Hadron Spectroscopy and Resonances : Review M. Padmanath Regensburg, Germany 25 th July 2018 Lattice 2018 M. Padmanath (UR) @ Lattice 2018, East Lansing, MI @ Hadron spectroscopy and resonances (0/32)
Outline Introduction 1 Ground state hadron spectroscopy 2 Excited hadron spectroscopy 3 Resonances on the lattice 4 Meson resonances on the lattice 5 Light baryon resonances 6 Beyond baryons and mesons 7 M. Padmanath (UR) @ Lattice 2018, East Lansing, MI @ Hadron spectroscopy and resonances (0/32)
Outline Introduction 1 Ground state hadron spectroscopy 2 Excited hadron spectroscopy 3 Resonances on the lattice 4 Meson resonances on the lattice 5 Light baryon resonances 6 Beyond baryons and mesons 7 M. Padmanath (UR) @ Lattice 2018, East Lansing, MI Introduction @ Hadron spectroscopy and resonances (1/32)
Hadron spectroscopy on the lattice Euclidean two point current-current correlation functions Z n ∗ Z n C ji ( t f − t i ) = � 0 | O j ( t f ) ¯ 2 E n e − E n ( t f − t i ) O i ( t i ) | 0 � = � i j n Correlation matrices out of large basis of hadron interpolating operators ( O j ( t )) with desired quantum numbers. � O j ( t ) = q ( x , t )Γ j ( x , t ) q ( x , t ) x Quark smearing to improve the overlap with ground states! � q ( x , t ) = S ( x , y ) q b ( y , t ) y Variational study (GEVP) to extract physical information C ji ( t ) v n i = λ n ( t , t 0 ) C ji ( t 0 ) v n i M. Padmanath (UR) @ Lattice 2018, East Lansing, MI Introduction @ Hadron spectroscopy and resonances (1/32)
Outline Introduction 1 Ground state hadron spectroscopy 2 Excited hadron spectroscopy 3 Resonances on the lattice 4 Meson resonances on the lattice 5 Light baryon resonances 6 Beyond baryons and mesons 7 M. Padmanath (UR) @ Lattice 2018, East Lansing, MI Ground state hadron spectroscopy @ Hadron spectroscopy and resonances (2/32)
Light baryons ETMC PRD 90 074501 ’14 PACS-CS PRD 87 094512 ’13 QCDSF-UKQCD PRD 84 054509 ’11 BMW Science 322 1224 ’08 ETMC, N f = 2 : Alexandrou and Kallidonis, PRD 96 034511 ’17 Calculations at physical pion mass (ETMC, N f = 2) Other measurements with chiral extrapolation to physical pion mass. ETMC, N f = 2 + 1 + 1 and BMW results with continuum extrapolation. Recently baryon masses and mass splittings : BMW Science 347 1452 ’15; QCDSF-UKQCD 1711.02485; Liu 1612.00103. M. Padmanath (UR) @ Lattice 2018, East Lansing, MI Ground state hadron spectroscopy @ Hadron spectroscopy and resonances (2/32)
Heavy baryons 4100 3200 : Expt ′ 17 : HSC ′ 15 : Expt ′ 17 : HSC ′ 15 : ILGTI ′ 13 - ′ 18 : Brown et.al. ′ 14 : ILGTI ′ 13 - ′ 18 : Brown et.al. ′ 14 4000 : TWQCD ′ 17 : PACS-CS ′ 13 : TWQCD ′ 17 : PACS-CS ′ 13 3000 : ETMC ′ 17 : Briceno et.al. ′ 12 : ETMC ′ 17 : Briceno et.al. ′ 12 3900 : RQCD ′ 15 : Durr et al. ′ 12 : RQCD ′ 15 : Durr et al. ′ 12 M cc (MeV) M c (MeV) 2800 3800 2600 3700 2400 3600 2200 3500 * * * * * ′ c c c c cc cc c c c c cc cc 2000 3400 PDG MP et al. (HSC) PRL 119 042001 ’17; PRD 