Charm baryons on the lattice M. PADMANATH Institute for Physics, - - PowerPoint PPT Presentation

SLIDE 1

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)

SLIDE 2

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)

SLIDE 3

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)

SLIDE 4

ABC?

◮ ABC : Aspiring study of Baryons with Charm 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 Ωccc.

◮ 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)

SLIDE 5

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(mQ → ∞) Jlight 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(mQ → ∞) Jlight is a conserved quantum number. Light quark dynamics around a static color source. Corrections of the O(ΛQCD/mQ).

CHARM BARYONS ON THE LATTICE

• M. PADMANATH (Charm 2015)

Institute of Physics, University of Graz, Austria (5/36)

SLIDE 6

Indications from finite temperature studies

Ebert et al., PRD 84 014025

ΛC [GeV]

experimentally established states 2 2.5 3 3.5 4 1/2+ 3/2+ 5/2+ 7/2+ 9/2+ 1/2- 3/2- 5/2- 7/2- 9/2-11/2-

◮ Charm hadron pressure (HRG) :

P(ˆ µC, ˆ µB) = PMcosh(ˆ µC) +PB,C=1cosh(ˆ µC + ˆ µB) χBC

kl

= ∂(k+l)[P(ˆ µC, ˆ µB)/T 4] ∂ˆ µk

B∂ˆ

µl

C

Bazavov et al., PLB 737, 210

Nτ: 8 6 0.3 0.5 0.7 140 150 160 170 180 190 200 210

• χ112

BSC/(χ13 SC-χ112 BSC)

Strange-charm T [MeV] 0.3 0.4 0.5 χ112

BQC/(χ13 QC-χ112 BQC)

Charged-charm non-int. quarks QM-HRG-3 QM-HRG PDG-HRG 0.2 0.3 0.4 0.5 χ13

BC/(χ4 C-χ13 BC)

Charm baryon/meson

⇒ 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)

SLIDE 7

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)

SLIDE 8

Charm baryons : SU(4) classifications

4 ⊗ 4 ⊗ 4 = 20S ⊕ 20M ⊕ 20M ⊕ 4A 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)

SLIDE 9

Charm baryons : HQET + SU(3)

C = 1 : 3 ⊗ 3 = ¯ 3A ⊕ 6S 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)

SLIDE 10

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)

SLIDE 11

QCD spectrum from Lattice QCD

◮ Aim : to extract the physical states of QCD. ◮ Euclidean two point current-current correlation functions

Cji(tf − ti) = 0|Φj(tf )¯ Φi(ti)|0 =

n Z n∗

i

Z n

j

2mn e−mn(tf −ti)

where Φj(tf ) and ¯ Φi(ti) are the desired interpolating

• perators and Z n

j = 0|Φj|n. ◮ Effective mass defined as

log[

C(t) C(t+1)]

0.24 0.26 0.28 0.3 0.32 0.34 0.36 0.38 0.4 2 4 6 8 10 12 14

log[C(t)/C(t+1)] t/at E1 E1, E2, ...

◮ 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)

SLIDE 12

Lattices in use

Gauge actions SIa LW Iw : Symanzik improved anisotropic gluonic action : L¨ uscher-Weisz gluonic action : Iwasaki gluonic action Fermion actions HISQ TM DW AsqTad OS : Highly Improved Staggered Quarks : Twisted Mass : Domain Wall : O(a2), Tadpole improved staggered : Osterwalder-Seiler All calculations with mu = md 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 (χPT) 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)

SLIDE 13

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)

SLIDE 14

Low lying singly charm baryons

✷✳✷ ✷✳✹ ✷✳✻ ✷✳✽ ✸ ✸✳✷ ✸✳✹ Σc Σ∗

c

Ξ

′

c

Ξ∗

c

Ωc Ω∗

c

Λc Ξc ▼ ✭●❡❱✮ ▲✐✉ ❇r✐❝❡ñ♦ ❉✉rr P❆❈❙✲❈❙ ❊❚▼❈ ❇r♦✇♥

❘◗❈❉ ❘◗❈❉ ♥❡❣ P

■▲●❚■ ■▲●❚■ ♥❡❣ P

❊❳P ♣♦s P ❊❳P ♥❡❣ P ◗❯❆❘❑❙✿ ✭✉✉❝✮ ✭ss❝✮ ✭✉s❝✮ ✭✉❞❝✮ ✭✉s❝✮ ❙P■◆✿

1 2 3 2 1 2 3 2 1 2 3 2 1 2 1 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)

