LHCb Results on Penta(tetra)-Quark Search...Up to now severalother exotic states have been observed, all involving heavy quark systems. The LHCb experiment has al-ready collected an

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LHCb results on penta(tetra)-quark searchMarcin Kucharczyk1 (on behalf of the LHCb collaboration)1Henryk Niewodniczanski Institute of Nuclear Physics PAN, Krakow, Poland

E-mail: [email protected]

(Received October 17, 2016)

The LHCb experiment is designed to study the properties and decays of heavy flavored hadronsproduced in pp collisions at the LHC. The data collected in the LHC Run I enables precision spec-troscopy studies of beauty and charm hadrons. The latest results on spectroscopy of conventional andexotic hadrons are reviewed, such as the discovery of the first charmonium pentaquark states in theJ/ψp system or the confirmation of resonant nature of the Z(4430)− mesonic state. LHCb has alsomade significant contributions to determination of the quantum numbers for the X(3872) state and toexclude the existence of the X(5568) tetraquark candidate. The LHCb results described in the presentdocument have dramatically increased the interest on spectroscopy of heavy hadrons.

KEYWORDS: pentaquarks, heavy flavor spectroscopy, exotic states

1. Introduction

In the simple quark model, only two types of quark combinations are required to account for theexisting hadrons, i.e. qq̄ combinations form mesons, while baryons are made up of three quarks. How-ever, in the quark model proposed by Gell-Mann and Zweig in 1960s [1] other SU(3) color-neutralcombinations of quarks and gluons such as gg glueballs, qq̄g hybrids, qq̄qq̄ tetraquarks, q̄qqqq pen-taquarks etc. were predicted. The world’s largest data sample of beauty and charm hadrons collectedby LHCb during LHC Run I provides great opportunities for studying the production and propertiesof heavy hadrons. Since such exotic states are experimentally hard to find in the light quark sector,the first discovery of the narrow exotic tetraquark state X(3872) by the Belle collaboration [2] wasmade only in 2003, leading to a revolution in the exotic hadron spectroscopy. Up to now several otherexotic states have been observed, all involving heavy quark systems. The LHCb experiment has al-ready collected an impressive set of results on exotic heavy flavour states, with the first unambiguousspin-parity assignments of the X(3872) [3], confirmation of resonant nature of the Z(4430)− [4] or ob-servation of two resonant states, Pc(4380)+ and Pc(4450)+ in the decay Λ0

b → J/ψpK− [5], which areconsistent with charmonium pentaquarks. The present document describes some recent results fromLHCb in exotic hadron spectroscopy. For all the studies the LHCb data corresponding to 3 fb−1ofintegrated luminosity in 7 and 8 TeV pp collisions has been used.

2. Pentaquark candidates in Λ0b→ J/ψpK−

First observation of the Λ0b → J/ψpK− with 1 f b−1 had unexpected large yield. It was orig-

inally used to precisely measure the Λ0b lifetime [6]. The sample of 26,007±166 signal candidates

subtracted of 5.4% background candidates within ±15 MeV of the J/ψK−p mass peak has been se-lected using full Run I dataset. An anomalous peaking structure in the J/ψp invariant mass spectrummight be observed on the Dalitz plot shown in Fig. 1. Since the contribution of Λ∗ → K−p reso-nances corresponding to the vertical bands only dominates the low m2

K p region, it is unlikely that the

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horizontal band is an effect of interference between the Λ∗ states. This structure can also be seen inthe invariant mass projections shown in Fig. 2. If the peak structure observed in Fig. 2b represents aresonance strongly decaying into J/ψp, the minimal valence quarks should be cc̄uud - a charmoniumpentaquark state. Many checks have been done in order to avoid the possibility that the peak structureis introduced by possible artificial effects, for example the background from B̄0

s and B̄0 decaying toJ/ψK+K− has been vetoed or the fake tracks have been suppressed. The full six-dimensional ampli-tude fit with resonance invariant mass, three helicity angles and two differences between decay planeshas been applied to describe the data. It allowed interference between the decays Λ0