91 094502 ’15 Alexandrou et al. (ETMC) PRD 96 034511 ’17 Brown et al. PRD 90 094507 ’14 Brice˜ no et al. PRD 86 094504 ’12 P´ erez-Rubio et al. (RQCD) PRD 92 034504 ’15 Namekawa et al. (PACS) PRD 87 094512 ’13 ILGTI 1807.00174, 1312.3050 Durr et al. PRD 86 114514 ’12 Chen & Chiu (TWQCD) PLB 767 193 ’17 Recently baryon masses and mass splittings : BMW Science 347 1452 ’15; QCDSF-UKQCD 1711.02485. Early quenched lattice calculations : Lewis et al. ’01; Mathur et al. ’02; Flynn et al. ’03 Dynamical (light quark) investigations : Liu et al. ’10 M. Padmanath (UR) @ Lattice 2018, East Lansing, MI Ground state hadron spectroscopy @ Hadron spectroscopy and resonances (3/32)
Recent highlight : Ξ cc 3800 : Expt ′ 17 : HSC ′ 15 : ILGTI ′ 13 - ′ 18 : Brown et.al. ′ 14 3750 : ETMC ′ 17 : PACS-CS ′ 13 : RQCD ′ 15 : Briceno et.al. ′ 12 cc (MeV) 3700 3650 M 3600 3550 3500 Aaij et al. (LHCb) PRL 119 112001 ’17 MP et al. (HSC) PRD 91 094502 ’15 Alexandrou et al. (ETMC) PRD 96 034511 ’17 Brown et al. PRD 90 094507 ’14 Brice˜ no et al. PRD 86 094504 ’12 P´ erez-Rubio et al. (RQCD) PRD 92 034504 ’15 Namekawa et al. (PACS) PRD 87 094512 ’13 ILGTI 1807.00174, 1312.3050 Ξ cc isospin splitting (LQCD), 2.16(11)(17) MeV : BMW Science 347 1452 ’15 SELEX measurement (3519 MeV) : Mattson et al. PRL 89 112001 ’02 New papers from LHCb on properties of Ξ cc : 1807.01919; 1806.02744 M. Padmanath (UR) @ Lattice 2018, East Lansing, MI Ground state hadron spectroscopy @ Hadron spectroscopy and resonances (4/32)
More predictions for heavy hadrons from lattice 4600 12. Postdiction � � cbb ILGTI ′ 18 Brown et al. ′ 14 � cbb TWQCD ′ 17 PACS-CS ′ 13 Prediction : Mesons 11. 4400 ETMC ′ 17 Briceno et al. ′ 12 Prediction : Baryons RQCD ′ 15 Durr et al. ′ 12 cc (MeV) HSC ′ 15 10. 4200 E � GeV � 9. 4000 � � ccb � ccb 8. E 3800 � � � � � cb � cb � cb � cb � cb � cb 7. B c � 0 � � B c � 1 � � 3600 � � 1 � � B c � 0 � � B c 6. 1/2 + 3/2 + 1/2 3/2 Mathur & MP (ILGTI) 1807.00174, 1312.3050 Mathur, MP et al. (ILGTI) 1806.04151 Ω cc : probably the next doubly charm baryon to be observed in LHCb. Precise predictions for charmed-bottom hadrons. Consistent results with other calculations Brown et al. PRD 90 094507 ’14 Both calculations treat bottom quarks with NRQCD. In this conference, bottom quarks with relativistic action : Salerno Thu. 09.50 [WDME]; Lytle Fri. 14.20 [HSI] M. Padmanath (UR) @ Lattice 2018, East Lansing, MI Ground state hadron spectroscopy @ Hadron spectroscopy and resonances (5/32)
Outline Introduction 1 Ground state hadron spectroscopy 2 Excited hadron spectroscopy 3 Resonances on the lattice 4 Meson resonances on the lattice 5 Light baryon resonances 6 Beyond baryons and mesons 7 M. Padmanath (UR) @ Lattice 2018, East Lansing, MI Excited hadron spectroscopy @ Hadron spectroscopy and resonances (6/32)