SLIDE 15

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)

SLIDE 16

Low lying doubly charm baryons

✸✳✹ ✸✳✻ ✸✳✽ ✹ ✹✳✷ ✹✳✹ ✹✳✻ ✹✳✽ Ξcc Ξ∗

cc

Ωcc Ω∗

cc

▼ ✭●❡❱✮

▲✐✉ ❇r✐❝❡ñ♦ ❉✉rr ■▲●❚■ ■▲●❚■ ♥❡❣ P P❆❈❙✲❈❙ ❊❚▼❈ ❇r♦✇♥ ❘◗❈❉ ❘◗❈❉ ♥❡❣ P ❍❙❈ ❍❙❈ ♥❡❣ P

◗❯❆❘❑❙✿ ✭✉❝❝✮ ✭s❝❝✮ ❙P■◆✿

1 2 3 2 1 2 3 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)

SLIDE 17

Ξcc Isospin splittings

◮ The lowest isospin doublet (SELEX) has splitting 9 MeV. ◮ The largest isospin splitting ever observed in Ξssq : 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/Nc/m2

b, α2).

◮ Coleman-Glashow relation : ∆CG = ∆MN − ∆MΣ + ∆MΞ=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)

SLIDE 18

The doubly heavy picture (BQQ)

◮ quark-diquark picture :

HQET motivated Heavy-light meson-like system. HQS : lim(mQ → ∞) M(B∗

QQ) − M(BQQ)

M(VQ) − M(PSQ) → 3 4

Brambilla et al., hep-ph/0506065

Low lying levels.

◮ Charmonium-like system :

Valid for excited states. Demands precision measurements

• f excited levels

CHARM BARYONS ON THE LATTICE

• M. PADMANATH (Charm 2015)

Institute of Physics, University of Graz, Austria (18/36)

SLIDE 19

HQET expectations

For a heavy-light meson-like system of doubly charm baryons (BQQ) M(B∗

QQ) − M(BQQ)

M(VQ) − M(PSQ) → 3 4

Brambilla et al., hep-ph/0506065

0.25 0.5 0.75 1

HSC ILGTI Brown RQCD PACS-CS

Ωcc

0.25 0.5 0.75 1

HSC Brown RQCD PACS-CS

Ξcc

♠ Ωcc consistently below 0.75 in all measurements. ♠ The study of systematics in ‘ILGTI’ are in process. ♠ Systematic uncertainties in ‘HSC’ and ‘PACS-CS’! ♠ Results from ‘Brown’ and ‘RQCD’ indicates similar pattern in Ωcc and Ξcc.

CHARM BARYONS ON THE LATTICE

• M. PADMANATH (Charm 2015)

Institute of Physics, University of Graz, Austria (19/36)

SLIDE 20

The triply charm baryon

HSC ILGTI BMW PACS-CS Brown 0.06 0.09 0.12 0.15 0.18 0.21 massΩccc - 3/2 massJ/ψ [GeV]

a=0.0888fm at=0.04fm a=0.0582fm a=0.09fm a=0.07fm a -> 0 MP et al., PRD 90 074504.

CHARM BARYONS ON THE LATTICE

• M. PADMANATH (Charm 2015)

Institute of Physics, University of Graz, Austria (20/36)

SLIDE 21

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 (21/36)

SLIDE 22

Excited charm baryon spectrum

♣ Prospects include zero to finite temperature physics.

◮ Answering fundamental questions ◮ Compare, inform and guide the experimental programs ◮ Finite temperature prospects

♣ Challenges include extracting densely populated spectra.

