechanism are weighted0.20 at RHIC and LHC energies. We thus401 focusquark. here on the The production gluon channels then which hadronizes do not involve beautyproducing decays; these a J/y. were discussed in the Section 2.2.3. 0.15 Figure 1.15:0.150.15by Left: the factors Prompt in Eq. J/ (2)y asyield before. as The measured FJF is appropri-0.150.15 by0.15by the LHCb factors [57] in Eq. at (2) 7 as TeV before. compared The FJF is to appropri-0.150.15by the factors in Eq. (2) as before. The FJF is appropri-0.15 402 These calculations can bedifferent implemented theoryate for predictions:n-jet in crossPYTHIA sections Prompt likeusing Eq. NLO (1). Inclusive two NRQCD methods. FJFsate [59], for n-jet Direct cross The NLO sections first CSM like is Eq. [60], Gluon (1). Direct Inclusive FJFsate for n-jet cross sections like Eq. (1). Inclusive FJFs Historically, promptly produced J/ and (2S)0.10 have always been studied in the dilepton0.10 channels.0.10[26–29] di Except↵er by a for contribution the from out-of-jet radiation0.100.100.10[26–29] di↵er by a contribution from out-of-jet radiation0.100.10[26–29] di↵er by a contribution from out-of-jet radiation0.10 PHENIX, STAR and ALICE experiments, the recent studies in fact only considerNNLO dimuons⇤ whichCSMthat o [61]↵ iser power a and better suppressed Prompt signal- for NLOR O(1) CEM [37]. [62]. Right:that is power Polarisation suppressed for parameterR O(1) [37].lq for that is power suppressed for R O(1) [37]. 403 Fragmentation0.05 Improved PYTHIA0.050.05(GFIP), where events⇠ corresponding0.050.050.05 to hard⇠ produc- 0.050.05 ⇠ 0.05 over-background ratio and a purer triggering. There are manyGFIP recentFJF experimentalprompt studies. J/y from InFig. Figure 2LHCb shows9,GFIP we [58]the show predicted comparedFJFz(J/ to) distributions different model forFig. 2 predictions: showsGFIP the predicted directFJFz(J/ NLO) distributions CSM forFig. 2 shows the predicted z(J/ ) distributions for / / p = 4 only two of these. First we show404 d dptionT for prompt0.00 of c Jareat generateds 7 GeV as measured using[63] and by MadGraph three LHCb0.000.00the NLO three compared choices NRQCD [68], to of a LDME’s few calculations then in TablePYTHIA I [63, using 64, theis0.00 65]. GFIP0.000.00the used three choices to shower of LDME’s in the Table event I using the0.00 GFIP0.00the three choices of LDME’s in Table I using the0.00 GFIP predictions for the prompt yield from the CEM and from0.2 NRQCD0.4 at NLO0.6 9 as well0.8 as the direct(gray) yield0.2 and0.210 FJFcompared0.4 (red)0.4 methods, to 0.60.6 which0.8 are0.8 in good agree-(gray)0.20.2 and0.2 FJF0.40.4 (red)0.4 methods,0.60.60.6 which0.80.80.8 are in good agree-(gray)0.20.2 and FJF0.40.4 (red) methods,0.60.6 which0.80.8 are in good agree- 0.2 0.4 0.6 0.8 ? 0.30 a0.30 NNLO0.30 CS evaluation. Our point405 heredown is to emphasise0.300.300.30 to a the scale precision of of the2m datac, and where to illustrate0.30 jetsment.0.30 that are Uncertainties at low reclustered and mid are due to the using LDMEs jet only.0.30 algorithms0.30ament. Inz(J/ Uncertainties) distribution like are fordue each the to of anti- the the LDMEs fivek mechanisms.T. only.0.30ment. In Uncertainties are due to the LDMEs only. In the case of Ref. [13], the errors in Table I are supple-Fromthe case the of GFIP Ref. calculations, [13], the errors we inknow Table asa I arefunction supple-the of case of Ref. [13], the errors in Table I are supple- pT –which is the region where heavy-ion studies areChao carried et out– al. none of⇠ the models can simply be ruledChaoB&K out et owingal. to Chao et al. 0.25 0.250.25 406 The0.25 second0.250.25 method is the Fragmentation0.250.25 Jet Function (FJF), where0.250.25 the jet fragmentation 0.25 their theoretical uncertainties (heavy-quark mass, scales, non-perturbative parameters, unknownmented QCD with and an relativistic error correlation matrix [40]. In Ref. [12]zmentedthe fraction with an of errorJ/ correlationthat survive matrix the muon [40]. cut In Ref. and [12]mented we with an error correlation matrix [40]. In Ref. [12] 384 3 [8] 3 [8] apply thisPYTHIA correction to our analytic3 [8] calculations.3 [8] The 3 [8] 3 [8] 0.20 0.200.20 0.200.200.20 nonprompt0.20 J/a0.20 fixedy to relationship the NRQCD between predictions the S1 and implementedPJ LDMEs0.20a fixed in relationship between8. The the nonpromptS1 and PJ re-LDMEsa fixed relationship between the S1 and PJ LDMEs corrections, ...). Second, we show407 the fractionfunctions of J/ from areb combineddecay for y close with to 0 at hardps =0.207 events TeV as function generated of at LO. It starts0.20z(J/ ) backwards, distributions from each by mechanism resum- are weighted0.20 385 sults are consistentis required with to obtain the unpolarizedPYTHIA J/8 prediction,. This constraint whereis is required both to obtaindataand unpolarized simulationJ/ . This show constraintis is required to obtain unpolarized J/ . This constraint is pT as measured by ALICE [108], ATLAS [170] and CMS [171]. At low pT, the di↵erence between the inclusive by the factors in Eq. (2) as before. The FJF is appropri- 0.15 0.150.15 408 0.150.150.15 0.15taken0.15 into account when computing the uncertainty0.150.15 duetaken into account when computing the uncertainty0.15 duetaken into account when computing the uncertainty due ming the logarithms386 of mJ/y/EJ from the scale of 2mc to EJ. MadGraph then continues and prompt yield should not exceed 10% – from the determination of the bb,a it sizeable is expected jetto to theactivity be LDMEs. a few accompanying percent These constraints at significantly the J/y. reduce However,ate theto the for LDMEs.n for-jet cross the These sections prompt constraints like component, Eq. significantly (1). Inclusive reduce a FJFsto the the LDMEs. These constraints significantly reduce the 0.10 0.100.10 0.100.100.10 0.100.10 0.10 RHIC energies [111]. It however steadilywith grows the with factorizationpT. At the highest p387T withreacheddiscrepancy LO at the perturbation LHC,0.10uncertainty is seen the majority between in the ofpredictions processes. the data and relative the to LO naively NRQCD-based adding0.10[26–29]uncertainty di↵er inprediction by the a contribution predictions implemented relative from out-of-jet to naively in radiation0.10 addinguncertainty in the predictions relative to naively adding inclusive J/ is from b decays. At p 10 GeV, which could be reached in future quarkoniumuncertainties measurements in Table in I in quadrature. Other sourcesthatuncertainties is power suppressedin Table I for in quadrature.R O(1) [37]. Other sourcesuncertainties in Table I in quadrature. Other sources 0.05 0.050.05 ...but the situa on is by far much more complicateT ' 0.050.050.05 GFIP FJF388 PYTHIA 8, which0.050.05 includesGFIP both color-octetFJF and color-singlet 0.050.05 mechanisms.GFIP FJF Prompt⇠ pp J/y are0.05 Pb–Pb collisions, it is already 3 times higher than at low p :1J/ out of 3 comes from b decays.of uncertaintyGFIP such as scaleFJF variation have not beenof in-Fig. uncertainty 2 shows such the as predicted scale variationz(J/ ) have distributions not beenof for in- uncertainty such as scale variation have not been in- T 4 0.00 0.000.00 0.000.000.00 observed to0.00cluded. be0.00 much Estimating less isolated theory uncertainties in data than reliably predicted in0.000.00the cluded. three by Estimating choices LO NRQCD. of LDME’s theory uncertainties in Table I using reliably the0.00 inGFIPcluded. the Estimating theory uncertainties reliably in the 0.2 0.4 0.6 0.8 0.20.2 • 0.40.4Fragmenta on0.60.6 0.80.8 of J/0.20.2ψ0.2 in jets: 0.40.40.4 0.6J/0.60.6ψ much0.80.80.8 lessabsence isolated0.2 of0.2 a complete0.40.4 in data factorization0.60.6 theorem0.8than0.8 is dipredicted cult.(gray)absence0.2 and0.2 of FJFa complete 0.4 (red)by0.4 LO NRQCD methods, factorization0.60.6 which theorem0.8 are0.8 in good is di agree-cult.absence0.2 of a complete0.4 factorization0.6 0.8 theorem is di cult. 4 0.300.30 3.50.300.30 0.3 0.303.50.30aFor0.30z(J/ example,) distribution using the for FJF each method, of the the fiveµ mechanisms.dependence0.300.303.50.30ment.For example, Uncertainties using the are FJF due method, to the LDMEsthe µ dependence only.0.30For In example, using the FJF method, the µ dependence σ
B 1 / 10 f rience with single inclusiveFrom the LHC GFIP data calculations, [29], oneLHCb we expects know as a function of σ Dataof the (syst) FJF shouldDPS be cancelled by µ dependence in hardtheof the case FJF of should Ref. [13], be cancelled the errors by inµ Tabledependence I are supple-in hardof the FJF should be cancelled by µ dependence in hard 3.0 BodwinB&K et al. ALICE, |y |<0.9 pp, s3.0=7 TeV ChaoBodwin et al.et al. 3.0 Bodwin et al.