b → J/ψΛ∗ andΛ0

b → P+c K−, with Λ∗ → pK− and P+c → J/ψp. As it may be seen in Fig. 3 the fit gives a gooddescription of the Λ∗ states as can be seen in the mK p spectrum but it fails to reproduce the structurein mJ/ψp. Adding non-resonant terms, two additional Λ∗ allowing their masses and widths to floator extra isospin-violating Σ∗ states could not improve the fit much. Adding two pentaquark statesimproves the fit quality a lot, as shown in Fig. 4b. The amplitude model in the fit contains 14 well-defined Λ∗ states listed by Particle Data Group [7] and two P+c states: Pc(4380)+ and Pc(4450)+. Witha full amplitude analysis, the masses of these two states are measured to be 4380 ±8(stat) ±29(syst)MeV and 4449.8 ±1.7(stat) ±2.5(syst) MeV, with the widths 205 ±18(stat) ±86(syst) MeV and 39±5(stat) ±19(syst) MeV, respectively. The preferred spin-parity values are (3/2−,5/2+), (3/2+,5/2−)and (5/2+,3/2−), where the first one is the JP assignment given by the best fit.

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Fig. 1. Dalitz plot for Λ0b → J/ψpK−. Figure taken from [5].

One of the most important sources of systematic uncertainty for pentaquark candidates in Λ0b →

J/ψpK− is commonly the poor knowledge of the spectrum of the conventional hadronic resonances,i.e. the excited Λ∗J → K−p states of spin-J. This is why the LHCb analysis has been extended with amodel-independent approach [8] as first proposed by the BaBar collaboration for the Zc(4430) anal-ysis [9]. The method is based on the Legendre polynomial moments extracted from the K p system.If the highest spin of the contributing J states is Jmax, then the maximal power of x = cos(θpK) in thedifferential decay rate is given by the Legendre polynomial, Plmax(x), of order lmax = 2Jmax+1, whereθpK represents the helicity angle of the daughter kaon in the mother Λ∗J rest-frame. Fig. 5(left) showsthat the physical J resonances occurring at a given mpK mass have a limited ranges of lmax, where thehorizontal lines indicate allowed kinematic range, and in general higher-spin resonances are heavier,as illustrated by the red and blue lines. Possible exotic states in the J/ψp or J/ψK systems affectentire spectrum of spin-J pK states in the 3-body Dalitz plane in Λ0

b → J/ψpK−. The presence ofsuch unexpected large spin-J components at a given mpK beyond the limits in Fig. 5(left) indicatesthe exotic activity. A model independent analysis allows to exclude that data can be described by

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represent data, while the red curve indicates the expectation from the phase space. Figure taken from [5].

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Fig. 3. Results for (a) mpK and (b) mJ/ψp for the extended Λ∗ model fit without P+c states. The black squareswith error bars represent data, while red circles indicate the results of the fit. Figure taken from [5].

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Fig. 4. Best fit projections for (a) mpK and (b) mJ/ψp for 14 well-defined Λ∗ states and two P+c states in thedecay Λ0

b → J/ψpK−. Figure taken from [5].

the pK contributions alone. Fig. 5(right) shows the efficiency-corrected and background-subtracteddistribution in mJ/ψp, superimposed with the exotic (black broken lines) and non exotic (blue line)models. The non-exotic model, representing the null-hypothesis, assumes that Λ0

b → J/ψpK− sig-nal originates uniquely from the decay chain Λ0

b → J/ψΛ∗ with Λ∗ → K−p, and that the spin andlineshape of possible Λ∗ contributions are limited to physically meaningful values. The exotic model

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allows Legendre moment of rank lmax = 31, corresponding to the Λ∗ resonance spin of 31/2, to repro-duce structures in the data induced by contributions of J/ψp and J/ψK−. Based on a likelihood ratiostudy using pseudo-experiments, between the null hypothesis and exotic models, LHCb was able toexclude the null hypothesis by more than 9σ.

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Fig. 5. (Left) The range of expected spin-J physical Λ∗J resonances at a given mpK− , where lmax = 2Jmax + 1and the green bands represent the experimentally observed states. (Right) Invariant mass distribution of J/ψpcombination for Λ0

b → J/ψpK− decays (black points) superposed with fit results based on the null hypothesis(blue solid line) and exotic model (black dashed). The data is efficiency-corrected and background-subtracted.Figure taken from [8].

The evidence of the resonant character of the discovered pentaquark states is obtained observingthe evolution of the complex amplitude in the Argand diagram [7]. Replacing Breit-Wigner amplituderepresentation of the Pc state by the combination of independent complex amplitudes at six equidis-tant points in the range ±Γ around the mass, the Pc shape may be constrained only by amplitudesin K p sector. The resulting Argand diagram, shown in Fig. 6(a) for Pc(4450)+, is consistent with arapid counter-clockwise change of the phase when its magnitude reaches the maximum, a behaviorcharacteristic for a resonance. A similar study for the Pc(4380)+ leads to less conclusive results.