◮ Extracting densely populated states ◮ Extracting radial and orbital excitations ◮ Extracting excitations with spin > 3/2 ◮ Systematic spin identification ◮ Multiple scattering channels affecting the single hadron spectra

♣ Scattering parameters from finite volume energy shifts. L¨ uscher’s formalism and its various generalizations. ♣ Encouraging achievements in the light and heavy meson spectra

Dudek et al. [HSC] PRL 113, 182001 Talk by Sasa Prelovsek (Mon, S1), Daniel Mohler (Mon, S2)

CHARM BARYONS ON THE LATTICE

• M. PADMANATH (Charm 2015)

Institute of Physics, University of Graz, Austria (22/36)

SLIDE 23

The variational method

• R. G. Edwards slides

CHARM BARYONS ON THE LATTICE

• M. PADMANATH (Charm 2015)

Institute of Physics, University of Graz, Austria (23/36)

SLIDE 24

Baryon operators

Edwards et al., PRD 84 074508

• R. G. Edwards slides

CHARM BARYONS ON THE LATTICE

• M. PADMANATH (Charm 2015)

Institute of Physics, University of Graz, Austria (24/36)

SLIDE 25

HSC lattices and caveats

♣ Anisotropic lattices : as = at Non-perturbative tuning of action parameters : ξ = as/at ∼ 3.5 ♣ Nf = 2 + 1 dynamical configurations ♣ 163 × 128 lattices with L ∼ 2fm. ♣ 96 gauge field configurations. ♣ Continuum limit not taken. ♣ Finite size effects; only one volume, L ∼ 2fm ♣ Heavy pion mass; mπ ∼ 400MeV ♣ only single hadron operators ⇒ No resonance properties ♣ Pioneering work on study of charm baryon excited states. Precision and systematics : temporarily relaxed (costly). Precision determination of excited states : A challenge we are working for.

CHARM BARYONS ON THE LATTICE

• M. PADMANATH (Charm 2015)

Institute of Physics, University of Graz, Austria (25/36)

SLIDE 26

Ωccc spectrum

1/2

+

3/2

+

5/2

+

7/2

+

1/2

• 3/2
• 5/2
• 7/2
• 0.0

0.4 0.8 1.2 1.6 2.0 2.4 m - 3/2 m ηc (GeV)

MP et al., PRD 90 074504; mπ = 391 MeV

CHARM BARYONS ON THE LATTICE

• M. PADMANATH (Charm 2015)

Institute of Physics, University of Graz, Austria (26/36)

SLIDE 27

Ωccc spectrum

Consistent with SU(3)F ⊗ SU(2)S ⊗ O(3) expectations

CHARM BARYONS ON THE LATTICE

• M. PADMANATH (Charm 2015)

Institute of Physics, University of Graz, Austria (27/36)

SLIDE 28

Ωccc spectrum

Consistent with SU(3)F ⊗ SU(2)S ⊗ O(3) expectations

CHARM BARYONS ON THE LATTICE

• M. PADMANATH (Charm 2015)

Institute of Physics, University of Graz, Austria (28/36)

SLIDE 29

A comparison between Ωccc and Ωbbb

1/2

+

3/2

+

5/2

+

7/2

+

1/2

• 3/2
• 5/2
• 7/2
• 0.0

0.4 0.8 1.2 1.6 2.0 2.4 m - 3/2 m ηc (GeV)

Ωccc : MP et al., PRD 90 074504 Ωbbb : Meinel, PRD 85 114510 ◮ The spectral pattern remains same up to second excitation band. ◮ PRD90 with considers relativistic operators also.

Hence the multitude of states.

CHARM BARYONS ON THE LATTICE

• M. PADMANATH (Charm 2015)

Institute of Physics, University of Graz, Austria (29/36)

SLIDE 30

Quark mass dependence : ∆-like baryons

MP et al., PRD 90 074504 ◮ The spectral pattern remain more or less same from light to bottom mq. ◮ The binding energy decreases with increasing mq.