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dy agreementCMS, |y |<0.9 with data at large p . It is very interesting to ! 0.7 J/ψ 0.2 z(J/ ) distributions⊥ from each mechanism are weighted Ψ
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However, 0.050.05 0.050.05 333 of jet-grooming techniques0.050.050.05 might also be helpful⇠ in further removing0.050.050.05uncertainties contributions in Table of I softin quadrature. radiation, Other and sources0.05 0.5 GFIP 0.3 FJFthe small x formalism0.5 [50]. SinceGFIPGFIP leading orderFJFFJF collinear 0.5 GFIP FJF 334 allow for an improvedit convergenceFig. is not 2 clear shows how ofthe estimate experimental predicted thesez(J/ uncertainties. studies) distributions and theoreticalofit for isuncertainty not clear calculations. how such estimate as scale these variation uncertainties. have not beenit in- is not clear how estimate these uncertainties. FIG. 2. J/ψ differential cross section as a function of J/ rapidityψ producedfactorization results for heavy quark pair production are 0.000.00 at LHC. 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LHCb data than default PYTHIA shown in Ref. [1]. 305 tweencomplemented the two formalisms. with subsequent In the parton low showering.p⊥ region, The a further observable measured in both experiments is the 0.30 0.30 0.30 0 0.2 0.4 0.6 0.8 1 0.30 3360 Multiplicity-dependentrefinement of our formalism3.50.30ment.This studies gives Uncertainties will of support include quarkoniajet to are resummation the due production picture to the of LDMEs of quarkonium give insight only.0.30 pro-ForThis In into example, gives the potentialsupport using the to correlations the FJF picture method, of between the quarkoniumµ dependence pro-This gives support to the picture of quarkonium pro- unintegrated pdfs at large x is important. Note that this 306 1 10 p (GeV/c) = / / logarithmstransverse momentum of p⊥/M for fraction,t p⊥ z MP [52–54].P , carried outz by(J/ theψ ) quarkonium state J inside the correspond- FIG. 2. Predicted z(J/ ) distribution337 hard using (heavy-quark GFIP (gray)FIG. production) 2.theduction Predicted case≪ in of Ref.and Ref.z(TJ/ [33] soft[13],)T distribution and the(charged this errors letter. using in particle Table GFIP The LDMEsI (gray)multiplicity) areFIG. supple- 2. fromofduction Predictedthe processes.FJF in shouldRef.z(J/ [33]) be distribution It and cancelled improves this letter. usingby µ ourdependence GFIP The under- LDMEs(gray) in hardfromduction in Ref. [33] and this letter. The LDMEs from matching condition allowed us to fix the radiusChao Retp al.which Most of the experimental3.0 Bodwin data presented et al. are for inclu- NLL’: a hard gluon is first produced 0.25 0.25 0.250.25 307 ing jet. This observable0.25 is indicative of the fragmenting parton’s momentum0.25 carried by the quarkonium was the only normalization parameterand FJF (red) in Eqs. for the (2) three and choices (6)338 ofstandingsive LDMEJ/ inψ Tableofproduction. the 1 andand initial FJFmentedglobal These states (red) fitsfor includewith of the [5, hadronic an three6] error giveJ/ choicesψ worsecorrelation’s collisions produced of agreement LDME matrix such fromin Table than [40]. as the1 multiparton Inand fitsRef. FJF from [12]andglobal (red) soft interactions for fits functions the [5, three 6] give choices that (MPI). worse have of agreement LDME Figurenot been in Table2 than computed.and 1 the and3 fits Note fromglobal fits [5, 6] give worse agreement than the fits from –theapparentOur interpreta onαs dependence(a) the cancels of R LHCb measurements out whenrelies Eq. of zon( (4)J/339 ).the308showBstate.-meson assump on the Theoretical normalised(b)decaysthe as predictions LHCb well2.5 of cc aRefs. yields fixed measurements as [12, promptrelationship for ofproduced 13]. the quarkonia The LHCb of productionz between(LHCbJ/ data). production data havebefore the of is3 beenJ/S a[8]ψ decreasingand’s. provided at the3 mid-P [8]the QGP functionLDMEs in LHCb and [78thatRefs.] forward-rapidity measurements by since [12, J/ using the13].ψ fragmentation-jet-produced normalization The of z( LHCbJ/ as). a data of function at theoretical islater a decreasing of mes curves the function is fixedRefs. [12, 13]. The LHCb data is a decreasing function 0.20 0.20 is substituted in these equations. It0.20 is0.20 thereforeAA striking The latter includes feeddown0.20 from higher excited char-1 J 0.20 340 chargedFigure particle 1.16: multiplicity z distributions at mid-rapidity for dpromptNch/d⌘ for (left)pp andcollisions nonprompt at ps = (right)5.02 and J/ 13y compared TeV, respec- to that our results explain both the overall normalization 309 moniumfunctions. states as well2.0isof required asz(J/ direct) to as obtainJ/z(J/ψ production.) unpolarized1. ThisJ/ How- is. a This property constraint ofto theof is thez(J/ LHCb) as data,z(J/ any) scale1. Thisvariation is a that property a↵ects of nor-of thez(J/ ) as z(J/ ) 1. This is a property of the 341 tively [82]. The quarkonium production increases linearly as a function of multiplicity at forward rapidity at Y = 0 and the relative normalization at forward ra- ever we only considered[1] direct J/[8]ψ production! contribu-[8] [8] [1] [8] ! [8] [8] [1] [8] ! [8] [8] 0.15 0.15 / 0.150.15 p = 310 ↵ predictions0.15 obtainedtaken3 into1 account from whenPYTHIA computing8. The3 the (DPS) uncertainty3 double0.15 duemalization3 and1 (SPS) but not single the shapes parton of the3 scatteringz(J/ ) distribution3 3 1 3 3 Figure 9: (a) Prompt J yield as measured by LHCb [172] at s 7 TeV compared342 towhile di erentAs at theory shown mid-rapidity, predictions in Fig. 1, referred forS theJ predictionsand/ to, asS a “prompt fasterFJFs, that thanNLO rely but onnot linear the the fragmentation increaseS and isP observed pictureFJFs,S inand NRQCD bothS for reproduceFJFs, the p but-integrated many not the S andandp P- FJFs,S and S FJFs, but not the S and P FJFs, pidities after matching the pdfsof the smoothly? data in these to the bins. dipole tion in our theoryof the results.1.5 data1 in these Nevertheless,0 bins. the compari-1 ofJ the data1 in these0 bins. T 1 T J 1 0 1 J NRQCD”[173amplitude], ”DirectNLO at x CS”[=057.,01.58], “DirectFigure NNLO CS” 1.17:[61, 62] and Predicted “Prompt NLO311dison↵important CEM”erential is z meaningful. [distribution174 features]. cases. (b) Fraction Noof Firstly, thetowhich strong of data.the J/ LDMEs. using theactuallyfrom However,energyB B-meson as These diverge measuredand GFIP the constraintsquarkoniumquantitative decay as z (gray) contribu- significantly1. agreement state In orderand dependence strongly reduce to FJF obtain thewillwhich depends (red) not is actuallyobserved contribute on for the diverge used atthree to forwardthe values as uncertainty.z choices of rapidity.1. In Especially order of to atobtain lowwhich actually diverge as z 1. In order to obtain 0.10 0.10 • Quarkonium vs Our0.10 second0.10mul plici es method, which we can refer tocontributions asimprove the FJFOur0.10 second our to the method, understanding prompt which prediction we refer to are as of the also FJFthe shownOur0.10 second ini al [66]. method, & final which we refereffects to as the FJF by ALICE[108], ATLAS [170] and CMS [171] at ps = 7 TeV in the central rapidity region.tion in the small p⊥1.0uncertaintyregion is small,in the predictions of order! lessrelative than to3 naively[8] adding3 values[8] of z, the underlying event! and double3 [8] parton scat-3 [8] ! 3 [8] 3 [8] 312 negligible polarization at high p ,the S and Pnegligible polarization at high p ,the S and Pnegligible polarization at high p ,the S and P method, employs FJFs combined with10%.LDMEs. hard Secondly, events Even-though gen-method, the LDMEs these employs exploratory in FJFs [4] combined are studies obtained have with given hardT by fit-a events great1 gen-insightmethod, intoJ employs the quarkonium FJFs combined production with hardT events1 gen- J T 1 J LDMECGC%NRQCD and the LHCb measurementsuncertainties of z in [67]. Table I in quadrature. Other sourcestering give additional theoretical uncertainties. However, 0.05 0.05 S &0.2 TeV for RHIC NLO0.05 NRQCD0.05 313 ting prompt J/ψ data.0.05LDMEs Thus of feeddown Refs. [12, contributions 13] have relative are signs such0.05 thatLDMEs of Refs. [12, 13] have relative signs such thatLDMEs of Refs. [12, 13] have relative signs such that 105 erated by MadgraphGFIP at LO. In calculatingFJFat large the momentum, FJFs, log-erated more0.5 by Madgraph detailed studiesGFIP at LO. are In necessary calculatingFJF to the obtain FJFs, a more log-erated comprehensive by Madgraph at picture. LO. In calculating the FJFs, log- S &7 TeV for LHC For Ψ' Ini al- 100'LHCb,2(y(4.5 already389 roughly estimatedof uncertainty in our such results. as scale With variation1 [8] the ex- have not beenit in- is not clear how estimate these1 [8] uncertainties. 1 [8] 4 For J!Ψ they roughly cancel, so the S dominates productionthey roughly cancel, so the S dominates productionthey roughly cancel, so the S dominates production 10 artihms of m /EJ are resummedpressions using leading in [11] orderartihms for the of higherm /E charmoniumJ are resummed states, using0 a fullyleading orderartihms of m /EJ are resummed using0 leading order 0 0.00 0.00 ALICE,0.000.00$y$(0.9J/ /0.00.00 cluded.+ ⇡⇡J/ Estimating theory uncertainties reliably in0.00 the J/ For excited states, there is an interestingATLAS, alternative$y$(0.75 to the sole dileptonconsistent channel,390 An treatment namely alternative J of prompt to. the ThisJ/ standard isψ particu-production production data is approach,All also three based choices on of LDMEs NRQCD, give better is the agreement J/y to # and J/ 0.2are unpolarized.0.4 0.6 The same0.8 cancellation hereand al- J/ are unpolarized. The same cancellation hereand al- J/ are unpolarized. The same cancellation here al- 0.2 0.4 0.6 0.8 0.2 0.4103 0.6 0.8 DGLAP0.2'LHCb,2 equations(y0.2(0.24.5 to evolve0.40.4state the fragmentation0.6 0.6 0.80.8 functionsDGLAP equations0.2 to evolve+0.4 the fragmentation0.6 0.8 functionsDGLAP equations0.2 to evolve0.4 the fragmentation0.6 0.8 functions 0.1'PHENIX,$y$(0.35 feasible in the near future.absence Asof a a complete first step, factorization we compare theorem is di cult. GeV / +⇡⇡ µ µ +⇡⇡ the LHCb data than default PYTHIA shown in Ref. [1]. larly relevant since! more than 50% of the (2S)0.1'STAR, decay$y$( in1 this channel. The decay chain (2S) J 2 409 391 ′ lows the z(J/ ) distribution go to zero as z(J/ ) lows1. the z(J/ ) distribution go to zero as z(J/ ) lows1. the z(J/ ) distribution go to zero as z(J/ ) 1. nb 10 from the' scale 2m($c$(to the jet energyour scale, resultsproductionEJ . for Mad- thefromψ the withindi scalefferential 2m partonc to cross the showers section jet energy as [67],scale, a func-E orJ . within Mad-from the jets. scale In 2m thisc toapproach, the jet energy analytical scale, EJ . Mad- cal- 0.30 " + 0.013.50.30PHENIX,1.2 y 2.2 0.30!For example,! using the FJF method, the µ dependence!This gives support to the picture of quarkonium! pro- !
