Scaling patterns in ATLAS & CMS quarkonium production data

Transcription

1 Scaling patterns in ATLAS & CMS quarkonium production data Pietro Faccioli, IST and LIP, Lisbon C. Lourenço M. Araújo J. Seixas Quarkonium Working Group, November 8 th shapes of the p T distributions in pp collisions 2. pp cross-section scaling with mass 3. centrality dependence in Pb-Pb collisions

2 p T distributions in pp collisions 2 Mid-rapidity cross section measurements show a common shape pattern for p T /M > 2 dσ/dp T vs p T /M arxiv: [PF et al. PLB 773, 476 (2017)]

3 p T distributions in pp collisions Scaling all data to match the J/ψ normalization 3 arxiv:

4 p T distributions in pp collisions 4 arxiv: Higher energy, broader distribution

5 Goodness of the global p T /M fit 5 Distribution of pulls (7 TeV fit)

6 Zoom : χ 1 vs χ 2 vs ψ 6 Purely kinematic scaling no sign of a dependence of the production dynamics on the quantum numbers!

7 Polarization 7 Polar decay anisotropy in the helicity frame vs p T CMS, TeV ϒ(1S): 40% χ b ψ(2s) J/ψ ϒ(1S) ψ(2s): feed-down free J/ψ: 25% χ c PLB 727 (2013) 382 PRL 110 (2013) S-wave quarkonia: small decay anisotropies with no significant p T dependences No indications of differences between states, despite very different feed-down contributions P-wave states

8 NRQCD vs simple data pattern 8 Considering e.g. cross-section SDC contributions (polarizations are as much diversified): NLO 1 S 3 S P J/ψ, ψ(2s) ϒ(1S), ϒ(2S), ϒ(3S) 3 S 1 3 P 1 3 S 1 χ c1, χ b1 3 P 2 3 S 1 χ c2, χ b2 3 P S 0 3 P 2 3 P 1 Negative P-wave contributions require exact cancellation for every p T /M to recover physical result Different final states come different pre-resonance mixtures, with rather diversified kinematic behaviours The variety of kinematic behaviours in NRQCD seems redundant with respect to the observed universal p T /M scaling and lack of polarization Conspiring SDC LDME combinations needed to reproduce data Curves H.-S. Shao et. al., PRL 108, ; PRL 112, ; Comput. Phys. Commun. 198, 238

9 A surprising agreement 9 Conspiracies actually happen: NRQCD is able to reproduce the simple data patterns New method of theory-data comparison [PF et al., PLB 773, 476 (2017)], unbiased by specific theoretical calculations of partonic cross sections: calculated NLO SDC combinations are in good agreement with the results of a fully data-driven fit of charmonium data, taking into account feed-down and constrained by polarization results dσ/dp T [a.u.] Experimental shapes of the direct-production cross sections J/ψ & ψ(2s) - data calc. NLO 1 S 0 [8] χ c1 - data calc. NLO 3 S 1 [8] + 3 P 1 [1] χ c2 - data calc. NLO 3 S 1 [8] + 3 P 2 [1] p T /M p T /M p T /M The three measured shapes are almost identical to one another Calculated shapes are within sigma data

10 Ultimate conspiracy or need for a better NRQCD? 10 Coincidentally, this seeming success of NRQCD brings along a strong prediction: the unmeasured χ c1 and χ c2 polarizations must be very different one another λ θ Δλ θ 1 at the barycentre of existing χ c cross-section data A potentially striking exception to the uniform picture of mid-rapidity quarkonium production! p T /M Will experiments find a large χ c2 χ c1 polarization difference? smoking gun! weak χ c1 and χ c2 polarizations as for S-wave states? need of improved (simpler?) NRQCD hierarchies or better perturbative calculations This prediction (PF et al., arxiv: ) is dramatically different that of H.-S. Shao et al., PRL 112, , because the huge acceptance-polarization correlations in the χ c -ratio data are properly considered

