Developments in heavy quarkonium spectroscopy

Developments in heavy quarkonium spectroscopy

S. Eidelman Budker Institute of Nuclear Physics SB RAS, Novosibirsk 630090, Russia Novosibirsk State University, Novosibirsk 630090, Russia    B. K. Heltsley Cornell University, Ithaca, NY 14853, USA    J. J. Hernàndez-Rey Instituto de Física Corpuscular, Universitat de València–CSIC, Edificio de Investigación de Paterna, Apdo. 22085, E-46071 Valencia, Spain    S. Navas Departamento de Física Teórica y del Cosmos & CAFPE, Universidad de Granada, 18071 Granada, Spain    C. Patrignani Dipartimento de Fisica e INFN, Università de Genova. I-16146 Genova, Italy
July 27, 2019
Abstract

We summarize recent developments in heavy quarkonium spectroscopy, relying on previous review articles for the bulk of material available prior to mid-2010. This note is intended as a mini-review to appear in the 2012 Review of Particle Physics published by the Particle Data Group.

A golden age for heavy quarkonium physics dawned a decade ago, initiated by the confluence of exciting advances in quantum chromodynamics (QCD) and an explosion of related experimental activity. The subsequent broad spectrum of breakthroughs, surprises, and continuing puzzles had not been anticipated. In that period, the BESII program concluded only to give birth to BESIII; the -factories and CLEO-c flourished; quarkonium production and polarization measurements at HERA and the Tevatron matured; and heavy-ion collisions at RHIC opened a window on the deconfinement regime. For an extensive presentation of the status of heavy quarkonium physics, the reader is referred to several reviews Brambilla:2004wf (); Eichten:2007qx (); Eidelman:2008zzc (); Godfrey:2008nc (); Barnes:2009zza (); Pakhlova:2010zz (); Brambilla:2010cs (), the last of which covers developments through the middle of 2010, and which supplies some tabular information and phrasing reproduced here (with kind permission, copyright 2011, Springer). This note focuses solely on experimental developments in heavy quarkonium spectroscopy, and in particular on those too recent to have been included in Brambilla:2010cs ().

  State  (MeV)  (MeV)     Process (mode) Experiment (#) Year Status
  1 CLEO Rubin:2005px (); Rosner:2005ry (); Dobbs:2008ec () (13.2) 2004 OK
CLEO Rubin:2005px (); Rosner:2005ry (); Dobbs:2008ec () (10), BES Ablikim:2010rc () (19)
E835 Andreotti:2005vu () (3.1)
BESIII Ablikim:2010rc () (9.5)
104 Belle Choi:2002na (); Vinokurova:2011dy () (6.0) 2002 OK
BABAR delAmoSanchez:2011bt (); Aubert:2003pt () (7.8),
CLEO Asner:2003wv () (6.5), Belle Nakazawa:2008zz () (6)
BABAR Aubert:2005tj () (np), Belle Abe:2007jn () (8.1)
246 Belle Uehara:2005qd () (5.3), BABAR :2010hka (); delAmoSanchez:2010jr () (5.8) 2005 OK
- CDF Abe:1998wi (); Aaltonen:2007gv () (8.0), DØ Abazov:2008kv () (5.2) 2007 OK
12.4 0 BABAR :2008vj () (10), CLEO Bonvicini:2009hs () (4.0) 2008 OK
BABAR :2009pz () (3.0)
Belle Adachi:2011ch () (14)
? Belle Adachi:2011ji (); Adachi:2011ch () (5.5) 2011 NC!
BABAR Lees:2011zp () (3.0)
? 2 CLEO Bonvicini:2004yj () (10.2) 2004 OK
BABAR Sanchez:2010kz () (5.8)
Belle Adachi:2011ji () (2.4)
? Belle Adachi:2011ji () (11.2) 2011 NC!
? ? ATLAS Aad:2011ih () (6) 2011 NC!
Table 1: New conventional states in the , , and regions, ordered by mass. Masses and widths represent the weighted averages from the listed sources. Quoted uncertainties reflect quadrature summation from individual experiments. In the Process column, the decay mode of the new state claimed is indicated in parentheses. Ellipses (…) indicate inclusively selected event topologies; i.e., additional particles not required by the Experiments to be present. A question mark (?) indicates an unmeasured value. For each Experiment a citation is given, as well as the statistical significance in number of standard deviations (#), or “(np)” for “not provided”. The Year column gives the date of first measurement cited. The Status column indicates that the state has been observed by at most one ( NC!-needs confirmation) or at least two independent experiments with significance of 5 (OK). The state labelled has previously been called . See also the reviews in Brambilla:2004wf (); Eichten:2007qx (); Eidelman:2008zzc (); Godfrey:2008nc (); Barnes:2009zza (); Pakhlova:2010zz (); Brambilla:2010cs (). Adapted from Brambilla:2010cs () with kind permission, copyright (2011), Springer.

