CKallidonis_talk_Bonn

Hyperon and charmed baryon masses from twisted mass Lattice QCD(Nf = 2 + 1 + 1, Nf = 2 plus clover)

Christos KallidonisComputation-based Science and Technology Research Center

The Cyprus Institute

C. Alexandrou et al. arXiv:1406.4310

withC. Alexandrou, V. Drach, K, Hadjiyiannakou, K. Jansen, G. Koutsou

Rheinische Friedrich-Wilhelms-Universitat BonnBonn, Germany1 April 2015

C. Kallidonis (CyI) Baryon Spectrum Bonn University 1 / 27

Outline

1 Introduction - Motivation

2 Lattice evaluationWilson twisted mass actionSimulation detailsScale settingInterpolating fields - Effective mass

3 Tuning of the strange and charm quark mass

4 ResultsChiral and continuum extrapolation for Nf = 2 + 1 + 1Isospin symmetry breaking

5 Comparison

6 Conclusions


Introduction - Motivation

Why we want to calculate baryon masses?

I easy to calculate

first quantities one calculates before proceeding with more complex observables

I large signal to noise ratio

reliable way to study lattice effects

I significant for on-going experiments

observation of doubly-charmed Ξ baryons (SELEX, hep-ex/0208014, hep-ex/0209075,hep-ex/0406033) - interest in charmed baryon spectroscopy (G. Bali et al. arXiv:1503.08440, M.

Padmanath et al. arXiv:1502.01845)

I are the experimentally known masses reproduced?

safe and reliable predictions for the rest


Lattice evaluationWilson twisted mass action for Nf = 2 + 1 + 1

doublet of light quarks: ψ =

(ud

)R. Frezzotti et al. arXiv:hep-lat/0306014

Transformation of quark fields:ψ(x) = 1√

2

(11 + iτ3γ5

)χ(x)

ψ(x) = χ(x) 1√2

(11 + iτ3γ5

)

mass term

ψmψ → χiγ5τ3mχ

S(l)F = a4

∑x

χ(x)

[1

2γµ(∇µ +∇∗µ)− ar

2∇µ∇∗µ +m0,l + iγ5τ

3µ

]χ(x)

heavy quarks: χh =

(sc

)In the sea we use the action: R. Frezzotti et al. arXiv:hep-lat/0311008

S(h)F = a4

∑x

χh(x)

[1

2γµ(∇µ +∇∗µ)− ar

2∇µ∇∗µ +m0,h + iµσγ5τ

1 + τ3µδ

]χh(x)

presence of τ1 introduces mixing of the strange and charm flavorsvalence sector: use Osterwalder-Seiler valence heavy quarks χ(s) = (s+, s−) , χ(c) = (c+, c−)

re-tuning of the strange and charm quark masses required

Wilson TM at maximal twist

cut-off effects are automatically O(a) improved

no operator improvement is needed (important for nucleon structure)


Lattice evaluationWilson twisted mass action for Nf = 2 + 1 + 1

doublet of light quarks: ψ =

(ud

)R. Frezzotti et al. arXiv:hep-lat/0306014

Transformation of quark fields:ψ(x) = 1√

2

(11 + iτ3γ5

)χ(x)

ψ(x) = χ(x) 1√2

(11 + iτ3γ5

)

mass term

ψmψ → χiγ5τ3mχ

S(l)F = a4

∑x

χ(x)

[1

2γµ(∇µ +∇∗µ)− ar

2∇µ∇∗µ +m0,l + iγ5τ

3µ

]χ(x)

heavy quarks: χh =

(sc

)In the sea we use the action: R. Frezzotti et al. arXiv:hep-lat/0311008

S(h)F = a4

∑x

χh(x)

[1

2γµ(∇µ +∇∗µ)− ar

2∇µ∇∗µ +m0,h + iµσγ5τ

1 + τ3µδ

]χh(x)

presence of τ1 introduces mixing of the strange and charm flavorsvalence sector: use Osterwalder-Seiler valence heavy quarks χ(s) = (s+, s−) , χ(c) = (c+, c−)

re-tuning of the strange and charm quark masses required

Wilson TM at maximal twist

cut-off effects are automatically O(a) improved

no operator improvement is needed (important for nucleon structure)


Lattice evaluationWilson twisted mass action for Nf = 2 plus clover

S(l)F = a4

∑x

χ(x)

[1

2γµ(∇µ +∇∗µ)− ar

2∇µ∇∗µ +m0,l + iγ5τ

3µ+i

4CSWσ

µνFµν(U)

]χ(x)

Clover term

stable simulations

control O(a2) effects

O(a) improvement remains!