11 Mass scaling charm to beauty 11 Exploiting p T /M scaling we can determine the mass scaling of the cross section without model-dependent extrapolations to low p T : it is sufficient to measure the ratio of the fitted p T /M distributions at one (arbitrary!) p T /M point How does the production cross section scales charmonium (m c ) to bottomonium (m b )? We consider the two mesons closer to ground state, J/ψ and ϒ(1S), correcting for feed-down. Assumption for ϒ(1S): f DIR = (50 ± 10)% dσ/dp T (ϒ(1S)) dσ/dp T (J/ψ) m α = b m c α = 6.6 ± ± TeV 13 TeV

12 Comparison to a simple reference: Drell-Yan 12 quarkonium, 7 TeV: dσ/dp T (ϒ(1S)) dσ/dp T (J/ψ) m (6.6 ± 0.1) = b m c Drell-Yan at 7 8 TeV for M < M Z : dσ/dm(m 2 ) dσ/dm(m 1 ) From dimensional analysis: dσ DY dm dσ DY dm M 3 (3 + β) M including β = 0.63 ± 0.03 M (3.63 ± 0.03) = 2 M 1 at partonic level JHEP 06 (2014) 112 JHEP 12 (2013) 030 EPJ C 75 (2015) 147 parton-luminosity factor ( s/m) β, common to all processes the PDF-undressed quarkonium cross section goes like m Q (6.0 ± 0.1) Note: the power-3 difference of quarkonium wrt DY is just what is needed to accommodate the [m Q3 ]-dimensional bound-state wave function

13 Implications of the observed scaling patterns Inclusive quarkonium production cross section pure dimensional analysis: 13 dσ dp T = Σ i m Q 3 global dimensionality L i (m Q, M, p T /M, y, s/m) m Q 3 L = purely formal LDME terms, defined to have the same [m Q3 ] dimensionality of the bound-state wave function F i (m Q, M, p T /M, y, s/m) generic dimensionless factors s M parton luminosity β = 0.63 ± 0.03 for s = 7-8 TeV L i and F i here a priori generic (and redundant) functions _ of the relevant variables. No assumption about possible factorization into QQ creation bound-state formation ATLAS and CMS data at y < 2 and p T /M > 2 tell us that: 1) the p T /M dependence is the same irrespectively of m Q and M 2) charmonium to bottomonium the partonic-level (PDF-undressed) cross section scales like m 6 Q, with no observed dependence on s y dependence to be studied ( LHCb data) 1) p T /M and {m Q, M} do not mix: L F writeable as L (m Q, M, s/m) F (p T /M, y, s/m) an experimental evidence that short- and long-distance effects factorize (*) 2) further specification of the LDME : L = L(M/m Q ), independent of m Q and s (*) β

14 Implications of the observed scaling patterns Inclusive quarkonium production cross section pure dimensional analysis: 14 dσ dp T = Σ i m Q 3 global dimensionality L i (m Q, M, p T /M, y, s/m) m Q 3 L = purely formal LDME terms, defined to have the same [m Q3 ] dimensionality of the bound-state wave function F i (m Q, M, p T /M, y, s/m) generic dimensionless factors s M parton luminosity β = 0.63 ± 0.03 for s = 7-8 TeV L i and F i here a priori generic (and redundant) functions _ of the relevant variables. No assumption about possible factorization into QQ creation bound-state formation ATLAS and CMS data at y < 2 and p T /M > 2 tell us that: 1) the p T /M dependence is the same irrespectively of m Q and M 2) charmonium to bottomonium the partonic-level (PDF-undressed) cross section scales like m 6 Q, with no observed dependence on s y dependence to be studied ( LHCb data) 1) p T /M and {m Q, M} do not mix: L F writeable as L (m Q, M, s/m) F (p T /M, y, s/m) an experimental evidence that short- and long-distance effects factorize (*) 2) further specification of the LDME : L = L(M/m Q ), independent of m Q and s (*) β

