Heavy hadron interactions from Lattice QCD Daniel Mohler Wien, Sep - PowerPoint PPT Presentation

Heavy hadron interactions from Lattice QCD Daniel Mohler Wien, Sep 14th, 2017 Daniel Mohler (HIM) Heavy hadron interactions from Lattice QCD Wien, Sep 14th, 2017 1 / 29

Observation of a doubly-charmed Ξ ++ cc by LHCb Roel Aaij et al. , LHCb collaboration arXiv:1707.01621 2 c 180 u u Candidates per 5 MeV/ LHCb 13 TeV 160 Λ + c c Data c 140 Total d 120 Signal Ξ ++ ¯ d Background cc 100 π + u 80 u ¯ 60 K − c s 40 20 u W + π + 0 ¯ d 3500 3600 3700 Ξ ++ m ( ) [MeV/ c 2 ] cc cand Ξ ++ with mass 3621 . 40 ± 0 . 72 ± 0 . 27 ± 0 . 14 cc seen in both 13 TeV and 8 TeV data Previous claim of Ξ cc by SELEX wit mass ≈ 3519 MeV not seen by BaBar, Belle, LHCb What about Lattice QCD Predictions? Daniel Mohler (HIM) Heavy hadron interactions from Lattice QCD Wien, Sep 14th, 2017 2 / 29

Ξ cc – Recent Lattice QCD predictions Alexandrou et al., PRD90 074501 (2014) Briceno et al., PRD86 094504 (2012) Brown et al. 094507 (2014) Namekawa et al. PRD87, 094512 (2013)) Perez Rubio et al., PRD92 034504 (2015) Mathur, Padmanath, Mondal (preliminary) Observation claimed by SELEX 3500 3550 3600 3650 3700 3750 3800 3850 Full symbols: Good control of systematic uncertainty Empty symbols: Continuum extrapolation missing All simulations neglect isospin splittings Ξ ++ – Ξ + cc cc Publications also contain a number of further predictions and successful postdictions History of earlier calculations, most notably Mathur, Lewis, Woloshyn, PRD 64 094509 (2001);PRD 66 014502 (2002) Daniel Mohler (HIM) Heavy hadron interactions from Lattice QCD Wien, Sep 14th, 2017 3 / 29

Ξ cc – Recent Lattice QCD predictions Alexandrou et al., PRD90 074501 (2014) Briceno et al., PRD86 094504 (2012) Brown et al. 094507 (2014) Namekawa et al. PRD87, 094512 (2013)) Perez Rubio et al., PRD92 034504 (2015) Mathur, Padmanath, Mondal (preliminary) Observation claimed by SELEX 3500 3550 3600 3650 3700 3750 3800 3850 Full symbols: Good control of systematic uncertainty Empty symbols: Continuum extrapolation missing All simulations neglect isospin splittings Ξ ++ – Ξ + cc cc Publications also contain a number of further predictions and successful postdictions History of earlier calculations, most notably Mathur, Lewis, Woloshyn, PRD 64 094509 (2001);PRD 66 014502 (2002) Daniel Mohler (HIM) Heavy hadron interactions from Lattice QCD Wien, Sep 14th, 2017 3 / 29

Observation of 5 narrow Ω c states Roel Aaij et al. , LHCb collaboration PRL 118 182001 (2017) Candidates / (1 MeV) 400 LHCb Γ [MeV] Resonance Mass [MeV] 3000 . 4 ± 0 . 2 ± 0 . 1 + 0 . 3 Ω c ( 3000 ) 0 4 . 5 ± 0 . 6 ± 0 . 3 − 0 . 5 300 3050 . 2 ± 0 . 1 ± 0 . 1 + 0 . 3 Ω c ( 3050 ) 0 0 . 8 ± 0 . 2 ± 0 . 1 − 0 . 5 Ω c ( 3066 ) 0 3065 . 6 ± 0 . 1 ± 0 . 3 + 0 . 3 3 . 5 ± 0 . 4 ± 0 . 2 200 − 0 . 5 3090 . 2 ± 0 . 3 ± 0 . 5 + 0 . 3 Ω c ( 3090 ) 0 8 . 7 ± 1 . 0 ± 0 . 8 − 0 . 5 3119 . 1 ± 0 . 3 ± 0 . 9 + 0 . 3 Ω c ( 3119 ) 0 1 . 1 ± 0 . 8 ± 0 . 4 100 − 0 . 5 0 3000 3100 3200 3300 − Ξ + m ( K ) [MeV] c Observation of 5 new Ω c resonances J P not identified All states are narrow → can compare to Lattice QCD simulations treating them as stable Daniel Mohler (HIM) Heavy hadron interactions from Lattice QCD Wien, Sep 14th, 2017 4 / 29