dy µ µ / effects+ ⇡⇡ : is four times more! likely than (2S) . The final state J istion also of thep⊥ onewith via data which inSuch the Fig. aX cancellation3.(3872) In this was comparison, does first not occur we for set the LDMEs fromSuch a cancellation does not occur for the LDMEs fromSuch a cancellation does not occur for the LDMEs from
! 10 graph calculates the remaining terms in the factorizationgraph calculates the remaining terms in the factorizationgraph calculates the remaining terms in the factorization 410! 392 culationsFIG. were 2.of thePredicted performed FJF shouldz(J/ ′) be todistribution cancelled next-to-leading-log-prime byusingµ dependence GFIP (gray) in hard (NLL’). To understand NLL’ cal- dp The z distributions predictedthe charm quark by mass this to be approach,m = M /2 1 calculated.84 GeV and using both GFIP and FJF meth- ! 3.0 Bodwin et al. ψ duction in Ref. [33] and this letter. The LDMEs from seen at pp collidersΣ [175, 181]. ATLAS released [136] the most precise study to date of (2S)the production global fits up so to thep z≈of(J/ ) distribution starts to turnthe global fits so the z(J/ ) distribution starts to turnthe global fits so the z(J/ ) distribution starts to turn 0.25 2 theorem0.25 to LO in perturbation theory. This does nottheorem in- 0.25 to LO in perturbationT theory. This does nottheorem in- to LO in perturbation theory. This does not in- d 1. Satura onused the CO LDMEsand FJFand extracted (red) soft for functions the in three [49]. choicesthat Theory have of LDME not and been indata Table computed. 1 and Noteglobal fits [5, 6] give worse agreement than the fits from agree well. However,up if weat large set mz(J/=1)..5GeVforψ′,the up at large z(J/ ). up at large z(J/ ). !1 411 clude NLL’2.5 resummation for the remaining terms in theclude NLL’ resummation for the remaining terms include the NLL’ resummation for the remaining terms in the 10 ods are shown in Fig. 1.17 forthe LHCb threethat measurements since choices the normalization of z(J/ of). NRQCD of theoretical curves LDME: is fixedRefs. [12, B&K 13]. The [69, LHCb 70], data is Chao a decreasing et function 0.20 factorization0.20 thereom, howeverin high theresultsz( J/ )dependence overshootfactorization the0.20 data.To summarize, thereom, As noted, however we one have anticipates theanalyzedz(J/ the)dependence the recent LHCbfactorization dataTo summarize, thereom, however we have the analyzedz(J/ the)dependence recent LHCb dataTo summarize, we have analyzed the recent LHCb data 9 10!2 2.0 sensitivity to the quarkto the mass LHCb in the data, short any scale distance variation cross that a↵ects nor-of z(J/ ) as z(J/ ) 1. This is a property of the Let us stress that the NRQCD band in Figure 9(a) is not drawn for pT lower than 5 GeV because such a NLO NRQCD fit overshoots the data 412 al.of the [65], cross section and is controlled Bodwin primarilysections et by al. to the be [71]. FJF. oofffset the by crosson When theirJ/ sectionproduction dependence compared is controlled within in theprimarily jets. LDMEs. Weto usedby the the a combination FJF. LHCbof the crosson[1]J/ data sectionproduction[8] is for controlled within prompt! primarily jets. We J/by used[8] y the aat FJF.combination[8] on J/ production within jets. We used a combination 0.15 0.15 ′ 0.15malization but not the shapes of the z(J/ ) distribution3 1 3 3 in this region and since data0 at low5 pT are10 in fact not15 used in20 this fit. For25 a complete30 mul plicity discussionHowever, of NLO for CSMψ/NRQCD, only two results linear for the combinationspT-integrated of the three S1 and S0 FJFs, but not the S1 and PJ FJFs, The energy1.5 distribution of hard partons is combined withofThe the′ energy dataof Madgraph, indistribution these bins. PYTHIA, of hard partons and LO is NRQCD combined fragmentation withThe energyof Madgraph, distribution PYTHIA, of hard partons and LO is NRQCD combined fragmentation with of Madgraph, PYTHIA, and LO NRQCD fragmentation p!"GeV# CO LDMEs of ψ canwill be not determined contribute to [49]; the uncertainty.because it Especiallyis at low yields, see [67]. As regards the CEM curves, an uncertainty band should also be drawn (see for instance [169]). ′ Excitedwhich over actually ground diverge as statez 1. to In order to obtain 0.10 Satura on physics at low 413 13the FJFs TeV,0.10 for theseanti-pT kT jets calculations [39] with R =0.5 to showed producethe Our FJFs0.10functions second a forψ better anti-3 method, first[8]kT jets introduced agreement which [39] with we in referR Ref.=0 to [33]′.5 withas to as the produce well FJFthe data as anFJFs ap-functions than for anti- firstkPYTHIAT jets introduced [39] with8. inR Ref.=0 [33].5 to as produce well as anfunctions ap- first introduced in Ref. [33] as well as an ap- 10 ↵ 1.0 pp? unconstrained, we setvalues( ofPz0, the) underlying=0here.Thus event andψ doublehas parton scat- ! 3 [8] 3 [8] The expected di erence′ between prompt and direct is discussed later on. ⟨O ⟩ negligible polarization at high p ,the S and P FIG. 3. The ψ (top curve) and J/ψ (other four curves) differ- larger systematicmethod, uncertainties employs FJFs relative combined to J/ withψ that hard sub- events gen- T 1 J collinear factoriza on at high p ALI-PUB-348246 tering give additional theoretical uncertainties. However,measure final-state effects 0.05 ential cross section as a function414 of p⊥.Datafrom[37,40,45–0.50.05 T sume the sensitivityy 0.05 of results to the quark mass. Based LDMEs of Refs. [12, 13] have relative signs such that In this newGFIP approach,FJF the J/ is produced′ at later times than what is assumed in the clas- 48]. NLO NRQCD predictions are taken from [49].20 on our presenterated work, by all Madgraph three ψ atCO LO. LDMEs In calculating can be the de- FJFs, log- Figure 2: Normalised inclusiveit is/ not J/ clearyield how at mid-rapidity estimate these as uncertainties. a function/ of normalised charged-particle pseudorapidity1 [8] density at terminedFigure 1: Comparisons from a global of the z( fit.J ) ALHCb consistent measurements treatment to the predicted of allz(J ) distributionthey with roughly the fragmentation-jet-functions cancel, so the S dominates production 0.0 mid-rapidity for theartihmsp -integrated of mJ/ (left)/EJ andarep resummeddi↵erential using (right) leading cases. order The data [82] are compared to theoretical0 predictions from 0.00 E. G. Ferreiro USC 415 0.00 charmonium(red)Quarkonium & related observables from pp to AA for the three and choicesT bottomonium0.00 of LDMEsAll three (left, choices states center,T right). ofis inLDMEs The progress gray give bands better[25]. correspond agreement to a6 modified to parton showerSnowMass2021 16/12/2020 approach where sic picture.0.2 This0.4 doesn’t0.6EPOS-30.8 [83 just], the coherent change particle J/ productiony production model (CPP) [84], in the pp percolation collisions. modeland J/ [85are], the unpolarized. It CGC can model alsoThe [86 same], the changecancellation 3-Pomeron here al- 0.2 In Fig.0.4 3, we0.6 compare0.8 our results for 0.2J/ψ diff0.4eren- 0.6In the latter0.8 case,DGLAP we equations anticipate0.2 to evolve0.4 a larger the fragmentation0.6 contribution0.8 functions CGCthe modelquarkonium [87] fragmentation and pythiathe8.2 is LHCb only [88 implemented]. data than at default the end ofPYTHIA the shower. shown For details in Ref. see [1]. [78]. tial cross section as a function of p⊥ with experimen- from the logarithmicfrom the resummation scale 2mc to of the [52–54]. jet energy scale, EJ . Mad- lows the z(J/ ) distribution go to zero as z(J/ ) 1. 416 our interpretation343 of J/y results inThis HI gives collisions. support to the The picture interpretation of quarkonium pro- of the J/y R results ! tal data at several c.m energies and rapidity regions. Comparing ourgraph results calculates to related the remaining work, J/ termsψ total in the cross factorization Such a cancellation does not occurAA for the LDMEs from It is clear that small p⊥ dataFIG. is well2. Predicted describedz(J/ by) ourdistribution344 sections usingThe GFIPratios were (gray) between studiedduction recentlythe yields in Ref. in of the[33] excited and CSM this states within letter. over the The those LDMEs for from the ground state show no dependence on 314 At the HL-LHC,theorem we identifyto LO in the perturbation followingmajor theory. subsequent This does notstudies in- withthe significant global fits phenomenological so the z(J/ ) distribution starts to turn CGC+NRQCD formalism.417 Further,inand FJF nucleus-nucleus as (red) anticipated for the three in choices the345 ofmultiplicity, collisionsbroadLDME inframework Table and 1 and relies are of collinear alwaysglobal on fits consistentfactorization the [5, 6] give assumption worse with [55, agreement unity 56]. While within than that the the fitssystematic the fromc and uncertaintiesc¯ are produced at forward rapidity. be- previous discussion, the results in this formalism begin 315 theimpact: trend of the total cross section is described, the theory up at large z(J/ ). the LHCb measurements of z(J/346). Figure 3 illustratesclude comparisons NLL’ resummation between for the⌥ remainingstates as terms well in as the (2S) and J/ . Theoretical predictions are to disagree with data at higher p⊥. From previous expe- uncertainties have toRefs. be as [12, large 13]. as The a factor LHCb of data 10 for is a data decreasing function 347 compared with thefactorization mid-rapidity thereom, results however and the somez(J/ models)dependence described theTo results summarize, very we well. have analyzedModel predictions the recent LHCb data 418 fore the formation of the QGP andof z(J/ are) as thenz(J/ ) screened1. This is a when property of the the hot medium is created 348 316are neededThe transverseto understand momentum the mechanism fraction, z, measured at work with at forward finer binning rapidities. and for a wider range of jet trans- • of the cross3 [1] section1 [8] is controlled! primarily3 by[8] the FJF.3 [8] on J/ production within jets. We used a combination 349 S and S FJFs, but not the S and P FJFs, 419 whichof the data in causes these bins. the suppression317 Theverse measurements momentum.The of energy the outlined1 The distribution J/ transversey here0meson. of aremomentum hard currently partons of is the limited combined jet,1 that by with sets systematicJ theof hard Madgraph, scale uncertainties of PYTHIA, the process, that and con-will LO be NRQCD mitigated fragmentation 350 with the upcoming HL-LHCwhich actually quarkonium diverge asdata.z With1. In the order expected to obtain much larger data samples and enlarged Our second method, which we318 refer totrols as the the FJF sizethe of FJFs evolution. for anti- ThiskT jets will [39] allow with us toR test=0. various5 to produce aspects offunctions the quarkonium first introduced fragmentation in Ref. [33] as well as an ap- 351 rapidity coverage, LHC experiments have good! prospects3 [8] to perform3 [8] multi-di↵erential studies among dif- negligible polarization at high pT ,the S and P 420 Onmethod, the employs left FJFs of combined Fig. 1.18319 with hard the events R gen-of prompt J/y is shown, in1 orange,J as a functionz of p [27]. 