CMS-BPH-13-001

CMS-BPH-13-001 ; CERN-EP-2019-279
Measurement of the ${\chi_{\mathrm{c}1}}$ and ${\chi_{\mathrm{c}2}}$ polarizations in proton-proton collisions at $\sqrt{s} = $ 8 TeV
CMS Collaboration
16 December 2019
Phys. Rev. Lett. 124 (2020) 162002
Abstract: The polarizations of promptly produced ${\chi_{\mathrm{c}1}}$ and ${\chi_{\mathrm{c}2}}$ mesons are studied using data collected by the CMS experiment at the LHC, in proton-proton collisions at $\sqrt{s} = $ 8 TeV. The ${\chi_{\mathrm{c}}}$ states are reconstructed via their radiative decays ${\chi_{\mathrm{c}}} \rightarrow \mathrm{J}/\psi\, \gamma$, with the photons being measured through conversions to $\mathrm{e^{+}}\mathrm{e^{-}}$, which allows the two states to be well resolved. The polarizations are measured in the helicity frame, through the analysis of the ${\chi_{\mathrm{c}2}}$ to ${\chi_{\mathrm{c}1}}$ yield ratio as a function of the polar or azimuthal angle of the positive muon emitted in the $\mathrm{J}/\psi \to \mu^+\mu^-$ decay, in three ranges of $\mathrm{J}/\psi$ transverse momentum. While no differences are seen between the two states in terms of azimuthal decay angle distributions, they are observed to have significantly different polar anisotropies. The measurement favors a scenario where at least one of the two states is strongly polarized along the helicity quantization axis, in agreement with nonrelativistic quantum chromodynamics predictions. This is the first measurement of significantly polarized quarkonia produced at high transverse momentum.
Links: e-print arXiv:1912.07706 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ;

Figures	Summary	References	CMS Publications

Figures
png pdf	Figure 1: Example of a fitted ${\mathrm{J}/\psi} \, \gamma $ invariant mass distribution, for the 0.15 $ < {{\| \cos\vartheta \|}} < $ 0.225 bin, in the 12-18 GeV ${p_{\mathrm {T}}}$ range. The vertical bars on the points indicate the statistical uncertainties. The lines show the various fit contributions.
png pdf	Figure 2: The $ {{\chi _{{\mathrm{c}}2}}} $/$ {{\chi _{{\mathrm{c}}1}}} $ yield ratio vs. $\varphi $ (left) and ${{\| \cos\vartheta \|}}$ (right), in the helicity frame, for the three ${\mathrm{J}/\psi}$ $ {p_{\mathrm {T}}}$ ranges. The grey markers (slightly shifted horizontally) show the values before acceptance and efficiency corrections, scaled vertically for an easier shape comparison. The vertical bars represent the statistical uncertainties and the horizontal bars the bin widths. The solid and dashed curves show, respectively, the "NRQCD" [44] and "unpolarized" scenarios. The dotted and dash-dotted curves illustrate maximally different natural polarizations in the Collins-Soper frame, leading to large differences in azimuthal anisotropy.
png pdf	Figure 3: Two-dimensional $ {\lambda _\vartheta} ^{\,{{\chi _{{\mathrm{c}}2}}}}$ vs. $ {\lambda _\vartheta} ^{\,{{\chi _{{\mathrm{c}}1}}}}$ contours, at 68.3, 95.5, and 99.7% confidence levels (CL), measured combining the three ${\mathrm{J}/\psi}$ $ {p_{\mathrm {T}}}$ ranges. The physically allowed region (red rectangle) and six pure angular momentum configurations (markers) are also shown. The crossing of the two dashed lines represents the unpolarized case.
png pdf	Figure 4: The $ {\lambda _\vartheta} ^{\,{{\chi _{{\mathrm{c}}2}}}}$ values (circles) measured when the $ {\lambda _\vartheta} ^{\,{{\chi _{{\mathrm{c}}1}}}}$ values (squares) are fixed to the unpolarized (left) or the NRQCD (right) scenarios (green curves), as a function of $ {p_{\mathrm {T}}} /M$ of the ${\mathrm{J}/\psi}$. The purple band on the right is the NRQCD prediction for $ {\lambda _\vartheta} ^{\,{{\chi _{{\mathrm{c}}2}}}}$ [44], while in the unpolarized scenario $ {\lambda _\vartheta} ^{\,{{\chi _{{\mathrm{c}}2}}}} = {\lambda _\vartheta} ^{\,{{\chi _{{\mathrm{c}}1}}}} = $ 0. The markers are shown at the average $ {p_{\mathrm {T}}} /M$ values in each bin, the vertical bars represent the total uncertainties, and the horizontal bars the bin widths. The dashed lines indicate the physically allowed range of $ {\lambda _\vartheta} ^{\,{{\chi _{{\mathrm{c}}2}}}}$.

Summary

In summary, the polarizations of promptly produced $\chi_{\mathrm{c}1}$ and $\chi_{\mathrm{c}2}$ mesons have been measured in pp collisions at $\sqrt{s} = $ 8 TeV. The analysis uses the $\mathrm{J}/\psi \, \gamma$ decay channel in three $\mathrm{J}/\psi$ $p_{\mathrm{T}}$ ranges between 8 and 30 GeV. The measurement, made in the helicity frame, shows a significant difference between the polar anisotropy parameters ${\lambda_{\vartheta}}^{\chi_{\mathrm{c}1}}$ and ${\lambda_{\vartheta}}^{\chi_{\mathrm{c}2}}$. The result strongly disfavors, in particular, the unpolarized scenario uniformly observed in the $\mathrm{J}/\psi$, $\psi\text{(2S)}$, and $\Upsilon$ measurements. Remarkably, the measurement agrees with the NRQCD prediction. This result provides a new piece in the experimental scenario of quarkonium production at mid-rapidity and the first significant indication of kinematic differences between the various quarkonia. It should improve the understanding of hadron formation and of the interplay between the long- and short-distance aspects of the strong interaction.

References
1	G. Bodwin, E. Braaten, and P. Lepage	Rigorous QCD analysis of inclusive annihilation and production of heavy quarkonium	PRD 51 (1995) 1125	hep-ph/9407339
2	M. Butenschoen and B. A. Kniehl	$ \mathrm{J}/\psi $ polarization at Tevatron and LHC: nonrelativistic-QCD factorization at the crossroads	PRL 108 (2012) 172002	1201.1872
3	M. Butenschoen and B. A. Kniehl	Next-to-leading-order tests of NRQCD factorization with $ \mathrm{J}/\psi $ yield and polarization	MPLA 28 (2013) 1350027	1212.2037
4	K.-T. Chao et al.	$ \mathrm{J}/\psi $ polarization at hadron colliders in nonrelativistic QCD	PRL 108 (2012) 242004	1201.2675
5	B. Gong, L.-P. Wan, J.-X. Wang, and H.-F. Zhang	Polarization for prompt $ \mathrm{J}/\psi $ and $ \psi $(2S) production at the Tevatron and LHC	PRL 110 (2013) 042002	1205.6682
6	H.-S. Shao, Y.-Q. Ma, K. Wang, and K.-T. Chao	Polarizations of $ {\chi _{{\mathrm{c}}1}} $ and $ {\chi _{{\mathrm{c}}2}} $ in prompt production at the LHC	PRL 112 (2014) 182003	1402.2913
7	H.-S. Shao and K.-T. Chao	Spin correlations in polarizations of P-wave charmonia $ {\chi _{{\mathrm{c}}J}} $ and impact on $ \mathrm{J}/\psi $ polarization	PRD 90 (2014) 014002	1209.4610
8	G. T. Bodwin et al.	Fragmentation contributions to hadroproduction of prompt $ \mathrm{J}/\psi, {\chi _{{\mathrm{c}}J}}, $ and $ \psi $(2S) states	PRD 93 (2016) 034041	1509.07904
9	CDF Collaboration	J/$ \psi $ and $ \psi(2S) $ production in $ {\mathrm{p}}\bar{{\mathrm{p}}} $ collisions at $ \sqrt{s} = $ 1.8 TeV	PRL 79 (1997) 572
10	R. Baier and R. Ruckl	Hadronic production of $ \mathrm{J}/\psi $ and $ \Upsilon $: transverse momentum distributions	PLB 102 (1981) 364
11	J.-P. Lansberg	On the mechanisms of heavy-quarkonium hadroproduction	EPJC 61 (2009) 693	0811.4005
12	CMS Collaboration	Measurement of $ \mathrm{J}/\psi $ and $ \psi^\prime $ prompt double-differential cross sections in pp collisions at $ \sqrt{s}= $ 7 TeV	PRL 114 (2015) 191802	CMS-BPH-14-001 1502.04155
13	ATLAS Collaboration	Measurement of the production cross-section of $ \psi^\prime \to \mathrm{J}/\psi (\to \mu^{+} \mu^{-}) \pi^{+} \pi^{-} $ in pp collisions at $ \sqrt{s} = $ 7 TeV at ATLAS	JHEP 09 (2014) 079	1407.5532