Excited charmonium spectrum : An example Established states in yellow Predicted, undiscovered Neutral XYZ mesons Charged XYZ mesons Need for a rigorous excited state determination Open scattering channels? Olsen, 1511.01589 M. Padmanath (UR) @ Lattice 2018, East Lansing, MI Excited hadron spectroscopy @ Hadron spectroscopy and resonances (6/32)
Methodology and literature Large basis of carefully constructed hadron interpolators Mesons : Liao & Manke hep-lat/0210030 ’02; Thomas (HSC) PRD 85 014507 ’12 Baryons : Basak et al. (LHPC) PRD 72 074501, PRD 72 094506 ’05 Morningstar et al. PRD 88 014511 ’13 . Matrix of correlation functions & Variational study Dudek et al. PRD 77 034501 ’08, Michael NPB 259 58 (1985) Established and practised by many groups Light mesons : Dudek et al. (HSC) PRL 103 262001 ’09, PRD 82 034508 ’10 1 Dudek et al. (HSC) PRD 85 014507 ’12 Light baryons : Bulava et al. (HSC) PRD 82 014507, ’10 2 Edwards et al. (HSC) PRD 84 074508 ’11, PRD 87 054506 ’13 Heavy mesons : Liu et al. (HSC) JHEP 1207 126; Moir et al. JHEP 1305 021 3 Cheung et al. JHEP 1612 089; Mohler et al. PRD 87 034501 ’13 Bali et al. PRD 84 094506 ’11; Wurtz et al. PRD 92 054504 ’15 Heavy baryons : Meinel, PRD 85 114510 ’12 4 MP et al. (HSC) PRD 90 074504 ’14, PRD 91 094502 ’15 MP & Mathur (HSC) PRL 119 042001 ’17, 1508.07168. Single hadron approximation. Naive expectation : correct up to O (Γ) M. Padmanath (UR) @ Lattice 2018, East Lansing, MI Excited hadron spectroscopy @ Hadron spectroscopy and resonances (7/32)
Excited hadron spectroscopy on lattice : An example p 2 � 0 1.8 1.8 p 2 � 0 1.7 1.7 1.6 D s D s 1.6 D s D s DD a E n 1.5 a E n DD 1.5 1.4 1.4 1.3 1.3 1.2 1.1 1.2 T1 �� T2 �� E �� T1 �� T2 �� E �� T1 �� T2 �� E �� T1 �� T2 �� E �� A1 �� A2 �� A1 �� A2 �� A1 �� A2 �� A1 �� A2 �� 1.8 1.8 p 2 � 1 p 2 � 2 1.7 1.7 D s D s DD D s D s 1.6 1.6 DD a E n a E n 1.5 1.5 1.4 1.4 1.3 1.3 1.2 1.2 A1 � A2 � B1 � B2 � E2 � A1 � A2 � B1 � B2 � E2 � A1 � A2 � B1 � B2 � A1 � A2 � B1 � B2 � Charmonium spectrum in different inertial frames ( L ∼ 2 fm ) Spin 0, 1, 2, 3 Piemonte Fri. 15.20 [HSI]; Collins, MP, et al. (RQCD) M. Padmanath (UR) @ Lattice 2018, East Lansing, MI Excited hadron spectroscopy @ Hadron spectroscopy and resonances (8/32)
Excited baryon spectroscopy : Example 2.6 � c 2.4 m � 0.5 m Η c � GeV � 2.2 2. 1.8 � ' c K � c K 1.6 1.4 1.2 1 � 2 � 3 � 2 � 5 � 2 � 7 � 2 � 1 � 2 � 3 � 2 � 5 � 2 � 7 � 2 � Edwards, et al. (HSC) PRD 84 074508 ’11; MP & Mathur (HSC) PRL 119 042001 ’17 PRD 87 054506 ’13 Baryon interpolators : Basak et al. (LHPC) PRD 72 074501, PRD 72 094506 ’05 Morningstar et al. PRD 88 014511 ’13 . Light baryons : Bulava et al. PRD 82 014507, ’10 Edwards et al. (HSC) PRD 84 074508 ’11, PRD 87 054506 ’13 Heavy baryons : Meinel, PRD 85 114510 ’12 MP et al. (HSC) PRD 90 074504 ’14, PRD 91 094502 ’15 MP & Mathur (HSC) PRL 119 042001 ’17, 1508.07168 . M. Padmanath (UR) @ Lattice 2018, East Lansing, MI Excited hadron spectroscopy @ Hadron spectroscopy and resonances (9/32)
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