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Fig. 6. Argand diagrams for the states (a) Pc(4450)+ and (b) Pc(4380)+. Points with error bars are the fittedvalues of the real and imaginary parts of the amplitudes in six independent bins of mJ/ψp. The red solid curvesare Breit-Wigner formula predictions. Figure taken from [5].

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2.1 Exotic baryonic resonances in Λ0b → J/ψpπ−

The possible way for independent confirmation of the discovered Pc(4380)+ and Pc(4450)+ statesin the Cabibbo-favored decay Λ0

b → J/ψpK− is to check if such states occur also in the the Cabibbo-suppressed decay Λ0

b → J/ψpπ−. If the P+c states are generated by kinematic effects, it is not neces-sary that they will be observed in the decay Λ0

b → J/ψpπ−. Analyzing the same Run I dataset, butnow in the Cabibbo suppressed mode, the signal yield is 1885±50, about 15 times less than that of theCabibbo-favored channel and with relatively high background level [10]. The following possible con-tributions to the decay amplitude are taken into account in the analysis:Λ0

b → J/ψN∗ with N∗ → pπ−,Λ0

b → P+c π− with P+c → J/ψp, and Λ0

b → Zc(4200)−p with Z−c → J/ψπ−. N∗ resonances are modeledusing relativistic Breit-Wigners, except the N(1535), which is modeled by a Flatte lineshape, as itcouples also to the near-threshold nη mode. The Zc(4200)− tetraquark candidate has been discoveredby the Belle collaboration [11]. The full amplitude analysis following the original formalism used inpentaquark analysis [5] has been applied for limited statistics of Cabibbo suppressed signal, with theproperties of the Pc and Zc candidates taken from the world data. Both reduced and extended modelsof the N∗ contributions have been tested, the latter including a wider set of resonances and allowedcouplings. Fig. 7 shows the projections of the six-dimensional fit results to the background-subtracteddata onto the mpπ− and mJ/ψp. The data is found to be consistent with the two exotic candidates, butlimited statistics did not allow to distinguish between Pc and Zc exotic contributions.

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Fig. 7. Amplitude fit projection onto (left) mpπ and (right) mJ/ψp with mpπ > 1.8 GeV, compared withbackground-subtracted and efficiency-corrected data (black squares with error bars). Figure taken from [10].

3. Confirmation of resonant nature of Z(4430)−

The Z(4430)− state was first reported by the Belle collaboration [12] as a charged resonancestructure in the ψ(2S )π− invariant mass distribution of the decay B0 → ψ(2S )K+π−. A relativelynarrow peak has been found, Γ ≈ 45 MeV, in the ψ(2S ) mass spectrum with a mass of 4433±5 MeV.BaBar collaboration could explain the enhancement as a reflection of the known K∗ states, but didnot rule out the existence of Z(4430)− either [13]. Such a resonance cannot be comprised of only twoquarks and, therefore, is particularly interesting as it is most likely exotic, with minimal quark contentcc̄ud̄. In 2013 Belle performed a reanalysis using more data containing about 2000 signal events,based on a full amplitude analysis. This gave a significance of 5.2σ for the Z(4430)− state, with themass MZ = 4485±22+28

−11 MeV and width ΓZ = 200+41−46

+26−35 MeV, and favour the JP = 1+ spin-parity

assignment by more than 3.4σ. Using the 3 fb−1 of integrated luminosity available from LHC runningin 2011 and 2012, the LHCb experiment collected about 25,000 B0 signal events, a yield an order ofmagnitude larger than in BaBar or Belle and observed the Z(4430)− with a significance larger than

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13.9 sigma [4]. The LHCb collaboration performed both a model independent analysis (like BaBar)to check whether the mψ(2S )π− spectrum could be understood in terms of any combination of knownK∗ resonances as well as a full amplitude analysis (like Belle) to also extract quantitative informationabout the Z(4430)− mass, width and spin. The projection of the fit including Z(4430)− state in Fig. 8ais in a good agreement with the data. The measured mass is 4475±7+15

−25 MeV and width 172±13+37−34

MeV are consistent with the Belle values. The Argand diagram of the Z(4430)− amplitude (Fig. 8b)shows the resonance behaviour for the first time. The spin-parity is measured to be 1+, by excluding0−, 1−, 2− and 2+ hypotheses by at least 9.7σ. For a charged charmonium state, Z(4430)− has aminimum quark content of cc̄ud̄, which clearly does not fit into traditional quark model.