14	CMS Collaboration	Measurements of the $ \Upsilon $(1S), $ \Upsilon $(2S), and $ \Upsilon $(3S) differential cross sections in pp collisions at $ \sqrt{s} = $ 7 TeV	PLB 749 (2015) 14	CMS-BPH-12-006 1501.07750
15	ATLAS Collaboration	Measurement of $ \Upsilon $ production in 7 TeV pp collisions at ATLAS	PRD 87 (2013) 052004	1211.7255
16	CMS Collaboration	Measurement of quarkonium production cross sections in pp collisions at $ \sqrt{s}= $ 13 TeV	PLB 780 (2018) 251	CMS-BPH-15-005 1710.11002
17	ATLAS Collaboration	Measurement of $ \chi_{c1} $ and $ \chi_{c2} $ production with $ \sqrt{s} = $ 7 TeV pp collisions at ATLAS	JHEP 07 (2014) 154	1404.7035
18	CMS Collaboration	Measurement of the relative prompt production rate of $ \chi_{c2} $ and $ \chi_{c1} $ in pp collisions at $ \sqrt{s} = $ 7 TeV	EPJC 72 (2012) 2251	CMS-BPH-11-010 1210.0875
19	CMS Collaboration	Measurement of the production cross section ratio $ \sigma(\chi_{b2}{\rm (1P)}) / \sigma(\chi_{b1}{\rm (1P)}) $ in pp collisions at $ \sqrt{s} = $ 8 TeV	PLB 743 (2015) 383	CMS-BPH-13-005 1409.5761
20	CMS Collaboration	Measurement of the prompt $ \mathrm{J}/\psi $ and $ \psi^\prime $ polarizations in pp collisions at $ \sqrt{s} = $ 7 TeV	PLB 727 (2013) 381	CMS-BPH-13-003 1307.6070
21	CMS Collaboration	Measurement of the $ \Upsilon $(1S), $ \Upsilon $(2S), and $ \Upsilon $(3S) polarizations in pp collisions at $ \sqrt{s}= $ 7 TeV	PRL 110 (2013) 081802	CMS-BPH-11-023 1209.2922
22	P. Faccioli et al.	Quarkonium production in the LHC era: A polarized perspective	PLB 736 (2014) 98	1403.3970
23	P. Faccioli et al.	Quarkonium production at the LHC: A data-driven analysis of remarkably simple experimental patterns	PLB 773 (2017) 476	1702.04208
24	P. Faccioli, C. Lourenço, M. Araújo, and J. Seixas	Universal kinematic scaling as a probe of factorized long-distance effects in high-energy quarkonium production	EPJC 78 (2018) 118	1802.01102
25	E. Mirkes and J. Ohnemus	W and Z polarization effects in hadronic collisions	PRD 50 (1994) 5692	hep-ph/9406381
26	CDF Collaboration	First measurement of the angular coefficients of Drell--Yan e$ ^{+} $e$ ^{-} $ pairs in the Z mass region from $ {\mathrm{p}}\bar{{\mathrm{p}}} $ collisions at $ \sqrt{s} = $ 1.96 TeV	PRL 106 (2011) 241801	1103.5699
27	CMS Collaboration	Angular coefficients of Z bosons produced in pp collisions at $ \sqrt{s} = $ 8 TeV and decaying to $ \mu^+ \mu^- $ as a function of transverse momentum and rapidity	PLB 750 (2015) 154	CMS-SMP-13-010 1504.03512
28	D0 Collaboration	Measurement of the angular distribution of electrons from $ \mathrm{W} \to \mathrm{e} \nu $ decays observed in $ {\mathrm{p}}\bar{{\mathrm{p}}} $ collisions at $ \sqrt{s} = $ 1.8 TeV	PRD 63 (2001) 072001	hep-ex/0009034
29	CDF Collaboration	Measurement of the polar-angle distribution of leptons from W boson decay as a function of the W transverse momentum in $ {\mathrm{p}}\bar{{\mathrm{p}}} $ collisions at $ \sqrt{s} = $ 1.8 TeV	PRD 70 (2004) 032004	hep-ex/0311050
30	CDF Collaboration	Measurement of the azimuthal angle distribution of leptons from W boson decays as a function of the W transverse momentum in $ {\mathrm{p}}\bar{{\mathrm{p}}} $ collisions at $ \sqrt{s} = $ 1.8 TeV	PRD 73 (2006) 052002	hep-ex/0504020
31	CMS Collaboration	Measurement of the polarization of W bosons with large transverse momenta in W+Jets events at the LHC	PRL 107 (2011) 021802	CMS-EWK-10-014 1104.3829