CHARM BARYONS ON THE LATTICE

• M. PADMANATH (Charm 2015)

Institute of Physics, University of Graz, Austria (30/36)

SLIDE 31

Heaviness of the quark : SO splitting

MP et al., PRD 90 074504 ◮ mc found to be near to heavy with almost vanishing SO splitting

CHARM BARYONS ON THE LATTICE

• M. PADMANATH (Charm 2015)

Institute of Physics, University of Graz, Austria (31/36)

SLIDE 32

Doubly charm baryon spectrum

1/2

+

3/2

+

5/2

+

7/2

+

1/2

• 3/2
• 5/2
• 7/2
• 0.6

0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 mass - mηc [GeV] 1/2

+

3/2

+

5/2

+

7/2

+

1/2

• 3/2
• 5/2
• 7/2
• 0.6

0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 mass - mηc [GeV]

Ξcc Ωcc Ξcc Ωcc Ξcc Ωcc Ξcc Ωcc 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 ∆mass (GeV)

1.7 1.72 1.74 1.76 1.78 1.8 1.78 1.79 1.8 1.81 1.82 1.83 1.84 1.85 1.86

1/2

+

3/2

+

5/2

+

7/2

+

(a) (a) (b) (b)

Ξcc Ωcc Ξcc Ωcc Ξcc Ωcc Ξcc Ωcc 1.95 2.10 2.25 2.40 2.55 2.70 2.85 3.00 3.15 ∆mass (GeV)

1/2

• 3/2
• 5/2
• 7/2
• MP et al., PRD 91 094502

CHARM BARYONS ON THE LATTICE

• M. PADMANATH (Charm 2015)

Institute of Physics, University of Graz, Austria (32/36)

SLIDE 33

Singly charm baryons

1/2

+

3/2

+

5/2

+

7/2

+

1/2

• 3/2
• 5/2
• 7/2
• 1.4

1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 m - mρ [GeV]

⊕ ⊕ ⊗ ⊗ ⊕ ⊗ ? ⊗ ? ⊕

Λc

1/2

+

3/2

+

5/2

+

7/2

+

1/2

• 3/2
• 5/2
• 1.4

1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 m - mK

* [GeV]

⊗ ⊕ ⊕ ⊕ ⊗ ⊗ ⊕ ⊗ ? ⊗ ⊕ ?

Ξc

1/2

+

3/2

+

5/2

+

7/2

+

1/2

• 3/2
• 5/2
• 7/2
• 1.6

1.8 2.0 2.2 2.4 2.6 2.8 3.0 m - mφ [GeV]

⊗ ⊕ ⊕ ⊗

Ωc

1/2

+

3/2

+

5/2

+

7/2

+

1/2

• 3/2
• 5/2
• 7/2
• 1.6

1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 m - mρ [GeV]

⊗ ⊕ ⊕ ⊗ ⊗ ⊕ ?

Σc

CHARM BARYONS ON THE LATTICE

• M. PADMANATH (Charm 2015)

Institute of Physics, University of Graz, Austria (33/36)

SLIDE 34

Excited state studies

◮ Systematic extraction of various radial and orbital excitations. ◮ Systematic methodology for spin identification. ◮ Broadly consistent non-relativistic quark model. ◮ No “freezing degrees of freedom” nor parity doubling. ◮ Yes! There are caveats

• Continuum limit not taken.
• Finite size effects; only one volume, L ∼ 2fm
• Heavy pion mass; mπ ∼ 400MeV
• only single hadron operators ⇒ No resonance properties

However, a pioneering step towards precision excited state spectroscopy.

◮ Continuing efforts : Include the effects of baryon-meson interpolators,

investigate widths, improving control over systematics. Cost of computing increases.

CHARM BARYONS ON THE LATTICE

• M. PADMANATH (Charm 2015)

Institute of Physics, University of Graz, Austria (34/36)

SLIDE 35

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 (35/36)

SLIDE 36

Summary

◮ High precision lattice calculations of low lying charm baryons. ◮ High precision lattice measurement of Ξcc isospin splitting (2.16(11)(17) MeV).

Looking forward to see more results from BMW-c’s precision measurements.