CSW = 1.57551

B. Sheikholeslami et al. Nucl.Phys. B259 (1985), S. Aoki et al. hep-lat/0508031


Lattice evaluationSimulation details

Total of 10 Nf = 2 + 1 + 1 gauge ensembles produced by ETMC

Nf = 2 plus clover ensemble at the physical pion mass

R. Baron et al. (ETMC) arXiV:1004.5284, A. Abdel-Rehim et al. arXiv:1311.4522

β = 1.90, a = 0.0936(13) fm

323 × 64, L = 3.0 fm

aµ 0.0030 0.0040 0.0050

No. of Confs 200 200 200

mπ (GeV) 0.2607 0.2975 0.3323

mπL 3.97 4.53 5.05

β = 1.95, a = 0.0823(10) fm

323 × 64, L = 2.6 fm

aµ 0.0025 0.0035 0.0055 0.0075

No. of Confs 200 200 200 200

mπ (GeV) 0.2558 0.3018 0.3716 0.4316

mπL 3.42 4.03 4.97 5.77

β = 2.10, a = 0.0646(7) fm

483 × 96, L = 3.1 fm

aµ 0.0015 0.002 0.003

No. of Confs 196 184 200

mπ (GeV) 0.2128 0.2455 0.2984

mπL 3.35 3.86 4.69

β = 2.10, a = 0.0941(12) fm

483 × 96, L = 4.5 fm

aµ 0.0009

No. of Confs 524

mπ (GeV) 0.1303

mπL 2.99

two lattice volumes

pion masses from 210-430 MeV → chiral extrapolations

three values of the lattice spacing → investigation of finite lattice effects


Lattice evaluationScale setting

for baryon masses → physical nucleon mass

dedicated high statistics analysis on 17 Nf = 2 + 1 + 1 ensembles

use HBχPT leading one-loop order result mN = m(0)N − 4c1m

2π −

3g2A16πf2π

m3π

fit simultaneously for Nf = 2 + 1 + 1 and Nf = 2 plus clover for all β values

systematic error due to the chiral extrapolation → use O(p4) HBχPT with explicit ∆-degrees offreedom

0.8

0.9

1

1.1

1.2

1.3

1.4

0 0.05 0.1 0.15 0.2 0.25

mN

(G

eV)

mπ2 (GeV2)

β=1.90, L/a=32, L=3.0fmβ=1.90, L/a=24, L=2.2fmβ=1.90, L/a=20, L=1.9fmβ=1.95, L/a=32, L=2.6fmβ=1.95, L/a=24, L=2.0fmβ=2.10, L/a=48, L=3.1fmβ=2.10, L/a=32, L=2.1fm

β=2.10, CSW=1.57551, L/a=48, L=4.5fm

β a (fm)

1.90 0.0936(13)(35)

1.95 0.0823(10)(35)

2.10 0.0646(7)(25)

2.10 0.0941(12)(2)

fitting for each β separately yields consistent values - negligible cut-off effects for the nucleon case

light σ-term for nucleon σπN = 64.9(1.5)(13.2) MeV


Lattice evaluationEffective mass

Effective masses are obtained from two-point correlationfunctions

C±B (t, ~p = ~0) =∑xsink

[1

4Tr (1± γ0) 〈JB (xsink) JB (xsource)〉

], t = tsink − tsource

I Gaussian smearing at source and sink, APE smearing at spatial links

I source position chosen randomly

amBeff(t) = log

(CB(t)

CB(t+ 1)

)

0

0.4

0.8

1.2

1.6

2 4 6 8 10 12 14 16 18

amef

f

t/a

Σc*++

Λc+

Ω

Ξ0

N



Effective masses are obtained from two-point correlationfunctions

C±B (t, ~p = ~0) =∑xsink

[1

4Tr (1± γ0) 〈JB (xsink) JB (xsource)〉

], t = tsink − tsource

I Gaussian smearing at source and sink, APE smearing at spatial links

I source position chosen randomly

amBeff(t) = log

(CB(t)

CB(t+ 1)

)