352 mechanisms,AA and their relative contributions. In addition, a detailed study of the regime 1 1 T ferent kinematic variables,LDMEs also of Refs. at forward [12, 13] rapidity. have relative This signs will such enable that focused studies of the⌧ dependence in erated by Madgraph at LO. In353 calculating320specific thewill regions FJFs, give log- insights of phase into space the non-perturbative and precision aspects analyses of quarkonium of the higher hadronisation excited quarkoniumwhere the process states, is such as the 421 1 [8] The R shows354 a rising⌥(3S ). trend atthey high roughlyp cancel,that so the isS similar0 dominates to production what is seen in open charm artihms of AAmJ/ /EJ are resummed321 using leadingparticularly order sensitive to soft radiation.T DGLAP equations to evolve the fragmentation functions and J/ are unpolarized. The same cancellation here al- lows the z(J/ ) distribution go to zero as z(J/ ) 1. from the scale 2mc to the jet energy322 scale,JetE substructureJ . Mad- observables, such as thrust and other angularities, will give access to the details of • Such a cancellation does not occur for11 the LDMEs! from graph calculates the remaining terms323 in thethe factorization radiation surrounding the quarkonium within the jet. The distribution of radiation in the jet is theorem to LO in perturbation theory. This does not in- the global fits so the z(J/ ) distribution starts to turn 324 sensitive to the production mechanisms of quarkonium and could o↵er an additional handle onto the clude NLL’ resummation for the remaining terms in the up at large z(J/ ). 325 numerical values of the LDMEs. A theoretical investigation of the observables of this type has been factorization thereom, however the z(J/ )dependence To summarize, we have analyzed the recent LHCb data of the cross section is controlled326 primarilyperformed by the FJF. in Ref.on [79J/]. production within jets. We used a combination The energy distribution of hard partons is combined with of Madgraph, PYTHIA, and LO NRQCD fragmentation 327 Multi-di↵erential measurements of quarkonium energy fraction and transverse momentum with re- the FJFs for anti-kT jets [39] with R =0• .5 to produce functions first introduced in Ref. [33] as well as an ap- 328 spect to the jet axis [80, 81] can provide the three-dimensional picture of quarkonium fragmentation. 329 In addition, the gluon and quark rapidity anomalous dimension is a significant component of these 330 studies, and of great interest for improving our understanding of the structure of nucleons.
331 Compared to light hadrons, quarkonium production is anticipated to be less sensitive to the background 332 contribution from multiparton interactions and underlying event activity. However, at the HL-LHC, the use 10 Remarks on (2S) production
p+p p+A
Excited states: Comover interac on So color exchanges between Ma, Venugopalan, Transport model with final interac ons Du & Rapp (2015) ψ(2S) production in p-Pb B. Paul, Wed 16:50 cc & - comovers at later stage Zhang, Watanabe (2018) “similar in spirit to comoverComparison suppression” with LHC 1.2 ps =5.02 TeV ALICE : J/ àNew resultsDirect on ψcomparison(2S) with LHC data as ALICE : (2S) [Ma, Venugopalan, Zhang, KW, PRC97,014909(2018)] 1 2.035 pA 0.6 ⇤à=Final state effects are R Factorization breaking at needed (to reproduceE (2S )the) (Very O 0.4 Soft!). Model dependent.ψ(2S)cf. suppression. [Ferreiro, PLB 749, 98 (2015)] ALICE PRL 110 032301! (2013) (2S) 0.2 Durham QM2018 Light : Q2 =(1.5 2)Q2 ,⇤=(10 20) MeV The comover e ect could bringàStill problems complications for a for s0,A s0,p CIM result vs. data Dark : Q2 =(1.5 2)Q2 ,⇤=15MeV quantitative description of s0,A s0,p Measurements production not available for all in high multiplicity events. 0 (2S) 0 1 2 3 4 5 rapidity rangesTheory: for all species E.G. Ferreiro arXiv:1411.0549;the data. Plot from the SGNR review: arXiv:1506.03981; PHENIX PRL 111, 202301 (2013); ALICE JHEP 02 (2014) 072 P [GeV] • use AMPT simulation for dN/dη 1.6 ? pPb p Pb 5.02 TeV from Glauber model pp pp ] ] 1.6 1.6 R ψ ψ Ini al state d-Au s =200 GeV p-Pb s =5.02 TeV 41 azuhiro atanabe efferon ab Matt Durham – Quarkand Matternium 2018 production in p+p and p+ collisions 1.4 uark atter ay / K NNW (J L ) HF NNO A 36 Q M 2018, M 16, 2018 11 18 1.4 1.4 effects ALICE, inclusive J/ψ and ψ(2S) 1.2 (2S)/J/ (2S)/J/ ψ 1.2 ψ 1.2 / [ / [ -CGC, 1 pPb pPb ] 1 ] 1 ψ ψ nPDFs- 0.8 0.8 0.8 0.6 (2S)/J/ (2S)/J/ cancel in ATLAS,ϒ(1S) ψ 0.6 ψ 0.6 [ [ 0.4 LHCb, ϒ(1S) 0.4 0.4 Comovers & Durhan the double 0.2 ALICE, ϒ(1S) 0.2 PHENIX, inclusive J/ψ and ψ(2S) 0.2 nCTEQ15 COMOV - Ferreiro ra o 0 −4 −2 024 0 0 y c.m.s. 0 2 4 6 8 10 12 14 16 18 -4 -2 0 2 4 N y EGF & Lansberg (2018) coll EGF (2014) Given that all the other models discussed so far predict no difference and thatE. G. Ferreiro USC the comover cross sections from AA data atQuarkonium & related observables from pp to AA SPS were re-used, this is 7 SnowMass2021 16/12/2020 encouraging. . . J.P. Lansberg (IPNO) Quarkonium production in pA collisions July 8, 2015 28 / 31 co Survival probability from integration over time (with τf τ ρ b, s, y ρpp y ) ρco b, s, y Sco b, s, y exp σ co ρco b, s, y ln ρpp y co Survival probability from integration over time (with τf τ ρ b, s, y ρpp y ) ρco b, s, y Sco b, s, y exp σ co ρco b, s, y ln ρpp y Comover-interaction model (CIM) Comover-interaction model (CIM) In a comover model, one introduces a suppression fromIn a scatterings comover model, of the one nascent introduces a suppression from scatterings of the nascent with comoving particles S. Gavin, R. Vogt PRL () with;A.Capella comovinget al.PLB particles () S. Gavin, R. Vogt PRL () ;A.Capellaet al.PLB () By essence of their comoving character,Comover-interac on these can interactBy essence model with of the CIM their fully comoving formed character, these can interact with the fully formed states aer . . fm/c states aer . . fm/c • In a comover model: suppression from sca erings of the nascent Q with comoving Stronger comover suppression where the comover densitiesStronger are comover larger. suppression For where the comover densities are larger. For medium cons tuted byasymmetric par cles with collisions similar rapidi es as proton-nucleus, Gavin, Vogt, Capellastronger, Armesto in, Ferreiro the nucleus-going… (1997) direction asymmetric collisions as proton-nucleus, stronger in the nucleus-going direction • Stronger suppressionStronger where suppression the comover in nucleus-nucleus densi es (mul plici es collisions) are as welllarge Stronger suppression in nucleus-nucleus For collisionsasymmetric collisions as wellRate as p- equationnucleus governing, stronger the in quarkoniumthe nucleus-going density direc onat a given transverse coordinate s, Rate equation governing the quarkonium density at a givenimpact transverse parameter coordinateb and rapiditysy, , • Boltzman equa on governing impact parameter b and rapidity y , dρ the quarkonium density: τ b, s, y σ co ρco b, s, y ρ b, s, y dτ dρ co co τ b, s, y σ : cross sec on of quarkonium dissocia on due to interac ons with ρ b, s, y whereρ bσ,cos, y is the cross section of quarkoniumcomoving dissociation medium due to interactions dτ with the comoving medium of transverse density ρco b, s, y . co where σ is the cross section• of quarkoniumSurvival probability dissociation from due to interactions co with the comoving medium of transverse integra on density over me: ρ b, s, y . J.P. Lansberg (IPNO) Bottomonium prod. in AA and pA collisions September , / E. G. Ferreiro USC Quarkonium & related observables from pp to AA 8 SnowMass2021 16/12/2020 J.P. Lansberg (IPNO) Bottomonium prod. in AA and pA collisions September , / Binding Radius co ¯ Energy r [fm] σ bb [mb] [MeV] bb¯ Υ(nS) Υ(S) Υ . . pPb CIM CMS Υ(nS) Υ(S) pp χb . . Υ . . . st. . sy. Υ . . Υ . . . st. . sy. χb . . Υ . . χb . (?) . To Do: analyse why the t seems to allow for dierent couples of n, Eco BindingBinding RadiusRadius co co EnergyEnergy σ σ bb¯ b[mb]b¯ [mb] r r ¯ [fm][fm] [MeV][MeV] bb bb¯ Υ(nS)Υ(nS)Υ(ΥS)(S)pPb Υ Υ . . . . pPb CIMCIM CMS CMS Υ(nS)Υ(nS)Υ(ΥS)(S)pp pp χb χb . . . . Υ Υ .. . . ..st.st. ..sy.sy. Υ Υ . . . . χ . . Υ Υ .. . . ..st.st. ..sy.sy. b χb . . Υ Υ . . . . χ . (?) . b χb . (?) . ToTo Do: Do: analyse analyse why why the thet seemst seems to to allow allow for for di dierenterent couples couples of ofn,n,EcoEco To do so we assumed that: (i) the thresholds, EthrQ , approximately follow from the mass differences between the quarkonium, , and the lightest open beauty hadron pair, taking into account the Q comover mass; (ii) away from the thresholds, the cross section should scale like the geometrical cross 2 section, σgeoQ πr , where r is the quarkonium Bohr radius. It can be evaluated ≃ Q by solving the Schr¨odingerequationQ with a well-choosen potential reproducing the quarkonium spectroscopy [30]. Our parametrisation of the energy dependence thus simply amounts to interpolating JHEP10(2018)094 co co co co from σ (E = EQ ) = 0 at threshold up to σ (E EQ )=σ away from −Q thr −Q ≫ thr geoQ threshold but with the same dependence for all the states. It reads n co co EthrQ σ −Q(E )=σgeoQ 1 co (2.4) × ! − E " where EQ = M + mco 2MB is the threshold energy to break the quarkonium bound thr Q co 2 −2 state and E = p + mco is the energy of the comover in the quarkonium rest frame. In the case of a hadronic# medium (made of pions), mco =0.140 GeV, while it is zero for gluons. The geometrical cross sections σgeoQ which we used are shown in table 1, together with the threshold energies EthrQ and the bottomonium radii. The first free parameter of To do so we assumed that: our modeling, n, characterises how quickly the cross section approaches the geometrical cross section. Attempts to compute this energy dependence, using the multipole expansion (i) the thresholds, EthrQ , approximatelyTo do so we follow assumed from that: the mass differences between the quarkonium, , and the lightest open beauty hadron pair, taking intoin perturbative account the QCD at LO [30–32], would suggest that n is close to 4 for pion comovers Q (i) the thresholds, EthrQ , approximately follow from the mass differences between the comover mass; quarkonium, , and the lightest open beauty hadron pair, taking into account the Q by making the strong assumption that the scattering is initiated by gluons inside these comover mass; (ii) away from the thresholds, the cross section should scale like the geometricalpions. Hadronic cross models which take into account non-perturbative effects and thus most 2 section, σgeoQ πr , where(ii)rawayis the from quarkonium the thresholds,2 Bohr theradius. cross It section can be should evaluated scale like the geometrical cross ≃ Q Q 2 likely provide a better description of the physics at work [33] show a different energy by solving the Schr¨odingerequationsection, σ withgeoQ aπ well-choosenr , where r potentialis the quarkonium reproducing Bohr the radius. It can be evaluated a simple pattern related to the size and the binding energy of J/ and (2S) from proton-nucleus and nucleus-nucleus≃ Q col- Q all the bottomonium states, which renders our set-up predic- quarkoniumlisions. spectroscopy [30].by solving the Schr¨odingerequation withdependence. a well-choosen potential It effectively reproducing corresponds the to smaller n [34]. As such, we will consider n tive; To do soIn order we to assumed set the scene for that: bottomoniumquarkonium dissociation, spectroscopy one [30]. JHEP10(2018)094 (ii) the absolute ⌥ suppression in pPb collisions as measured Ourcan parametrisation not follow the same of approach. the energy No such dependence nucleus-nucleus thus simply amountsvarying to interpolating from 0.5 to 2. In fact, the discrepancies existing between the aforementioned LO by ALICE, ATLAS and LHCb is also well described andfrom the σdataco exist(Eco at= lowE energies) = and, 0 at inOur threshold fact, parametrisationthe CIM up was to neverσco ap- of( theEco energyE dependence)=σ away thus from simply amounts to interpolating JHEP10(2018)094 (i) the thresholds,−Q thrQ EQ , approximately follow−Q fromthrQ thegeoQ mass differences between the tension with nuclear PDFs with antishadowing is solved; plied to bottomonia before.thr We haveco then chosenco to develop a ≫ QCDco resultsco and these hadronic calculations are partly due to large higher order correction threshold but with the same fromdependenceσ −Q(E for all= theEQ states.) = 0 atIt reads threshold up to σ −Q(E EQ )=σQ away from (iii) even more striking, the entire relative suppression ob- new strategy. We are aware that the magnitude of thethr quarko- ≫ thr geo quarkonium, , andthreshold the lightest but with open the same beautydependencen hadron for nearall pair,thethe states. taking threshold It reads into account [35]. the served inSetting PbPb collisions is accounted the by scatterings scene with co- fornium absorption theQ cross bottomonium section in medium is not well underE family p ↵ co co thrQ n movers with the same interaction strength as for the Pb data;comovercontrol, andmass; that di erentσ theoretical−Q(E calculations,)=σQ as the1 ones Conventional(2.4) charmonia in nuclear medium geo co AsE forQ the energy distribution of the comovers in the transverse plane, we simply take (iv) the absolute magnitude is also very well reproduced up based on the multipole expansion in QCD, [24–26×] di!↵er− fromEσco" (Eco)=σ 1 thr (2.4) LHCb, JHEP 1603 (2016) 133 to the uncertaintiesNo in such the nuclearAA modificationdata of exist the gluon atthose low which energies include other non-perturbative e↵ects by orders E.G.−Q Ferreiro,geoQ J.P. Lansberg,co work in progress (ii) away from the thresholds, the cross section shoulda scale× Bose-Einstein! − likeE the" geometrical distribution cross densities. where EofQ magnitude= M [+27].m Thereco 2 areM neverthelessB is the threshold some common energy fea- to break the quarkonium bound turesthr to mostQ of the approaches:−In fact, the CIM was never applied to bottomonia The Comover Interaction Model. — Let us recall the main co 2 2 Towhere do soE weQ assumed= M + that:mco 2MB is the threshold energy to break the quarkonium bound 1 statesection, and(i) ETheσ quarkonium=geoQ p +π asymptoticmrco ,is where the cross energythr sectionr ofis forQ the the the comover interac- quarkonium− in the quarkonium Bohr rest radius. frame.Production It can be of evaluated quarkonia is modifiedco in nuclear collisions features of the CIM. Within this framework, the quarko- Comover-interac oncoQ 2 2 model CIM: The interac on(E ; Tcross) sec ons (2.5) tion with an energetic≃ particleQ state is commonly and E assumed= p to+ con-mco is the energy of the comover in the quarkonium rest frame. eff co nia are suppressede duerelative to the interaction suppression with the comovingIn the ofcase the of a hadronic excited medium(i) theΥ thresholds,is (made probably ofE pions),thrQ , approximatelymco the=0.cleanest140 follow GeV, from while theobservable it mass is zero diff forerences between to xthe the E /Teff by solving the# Schr¨odingerequationQ 2 with a well-choosen potentialcompared reproducing to that in the pp.P ∝ e 1 verge to the geometrical crossIn the section case of a⇡ hadronicr , being r mediumQ (made of pions), m =0.140 GeV, while it is zero for medium, constituted by particles with similar rapidities.gluons. The The geometrical crossquarkonium, sections σgeo ,which and#Q the we lightest used are open shown beauty in hadron table 1 pair,, togetherco taking into account the − comover suppressionquarkoniumthe magnitude Bohr radius spectroscopy of the• corresponding Rela ve quarkonium [[without30geoQ].Q' suppression bound interference state, of excited with other Υ: cleanest nuclear observable eect] to fix the comover suppression rate equation that governs the density of quarkonium at a given gluons.comover The mass; geometrical cross sections σgeoQ whichwhich we used introduces are shown in our table second1, together parameters, namely an effective temperature of these co- transverse coordinate s, impact parameter b and rapiditywithy, theat su threshold ciently large energies energies;EthrQ and the bottomonium radii. The first free parameter of s JHEP10(2018)094 ( p , y ) ⌥ (ii) The thresholdSettingSetting e↵ects canwith the be the the takenco scene threshold scene into account¯ for for energies through the theE bottomoniumQ bottomoniumand the bottomonium family family radii. The first free parameter of 1 pPb T ⇤ ⇢ (b, s, y), obeysHowever, the expression not enoughOurour data modeling, parametrisation to n,tallthe characterises•(ii) ofaway6 how theσ from quickly energy the thresholds, thebb involved[the dependencecross sectionfeed-downs the crossthr approaches section[ thusthe should discussedfeed-downs simplymovers. the scale geometrical amountslike above the are geometrical weretaken to interpolating used cross into !] RaccountpPb = ] the quarkonium binding energy, i.e. the di↵erence2 between No suchoursection,AA modeling,dataσ existnπ,r at characterises, low where energiesr is how the quarkonium quickly the Bohr crossE.G.E.G. radius. Ferreiro, section Ferreiro, It J.P.J.P. canapproaches Lansberg, Lansberg, be evaluated work work thein inprogress progress geometrical ⌥ crossco section.the quarkoniumco Attempts massesNo to andcompute such the openAA thisdata charmgeoQ energy exist or beauty dependence, at low thresh- energies usingco the multipoleco expansion co coA sppco( pT, y ⇤) d⇢ co ⌥ co ⌥ from σ (E EBinding= EQ ) = 0 at threshold≃ Q upQ to σ (E HavingEQ )=(σE ; Taway) fromand σ (E ), we derive the energy-averaged quarkonium- co ¯ −Q n −Q geoQ eff −Q ⌧ (b, s, y) = ⇢ (b, s, y) ⇢ b(b, s, y) , (1) thr• crossby solving section. the Attempts Schr¨odingerequation to computeIn fact, with this the aenergywell-choosen CIM dependence, was never potentialthr applied using reproducing the to multipolebottomonia the expansion d⌧ We use : σ σgeomin perturbativeold. QCDTo at do LO so [30where weGoing–32 assumed], would toE that: suggest a comicroscopicand that n nisIn closeare fact, to level the 4t for CIM pion was≫ comovers never appliedP to bottomonia E.G.F., J.P. Lansberg JHEP 10 (2018) threshold butBased with on theEco theabovesame statements,inquarkonium perturbativedependence we propose spectroscopy QCD a generic atfor[ LO for-30all]. [30the–32],states. would suggest It reads that n is close to 4 for pion comovers co ⌥ e relative suppression of the excited Υ is probablycomover-interaction the cleanest observable to crossxthe section where is the cross section of bottomonium dissociationby makingmula for the all strong the quarkonia assumptione statesrelative and that suggest suppression the a connection scattering of the with is excited initiatedΥ is by probably gluons inside the cleanestHigher these observable excited to statesxthe JHEP10(2018)094 are more suppressed, as they are (i) the thresholds,Ourby making parametrisationE thethrQ , strong approximately of the assumption energy dependence follow that fromthe thus scattering the simplyn mass amounts is di initiatedfferences to interpolating by between gluons inside the these due to interactions with the comoving medium of transverse the momentum distributioncomovercomover of the comovers suppression suppression in the transverse magnitude magnitude [without[without interference interference with with other other nuclear nuclear e eect]ect] co co co co σgeom πr pions. Hadronic modelsquarkonium, whichco take intoco, and account the lightest non-perturbative open beauty effEects hadronco andco thus pair, most taking into account the ∞ dE (E ; Teff ) σ −Q(E ) co bb¯ ↵frompions.