◮ Heavy diquark-antidiquark symmetry : With increasing precision

lattice measurements this will be put to test.

◮ Excited charm baryon spectra extraction using a systematic operator

construction procedure.

◮ First results suggest the spectrum to be broadly consistent with non-relativistic

quark model.

◮ Promising results, however expensive.

Currently studies made on single L, a and an unphysically heavy mπ. Efforts are on the way for calculations with controlled systematics.

◮ Not covered here : electromagnetic form factors[Can et al., JHEP(2014)125], σ

terms, axial charges [Hadjiyiannakou et al., Lattice 2014] and heavy baryon decay widths [Detmold et al., PRL 108 172003].

CHARM BARYONS ON THE LATTICE

• M. PADMANATH (Charm 2015)

Institute of Physics, University of Graz, Austria (36/36)

SLIDE 37

Thank you...

CHARM BARYONS ON THE LATTICE

• M. PADMANATH (Charm 2015)

Institute of Physics, University of Graz, Austria (37/36)

SLIDE 38

Backups

CHARM BARYONS ON THE LATTICE

• M. PADMANATH (Charm 2015)

Institute of Physics, University of Graz, Austria (38/36)

SLIDE 39

HQET expansion for energy splittings

◮ Consider the energy splittings

(Ξ∗

cc − D, Ω∗ cc − Ds, Ω∗ ccc − ηc and Ω∗ ccb − Bc),

(Ξ∗

cc − D∗, Ω∗ cc − D∗ s , Ω∗ ccc − J/ψ and Ω∗ ccb − B∗ c ) ◮ Extrapolation of the fit to these splittings → mB∗

c − mBc.

◮ Heavy Quark Effective Theory (HQET) : Mass of a heavy hadron,

mHn Q = n mQ + A + B/mQ + O(1/m2

Q). Jenkins, PRD 54, 4515 ◮ Splittings : ∆m ∼ a1[(n1 − n2)mQ + A1 − A2] + b1/mQ + O(1/m2 Q)

∼ a + b/mPS + O(1/m2

PS). ◮ Light quark data excluded from the fits. MP et al., PRD 91 094502

CHARM BARYONS ON THE LATTICE

• M. PADMANATH (Charm 2015)

Institute of Physics, University of Graz, Austria (39/36)

SLIDE 40

An HQET inspired fit on HSC results

MP et al., PRD 91 094502

1700 1750 1800 1850 1900 1950 2000 0.1 1 10 100

∆mass (MeV) (mπa)2 (GeV2) 3/2+

1600 1650 1700 1750 1800 1850 1900 0.1 1 10 100

∆mass (MeV) (mπa)2 (GeV2) 3/2+

mB∗

c − mBc = 80 ± 8 MeV

53(7) : Gregory et al., PRL 104 022001 54(3) : Dowdall et al., PRD 86 094510

mΩ∗

ccb = 8050 ± 10 MeV

8037(9)(20) : Brown et al., PRD 90 094507

CHARM BARYONS ON THE LATTICE

• M. PADMANATH (Charm 2015)

Institute of Physics, University of Graz, Austria (40/36)

SLIDE 41

Σb decay width

Detmold et al., PRL 108 172003

CHARM BARYONS ON THE LATTICE

• M. PADMANATH (Charm 2015)

Institute of Physics, University of Graz, Austria (41/36)

SLIDE 42

Known charm baryons

CHARM BARYONS ON THE LATTICE

• M. PADMANATH (Charm 2015)

Institute of Physics, University of Graz, Austria (42/36)

SLIDE 43

Chiral extrapolations

Brice˜ no et. al, PRD 86 094504 Brown et. al, PRD 90 094507

Chiral extrapolations based on Heavy hadron chiral perturbation theory.

Savage, PLB 359, 189; Mehen and Tiburzi, hep-lat/0607023.

CHARM BARYONS ON THE LATTICE

• M. PADMANATH (Charm 2015)

Institute of Physics, University of Graz, Austria (43/36)

SLIDE 44

Spectroscopy : baryon operator construction

◮ Aim : Extraction of highly excited states.