32	ATLAS Collaboration	Measurement of the polarisation of W bosons produced with large transverse momentum in pp collisions at $ \sqrt{s}= $ 7 TeV with the ATLAS experiment	EPJC 72 (2012) 2001	1203.2165
33	C. S. Lam and W.-K. Tung	A systematic approach to inclusive lepton pair production in hadronic collisions	PRD 18 (1978) 2447
34	P. Faccioli, C. Lourenço, and J. Seixas	Rotation-invariant relations in vector meson decays into fermion pairs	PRL 105 (2010) 061601	1005.2601
35	NA10 Collaboration	Angular distributions of muon pairs produced by negative pions on deuterium and tungsten	Z. Phys. C 37 (1988) 545
36	J. S. Conway et al.	Experimental study of muon pairs produced by 252 GeV pions on tungsten	PRD 39 (1989) 92
37	NuSea Collaboration	Measurement of angular distributions of Drell--Yan dimuons in p+d interactions at 800 GeV/c	PRL 99 (2007) 082301	hep-ex/0609005
38	NuSea Collaboration	Measurement of angular distributions of Drell--Yan dimuons in p+p interactions at 800 GeV/c	PRL 102 (2009) 182001	0811.4589
39	HERA-B Collaboration	Angular distributions of leptons from $ \mathrm{J}/\psi's $ produced in 920 GeV fixed-target proton-nucleus collisions	EPJC 60 (2009) 517	0901.1015
40	NuSea Collaboration	Observation of polarization in bottomonium production at $ \sqrt{s} = $ 38.8 GeV	PRL 86 (2001) 2529	hep-ex/0011030
41	N. Brambilla et al.	Heavy quarkonium: Progress, puzzles, and opportunities	EPJC 71 (2011) 1534	1010.5827
42	G. T. Bodwin, H. S. Chung, U.-R. Kim, and J. Lee	Fragmentation contributions to $ \mathrm{J}/\psi $ production at the Tevatron and the LHC	PRL 113 (2014) 022001	1403.3612
43	P. Faccioli and C. Lourenço	NRQCD colour-octet expansion vs. LHC quarkonium production: signs of a hierarchy puzzle?	EPJC 79 (2019) 457	1905.09553
44	P. Faccioli et al.	From identical S- and P-wave $ {p_{\mathrm{T}}} $ spectra to maximally distinct polarizations: probing NRQCD with $ \chi $ states	EPJC 78 (2018) 268	1802.01106
45	CMS Collaboration	The CMS experiment at the CERN LHC	JINST 3 (2008) S08004	CMS-00-001
46	CMS Collaboration	The CMS trigger system	JINST 12 (2017) P01020	CMS-TRG-12-001 1609.02366
47	CMS Collaboration	Description and performance of track and primary-vertex reconstruction with the CMS tracker	JINST 9 (2014) P10009	CMS-TRK-11-001 1405.6569
48	CMS Collaboration	Performance of CMS muon reconstruction in pp collision events at $ \sqrt{s}= $ 7 TeV	JINST 7 (2012) P10002	CMS-MUO-10-004 1206.4071
49	Particle Data Group, M. Tanabashi et al.	Review of particle physics	PRD 98 (2018) 030001
50	P. Faccioli, C. Lourenço, J. Seixas, and H. K. Wohri	Determination of $ \chi_c $ and $ \chi_b $ polarizations from dilepton angular distributions in radiative decays	PRD 83 (2011) 096001	1103.4882
51	J. C. Collins and D. E. Soper	Angular distribution of dileptons in high-energy hadron collisions	PRD 16 (1977) 2219
52	P. Faccioli, C. Lourenço, J. Seixas, and H. Wohri	Towards the experimental clarification of quarkonium polarization	EPJC 69 (2010) 657	1006.2738
53	P. Faccioli, C. Lourenço, and J. Seixas	New approach to quarkonium polarization studies	PRD 81 (2010) 111502(R)	1005.2855
54	P. Faccioli, C. Lourenço, J. Seixas, and H. K. Wohri	Model-independent constraints on the shape parameters of dilepton angular distributions	PRD 83 (2011) 056008	1102.3946
55	M. J. Oreglia	A study of the reactions $\psi' \to \gamma\gamma \psi$	PhD thesis, Stanford University, 1980 SLAC Report SLAC-R-236, see A