Charm baryons on the lattice M. PADMANATH Institute for Physics, University of Graz, Graz, Austria. CHARM 2015 May 21, 2015 ♠ Collaborators : R. G. Edwards, N. Mathur and M. Peardon (For HSC) ♠ Acknowledgements : TIFR, Mumbai & Austrian Science Fund (FWF) ♠ Thanks to those who provided me the material CHARM BARYONS ON THE LATTICE M. PADMANATH (Charm 2015) Institute of Physics, University of Graz, Austria (1/36)
Outline ABC? Low lying spectrum from lattice QCD Excited charm baryon spectrum Summary CHARM BARYONS ON THE LATTICE M. PADMANATH (Charm 2015) Institute of Physics, University of Graz, Austria (2/36)
Outline ABC? Low lying spectrum from lattice QCD Excited charm baryon spectrum Summary CHARM BARYONS ON THE LATTICE M. PADMANATH (Charm 2015) Institute of Physics, University of Graz, Austria (3/36)
ABC? ◮ ABC : A spiring study of B aryons with C harm quarks. ◮ The heavy flavor tag : Mechanism of confinement and systematics of hadron resonances that are obscure due to the chiral dynamics in light baryons. Particularly Ω ccc . ◮ Detection and isolation : relatively easy. Expected to be relatively free of nearby overlapping resonances. Production? : No known resonant production mechanism Rely on continuum production ◮ Spin identification : Most assignments based on quark model expectations! ◮ Heavy quark symmetry (HQS) : Qualitative insight into light baryon spectrum (hyperons). The quark-diquark picture and the missing baryon resonances. Shirotori et al. , JPCS 569, no. 1, 012085 CHARM BARYONS ON THE LATTICE M. PADMANATH (Charm 2015) Institute of Physics, University of Graz, Austria (4/36)
Baryons with C = 3 , 2 and 1 ◮ Triply charm baryons : Charmonia analogues in baryons. Platform to study quark confinement mechanism. The triply charmed baryons may provide a new window for understanding the structure of baryons. J. D. Bjorken, Report No. FERMILAB-CONF-85/69. ◮ Doubly charm baryons : Observations only by SELEX ( losing confidence ) Failed to be observed in FOCUS, Belle, BaBar and LHCb. Very large isospin splittings : 9 and 21 MeV. HQS : lim( m Q → ∞ ) J light is a conserved quantum number. ◮ Singly charm baryons : 20 states with *** or more. More levels expected to be observed. Interesting indications for the existence of many charm baryons from finite temperature lattice calculations HQS : lim( m Q → ∞ ) J light is a conserved quantum number. Light quark dynamics around a static color source. Corrections of the O (Λ QCD / m Q ). CHARM BARYONS ON THE LATTICE M. PADMANATH (Charm 2015) Institute of Physics, University of Graz, Austria (5/36)