Local operators → low lying states. Extended operators → States with radial and orbital excitations.

◮ Proceeds in two steps

Construct continuum operators with well defined quantum nos. Reduce/subduce into the irreps of the reduced symmetry.

◮ Used set of baryon continuum operators of the form

Γαβγqαqβqγ, Γαβγqαqβ(Diqγ) and Γαβγqαqβ(DiDjqγ)

◮ Excluding the color part, the flavor-spin-spatial structure

O[JP] = [FΣF ⊗ SΣS ⊗ DΣD]JP .

◮ γ-matrix convention : γ4 = diag[1,1,-1,-1];

Non-relativistic → purely based on the upper two component of q. Relativistic → All operators except non-relativistic ones.

◮ Subset of DiDj operators that include [Di, Dj] ∼ Fij → hybrid.

CHARM BARYONS ON THE LATTICE

• M. PADMANATH (Charm 2015)

Institute of Physics, University of Graz, Austria (44/36)

SLIDE 45

Charm baryon : Flavor symmetry structures (1)

20M I Iz S FMS FMA Λ+

c 1 √ 2(|cudMS − |udcMS) 1 √ 2(|cudMA − |udcMA)

Σ++

c

1 +1 |uucMS |uucMA Σ+

c

1 |ucdMS |ucdMA Σ0

c

1 −1 |ddcMS |ddcMA Ξ

′+

c 1 2

+ 1

2

−1 |ucsMS |ucsMA Ξ

′0

c 1 2

− 1

2

−1 |dcsMS |dcsMA Ξ+

c 1 2

+ 1

2

−1

1 √ 2(|cusMS − |uscMS) 1 √ 2(|cusMA − |uscMA)

Ξ0

c 1 2

− 1

2

−1

1 √ 2(|cdsMS − |dscMS) 1 √ 2(|cdsMA − |dscMA)

Ω0

c

−2 |scsMS |scsMA Ξ++

cc 1 2

+ 1

2

|ccuMS |ccuMA Ξ+

cc 1 2

− 1

2

|ccdMS |ccdMA Ω+

cc

−1 |ccsMS |ccsMA

FMS → Mixed Symmetric flavor structure FMA → Mixed Antisymmetric flavor structure

CHARM BARYONS ON THE LATTICE

• M. PADMANATH (Charm 2015)

Institute of Physics, University of Graz, Austria (45/36)

SLIDE 46

Charm baryon : Flavor symmetry structures (2)

20S I Iz S FS Σ++

c

1 +1 |uucS Σ+

c

1 |ucdS Σ0

c

1 −1 |ddcS Ξ+

c 1 2

+ 1

2

−1 |ucsS Ξ0

c 1 2

− 1

2

−1 |dcsS Ω0

c

−2 |sscS Ξ++

cc 1 2

+ 1

2

|ccuS Ξ+

cc 1 2

− 1

2

|ccdS Ω+

cc

−1 |ccsS Ω++

ccc

|cccS 4A I Iz S φA Λ+

c

|udcA Ξ+

c 1 2

+ 1

2

−1 |ucsA Ξ0

c 1 2

− 1

2

−1 |dcsA

20S → Symmetric flavor structure 20A → Antisymmetric flavor structure

CHARM BARYONS ON THE LATTICE

• M. PADMANATH (Charm 2015)

Institute of Physics, University of Graz, Austria (46/36)

SLIDE 47

Continuum → Lattice : Symmetries

O(3) lattice − − − − − − − − − − → Oh

◮ Eigenstates of lattice Hamiltonian transform under irreps, Λn, of Oh. ◮ Continuum states with same JP but different Jz : separated across

different lattice irreps.

◮ Subduce the continuum operators into the irreps of Oh.

CHARM BARYONS ON THE LATTICE

• M. PADMANATH (Charm 2015)

Institute of Physics, University of Graz, Austria (47/36)

SLIDE 48

Continuum → Lattice : Irreps (1)

O(3) lattice − − − − − − − − − − → Oh

◮ Integer spin objects see an Oh symmetry on lattice.