0

0.4

0.8

1.2

1.6

2 4 6 8 10 12 14 16 18

amef

f

t/a

Σc*++

Λc+

Ω

Ξ0

N


Lattice evaluationInterpolating fields

constructed such that they have the quantum numbers of the baryon in interest

4 quark flavors

baryons (qqq)

SU(3) subgroups

of SU(4)

Examples

p (uud) J = εabc(uTaCγ5db

)uc

Σ0 (uds) J = 1√2εabc

[(uTaCγ5sb

)dc +

(dTaCγ5sb

)uc

]Ξ+c (usc) J = εabc

(uTaCγ5sb

)cc

Ξ?0 (uss) Jµ = εabc(sTaCγµub

)sc

Σ?++c (uuc) Jµ = 1√

3εabc

[(uTaCγµub

)cc + 2

(cTaCγµub

)uc

]Ω?0c (ssc) Jµ = εabc

(sTaCγµcb

)sc

20plet of spin-1/2 baryons20 = 8⊕ 6⊕ 3⊕ 3

20plet of spin-3/2 baryons20 = 10⊕ 6⊕ 3⊕ 1



incorporation of spin-3/2 and spin-1/2 projectors

Pµν3/2 = δµν − 1

3γµγν , J µB3/2

= Pµν3/2JνBPµν1/2 = δµν − Pµν3/2 , J

µB1/2

= Pµν1/2JνB

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 4 8 12 16 20

ame↵++

c

t/a

3/2 projection1/2 projectionNo projection

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 4 8 12 16 20

ame↵+

t/a


0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

2 4 6 8 10 12 14 16

ame↵

t/a

J0 3/2 projectionJ0 1/2 projectionJ0 No projection

J0

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

2 4 6 8 10 12 14 16

ame↵

t/a

J 3/2 projectionJ 1/2 projectionJ No projection

J




Pµν3/2 = δµν − 1



µB1/2

= Pµν1/2JνB0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 4 8 12 16 20

ame↵++

c

t/a


0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 4 8 12 16 20

ame↵+

t/a


0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

2 4 6 8 10 12 14 16

ame↵

t/a


J0

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

2 4 6 8 10 12 14 16

ame↵

t/a


J




Pµν3/2 = δµν − 1



µB1/2

= Pµν1/2JνB0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 4 8 12 16 20

ame↵++

c

t/a


0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 4 8 12 16 20

ame↵+

t/a


0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

2 4 6 8 10 12 14 16

ame↵

t/a


J0

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

2 4 6 8 10 12 14 16

ame↵

t/a


J


Tuning of the strange and charm quark mass (Nf = 2 + 1 + 1)

use Ω− for strange quark and Λ+c for charm quark

fix renormalized strange and charm masses using non-perturbatively determined renormalizationconstants (N. Carrasco et al. arXiv:1403.4504) in the MS scheme at 2 GeV

Strange quark mass tuning

use a set of strange quark masses to interpolate the mass of Ω− to a given value of

mRs and extrapolate to the continuum and physical pion mass using

mΩ = m0Ω − 4c

(1)Ω m2

π + da2

match with physical mass of Ω−

mΩphys

1.6

1.65

1.7

1.75

1.8

85 90 95 100 105 110 115

mΩ

-

(G

eV)

msR (MeV)

msR = 92.4(6) MeV

1.5

1.55

1.6

1.65

1.7

1.75

1.8

1.85

0 0.05 0.1 0.15 0.2 0.25

mΩ

- (G

eV)

mπ2 (GeV2)

β=1.90, L/a=32β=1.95, L/a=32β=2.10, L/a=48Continuum limit

MS : mRs (2 GeV) = 92.4(6)(2.0) MeV




fix renormalized strange and charm masses using non-perturbatively determined renormalizationconstants (N. Carrasco et al. arXiv:1403.4504) in the MS scheme at 2 GeV

Strange quark mass tuning

use a set of strange quark masses to interpolate the mass of Ω− to a given value of

mRs and extrapolate to the continuum and physical pion mass using

mΩ = m0Ω − 4c

(1)Ω m2

π + da2

match with physical mass of Ω−

mΩphys

1.6

1.65

1.7

1.75

1.8

85 90 95 100 105 110 115

mΩ

-

(G

eV)

msR (MeV)

msR = 92.4(6) MeV

1.5

1.55

1.6

1.65

1.7

1.75

1.8

1.85

0 0.05 0.1 0.15 0.2 0.25

mΩ

- (G

eV)

mπ2 (GeV2)