15 Mass scaling of S-wave cross sections 15 Refined determination of the mass scaling, using all S states and adopting the short long-distance factorized point of view: initial assumption (iteratively improved): two sections of same curve 7 TeV f DIR = ( ± 10)% for Y(1 2 3S) inspired by data including LHCb s forward-rapidity χ b [EPJ C 74, 3092] dσ/dp T (M 2m c ) short distance. dσ/dp T (M 2m b ) (dependence on m Q ):. dσ/dp T (M 2m b ) dσ/dp T (M 2m c ) m (6.63 ± 0.08) = b m c long distance (M/m Q )-dependent LDME : dσ/dp T (M = M ψ ϒ ) dσ/dp T (M 2m c b ) M (9.7 ± 0.3) = ψ ϒ 2m c b one common slope parameter fits well ψ and ϒ states Using: 2m Q = M ηc (1S) M ηb (1S)

16 Long-distance scaling: a universal pattern? 16 The LDMEs show a clear correlation with binding energy, common to charmonium and bottomonium identical at 7 and 13 TeV 7 TeV ϒ(1S) 13 TeV ϒ(1S) ϒ(2S) J/ψ ϒ(2S) J/ψ ϒ(3S) σ ψ ϒ σ QQ δ E binding ϒ(3S) ψ(2s) δ = 0.63 ± 0.02 δ = 0.63 ± 0.04 ψ(2s) 0.63 just as β: confusing coincidence E binding = E binding = further support to the assumption that the dependence on bound-state mass is a factorizable long-distance effect (= abstract lab momentum dependence)

17 The missing pieces of quarkonium feed-down Assuming that the universal Ebinding dependence hypothesis can be extended to the P-wave states, σχ 0.63 ± 0.02 E binding σqq χc data come to constrain the χb(1-2-3p) cross sections and, using BRs PDG, the feed-down structure of quarkonium production can be fully predicted Y1S Feed-down fractions in pp (%): Jpsi chic chic chic psi2s Y1S ( ) E-5 Y2S ( ) E-5 chic0 psi2s Y1S Y2S (3.4 (1.5 psi2s Y1S Y2S ( ) E-5 ( ) E-5 chic2 psi2s Y1S Y2S ( ) E-5 ( ) E-5 psi2s Y1S Y2S ( ) E-4 ( ) E-4 ( ) E-4 chic ) E-5 1.5) E-5 chib0_1p chib1_1p chib2_1p Y2S chib0_2p chib1_2p chib2_2p Y3S chib0_3p chib1_3p chib2_3p chib0_1p Y2S Y3S chib1_1p Y2S Y3S chib2_1p Y2S Y3S Y2S chib0_2p chib1_2p chib2_2p Y3S chib0_3p chib1_3p chib2_3p chib0_2p Y3S chib1_2p Y3S chib2_2p Y3S Y3S chib0_3p chib1_3p chib2_3p

18 Comparison with existing data 18 The predicted χ b ϒ feed-downs are in reasonable agreement with forward-rapidity LHCb data (considered for p T /M > 2) [EPJ C 74, 3092]

19 Nuclear modifications in Pb-Pb 19 How is the universal E binding -scaling modified in Pb-Pb? Can we describe Pb-Pb data assuming a minimal modification of the simple parametrization found for pp data? Hint data: the double charmonium ratio R AA (2S)/R AA (1S) is well below 1 already in peripheral events ψ(2s) has a very small binding energy a threshold effect in binding energy? CMS, PRL 118,

20 Nuclear modifications in Pb-Pb 20 We want to study the measured AA-to-pp production ratio R AA as a function of binding energy centrality