σ −coQ(E Hadronic= EcoQ models) = 0 at which threshold take up into to accountσthrQ−Q(E non-perturbativeEincreasinglyQ )=σgeoQ eawayffects from weakly andco thus most bound. 0 density ⇢ (b, s, y). plane, thus with an e ective temperatureQ of thethr comover. We coco bb¯ ¯ thr likely provide a betterHowever,However, descriptionσ not not− of enoughQ enough the(E physics data)= data toσ at togeoQtallthe worktallthe [331]σ showσ ab[theb di[theff feed-downserent feed-downs≫ energy discussed discussed above above were wereσ used used−Q !](2.4) !](Teff ,n)= P , (2.6) By integrating this equation between initial timeB ⌧0 and use comoverthreshold mass; but with the same dependence for all theco states. It reads co co EBinding M M bb¯ , i.e. the thresholdlikely provide energy a better to description break× the of− theE bound physics at state work [33] show a⟨ different⟩ energy ∞ dE (E ; Teff ) freeze-out time ⌧ , one obtains the survival probability coco ¯ EBindingEBindingn!n " n 0 f dependence. It effectivelyWe use corresponds : σ bb bb¯Q toσgeom smaller n [34]. Aswhere such,E weco willEand considern are t n $ P co We usedependence. : σ E Itσgeom effectivelyco EcoE correspondsco where toE smallerco thrQandnn are[34].t As such, we will consider n S ⌥ (b, s, y) of a ⌥ interactingE withco comovers:: the average energy of(ii) thecoawayQ comoversco fromQ the thresholds, inth n theσ quarkonium the−Q( crossEco )= sectionσQ should rest1 frame scale like the geometrical(2.4) cross LHCb, JHEP 11 (2018) 194 varying from 0.5 to 2. In(E fact,) = the geo(1 discrepancies) existing(3) betweengeo the aforementionedco LO where E = M + m varying2M from Eisco2 0.5 the to threshold 2. In fact, the energy discrepancies× ! − tofromE break existing" which the between quarkonium we the can aforementioned compute bound LO the (relative) NMFs. Our fits will thus simply amount to thrQ section,co σgeoQ B πr , where r is the quarkonium Bohr radius. It can be evaluated $ ) a t to theco CMS data gives Eco σgeomσgeomGeVπrπrand¯ n . 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JHEP10(2018)094 # a at totAs to the thefor CMS theCMS data energy data gives gives distributionEcoEco GeV ofGeV theandand comoversn n ..(see in(see the below) below) transversep plane,⌥(2S) we/⌥ simply(1S) take p ⌥(3S)/⌥(1S) p # ϒ ( ϒ ( with the comovers1. mean cross sectionOur is calculated parametrisation by averaging of over the a energy normal- dependence thus simply amounts1.4 to interpolating 1.4 gluons.a Bose-Einstein The geometrical distributiongluons. cross The sections geometrical crossσ sectionswhichσgeoQ wewhich used we used are are shown shown in in table table1, together1, together co a Bose-Einsteinco distributiongeoQ co co ℜ ℜ In order to compute the above survival probability, the den- ized Bose-Einsteinfrom σ phase-space−Q(E distribution= EQ ) of= the 0 atcomovers, threshold up to σ −Q(E EQ )=1.2σQ away from 1.2 cowith the thresholdthr energies EQ and the bottomonium radii. The firstthr free parametergeo of co E /Tef f 1thr 1 ≫ sity of comovers ⇢ is mandatory. It is directly connectedwith the to thresholdproportional to 1 energies/(e 1).E( ProceedingEQco; Tand) this the way, thebottomonium ob- co radii. The(2.5) first free parameter of thresholdour but modeling, withthr then,esameff characterisesdependenceEco/T how quickly for(Eall the;theTe crossff ) states. sectionco It approaches reads the1 geometrical (2.5) 1 the particle multiplicity measured at that rapidity for the cor- tained cross sections will dependP only on the∝ inversee e slopeff 1 P ∝ eE /Teff 1 Such difference in suppression of states 2 T cross section.n Attempts to compute− this energy dependence, usingn the multipole0.8 expansion 0.8 responding colliding system . our modeling,parametern,ef characterisesf and the exponent that how can be quickly extracted from the cross sectionEQ approaches− the geometrical Since we are interested in the study of pA, one can assumewhich introducesfits to the data. our secondwhich parameters, introduces namelyσco our( ansecondEco eff)=ective parameters,σ temperature1 namelythr of anthese effective co- temperature(2.4) of these co- in perturbative QCD at LO−Q [30–32], wouldgeoQ suggest that con is close to 4 for0.6 pion comoversLHCb, JHEP 11 (2018) 194 0.6 with the same quark content can be that the medium is made of pions. Nevertheless, wecross will showmovers. section.In order Attempts to proceed with tomovers. the compute fit, it is mandatory this to energy take into dependence,× ! − E using" the multipole expansion by• makingSuccesfully the strong assumption reproduces that the scatteringthe is initiated by gluons0.4 inside these –5–0.4 later that the nature of this medium –partonic or hadronic– do account theco feed-down contributions.co co In fact,co the observed co co p <25 GeV/c p <25 GeV/c explained with final-state effects. Having (E ; Teff )pions. and σ HadronicHaving−Q(E models),( weE which; deriveTeff ) take and the intoσ energy-averaged− accountQ(E ), non-perturbative we derive quarkonium- the eff energy-averagedects and thus most quarkonium-T T not change our results. in perturbative⌥(nS) yields QCDwhere containE atcontributionsthrQ LO= M [30 from+–m32 decaysco], would2 ofM heavierB is bot- the suggest threshold that energyn is to close break to the 4 quarkonium0.2 for pion bound comovers 0.2 P excited-over-groundQ P− rela ve s =8.16 TeV s =8.16 TeV comover-interactiontomonium states cross and,likely thus, sectioncocomover-interaction the provide measured2 a better suppression2 description cross can sectionbe of the physics at work [33] show a different energy NN NN The only adjustable parameter in the CIM is theby cross making sec- the strongstate and assumptionE = p + m thatco is the energy scattering of the comover is initiated in the quarkonium by gluons0 rest inside frame. these 0 tion of bottomonium dissociation due to interactions with the a↵ected by the dissociationdependence.suppression of these Itstates. effectively Thisco feed-down versus correspondsco corapidity to smallerco∞ dEnco [34].(Eco As; T such,) σco we will(Eco consider)−4 n−2 0 2 4 −4 −2 0 2 4 co ⌥ In the caseJ.P.J.P. of Lansberg Lansberg a hadronic (IPNO) (IPNO)∞ dE medium(EcoBottomoniumBottomonium; (madeTeff ) σ ofprod.− prod.Q pions),( inEAA in0AA)andandmpAcopAcollisionscollisions=0.140eff GeV,−September whileQSeptember it is,, zero for/ / comoving medium, . In our previous works, relative contribution to theco⌥(1S) state is# usually0 taken of the order P pions. Hadronic modelsσ −Qvarying(T whicheff ,n from)= 0.5 take to 2. into InP fact,σ account− theQ (T discrepancieseff ,n)= non-perturbative existing, betweenco (2.6) theco e aforementionedffects and, LOthus most(2.6) y* y* of 50%, accordinggluons. to The CDF geometrical Collaboration cross measurements⟨ sectionsco ⟩ atcoσQ which we used∞ dE are( shownE ; Teff in) tableStronger1, together suppression in the nucleus-going direc on to charmonium production,J.P. Lansberg the cross sections (IPNO) of charmonium Bottomonium⟨ ⟩ prod. in AA and0∞ pAdE collisions(E ;geoTeff ) $ 0 September , / > QCD results and$ these hadronicP calculations are partly due to largeP higher order correction dissociation were obtained from fits to low-energylikely experimen- providepT 8 a GeVwith better [28 the]. However, threshold description following energies the of newE theQ dataand mea- physics the bottomonium at work radii. [33] The show first a free di parameterfferent energy of co J/ co (2S ) nearfrom the threshold which we [35]. canthr compute the (relative) NMFs. Our fits will thus simply amount to tal data [14], = 0.65 mb and = 6 mb. Thesefrom whichsured by we LHCb can CollaborationcomputeE. G. Ferreiro USC the [29 (relative)], this assumption NMFs. needs Our to fits will thus simply$ amountQuarkonium & related observables from pp to AA to 9 SnowMass2021 16/12/2020 $ [email protected] Multiplicity dependent production of cc1 (3872) LHCP2020 4 / 13 dependence.be revisited, Itour e inff particularectively modeling, atAsdetermine low forn corresponds,pthe characterises. Inenergy the fact, best distributionif one value how to is inter-T smaller quickly offor the fixed comovers then values cross[34 in]. of the sectionn transversein As the approaches such, aforementioned plane, we we the simply will geometrical ranges take consider reproducingn values have been also successfully applied at higher energiesdetermine the best value Teff for fixedT values of n in the aforementionedeff ranges reproducing to reproduced the RHIC [19, 21] and LHC [20, 21] data on ested on pTcrossintegrated section.a results Bose-Einsteinthe Attempts the selected feed-down distribution toexperimental fractions compute for this the data. energy dependence, using the multipole expansion varyingthe selected from⌥(1S)0.5experimental can be to estimated 2. In data. as: fact, 70% of the direct discrepancies⌥(1S), 8% from existing between the aforementioned LO in perturbative QCD at LO [30–32], wouldco suggest that1 n is close to 4 for pion comovers ⌥(2S) decay, 1% from ⌥(3S), 15% from B1, 5% from (B2E ; Teff ) co (2.5) QCD results and these hadronic calculationsP are partly∝ eE due/Teff to1 large higher order correction and 1% fromby B3 making, while for the the strong⌥(2S) the assumption di↵erent contribu- that the scattering− is initiated by gluons inside these 1 which introduces our second parameters, namely an effective temperature of these co- We assume that the interaction stops when the densities havenear diluted, reach- the thresholdtions wouldpions. be: [ 63%35 Hadronic]. direct ⌥(2S), models 4% of ⌥ which(3S), 30% take of intoB2 account non-perturbative effects and thus most ing the value of the pp density at the same energy, ⇢pp. and 3% of B3 [30]. Notemovers. also that for the ⌥(3S), 40% of the 2 In fact, within this approach, a good description of the centrality depen- likely provide a betterco descriptionco of theco physics at work [33] show a different energy As forcontribution the energy will come distribution fromHaving decays of(E B3 of.; Teff the) and comoversσ −Q(E ), in we the derive–5– transverse the energy-averaged plane, quarkonium- we simply take dence of charged multiplicities in nuclear collisions is obtained both at dependence. It effPectively–5– corresponds to smaller n [34]. As such, we will consider n RHIC [22] and LHC energies [23]. Tackling the CMS puzzle.