MS : mRs (2 GeV) = 92.4(6)(2.0) MeV



Charm quark mass tuning

follow the same procedure using Λ+c and fit using

mΛc = m0Λc + c1m

2π + c2m

3π + da2

mΛcphys

2.26

2.28

2.3

2.32

1150 1160 1170 1180 1190 1200

mΛ

c+ (

GeV

)

mcR (MeV)

mcR = 1173.0(2.4) MeV

2.2

2.25

2.3

2.35

2.4

2.45

2.5

2.55

2.6

0 0.05 0.1 0.15 0.2 0.25

mΛ

c+ (

GeV

)

mπ2 (GeV2)


MS : mRc (2 GeV) = 1173.0(2.4)(17.0) MeV


Tuning of the strange and charm quark mass (Nf = 2 plus clover)


use a set of strange and charm quark masses and interpolate to the physical Ω− and Λ+c mass

mphysΩ

1.6

1.65

1.7

1.75

0.023 0.024 0.025 0.026 0.027 0.028

mΩ

(G

eV)

aμs

aμsphys = 0.0264(3)

mphysΛc

+

2.15

2.2

2.25

2.3

2.35

2.4

0.3 0.31 0.32 0.33 0.34 0.35 0.36

mΛ

c+ (

GeV

)

aμc

aμcphys = 0.3346(15)

I interpolate all the rest hyperons and charmed baryons to the tuned valuesof aµs and aµc


Tuning of the strange and charm quark mass (Nf = 2 plus clover)


use a set of strange and charm quark masses and interpolate to the physical Ω− and Λ+c mass

mphysΩ

1.6

1.65

1.7

1.75

0.023 0.024 0.025 0.026 0.027 0.028

mΩ

(G

eV)

aμs

aμsphys = 0.0264(3)

mphysΛc

+

2.15

2.2

2.25

2.3

2.35

2.4

0.3 0.31 0.32 0.33 0.34 0.35 0.36

mΛ

c+ (

GeV

)

aμc

aμcphys = 0.3346(15)

I interpolate all the rest hyperons and charmed baryons to the tuned valuesof aµs and aµc


Tuning of the strange and charm quark mass (Nf = 2 plus clover)Interpolation

Hyperons - Charmed baryons mass Mint

μ1 μ2 μt μ3 μ

Charmed baryons with strange quarks

mass μc = μc,1 Ms,1

μs,1 μs,2 μs,t μs,3 μs

mass μc = μc,2 Ms,2

μs,1 μs,2 μs,t μs,3 μs

...

mass Mint

μc,1 μc,2 μc,t μc,3 μc


Results I: Chiral and continuum extrapolation for Nf = 2 + 1 + 1

fit in the whole pion mass range 210-430 MeV

include all β’s

allow for cut-off effects by including a term ∝ a2

Hyperons

use leading one-loop order continuum HBχPT

systematic error due to the chiral extrapolation → use O(p4) HBχPT

1.05

1.1

1.15

1.2

1.25

1.3

1.35

1.4

1.45

0 0.05 0.1 0.15 0.2 0.25

mΣ

0 (G

eV)

mπ2 (GeV2)

NLO HBχPTLO HBχPT

β=2.10, L/a=48β=1.95, L/a=32β=1.90, L/a=32

1.4

1.45

1.5

1.55

1.6

1.65

1.7

1.75

1.8

0 0.05 0.1 0.15 0.2 0.25

mΞ

* (G

eV)

mπ2 (GeV2)

NLO HBχPTLO HBχPT

β=2.10, L/a=48β=1.95, L/a=32β=1.90, L/a=32



fit in the whole pion mass range 210-430 MeV

include all β’s

allow for cut-off effects by including a term ∝ a2

Hyperons

use leading one-loop order continuum HBχPT

systematic error due to the chiral extrapolation → use O(p4) HBχPT

1.05

1.1

1.15

1.2

1.25

1.3

1.35

1.4

1.45

0 0.05 0.1 0.15 0.2 0.25

mΣ

0 (G

eV)

mπ2 (GeV2)

NLO HBχPTLO HBχPT

β=2.10, L/a=48β=1.95, L/a=32β=1.90, L/a=32

1.4

1.45

1.5

1.55

1.6

1.65

1.7

1.75

1.8

0 0.05 0.1 0.15 0.2 0.25

mΞ

* (G

eV)

mπ2 (GeV2)