21 One hypothesis, different interpretations 21 Base assumption: nuclear effects modify the universal bound-state formation pattern as follows: pp σ ψ ϒ σ QQ δ E binding AA σ ψ ϒ σ QQ δ (E binding ΔE) With increasing ΔE it becomes less and less probable to form the bound state. For ΔE >= E binding the QQbar never transforms into quarkonium An empirical parametrization with different interpretations and possibly including different physics effects, e.g.: E binding (J/ψ) = 2M(D 0 ) M(J/ψ) [2M(D 0 ) ΔE] M(J/ψ)? E binding (J/ψ) ΔE = 2M(D 0 ) [M(J/ψ) + ΔE]? screening effectively reduces di-meson threshold? multiple scattering effectively increases Q Qbar relative momentum and invariant mass? J. Qiu et al., PRL 88 (2002)

22 Parameters and ingredients 22 pp σ ψ ϒ σ QQ δ E binding AA σ ψ ϒ σ QQ δ (E binding ΔE) ΔE is determined data in each condition (centrality, energy), but we test the approximation that it is always the same for all states Additional parameter: the width of the ΔE distribution, σ ΔE, for simplicity centrality-independent All the rest is fixed pp data: same parameter δ = 0.63 ± 0.04 used in AA as in pp same short-distance cross-section dependence used in AA as in pp cross sections of all states calculated in pp and AA for each condition; all varying feed-down effects included in the parametrization

23 Examples Curves: suppression of directly produced states Points: including effect of feed-down specific to each state 23 ΔE = 0.02 GeV ΔE = 0.25 GeV χ b0 (3P) χ b1 (3P) χ b2, χ b1, χ b0 (1P) ϒ(1S) ΔE = 0.55 GeV σ ΔE = 0.03 GeV ψ(2s) χ b2 (3P) χ c0 χ b1 (2P) χ b2 (2P) ϒ(3S) ϒ(2S) χ b0 (2P) J/ψ χ c1 χ c2

24 Examples Curves: suppression of directly produced states Points: including effect of feed-down specific to each state 24 ΔE = 0.55 GeV σ ΔE = 0.03 GeV ϒ(1S) ψ(2s) ϒ(3S) ϒ(2S) J/ψ

25 Global data fit: R AA vs centrality 25 J/ψ ψ(2s) ψ(2s) / J/ψ ratio (not fitted) These are the 37 points entering the fit ϒ(1S) ϒ(2S) ϒ(3S) (no data) ΔE = a + b log(n part ) a, b free parameters σ ΔE = (30 ± 5) MeV (free parameter) CMS & ATLAS 5.02 TeV CMS-PAS HIN CMS-PAS HIN ATLAS-CONF free parameters - 70 nuisance parameters (BRs, pp cross sections, global experimental uncertainties) Good fit quality P(χ 2 ) = 22% Improves if the absolute energy shift ΔE is allowed to be different for charmonium and bottomonium

26 Global data fit: R AA vs E binding Examples of projections at some N part values CMS & ATLAS 5.02 TeV CMS-PAS HIN CMS-PAS HIN ATLAS-CONF N part = 21 N part = 53 N part = 87 CMS & ATLAS 5.02 TeV ψ(2s) J/ψ ϒ(1S) gray: direct production coloured: + feed-down ϒ(3S) ϒ(2S) N part = 131 N part = 189 N part = 264

27 Summary 27 At the current level of experimental precision, mid-rapidity LHC pp data for charmonium and bottomonium are well described by a simple parametrization reflecting a universal (=state-independent) scaling with two variables: 1. shapes of the p T distributions in pp collisions p T /M 2. pp cross-section scaling with mass E binding This parametrization mirrors well the general idea of factorization of NRQCD. While the observed simplicity is in seeming contradiction with the calculated SDCs, cancellations ultimately enable NRQCD to succeed. Will the striking χ c1 and χ c2 polarization predictions bring us to a new theory-data clash? Also PbPb data (for S-waves) show a surprisingly simple pattern: R AA can be parametrized assuming a (centrality/energy-dependent) shift of the binding-energy, equal in magnitude, at least in first approximation, for all c-cbar and b-bbar states 3. centrality dependence in Pb-Pb collisions E binding ΔE