—comover-interactionWe have used crossthe CMS section [1] and a Bose-Einsteinvarying distribution from 0.5 to 2. In fact, the discrepanciesco existingco betweenco co the aforementioned LO ∞ dE (E ; Teff ) σ −Q(E ) σco (T ,n)= 0 P , (2.6) QCD results and these hadronic−Q calculationseff are1 partlyco dueco to large higher order correction ⟨ co ⟩ ∞ dE (E ; Teff ) (E ; Teff ) $ co 0 P (2.5) near the threshold [35]. E /Teff from which weP can compute the∝ (relative)e $ NMFs.1 Our fits will thus simply amount to As for the energy distribution of the comovers− in the transverse plane, we simply take which introduces ourdetermine second the parameters, best value Teff for namely fixed valuesan of n in eff theective aforementioned temperature ranges reproducing of these co- a Bose-Einsteinthe selected distribution experimental data. movers. co 1 (E ; Teff ) co (2.5) co co coP ∝ eE /Teff 1 Having (E ; Teff ) and σ −Q(E ), we derive the− energy-averaged quarkonium- P which introduces our second parameters, namely an effective temperature of these co- comover-interaction cross section movers. –5– co co co co co co co Having (E ; Teff ) and ∞σ dE−Q(E ),(E we; deriveTeff ) σ the− energy-averagedQ(E ) quarkonium- co P 0 P comover-interactionσ −Q (Teff ,n cross)= section co co , (2.6) ⟨ ⟩ 0∞ dE (E ; Teff ) $ ∞ dEco P(Eco; T ) σco (Eco) co 0 P eff −Q σ −Q (Teff ,n)= co co , (2.6) from which we can compute the⟨ (relative)⟩ $ NMFs.∞ dE Our fits(E ; willTeff ) thus simply amount to $ 0 P determine the bestfrom value whichT weeff canfor compute fixed values the (relative) of n in$ NMFs. the aforementioned Our fits will thus ranges simply amount reproducing to the selected experimentaldetermine the data. best value Teff for fixed values of n in the aforementioned ranges reproducing the selected experimental data. –5– –5– The mysterious cc1(3872) The cc1(3872) exotic hadron was first observed in 2003 by Belle in decays of + B J/yp p . Belle, PRL 91 (2003) 262001 Applica on of final state comover interac on! to pp collisions Quantum numbers of c (3872) were determined as JPC = 1++. c1 y(2S) 1 • Mo va on: recent LHCbRatio results of on cross X(3872) versus ”This result rulessections out the explanationmul plicity of the X(3872 ) meson as a conventional hc2(1 D2) state. Among the 3 remaining possibilities are the cc1(2 P1) charmonium, disfavored by the value of the X(3872) mass, and 0 ¯ 0 unconventional explanations such as a D⇤ D molecule, tetraquark state or a charmonium-molecule mix.” LHCb, PRL 110 (2013) 222001 ) ) Prompt Component: - - LHCb Preliminary ) ) p p - - 0.12 Increasing suppression of + p + p pp s = 8 TeV p p + + p p , -./0 production relative to Prompt cc1(3872) y y R(X/2S) 0.1 y y Prompt 1 02 as event activity increases J/ J/ b decays J/ J/ ® ® 0.08 ® ® 0.06 (2S) (2S) (3872) (3872) y y c1 c1 c c 0.04 Χ/ψ(2S) BR( BR( BR( BR( p > 5 GeV/c 0.02 T Ma Durham QM2019 Courtesy of Matt Durham (2S) (2S) (3872) 0 (3872) 0 y y c1 0 20 40 60 80 100 120 140 160 180 200 c1 0 20 40 60 80 100 120 140 160 180 200 c c s s Ma Durham QM2019 VELO s s N [email protected] Multiplicity dependent production of cc1 (3872) LHCP2020 2 / 13 LHCb-CONF-2019-005 tracks Matt Durham - LANL 27 E. G. Ferreiro USC Quarkonium & related observables from pp to AA 10 SnowMass2021 16/12/2020 Applica on of final state comover interac on to pp collisions • In fact, the effect foundRatio by LHCb of is cross similar to sections the one previously found for Υ by CMS 5.1 Excited-to-ground state cross section ratios: U(nS)/U(1S) 7 0.5 ) ) Prompt Component: - - LHCb Preliminary (1S) ) ) p p CMS pp s = 2.76 TeV CMS pPb s = 5.02 TeV - - NN ϒ 0.12 Increasing0.45 suppression of + p + p pp s = 8 TeV ϒ(2S)/ϒ(1S) ϒ(2S)/ϒ(1S) p p + + (nS)/ 0.4 ϒ p p Prompt , -./0 ϒproduction(3S)/ϒ(1S) relative ϒ(3S)/ toϒ(1S) y y R(X/2S) 0.1 y y Prompt 1 020.35 as event activity increases J/ J/ b decays |y |< 1.93 J/ J/ CM ® ® 0.08 0.3 ® ® 0.25 0.06 (2S) (2S) 0.2 (3872) (3872) y y c1 c1 Υ(2S)/Υ(1S) c c 0.04 Χ/ψ(2S) 0.15 BR( BR( 0.1 BR( BR( p > 5 GeV/c 0.02 T Υ(3S)/Υ(1S) Ma Durham QM2019 0.05 CMS collabora on JHEP 103 (2014) (2S) (2S) (3872) 0 (3872) 0 0 y y c1 0 20 40 60 80 100 120 140 160 180 200 c1 0 20 40 60 80 100 120 140 160 180 200 0 20 40 60 80 100 120 140 c c |η|<2.4 s s VELO N s s N tracks LHCb-CONF-2019-005 tracks Figure 3: Single cross section ratios U(2S)/U(1S) and U(3S)/U(1S) for y < 1.93 versus trans- | CM| verse energy measured in 4.0 < h < 5.2 (left) and number of charged tracks measured Matt Durham| | - LANL 27 in h < 2.4 (right), for pp collisions at ps = 2.76 TeV (open symbols) and pPb collisions at | | psNN = 5.02 TeV (closed symbols). In both figures, the error bars indicate the statistical uncer- tainties, and the boxes represent the point-to-point systematic uncertainties. The global uncer- E. G. Ferreiro USC tainties on the pp results areQuarkonium & related observables from pp to AA 7% and 8% for U(2S)/U(1S) and U(3S)/11 U(1S), respectively,SnowMass2021 16/12/2020 while in the pPb results they amount to 8% and 9%, respectively. The results are available in tabulated form in Table 4, with binning information provided in Table 3. pp to pPb to PbPb systems, as a function of event multiplicity. The impact of additional underlying particles on the decreasing trend of the U(2S)/U(1S) and h <2.4 | | U(3S)/U(1S) versus Ntracks in pp and pPb collisions is studied in more detail. The pp sample contains on average two extra charged tracks in the U(1S) events when compared to the U(2S) and U(3S) events, consistent with the pPb sample, though the average number of charged par- ticles rises from 13 (pp) to 50 (pPb). The trend shown in the right panel of Fig. 3 is found to weaken (or even reverse) if one artificially lowers the number of charged particles in the U(1S) sample by two or three tracks for every event. In contrast, the number of extra charged particles h <2.4 | | does not vary when lowering the pT threshold down to 200 MeV/c in the Ntracks computation, or when removing particles located in a cone of radius DR = p(Df)2 +(Dh)2 = 0.3 or 0.5 around the U momentum direction. Extra charged particles are indeed expected in the U(1S) sample because of feed-down from higher-mass states, such as U(2S) U(1S)p+p , but decay ! kinematics [24], with typically assumed feed-down fractions [4], do not lead to a significant rise of the number of charged particles with pT > 400 MeV/c. While most feed-down contributions should come from the decays of P-wave states, such as c U(1S)g, the probability for a pho- b ! ton to convert in the detector material and produce at least one electron with pT > 400 MeV/c, that is further reconstructed and selected, is very low (<0.2%). This makes the number of re- constructed electrons not sufficient to produce the measured trend. Therefore, it is concluded that feed-down contributions cannot solely account for the observed features in the measured ratios. It is noted also that if the three U states are produced from the same initial partons, the mass difference between the U(1S) and the U(2S) (>500 MeV), or the U(1S) and the U(3S) (>800 MeV), could be found not only in the momentum of the U(1S), but also in extra particles created together with the U(1S). To do so we assumed that: 3 (i) the thresholds, EthrQ , approximately follow from the mass differences between the quarkonium, , and the lightest open beauty hadron pair, taking into account the co Q EQ size geoQ Q comover mass; thr Q (2S) 50MeV 0.90fm 6.36mb 5.15 0.84 mb ± (ii) away from the thresholds, the cross section should scale like the geometrical cross 2 X(3872) tetraquark 21 MeV 1.3 fm 13.27 mb 11.10 1.56 mb section, σgeoQ πr , where r is the quarkonium Bohr radius. It can be evaluated ± ≃ Q X(3872) molecular 0.01 MeV 7 fm 384.84 mb 329.43 55.39 mb by solving the Schr¨odingerequationQ with a well-choosen potential reproducing the ± quarkonium spectroscopy [30]. TABLE I. Fixed valuesBehaviour used in our of X(3872)/ parametrisation ofψ the(2S) comoverwith cross mul plicity sections and the resultingOur parametrisation values. of the energy dependence thus simply amounts to interpolating JHEP10(2018)094 co co co co from σ (E = EQ ) = 0 at threshold up to σ (E EQ )=σ away from −Q thr −Q ≫ thr geoQ • Let’s consider X(3872) as a compact object => interac onthreshold cross but sec ons with the same can be dependencecalculated for all the states. It reads co n EQ r geoQ Q For the 2S: Satz 0512217 co co EthrQ thr Q σ (E )=σ 1 (2.4) For the X tetraquark: −Q geoQ co (2S) 50 MeV 0.45 fm 6.36 mb 5.15 0.84 mb × ! − E " ± Esposito,Polosa 1807.06040 X(3872) tetraquark 200 keV 0.65 fm 13.3 mb 11.61 1.69 mb Maianiwhere et al. 0412098 EQ = M + mco 2MB is the threshold energy to break the quarkonium bound thr Q ± co 