What can Lattice QCD say about their spin-parity? Padmanath, Mathur, PRL 119 042001 (2017) 3 � 2 � � c Η 1 � 2 � � ' c K � S � 600 + ) L 1 + ) L 2 : ∆ E ( 3 : ∆ E ( 3 0.5 � D : Expt 2 2 − ) L 1 − ) L 2 5 � 2 � : ∆ E ( 1 : ∆ E ( 1 2 2 − ) L 1 − ) L 2 500 : ∆ E ( 3 : ∆ E ( 3 3 � 2 � 0.4 � c K � S � 2 2 E � E 1 � 2 � � GeV � � ' c K 3 � 2 � 1 � 2 � 400 1 � 2 � 0.3 � c K ∆ E Ω 0 c 300 0.2 200 0.1 3 � 2 � 100 1 � 2 � 0. 0 0.000 0.005 0.010 0.015 0.020 Expt. Lattice a 2 Pattern of lattice states agrees well with experiment second study with smaller basis can not resolve two states with same J P ; checks systematics Scattering thresholds somewhat unphysical Daniel Mohler (HIM) Heavy hadron interactions from Lattice QCD Wien, Sep 14th, 2017 5 / 29

Outline Motivation – Charmed baryons 1 Recent progress in Lattice QCD 2 D , D s , and B s 3 Charmonium(-like) states 4 Charmonium-like states: Z c Charmonium-like states: X(3915) Charmonium-like states: X ( 3872 ) Exotic doubly-heavy states 5 Daniel Mohler (HIM) Heavy hadron interactions from Lattice QCD Wien, Sep 14th, 2017 6 / 29

Lattice Quantum Chromodynamics: What do we calculate? Regularization of QCD by a 4-d Euclidean space-time lattice. (Kenneth Wilson 1974) Provides a calculational method for QCD Euclidean correlator of two Hilbert-space operators ˆ O 1 and ˆ O 2 . � � O 2 ( t )ˆ ˆ � e − t ∆ E n � 0 | ˆ O 2 | n �� n | ˆ O 1 ( 0 ) = O 1 | 0 � n = 1 � D [ ψ, ¯ ψ, U ] e − S E O 2 [ ψ, ¯ ψ, U ] O 1 [ ψ, ¯ ψ, U ] Z Path integral over the Euclidean action S E , QCD [ ψ, ¯ ψ, U ] ; (a sum over quantum fluctuations) Can be evaluated with Markov Chain Monte Carlo (using methods well established in statistical physics) Daniel Mohler (HIM) Heavy hadron interactions from Lattice QCD Wien, Sep 14th, 2017 7 / 29

Recent progress in Lattice QCD Dynamical simulations with 2+1(+1) flavors of sea quarks Simulations at physical pion (light-quark) masses Isospin splitting and QCD+QED simulations Improved heavy quark actions for charm Efficient methods for all-to-all propagation (disconnected diagrams) 10 ΔΣ experiment 8 QCD+QED ΔΞ prediction 6 Δ M [MeV] Δ D 4 ΔΞ cc Δ N 2 Δ CG 0 BMW 2014 HCH BMW Collaboration, Borsanyi et al. Science 347 1452 (2015) Daniel Mohler (HIM) Heavy hadron interactions from Lattice QCD Wien, Sep 14th, 2017 8 / 29