Table 1 lists properties of newly observed conventional heavy quarkonium states, where “newly” is interpreted to mean within the past decade. The is the state of charmonium, singlet partner of the long-known triplet . The is the first excited state of the pseudoscalar ground state , lying just below the mass of its vector counterpart, . The state originally dubbed is now regarded by many as the first observed state of , the . The first -meson seen that contains charm is the . The ground state of bottomonium is the , recently confirmed with a second observation of more than 5 significance. The  is the lowest-lying -wave triplet of the system. Both the , the bottomonium counterpart of , and the next excited state, , were very recently observed by Belle Adachi:2011ji (), as described further below, in dipion transitions from either the or . All fit into their respective spectroscopies roughly where expected. Their exact masses, production mechanisms, and decay modes provide guidance to their descriptions within QCD. The states still need experimental confirmation at the 5 level, as does the triplet.

  State  (MeV)  (MeV)     Process (mode) Experiment (#) Year Status
  3871.680.17 Belle Choi:2003ue (); Choi:2011fc () (12.8), BABAR Aubert:2008gu () (8.6) 2003 OK
CDF Acosta:2003zx (); Abulencia:2006ma (); Aaltonen:2009vj () (np), DØ Abazov:2004kp () (5.2)
Belle Abe:2005ix () (4.3), BABAR delAmoSanchez:2010jr () (4.0)
Belle Gokhroo:2006bt (); Aushev:2008su () (6.4), BABAR Aubert:2007rva () (4.9)
Belle Bhardwaj:2011dj () (4.0), BABAR Aubert:2006aj (); Aubert:2008rn () (3.6)
BABAR Aubert:2008rn () (3.5), Belle Bhardwaj:2011dj () (0.4)
LHCb Aaij:2012lhcb () (np)
28 Belle Abe:2004zs () (8.1), BABAR Aubert:2007vj () (19) 2004 OK
Belle Uehara:2009tx () (7.7), BABAR delAmoSanchez:2010jr () (np)
Belle Abe:2007sya () (6.0) 2007 NC!
Belle Abe:2007jn () (5.0)
5211 BABAR Aubert:2006mi () (np), Belle Pakhlova:2008zza () (np) 2007 OK
22697 Belle Belle:2007sj () (7.4) 2007 NC!
? Belle Mizuk:2008me () (5.0), BABAR Lees:2011ik () (1.1) 2008 NC!
CDF Aaltonen:2009tz (); Aaltonen:2011at () (5.0) 2009 NC!
Belle Abe:2007sya () (5.5) 2007 NC!
177 ? Belle Mizuk:2008me () (5.0), BABAR Lees:2011ik () (2.0) 2008 NC!
9514 BABAR Aubert:2005rm (); Aubert:2008ic () (8.0) 2005 OK
CLEO He:2006kg () (5.4), Belle Belle:2007sj () (15)
CLEO Coan:2006rv () (11)
CLEO Coan:2006rv () (5.1)
CDF Aaltonen:2011at () (3.1) 2010 NC!
0/2 Belle Shen:2009vs () (3.2) 2009 NC!
7418 BABAR Aubert:2006ge () (np), Belle :2007ea () (8.0) 2007 OK
? Belle Choi:2007wga (); Mizuk:2009da () (6.4), BABAR :2008nk () (2.4) 2007 NC!
Belle Pakhlova:2008vn () (8.2) 2007 NC!
466412 4815 Belle :2007ea () (5.8) 2007 NC!
10607.22.0 18.42.4 Belle Adachi:2011XXX (); Bondar:2011pd () (16) 2011 NC!
10652.21.5 11.52.2 Belle Adachi:2011XXX (); Bondar:2011pd () (16) 2011 NC!
10888.43.0 30.7 Belle Chen:2008pu (); Abe:2007tk () (2.0) 2010 NC!
Table 2: As in Table 1, but for new unconventional states in the and regions, ordered by mass. For , the values given are based only upon decays to . and have been subsumed under due to compatible properties. The state known as appears as the in Table 1. In some cases experiment still allows two values, in which case both appear. See also the reviews in Brambilla:2004wf (); Eichten:2007qx (); Eidelman:2008zzc (); Godfrey:2008nc (); Barnes:2009zza (); Pakhlova:2010zz (); Brambilla:2010cs (). Adapted from Brambilla:2010cs () with kind permission, copyright (2011), Springer.