2 −2 X(3872) molecule 200 keV 5.0 fm 785 mb 687 98 mb Forstate X molecular: and E = Beverenp + mco & isRupp the energy of the comover in the quarkonium rest frame. ± In the case of a hadronic# medium (made of pions), mco =0.140 GeV, while it is zero for TABLE II. Fixed values used inCross our parametrisationsec ons very of close the comover to their cross geometrical sections and thevalue resulting due gluons.to values. small The By geometrical bindingr we cross indicate energies sections σgeoQ whichinvolved we used are shown in table 1, together 2 Q the expectation value of the radius of the state, and by geoQ = ⇡r the geometrical cross section.with the The threshold average energies overEthrQ theand the bottomonium radii. The first free parameter of co Q comover distribution Q and0.12 its uncertainties are described in the text. For the (2S), the thresholdour modeling, is setn, at characterises the average how quickly the cross section approaches the geometrical 0 ¯ 0 + cross section. Attempts+ to compute this energy dependence, using the multipole expansion D D -D D mass, which is the lightest OZI-favored mode available. ForX(3872)/ the tetraquark,ψ(2S) the OZI-favored• Cross sec ons mode ⇤c ⇤calculatedc [10–12] as for Υ 0 0 R(X/2S) 0.1 is not kinematically allowed at the typical comover energy. We consider the next favored decay is intoin perturbative open charm, QCDD at¯ LOD⇤ [30–[3213],]. would suggest that n is close to 4 for pion comovers The PDG average for this binding energy is 16 200 keV. In our calculations, we use as bindingby energy making the the strong 1 error. assumption The that the scattering is initiated by gluons inside these 0.08 ± • Parameters involved: size & binding E radius of the tetraquark is taken from [3, 13]. tetraquark: 1 to 1.5 fm pions. Hadronic models which take into account non-perturbative effects and thus most 0.06 • Ourlikely results provide a are betternormalized description of the physicsto the at work [33] show a different energy 0.04 dependence. It effectively corresponds to smaller n [34]. As such, we will consider n experimental varying from 0.5 to 2.value In fact, obtained the discrepancies for existing the between the aforementioned LO 0.02 III. RESULTS FOR PROTON-PROTONmolecula: size 5 to2013, 10 fm the ratios of the excitedfirst toQCD the bin results ground and these state hadronic cross calculations are partly due to large higher order correction COLLISIONS0 near the threshold [35]. 1 1.5 2 2.5sections, 3 3.5 ⌥(nS)/ 4⌥(1S), 4.5 both in pp and pPb collisions at 2.76 TeV and 5.02n/ Recombination e↵ects on compact objects has been ex- tensively confirmed to be negligible by experimental data. Conversely, for hadron molecules it has been already advo- cated that the interaction with comoving particles could sensibly increase their production [15–19]. Indeed, recent measurements by the ALICE collaboration have shown that the number of deuterons produced in pp collisions at 7 and 13 TeV increases with multiplicity [20, 21]. Were a molecular X to behave like that, it would be in striking X n contrast with the data presented by LHCb [4]. FIG. 2. R[ (2S) ]vs E. G. Ferreiro USC Quarkonium & related observables from pp to AA 14 SnowMass2021 16/12/2020 4 the CIM to proton-proton data, we can extract informa- to-ground upsilon states in pp collisions at 2.76 TeV, hap- tion on the structure of the X(3872). The main ingredient pened to be a factor 1.5 for ⌥(2S)/ ⌥(1S) and a factor of will be its interaction cross section with the comovers, 3 for ⌥(3S)/ ⌥(1S) when going from mean multiplicity calculated according to Eq. (5). As mentioned above, the to 4 times the mean multiplicity. fact that the X(3872) binding energy is very low –this is On the other hand, in case of a molecular X(3872) of 5 clearly the case if X(3872) is considered to be a molecu- fm, it will not survive at multiplicities twice the mean one. lar state, but this is also true for a X(3872) tetraquark If the molecula has a size of 10 fm, the X(3872) would be [3]– makes its interaction cross section very close to the destroyed by interactions with the comovers already at geometrical value. We will consider di↵erent sizes for the multiplicities of 1.5 the mean one. X(3872), from 1 to 2 fm in the tetraquark case, and from In the present implementation of the final state inter- 5 to 10 fm in the molecular case. actions, no secondary charmonium production has been In order to measure the e↵ects of the comovers with in- considered. Coalescence e↵ects, similar to the ones ap- creasing multiplicity, we have calculated the rate X(3872) (2S) plied to reproduce the deuteron-to-proton ratio in pp n versus Recombination e↵ects on compact objects has been ex- tensively confirmed to be negligible by experimental data. Conversely, for hadron molecules it has been already advo- cated that the interaction with comoving particles could sensibly increase their production [15–19]. Indeed, recent measurements by the ALICE collaboration have shown that the number of deuterons produced in pp collisions at 7 and 13 TeV increases with multiplicity [20, 21]. Were a molecular X to behave like that, it would be in striking X n contrast with the data presented by LHCb [4]. FIG. 2. R[ (2S) ]vs the event multiplicity, Nch: Appendix A: Boltzmann equation for hadron N v molecules and comovers m = h im N12 v hh + v m h i 0 h i In this derivation, we will follow [27]. In particular, we N v m (7) + m h i will use the standard noncovariant form of the Boltzmann N v + v ⇥ ✓ 12 hh m ◆ equation, and all the quantities discussed below are meant h i h i pp exp v hh + v m ⇢c ln(⇢c/⇢c ) , to be defined in the lab frame. We discuss the creation ⇥ h i h i and destruction of hadron molecules as due to elastic 0 were Nm is the⇥ number of molecules generated⇤ by scattering of a comover with one of the constituents[17– hadronization, but before any further interaction with 19]. For example, for the deuteron we restrict to processes 0 comovers. We expect Nm N12. The dependence on like ⇡pn )* ⇡d. ⌧ multiplicity enters through the comovers’ spatial density, Consider two hadrons, ‘1’ and ‘2’, with positions 3 ⇢c = Nch/ Nch/a. The factor 3/2 accounts for the and momenta (x , q ) and (x , q ). We adopt the co- 2 ⌘ 1 1 2 2 neutral comovers. From the eikonal-Glauber model [22], alescence picture, i.e. that the two hadrons bind if which successfully reproduces charged multiplicities in their relative momentum is smaller than some thresh- proton and nuclear collisions, we have estimated the old, q q < ⇤. The phase-space density for these two | 1 2| non-di↵ractive cross section to be 63.3 mb, which gives hadrons, n12(x1, x2, q1, q2,⌧), is such that a 42.2mb. 3 3 'We test the validity of this idea on data. For deuteron 3 3 d q1 d q2 Nm(⌧)= d x1d x2 3 3 n12(xi, qi,⌧) , we consider a coalescence momentum ⇤= 150 MeV [23– ⇤ (2⇡) (2⇡) Z ZR 3 3 25]. The momentum distributions for the free constituents 3 3 d q1 d q2 1 Pythia8 Nhh(⌧)= d x1d x2 n12(xi, qi,⌧) , and for the comovers are taken from [26], while ¯ (2⇡)3 (2⇡)3 those for deuteron are taken directly from data [20]. Z ZR⇤ d3q d3q With this information at hand one can compute the av- N = d3x d3x 1 2 n (x , q ,⌧) , 12 1 2 (2⇡)3 (2⇡)3 12 i i erage cross sections for creation and destruction of a Z Z deuteron (see Appendix B), obtaining v 0.51 mb (A1) h im ' and v hh 4.34 mb. We also estimate the number of ¯ h i ' where ⇤ is the domain where q1 q2 < ⇤, and ⇤ initial deuterons with Pythia8, by counting how many its complement.R N , N and N| are respectively| R the proton-neutron pairs have relative momentum initially m hh 12 0 4 number of molecules, free pairs and total pairs. Clearly below ⇤. We find N /N12 = O(10 ), which can be m N12 = Nm +Nhh, and it is assumed to be constant in time, neglected. All the above completely fix the dependence of hence neglecting creation/annihilation of the constituents the number of deuterons on multiplicity, up to an overall pp themselves. In the lab frame, the variable ⌧ can be taken factor, which we fit to data. We also set ⇢c =1/a,tolet simply as the time. the curve start at Nch = 1, as suggested by data. We assume that the spatial and momentum distribu- tions factorize as 1 ⇢m(xi,⌧) fm(qi,⌧) for q1 q2 < ⇤ In our simulations we define as a comover any long-lived particle n12 | | , (A2) ' ⇢ (x ,⌧) f (q ,⌧) for q q ⇤ which interacts with one of the constituents. ( hh i hh i | 1 2| Future X(3872) studies in HI collisions • For low PT produc on, dissocia on and recombina on of X(3872) similar to those of charmonium can happen in the hot QGP or in the hadronic gas So far, only the ra o between produc on yields of X(3872) and Ψ(2S) has been measured by the CMS collabora on in the pT = 10-50 GeV range Tetra- VERY PRELIMINAR R(X/2S) quark from 1 Integrated value: to 1.7 RPbPbψ(2S)=0.147, fm RPbPb(X(3872)=1.239 (for 1.7 fm) to 0.59 (for 1 fm) Our result: R(2S/X)PbPb= 0.5-0.9 2S E. G. Ferreiro USC Quarkonium & related observables from pp to AA 15 SnowMass2021 16/12/2020 New observables can help Observables Experiments CSM CEM NRQCD Interest J/ψ+J/ψ LHCb, CMS, ATLAS, D0 (+NA3) NLO, LO ? LO Prod. Mechanism (CS dominant) + DPS + gluon TMD NNLO* J/ψ+D LHCb LO LO ? LO Prod. Mechanism (c to J/psi fragmenta on) + DPS J/ψ+ϒ D0 (N)LO LO ? LO Prod. Mechanism (CO dominant) + DPS J/ψ+hadron STAR LO -- LO B feed-down; Singlet vs Octet radia on J/ψ+Z ATLAS NLO NLO Par al Prod. Mechanism + DPS NLO J/ψ+W ATLAS LO LO ? Par al Prod. Mechanism (CO dominant) + DPS NLO J/ψ vs mult. ALICE,CMS (+UA1) ------Density effects (Satura on/Hydro) J/ψ+b -- (LHCb, D0, CMS ?) -- -- LO Prod. Mechanism (CO dominant) + DPS ϒ+D LHCb LO LO ? LO DPS ϒ+γ -- NLO, LO ? LO Prod. Mechanism (CO LDME mix) + gluon TMD/PDF NNLO* ϒ vs mult. CMS ------Density effects (Satura on/Hydro) ϒ+Z -- NLO LO ? LO Prod. Mechanism + DPS ϒ+ϒ CMS NLO? LO? LO? Prod. Mechanism + DPS + gluon TMD Lansberg (2018) E. G. Ferreiro USC Quarkonium & related observables from pp to AA SnowMass2021 16/12/2020