Progress from an old idea: Lüscher’s finite-volume method M. Lüscher Commun. Math. Phys. 105 (1986) 153; Nucl. Phys. B 354 (1991) 531; Nucl. Phys. B 364 (1991) 237. Basic observation: Finite volume, multi-particle energies are shifted with regard to the free energy levels due to the interaction E = E ( p 1 ) + E ( p 2 ) + ∆ E E � m Π Energy shifts encode scattering amplitude(s) 4.0 Original method: Elastic scattering in the 3.5 rest-frame in multiple spatial volumes L 3 Coupled 2-hadron channels well understood 3.0 2 ↔ 1 and 2 ↔ 2 transitions well understood 2.5 (example ππ → πγ ∗ ) significant progress for 3-particle scattering 2.0 8L m Π 2 3 4 5 6 7 Reviews by R. A. Briceño arXiv:1411.6944 and M. Hansen arXiv:1511.04737 Daniel Mohler (HIM) Heavy hadron interactions from Lattice QCD Wien, Sep 14th, 2017 9 / 29

Fully systematic calculation vs. exploratory study Important lattice systematics from a ( g , m ) → 0 Taking the continuum limit : Taking the infinite volume limit : L → ∞ Calculation at (or extrapolation to) the physical pion mass I cover many exploratory results Should be compared only qualitatively to experiment Provide an outlook on future Lattice QCD results ± / ± FLAG average for = + + + ETM 14E FNAL/MILC 14A Example for fully systematic results: + ETM 13F HPQCD 13A MILC 13A = MILC 11 (stat. err. only) ETM 10E (stat. err. only) = + FLAG average for Flavor physics results listed in the RBC/UKQCD 14B RBC/UKQCD 12 Laiho 11 MILC 10 JLQCD/TWQCD 10 FLAG review RBC/UKQCD 10A + PACS-CS 09 BMW 10 JLQCD/TWQCD 09A (stat. err. only) = MILC 09A http://flag.unibe.ch/ MILC 09 Aubin 08 PACS-CS 08, 08A RBC/UKQCD 08 HPQCD/UKQCD 07 → See talk by U. Wenger NPLQCD 06 MILC 04 FLAG average for = ETM 14D (stat. err. only) ALPHA 13A = BGR 11 ETM 10D (stat. err. only) ETM 09 QCDSF/UKQCD 07 1.14 1.18 1.22 1.26 Daniel Mohler (HIM) Heavy hadron interactions from Lattice QCD Wien, Sep 14th, 2017 10 / 29

Exotic D s and B s candidates Established s and p-wave D s and B s hadrons: D s ( J P = 0 − ) and D ∗ B s ( J P = 0 − ) and B ∗ s (1 − ) s (1 − ) D ∗ s 0 ( 2317 ) (0 + ), D s 1 ( 2460 ) (1 + ), B s 1 ( 5830 ) (1 + ), B ∗ s 2 ( 5840 ) (2 + ) D s 1 ( 2536 ) (1 + ), D ∗ s 2 ( 2573 ) (2 + ) Corresponding D ∗ 0 ( 2400 ) and D 1 ( 2430 ) are broad resonances s ≈ M c ¯ → Peculiarity: M c ¯ exotic structure? (tetraquark, molecule) d B s cousins of the D ∗ s 0 ( 2317 ) and D s 1 ( 2460 ) not (yet) seen in experiment The LHCb experiment at CERN should be able to see these Daniel Mohler (HIM) Heavy hadron interactions from Lattice QCD Wien, Sep 14th, 2017 11 / 29

Exotic D s and B s candidates Established s and p-wave D s and B s hadrons: D s ( J P = 0 − ) and D ∗ B s ( J P = 0 − ) and B ∗ s (1 − ) s (1 − ) D ∗ s 0 ( 2317 ) (0 + ), D s 1 ( 2460 ) (1 + ), ? D s 1 ( 2536 ) (1 + ), D ∗ s 2 ( 2573 ) (2 + ) B s 1 ( 5830 ) (1 + ), B ∗ s 2 ( 5840 ) (2 + ) Corresponding D ∗ 0 ( 2400 ) and D 1 ( 2430 ) are broad resonances s ≈ M c ¯ → Peculiarity: M c ¯ exotic structure? (tetraquark, molecule) d B s cousins of the D ∗ s 0 ( 2317 ) and D s 1 ( 2460 ) not (yet) seen in experiment The LHCb experiment at CERN should be able to see these Daniel Mohler (HIM) Heavy hadron interactions from Lattice QCD Wien, Sep 14th, 2017 11 / 29