Correspondingly, the menagerie of new, heavy-quarkonium-like unanticipated states***For consistency with the literature, we preserve the use of , , , and , contrary to the practice of the PDG, which exclusively uses for unidentified states. is shown in Table 2; notice that just a handful have been experimentally confirmed. None can unambiguously be assigned a place in the hierarchy of charmonia or bottomonia; neither do any have a universally accepted unconventional origin. The occupies a unique niche among the unexplained states as both the first and the most intriguing. It is, by now, widely studied, yet its interpretation demands much more experimental attention. The and are vector states decaying to and , respectively, yet, unlike most conventional vector charmonia, do not correspond to enhancements in the hadronic cross section. The three and two states, each decaying to a charged pion and conventional heavy quarkonium state, would be manifestly exotic, but remain unconfirmed. Final states of the type from collisions acquired near the have a lineshape differing somewhat from that of multi-hadronic events, which suggested a new state , distinct from , which could be analogous to . The nature of , if it does mimic the behavior of the charmonium-region ’s, could help to explain the observed (and otherwise unexpected) high rate of dipion transitions to and seen in collisions near the region. It could also provide insight into the states, which appear to be intermediate resonances in the dipion transitions.

BABAR :2008nk (); Lees:2011ik () has searched for the three states in the charmonium mass region seen by Belle, and failed to observe any significant signals. The approach taken in searching for , where is or , is to first fit the data for all reasonable mass or angular structure, having demonstrated that the presence of one or more ’s cannot be accommodated by this procedure. After doing so, the finding is that some of what might be the Belle excess of events above Belle background gets absorbed into the structure of the BABAR background. As shown in Table 2, where Belle observes signals of significances , , and for , , and , respectively, BABAR reports , , and effects, setting upper limits on product branching fractions that are not inconsistent with Belle’s measured rates, leaving the situation unresolved.

Although measurements began to converge on a mass and width nearly a decade ago, refinements are still in progress. In particular, Belle Vinokurova:2011dy () has revisited its analysis of , decays with more data and methods that account for interference between the above decay chain, an equivalent one with the instead, and one with no intermediate resonance. The net effect of this interference is far from trivial; it shifts the apparent mass by +10  and blows up the apparent width by a factor of six. The updated mass and width are in better accordance with other measurements than the previous treatment Choi:2002na () not including interference. Complementing this measurement in -decay, BABAR delAmoSanchez:2011bt () updated their previous Aubert:2003pt () mass and width measurements in two-photon production, where interference effects, judging from studies of , appear to be small. In combination, precision on the mass has improved dramatically.

New results on , , and mostly come from Belle, all from analyses of 121.4 fb of collision data collected near the peak of the resonance. They also appear in the same types of decay chains: , , and, when the forms an , frequently . Previous unsuccessful searches for focused on what was considered the most easily detected production mechanism, . In early 2011 BABAR presented marginal evidence for this transition at the level, at a mass near that expected for zero hyperfine splitting.

Figure 1: From Belle Adachi:2011ji (), the mass recoiling against pairs, , in collision data taken near the peak of the (points with error bars). The smooth combinatoric and background contributions have already been subtracted. The fit to the various labeled signal contributions overlaid (curve). Adapted from Adachi:2011ji () with kind permission, copyright (2011) The American Physical Society.
Figure 2: From Belle Bondar:2011pd () collision data taken near the peak of the for events with a -missing mass consistent with a , (a) the maximum of the two possible single -missing-mass-squared combinations vs. the -mass-squared; and (b) projection of the maximum of the two possible single -missing-mass combinations (points with error bars) overlaid with a fit (curve). Events to the left of the vertical line in (a) are excluded from further analysis. The two horizontal stripes in (a) and two peaks in (b) correspond to the two states. Adapted from Bondar:2011pd () with kind permission, copyright (2011) The American Physical Society.