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Fig. 8. (Left) Distribution of m2ψ(2S )π− , where black dots represent data, the red solid and brown dashed lines

indicate the total fit with and without the Z(4430)− component. (Right) Fitted values of Z(4430)− amplitude insix m2

ψ(2S )π− bins shown in an Argand diagram. Figure taken from [4].

4. X(3872) composition

X(3872) is the first charmonium-like exotic state ever observed, which led to a revolution inexotic hadron spectroscopy. It was discovered by Belle in 2003 [2] as an unexpected structure inthe J/ψπ+π− invariant mass while investigating B+ → J/ψK+π+π− decays. It has been seen nowby seven different experiments in both B decays and the prompt production. Its quantum numberswere narrowed down by CDF collaboration to be 1++ or 2−+ [14], but the nature is still unclear,drawing a lot of theoretical interests. The X(3872) decaying into J/ψπ+π− may be interpreted as acharmonium excitation, but on the other hand having the mass close to the D∗+D− threshold it maybe an example of a hadron molecule with an extremely small binding energy [15]. Furthermore,the decay modes X(3872) → J/ψρ and X(3872) → J/ψω have comparable branching fractions,leading to the strong violation of isospin symmetry. This may suggest that X(3872) is a molecule,since D∗+D− state is a superposition of isospin 0 and 1. LHCb used first 7 TeV dataset to measuremass and production cross-section in B+ → X(3872)K+ with X(3872) decaying into J/ψπ+π− andJ/ψ → µ+µ− in order to pin down spin-parity to be 1++ [3]. More recently, using improved statisticsfrom the full 3 fb−1 LHC Run I dataset, LHCb has performed a full five-dimensional angular analysiswithout any assumptions on orbital angular momentum [16]. In this analysis the quantum numbersof the X(3872) are determined to be JPC = 1++, while the only alternative assignment allowed byprevious measurements JPC = 2−+ [14] is excluded with a significance of more than 8σ. Now theamplitude model has included also D-wave components, which were previously ignored. However, itturned out that D-wave components are negligible and the decay is mainly through S-wave. Usefulinformation about X(3872) state can be obtained from its radiative decay. Radiative transitions may

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be a sensitive probe of exotic structure, since electromagnetic transitions among charmonium statesare well-defined. Various interpretations predict very different values of the ratio Rψγ = B(X(3872)→ψ(2S )γ)/B(X(3872) → J/ψγ). LHCb has recently found a 4.4σ evidence of the X(3872) → ψ(2S )γin B+ → X(3872)K+ (see Fig. 9), and measured its branching fraction relative to X(3872) → J/ψγ,i.e. Rψγ = 2.46 ± 0.64(stat) ± 0.29(syst) [17]. This result is consistent with expectations for thecharmonium cc̄(23P1) or a molecule-charmonium mixture interpretation, but does not support a pureD∗+D− molecule interpretation.

Fig. 9. Invariant mass distributions of (left) J/ψγ and (right) ψ(2S )γ from B+ decays. Figure taken from [17].

5. No evidence of the X(5568) tetraquark

The evidence for X(5568)± → B0sπ± tetraquark candidate has been reported by D0 collaboration

with a significance of 3.9σ [18]. This new four-flavored b̄sud̄ exotic state has been found usingthe pp̄ collisions at

√s = 1.97 TeV. The relative production rate between the X(5568) and B0

s ,multiplied by the X → B0

s branching fraction has been found to be ρD0X (10 < pT (B0

s) < 15GeV)= 9.1±2.6(stat)±1.6(syst)% and ρD0

X (15 < pT (B0s) < 30GeV) = 8.2±2.7(stat)±1.6(syst)%, with an

average of ρD0X = 8.6±1.9(stat)±1.4(syst)%, being not particularly relevant without the actual limit. If

this value is universal, this is the rate that one would expect to be seen also in other experiments. Usingfull Run I dataset LHCb has a huge and clean sample of B0

s mesons, where the selection requirementsfor the B0

s and the companion follow those in previous well-understood LHCb analyses. LHCb hassearched for X(5568) decaying into B0

