Pentaquarks at LHCb Nathan Jurik Syracuse University On behalf of the LHCb Collaboration
2 Tetra- and Penta-quarks conceived at the birth of Quark Model … … • Searches for such states made out of the light quarks (u,d,s) are ~50 years old, but no undisputed experimental evidence have been found for them • However several charmonium and bottomonium-like tetraquark candidates have been observed
3 0 J/ y p K - At LHCb L b 26,007±166 PRL 115, 072001 L b 0 candidates Run I 3 fb -1 The background The sideband is only 5.4% in distributions are flat no major the signal region! reflections from the other b-hadrons after the selection • The decay first observed by LHCb and used to measure L b 0 lifetime PRL 111, 102003 (2013)
4 An unexpected structure in m J/ y p + J/ y p P c ? L (1520) and other L * ’s p K - LHCb Unexpected narrow peak in m J/ y p ! PRL 115, 072001 (2015)
5 Necessary Checks • Many checks done to ensure it is not an “artifact” of selection: – Efficiency across Dalitz plane is smooth, wouldn’t create peaking structures. + structure found using very different selections – The same P c by different LHCb teams – Suppress fake tracks – Split data shows consistency: 2011/2012, magnet up/down, L b / Λ 𝑐 , L b (p T low)/ L b (p T high) – Veto B s →J / y K - K + & B 0 →J/ y K - p + decays – Exclude X b or other high mass decays as a possible source
6 Amplitude Analysis of L b 0 J/ y pK - , J/ y + - • Could it be a reflection of interfering L * ’s p K - ? – Full amplitude analysis absolutely necessary! • Analyze all dimensions of the decay kinematics for 0 J/ y pK - , J/ y + - . L b Λ 𝑐 → Λ ∗ 𝐾 𝜔 with Λ ∗ → 𝐿𝑞 and 𝐾 𝜔 → 𝜈𝜈 Λ 𝑐 → 𝑄 𝑑 𝐿 with 𝑄 𝑑 → 𝐾 𝜔 𝑞 and 𝐾 𝜔 → 𝜈𝜈 • Write down (6D) matrix element with helicity formalism and allow the two decay chains to interfere:
7 L * resonance model • Large number of possibly contributing resonances, each contributing 4-6 complex helicity couplings which need to be determined by the data. We use two models in our fits to study the dependence on Λ ∗ • model. amplitudes ? Total fit parameters: 64 146
8 Fit with L * pK - contributions only • m Kp looks fine, but m J/ y p looks terrible • Addition of non-resonant terms, S * ’s or extra L * ’s doesn’t help. • There is no ability to describe the peaking structure with conventional resonances!
9 Fit with L * ’s and one P c + J /y p state (extended L * model) • Try all J P of P c + up to 7/2 ± and best fit has J P =5/2 ± . • Still not a good fit though, evidently something further is needed.
10 Fit with L * ’s and two P c + J /y p states P c (4450) + P c (4380) + (reduced L * model) • With two 𝑄 𝑑 resonances we are able to describe the peaking structure! • Obtain good fits even with the reduced L * model • Best fit has 𝐾 𝑄 (𝑄 𝑑 (4380), 𝑄 𝑑 (4450)) =(3/2 - , 5/2 + ), also (3/2 + , 5/2 - ) and (5/2 + , 3/2 - ) are preferred
11 Angular distributions • Good description of the data in angular distributions too!
12 + states Data preference for opposite parity P c Events/(20 MeV) m Kp <1.55 GeV 1.55< m Kp <1.70 GeV Positive interference between the P c states (display before efficiency) Events/(20 MeV) - + 2.00 GeV< m Kp 1.70< m Kp <2.00 GeV Negative interference between the P c states (display after efficiency) • Two opposite parity states necessary to generate the interference pattern
13 Results + states: • Parameters of the P c State Mass (MeV) Width (MeV) Fit fraction (%) P c (4380) + 4380 ± 8 ± 29 205 ± 18 ± 86 8.4 ± 0.7 ± 4.2 P c (4450) + 4449.8 ± 1.7 ± 2.5 39 ± 5 ± 19 4.1 ± 0.5 ± 1.1 • With the ℬ( L b 0 J/ y p K − ) measurement (arXiv:1509.00292) we can also calculate the branching fractions:
14 Resonance Phase Motion • Relativistic Breit-Wigner function is used to model resonances 2𝑀+1 𝑁 0 1 𝑟 ′ 𝑟, 𝑟 0 , 𝑒 2 𝐶𝑋 𝑛 𝑁 0 , Γ 0 = , Γ 𝑛 = Γ 0 𝑛 𝐶 𝑀 2 − 𝑛 2 − 𝑗𝑁 0 Γ(𝑛) 𝑟 0 𝑁 0 • The complex function 𝐶𝑋 𝑛 𝑁 0 , Γ 0 displayed in an Argand diagram exhibits a circular trajectory . 𝑁 0
15 Resonance Phase Motion • The Breit-Wigner shape for individual 𝑄 𝑑 ’s is replaced with 6 independent amplitudes in 𝑁 0 ± Γ 0 • 𝑄 𝑑 4450 : shows resonance behavior: a rapid counter- clockwise change of phase across the pole mass • 𝑄 𝑑 4380 : does show large phase change, but is not conclusive. Plot fitted values for amplitudes in an Argand diagram Breit-Wigner Prediction Fitted Values
16 Interpretations of the states diquarks molecular triquark baryon meson • Already a lot of activity on interpreting these states, with a variety of models being proposed. • Most common models employ molecular binding or additional hadron building blocks of diquarks or triquarks. • Additional explanations have been offered in terms of kinematical effects. However these cannot explain two states.