CHARM BARYONS ON THE LATTICE

• M. PADMANATH (Charm 2015)

Institute of Physics, University of Graz, Austria (48/36)

SLIDE 49

Continuum → Lattice : Irreps (2)

O(3) lattice − − − − − − − − − − → OD

h ◮ Half-integer spin objects see an OD h symmetry on lattice.

CHARM BARYONS ON THE LATTICE

• M. PADMANATH (Charm 2015)

Institute of Physics, University of Graz, Austria (49/36)

SLIDE 50

Continuum → Lattice : Operators (1)

O(3) lattice − − − − − − − − − − → Oh

◮ Operators in the continuum get distributed over the lattice irreps.

CHARM BARYONS ON THE LATTICE

• M. PADMANATH (Charm 2015)

Institute of Physics, University of Graz, Austria (50/36)

SLIDE 51

Continuum → Lattice : Operators (2)

O(3) lattice − − − − − − − − − − → Oh

◮ Multiple continuum operators with various spin-spatial structures

reducing onto same lattice irreps with varying lattice extensions : Excited states.

CHARM BARYONS ON THE LATTICE

• M. PADMANATH (Charm 2015)

Institute of Physics, University of Graz, Austria (51/36)

SLIDE 52

Local and extended operators

Meson two point correlators using local source operators Meson two point correlators using extended source operators We used a technique called “Distillation”. Aids in computing the correlation functions with much less computational requirements.

• M. Peardon et al., PRD 80, 054506, 2009

CHARM BARYONS ON THE LATTICE

• M. PADMANATH (Charm 2015)

Institute of Physics, University of Graz, Austria (52/36)

SLIDE 53

• No. of interpolating operators

Ωccc G1 H G2 g u g u g u Total 20 20 33 33 12 12 Hybrid 4 4 5 5 1 1 NR 4 1 8 1 3 Λcdu G1 H G2 g u g u g u Total 53 53 86 86 33 33 Hybrid 12 12 16 16 4 4 NR 10 3 17 4 7 1 Ωccs, Ξccu, Ωcss and Σcuu. G1 H G2 g u g u g u Total 55 55 90 90 35 35 Hybrid 12 12 16 16 4 4 NR 11 3 19 4 8 1 Ξcsu G1 H G2 g u g u g u Total 116 116 180 180 68 68 Hybrid 24 24 32 32 8 8 NR 23 6 37 10 15 2

CHARM BARYONS ON THE LATTICE

• M. PADMANATH (Charm 2015)

Institute of Physics, University of Graz, Austria (53/36)

SLIDE 54

Generalized eigenvalue problem

Solving the generalized eigenvalue problem for Cij(t). Cij(t)v (n)

j

(t, t0) = λ(n)(t, t0)Cij(t0)v (n)

j

(t, t0) Solve for many t0’s. Choice of t0’s crucial ⇒ Determine quality of extractions.

◮ Principal correlators given by eigenvalues

λn(t, t0) ∼ (1 − An) exp−mn(t−t0) +An exp−m′

n(t−t0)

Extraction of a tower of states.

◮ Eigenvectors related to the overlap factors

Z (n)

i

= 0|Oi|n = √2En expEnt0/2 v (n)†

j

Cji(t0) Spin identification.

• C. Michael, Nucl. Phys. B 259, 58, (1985).
• M. L¨

uscher and U. Wolff, Nucl. Phys. B 339, 222 (1990).

CHARM BARYONS ON THE LATTICE

• M. PADMANATH (Charm 2015)

Institute of Physics, University of Graz, Austria (54/36)

SLIDE 55

Spin identification using overlap factors : (Ωccc, Hg)

nrnh nrh rnh rh nrnh rnh rnh nrnh rnh 32 52 72

1 2 3 4 5 6 7 8 9 10 11

Operators States nr − nh = non − relativistic & non − hybrid nr − h = non − relativistic & hybrid r − nh = relativistic & non − hybrid r − h = relativistic & hybrid

CHARM BARYONS ON THE LATTICE

• M. PADMANATH (Charm 2015)

Institute of Physics, University of Graz, Austria (55/36)

SLIDE 56

Spin identification from overlap factors

◮ For example, a continuum operator Ojk = ¯

ψγjDkψ. Projects on to 2++.