Indications from finite temperature studies Ebert et al. , PRD 84 014025 Bazavov et al. , PLB 737, 210 Λ C [GeV] 0.5 4 BC /( χ 4 C - χ 13 BC ) Charm baryon/meson χ 13 0.4 3.5 QM-HRG-3 QM-HRG 3 0.3 PDG-HRG 2.5 0.2 experimentally established states BQC /( χ 13 QC - χ 112 BQC ) non-int. 0.5 χ 112 2 quarks 1/2 + 3/2 + 5/2 + 7/2 + 9/2 + 1/2 - 3/2 - 5/2 - 7/2 - 9/2 - 11/2 - 0.4 ◮ Charm hadron pressure (HRG) : 0.3 Charged-charm BSC /( χ 13 SC - χ 112 BSC ) - χ 112 Strange-charm 0.7 P (ˆ µ C , ˆ µ B ) = P M cosh (ˆ µ C ) + P B , C =1 cosh (ˆ µ C + ˆ µ B ) N τ : 8 6 0.5 = ∂ ( k + l ) [ P (ˆ µ B ) / T 4 ] µ C , ˆ T [MeV] χ BC 0.3 kl µ k µ l ∂ ˆ B ∂ ˆ 140 150 160 170 180 190 200 210 C ⇒ Existence of additional charm-light baryons in QGP formed in HIC. CHARM BARYONS ON THE LATTICE M. PADMANATH (Charm 2015) Institute of Physics, University of Graz, Austria (6/36)
Lattice study of charm baryons ◮ Non-perturbative study : A comprehensive lattice QCD study of spectrum, including excited states, of charm baryons. ◮ Predictions and postdictions : Confirm and guide the experimental searches. ◮ Precision Spectroscopy : Aimed at low lying spectrum. ◮ Excited state measurement : Understanding the spectral patterns. First step towards that goal made. Efforts on the way to ‘precision’ spectroscopy of excited states. CHARM BARYONS ON THE LATTICE M. PADMANATH (Charm 2015) Institute of Physics, University of Graz, Austria (7/36)
Charm baryons : SU(4) classifications 4 ⊗ 4 ⊗ 4 = 20 S ⊕ 20 M ⊕ 20 M ⊕ 4 A Broken flavor symmetry. Classification for enumerating the possible states. Physical states could be mixture of these multiplets. CHARM BARYONS ON THE LATTICE M. PADMANATH (Charm 2015) Institute of Physics, University of Graz, Austria (8/36)
Charm baryons : HQET + SU(3) C = 1 : 3 ⊗ 3 = ¯ 3 A ⊕ 6 S C = 2 : 3 The symmetries are with respect to the light quarks. The charm quarks are considered as spectators. CHARM BARYONS ON THE LATTICE M. PADMANATH (Charm 2015) Institute of Physics, University of Graz, Austria (9/36)
Outline ABC? Low lying spectrum from lattice QCD Excited charm baryon spectrum Summary CHARM BARYONS ON THE LATTICE M. PADMANATH (Charm 2015) Institute of Physics, University of Graz, Austria (10/36)
QCD spectrum from Lattice QCD ◮ Aim : to extract the physical states of QCD. ◮ Euclidean two point current-current correlation functions Z n ∗ Z n C ji ( t f − t i ) = � 0 | Φ j ( t f )¯ 2 m n e − m n ( t f − t i ) Φ i ( t i ) | 0 � = � i j n 0.4 where Φ j ( t f ) and ¯ Φ i ( t i ) are 0.38 the desired interpolating 0.36 operators and Z n log[C(t)/C(t+1)] E 1 , E 2 , ... j = � 0 | Φ j | n � . 0.34 0.32 0.3 ◮ Effective mass defined as 0.28 E 1 C ( t ) log[ C ( t +1) ] 0.26 0.24 2 4 6 8 10 12 14 t/a t ◮ The ground states : from the exponential fall off at large times. Non-linear fitting techniques. CHARM BARYONS ON THE LATTICE M. PADMANATH (Charm 2015) Institute of Physics, University of Graz, Austria (11/36)