The Belle discovery analysis Adachi:2011ji () selects hadronic events and looks for peaks in the mass recoiling against pairs, the spectrum for which, after subtraction of smooth combinatoric and backgrounds, appears in Fig. 1. Prominent and unmistakable and peaks are present. This search was directly inspired by a new CLEO result :2011uqa (), which found the surprisingly copious transitions and an indication that occurs at a comparable rate as the signature mode, . The presence of peaks in Fig. 1 at rates two orders of magnitude larger than expected for transitions requiring a heavy-quark spin-flip, along with separate studies with exclusive decays , allow precise calibration of the recoil mass spectrum and very accurate measurements of and masses. Both corresponding hyperfine splittings are consistent with zero within an uncertainty of about 1.5  (lowered to for in Adachi:2011ch ()).

Figure 3: From Belle Adachi:2011ch () collision data taken near the peak of the , the event yield vs. the mass recoiling against the (corrected for misreconstructed ), where the yield is obtained by fitting the mass recoiling against the (points with error bars). The fit results (solid histograms) for signal plus background and background alone are superimposed. Adapted from Adachi:2011ch () with kind permission, copyright (2011) The American Physical Society.

Belle soon noticed that, for events in the peaks of Fig. 1, there seemed to be two intermediate charged states nearby. For example, Fig. 2 shows a Dalitz plot for events restricted to the region of recoil mass. The two bands observed in the maximum of the two values also appear for , , , and samples, but do not appear in the respective sidebands. Belle fits all subsamples to resonant plus non-resonant amplitudes, allowing for interference (notably, between and ), and finds consistent pairs of masses for all bottomonium transitions, and comparable strengths of the two states. Angular analysis favors a assignment for both states, which must also have negative -parity. Transitions through to the saturate the observed cross sections. The two masses of states are just a few MeV above the and thresholds, respectively. The cannot be simple mesons because they are charged and have content.

The third Belle result to flow from these data is confirmation of the and measurement of the branching fraction, expected to be several tens of percent. To accomplish this, events with the recoil mass in the mass window and a radiative photon candidate are selected, and the recoil mass queried for correlation with non-zero population in the missing mass spectrun, as shown in Fig. 3. A clear peak is observed, corresponding to the . A fit is performed to extract the mass, and first measurements of its width and the branching fraction for (the latter of which is ). The mass determination has comparable uncertainty to and a larger central value (by 10 , or 2.4) than the average of previous measurements, thereby reducing the new world average hyperfine splitting by nearly 5 , as shown in Table 3.

  Process Ref.
(/d.o.f.)
  9394.22.0 2.0 BABAR :2009pz ()
9388.92.7 71.42.7 BABAR :2008vj ()
9391.86.62.0 68.56.62.0 CLEO Bonvicini:2009hs ()
Above Brambilla:2010cs () AvgAn inverse-square-error-weighted average of the individual measurements appearing above, for which all statistical and systematic errors were combined in quadrature without accounting for any possible correlations between them. The uncertainty on this average is inflated by the multiplicative factor if /d.o.f.1 (0.6/2)
9401.0 59.31.9 Belle Adachi:2011ch ()
All Avg (6.1/3)
Table 3: Measured  masses and hyperfine splittings, by experiment and production mechanism.

The states have recently been observed at the LHC by ATLAS Aad:2011ih () for , although in each case the three states are not distinguished from one another. Events are sought which have both a photon and an candidate which together form a mass in the region. Observation of all three -merged peaks is seen at significance in excess of for both unconverted and converted photons. The mass plot for converted photons, which provide better mass resolution, is shown in Fig. 4. This marks the first observation of the triplet, quite near the expected mass.

Figure 4: From ATLAS Aad:2011ih () collision data (points with error bars) taken at  TeV, the effective mass of candidates in which and the photon is reconstructed as an conversion in the tracking system. Fits (smooth curves) show significant signals for each triplet (merged-) on top of a smooth background. From Aad:2011ih () with kind permission, copyright (2012) The American Physical Society.

References

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