◮ In the continuum, 0|Ojk|2++ = Zǫjk. ◮ On lattice, Ojk gets subduced over two lattice irreps (ρ × ∇)T2 and

(ρ × ∇)E.

◮ Then

0|(ρ × ∇)i

T2)|2++ = αijk0|Ojk|2++ = Z1αijkǫjk

0|(ρ × ∇)i

E)|2++ = βijk0|Ojk|2++ = Z2βijkǫjk

where αijk and βijk are the Clebsch-Gordan coefficients.

◮ If “close” to the continnum, then Z ∼ Z1 ∼ Z2.

CHARM BARYONS ON THE LATTICE

• M. PADMANATH (Charm 2015)

Institute of Physics, University of Graz, Austria (56/36)

SLIDE 57

Overlap factors (Z) across multiple irreps : 5/2+

0.025 0.05 0.075 0.1 0.125 0.15 0.175 0.2

5/2

+

(1/2

+

)

1,M

⊗D

[2] L=2,M

100 (1/2

+

)

2,M

⊗D

[2] L=2,M

100 (1/2

+

)

1,S

⊗D

[2] L=2,S

100 (1/2

+

)

3,S

⊗D

[2] L=2,M

10 (3/2

+

)

1,M

⊗D

[2] L=2,M

(3/2

+

)

1,S

⊗D

[2] L=2,S

1000 (3/2

+

)

2,S

⊗D

[2] L=2,S

(3/2

• )

1,M

⊗D

[1] L=1,M

Hg: 0.949(3) G2g: 0.952(2)

CHARM BARYONS ON THE LATTICE

• M. PADMANATH (Charm 2015)

Institute of Physics, University of Graz, Austria (57/36)

SLIDE 58

Connecting lattice to continnum irreps

Lattice irrep, Λ Dimension Continuum irrep, J A1 1 0,4,... A2 1 3,5,... E 2 2,4,... T1 3 1,3,... T2 3 2,3,... G1 2

1 2, 7 2, 9 2,...

G2 2

5 2, 7 2, 9 2,...

H 4

3 2, 5 2, 7 2,...

Including the spatial inversions : doubles the group elements. A1g, A1u, A2g, A2u, Eg, Eu, T1g, T1u, T2g, T2u, G1g, G1u, G2g, G2u, Hg and Hu; g → + and u → −.

CHARM BARYONS ON THE LATTICE

• M. PADMANATH (Charm 2015)

Institute of Physics, University of Graz, Austria (58/36)

SLIDE 59

Joint fitting principal correlators for J = 5/2+

atE = 0.770(3) atE = 0.775(1)

0.6 0.8 1 1.2 1.4 1.6 1.8 2 5 10 15 20 25

Hg

0.6 0.8 1 1.2 1.4 1.6 1.8 2 5 10 15 20 25

G2g

λn(t, t0) expmn(t−t0) Vs t/at; atE = 0.771(3)

CHARM BARYONS ON THE LATTICE

• M. PADMANATH (Charm 2015)

Institute of Physics, University of Graz, Austria (59/36)

SLIDE 60

Λc (uuc) baryon spectrum in potential model

1/2

+

3/2

+

5/2

+

7/2

+

1/2

• 3/2
• 5/2
• 7/2
• ?

?

2.2 2.4 2.6 2.8 3.0 3.2 3.4

massΛc [GeV] Experiment QM

* ?

ΛC [GeV]

experimentally established states

2 2.5 3 3.5 4 1/2+ 3/2+ 5/2+ 7/2+ 9/2+ 1/2- 3/2- 5/2- 7/2- 9/2-11/2-

Capstick and Isgur, PRD 34 2809 Ebert et al., PRD 84 014025

CHARM BARYONS ON THE LATTICE

• M. PADMANATH (Charm 2015)

Institute of Physics, University of Graz, Austria (60/36)