Lattices in use Fermion actions Gauge actions HISQ : Highly Improved Staggered Quarks : Symanzik improved anisotropic SIa TM : Twisted Mass gluonic action DW : Domain Wall : L¨ uscher-Weisz gluonic action LW : O( a 2 ), Tadpole improved staggered AsqTad : Iwasaki gluonic action Iw OS : Osterwalder-Seiler All calculations with m u = m d and neglect QED ⇒ no isospin splittings. All baryons in the same isospin multiplet appears at same energy. Dynamical calculations from 2009 onwards. • Brice˜ no, Brown and ETMC : Chiral ( χ PT) and continuum extrapolated results • PACS-CS : Measurements at physical point • RQCD : Physical point approached based on Gell-Mann-Okubo relations. CHARM BARYONS ON THE LATTICE M. PADMANATH (Charm 2015) Institute of Physics, University of Graz, Austria (12/36)
Low lying heavy baryons Brown et al. , PRD 90 094507 . CHARM BARYONS ON THE LATTICE M. PADMANATH (Charm 2015) Institute of Physics, University of Graz, Austria (13/36)
Low lying singly charm baryons ▲✐✉ ❊❚▼❈ ■▲●❚■ ❇r✐❝❡ñ♦ ❇r♦✇♥ ■▲●❚■ ♥❡❣ P ❉✉rr ❘◗❈❉ ❊❳P ♣♦s P P❆❈❙✲❈❙ ❘◗❈❉ ♥❡❣ P ❊❳P ♥❡❣ P ✸✳✹ ✸✳✷ ✸ ▼ ✭●❡❱✮ ✷✳✽ ✷✳✻ ✷✳✹ ✷✳✷ ′ Σ c Σ ∗ Ξ Ξ ∗ Ω c Ω ∗ Λ c Ξ c c c c c ✭✉✉❝✮ ✭ss❝✮ ✭✉s❝✮ ✭✉❞❝✮ ✭✉s❝✮ ◗❯❆❘❑❙✿ 1 3 1 3 1 3 1 1 ❙P■◆✿ 2 2 2 2 2 2 2 2 Bali et. al. , arXiv:1503.08440[hep-lat] . ♠ Ground states more or less in agreement between all lattice results and experiments. ♠ Improving control over the systematic and statistical uncertainties. ♠ The excited state determination : challenging! ♠ Systematic spin identification : Even more challenging!! CHARM BARYONS ON THE LATTICE M. PADMANATH (Charm 2015) Institute of Physics, University of Graz, Austria (14/36)
Chiral extrapolations Chiral extrapolations based on Gell-Mann-Okubo formulae. Bali et. al. , arXiv:1503.08440[hep-lat] . CHARM BARYONS ON THE LATTICE M. PADMANATH (Charm 2015) Institute of Physics, University of Graz, Austria (15/36)
Low lying doubly charm baryons ▲✐✉ ■▲●❚■ ♥❡❣ P ❘◗❈❉ ❇r✐❝❡ñ♦ P❆❈❙✲❈❙ ❘◗❈❉ ♥❡❣ P ❉✉rr ❊❚▼❈ ❍❙❈ ■▲●❚■ ❇r♦✇♥ ❍❙❈ ♥❡❣ P ✹✳✽ ✹✳✻ ✹✳✹ ▼ ✭●❡❱✮ ✹✳✷ ✹ ✸✳✽ ✸✳✻ ✸✳✹ Ξ cc Ξ ∗ Ω cc Ω ∗ cc cc ✭✉❝❝✮ ✭s❝❝✮ ◗❯❆❘❑❙✿ 1 3 1 3 ❙P■◆✿ 2 2 2 2 Bali et. al. , arXiv:1503.08440[hep-lat] . ♠ The only experimental candidate (SELEX) : seems very low. ♠ On average lattice results agree between them. ♠ Improving control over the systematic and statistical uncertainties. ♠ The challenging excited states and spin identification! CHARM BARYONS ON THE LATTICE M. PADMANATH (Charm 2015) Institute of Physics, University of Graz, Austria (16/36)
Ξ cc Isospin splittings ◮ The lowest isospin doublet (SELEX) has splitting 9 MeV. ◮ The largest isospin splitting ever observed in Ξ ssq : 6 . 85 ± 0 . 21 MeV ◮ Fully controlled ab initio calculation with 1+1+1+1 flavor QCD+QED with clover improved Wilson quarks. ◮ Precision of low energy description is down to per mil level. ◮ Precision at a level of challenging the experimental numbers. ◮ Irreducible uncertainties is down to O (1 / N c / m 2 b , α 2 ). ◮ Coleman-Glashow relation : ∆ CG = ∆ M N − ∆ M Σ + ∆ M Ξ =0. Borsanyi, et. al. , Science Vol. 347 no. 6229 pp. 1452-1455 CHARM BARYONS ON THE LATTICE M. PADMANATH (Charm 2015) Institute of Physics, University of Graz, Austria (17/36)
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