17 Where else to look for these pentaquarks? • There are many ideas on where to look. None will be as ideal as the clean 𝐾 𝜔 signature plus two charged tracks forming a secondary vertex. This was a good channel to accidentally find this in. • They can be looked for in decays to other charmonium states: 𝜃 𝑑 𝑞 , 𝜓 𝑑 𝑞 • Or to open charm pairs: Λ 𝑑 𝐸, Λ 𝑑 𝐸 ∗ , Σ 𝑑 𝐸 • Would be very interesting to see them from different sources: • Direct production: However there is a difficulty from huge number of protons coming from primary vertices It’s been proposed to look for these states in 𝛿𝑞 → 𝐾 𝜔 𝑞 •
18 Conclusions Two pentaquark candidates decaying to J/ y p have been observed with • overwhelming significance in a state of the art amplitude analysis. Both are absolutely needed to obtain a good description of the data. • The nature of the states is unknown. For elucidation, more sensitive studies as well as searches for other pentaquark candidates will be absolutely necessary. • Towards this effort we continue to fully utilize the Run 1 data, and have increased statistics on the way. LHCb expects 8 fb -1 in Run 2 (-2018) followed by the detector/luminosity upgrade which will bring ~50 fb -1 by 2028. • We look forward to more input from theory and other experiments.
BACKUP SLIDES
20 0 J/ y p K - Selection L b • The data sample consists of the full LHCb Run 1 data set VELO of 3fb -1 • Candidates have a 𝜈 + 𝜈 − 𝐿𝑞 vertex, with the 𝜈 + 𝜈 − pair consistent with a 𝐾 𝜔 p • Standard selection to ensure good track and vertex quality, as well as cuts on particle identification, 𝑞 𝑈 cuts, and K separation from the primary vertex. • Reflections from 𝐶 0 and 𝐶 𝑡 are vetoed. • Final background suppression is done with a multivariate analyzer (boosted decision tree).
21 L * Matrix Element Completely describes the decay Λ 𝑐 → Λ ∗ 𝐾 𝜔 with Λ ∗ → 𝐿𝑞 and 𝐾 𝜔 → 𝜈𝜈 6 independent data variables: 4-6 independent complex helicity 1 mass, 5 angles couplings per L n * resonance Breit-Wigner Blatt-Weisskopf functions
22 + Matrix Element P c Completely describes the decay 𝑑 → 𝐾 𝜔 𝑞 and Λ 𝑐 → 𝑄 𝑑 𝐿 with 𝑄 𝐾 𝜔 → 𝜈𝜈 One more angle than in Λ ∗ decay: P c + production angles must be defined relative to the L b reference frame established for L b J/ yL * decay 1 mass ( m J/ y p ), 6 angles all derivable from the L * decay variables 3-4 independent complex helicity couplings + resonance depending on its J P per P c j Breit- Wigner Blatt-Weisskopf functions
23 + Matrix Element L * Plus P c • To add the two matrix elements together we need two additional angles to align the muon and proton helicity frames between the Λ ∗ and 𝑄 𝑑 decay chains. + interferences – This is necessary to describe L * plus P c properly 𝜄 𝑞 • With 𝜄 𝑞 , 𝛽 𝜈 the full matrix element is written as
24 No need for exotic J/ y K - contributions m Kp <1.55 GeV 1.55< m Kp • No evidence seen for <1.70 GeV a resonance in the Dalitz plane • J/ y K - system is well described by the Λ ∗ c + reflections. and P 1.70< m Kp <2.00 GeV 2.00 GeV< m Kp 𝑄 𝑑 All m Kp
25 Systematic uncertainties • Uncertainties in the L * model dominate • Quantum number assignment and resonance parametrization are also sizeable.
26 Significances • Significances assessed using the extended model. • This includes the dominant systematic uncertainties, coming from difference between extended and reduced L * model results. • Fit quality improves greatly, and simulations of pseudoexperiments are used to turn the D (-2ln L ) values to significances D (-2ln L ) Significance 14.7 2 0 → 1 𝑄 12𝜏 𝑑 11.6 2 1 → 2 𝑄 9𝜏 𝑑 18.7 2 0 → 2 𝑄 15𝜏 𝑑 • Each of the states is overwhelmingly significant.
27 Complete set of fit fractions
28 Extended Model with Two 𝑄 𝑑 Resonances
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