sπ±, with B0

s → D−s π+ and B0

s → J/ψϕ, where D−s → K+K−π−,J/ψ → µ+µ− and ϕ → K+K− [19]. The overall signal sample (about 110,000) is about twenty timeslarger than in D0, having much less background. Cut-based selection has been applied to clean B0

ssample together with the mass constraints on J/ψ and D−s to improve mass resolution. The polynomialhas been assumed for the background, and it comes from random combinations of pions with true orfake B0

s candidates. No significant X(5568) has been found for either of the three pT (B0s) (greater

than 5, 10, or 15 GeV) requirements (see Fig. 10), so the upper limits at the 95% confidence levelhave been calculated to be ρLHCb

X (pT (B0s) > 5GeV) < 0.011, ρLHCb

X (pT (B0s) > 10GeV) < 0.021 and

ρLHCbX (pT (B0

s) > 15GeV) < 0.018.

6. Conclusions

Many new exotic states have been discovered since the first observation of the X(3872). Someof them have been observed by many experiments, other need further confirmation, thus it is crucialto perform hadron spectroscopy searches in different production and decay modes. During the RunI phase of LHC running, the LHCb experiment has made several important measurements in heavyflavour spectroscopy studies. Two pentaquark candidates decaying to J/ψp have been observed byLHCb with overwhelming significance in both amplitude and moment analyses. The existence and

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Fig. 10. Fits to the B0sπ± spectrum showing no significant excess at the X(5568) mass for (left) pT (B0

s) >5 GeV and (right) pT (B0

s) > 15 GeV. Figure taken from [19].

resonant nature of Z(4430)− state has been decisively confirmed in both model independent andamplitude approaches. After having determined the X(3872) quantum numbers, the decay X(3872)→ψ(2S )γ is established with a significance of 4.4σ. These results, together with many others obtainedby LHCb with the Run I dataset demonstrate its excellent capability for hadronic spectroscopy.

ACKNOWLEDGEMENTS

I would like to express my gratitude to the National Science Centre NCN in Poland, for financialsupport under the contract no. 2013/11/B/ST2/03829.

References

[1] M. Gell-Mann, Phys. Lett. 8 (1964) 214.[2] S. K. Choi et al. (Belle collaboration), Phys. Rev. Lett. 91 (2003) 262001.[3] R. Aaij et al. (LHCb collaboration), Phys. Rev. Lett. 110 (2013) 222001.[4] R. Aaij et al. (LHCb collaboration), Phys. Rev. Lett. 112 (2014) 222002.[5] R. Aaij et al. (LHCb collaboration), Phys. Rev. Lett. 115 (2015) 072001.[6] R. Aaij et al. (LHCb collaboration), Phys. Lett. B734 (2014) 122.[7] K. A. Olive et al. (Partilce Data Group), Chin. Phys. C38 (2014) 090001.[8] R. Aaij et al. (LHCb collaboration), Phys. Rev. Lett. 117 (2016) 082002.[9] B. Aubert et al. (BaBar collaboration), Phys. Rev. D79 (2009) 112001.[10] R. Aaij et al. (LHCb collaboration), Phys. Rev. Lett. 117 (2016) 082003.[11] K. Chilikin et al. (Belle collaboration), Phys. Rev. D90 (2014) 112009.[12] S. K. Choi et al. (Belle collaboration), Phys. Rev. Lett. 100 (2008) 142001.[13] B. Aubert et al. (BaBar collaboration), Phys. Rev. D79 (2009) 112001.[14] A. Abulencia et al. (CDF collaboration), Phys. Rev. Lett. 98 (2007) 132002.[15] R. Aaij et al. (LHCb collaboration), JHEP 1306 (2013) 065.[16] R. Aaij et al. (LHCb collaboration), Phys. Rev. D92 (2015) 011102.[17] R. Aaij et al. (LHCb collaboration), Nucl. Phys. B886 (2014) 665.[18] V. M. Abazov et al. (D0 collaboration), Phys. Rev. Lett. 117 (2016) 022003.[19] R. Aaij et al. (LHCb collaboration), accepted by Phys. Rev. Lett.), 2016, arXiv:1608.00435.

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Documents

LHCb Results on Penta(tetra)-Quark Search...Up to now severalother exotic states have been observed, all involving heavy quark systems. The LHCb experiment has al-ready collected an