NLO HBχPTLO HBχPT

β=2.10, L/a=48β=1.95, L/a=32β=1.90, L/a=32



Charmed baryons

use Ansatz mB = m(0)B + c1m

2π + c2m

3π + da2

systematic error due to the chiral extrapolation → set c2 = 0 and restrict mπ < 300 MeV

2.35

2.4

2.45

2.5

2.55

2.6

0 0.05 0.1 0.15 0.2 0.25

mΞ

c0 (G

eV)

mπ2 (GeV2)

mπ < 0.300GeVmπ < 0.432GeVβ=2.10, L/a=48β=1.95, L/a=32β=1.90, L/a=32

2.4

2.45

2.5

2.55

2.6

2.65

2.7

2.75

0 0.05 0.1 0.15 0.2 0.25

mΣ

c* (G

eV)

mπ2 (GeV2)


systematic error due to the tuning for all baryons

finite-a corrections ∼ 1%− 9% - cut-off effects are small

reproduction of experimentally known baryon masses → Predictions



Charmed baryons

use Ansatz mB = m(0)B + c1m

2π + c2m

3π + da2

systematic error due to the chiral extrapolation → set c2 = 0 and restrict mπ < 300 MeV

2.35

2.4

2.45

2.5

2.55

2.6

0 0.05 0.1 0.15 0.2 0.25

mΞ

c0 (G

eV)

mπ2 (GeV2)


2.4

2.45

2.5

2.55

2.6

2.65

2.7

2.75

0 0.05 0.1 0.15 0.2 0.25

mΣ

c* (G

eV)

mπ2 (GeV2)


systematic error due to the tuning for all baryons

finite-a corrections ∼ 1%− 9% - cut-off effects are small

reproduction of experimentally known baryon masses → Predictions


Results I: Chiral and continuum extrapolation for Nf = 2 + 1 + 1Cut-off effects

Baryon d (GeV3)% correction

β = 1.90 β = 1.95 β = 2.10

Ξcc 1.08(7) 6.3 5.0 3.1

Ξ∗cc 1.01(10) 5.9 4.6 2.9

Ωcc 1.20(5) 6.9 5.4 3.4

Ω∗cc 1.10(7) 6.2 4.9 3.0

Ωccc 1.15(5) 5.1 4.1 2.6

1.6

1.65

1.7

1.75

1.8

1.85

1.9

0 0.05 0.1 0.15 0.2 0.25

mΩ

(GeV

)

a2 (1/GeV2)

mΩ = 1.672(7) + 0.466(4) a2

4.7

4.8

4.9

5

5.1

0 0.05 0.1 0.15 0.2 0.25

mΩ

ccc

(GeV

)

a2 (1/GeV2)

mΩccc = 4.734(9) + 1.154(10) a2


Results II: Isospin symmetry breaking

Wilson twisted mass action breaks isospin symmetry explicitly to O(a2)

it is expected to be zero in the continuum limit

manifests itself as mass splitting between baryons belonging to the same isospin multiplets due tolattice artifacts

u←→ d is a symmetry, e.g. ∆++(uuu), ∆−(ddd) and ∆+(uud), ∆0(ddu) are degenerate



∆ baryons

-0.08

-0.04

0

0.04

0.08

0.12

0 0.002 0.004 0.006 0.008 0.01

Δm

(G

eV)

a2 (fm2)

Δ++,- - Δ+,0

isospin splitting effects are consistent with zero for all lattice spacings and pion masses



Hyperons

-0.08

-0.04

0

0.04

0.08

0.12

0 0.002 0.004 0.006 0.008 0.01

Δm

(G

eV)

a2 (fm2)

Ξ0 - Ξ-

-0.08

-0.04

0

0.04

0.08

0.12

0 0.002 0.004 0.006 0.008 0.01

Δm

(G

eV)

a2 (fm2)

Ξ*0 - Ξ*-

small mass splittings for the spin-1/2 hyperons - decreased as a−→ 0

splitting is smaller for the Nf = 2 plus clover ensemble

isospin splitting consistent with zero for spin-3/2 hyperons



Charmed baryons

-0.08

-0.04

0

0.04

0.08

0.12

0 0.002 0.004 0.006 0.008 0.01

Δm

(G

eV)

a2 (fm2)

Ξcc++ - Ξcc

+

-0.08

-0.04

0

0.04

0.08

0.12

0 0.002 0.004 0.006 0.008 0.01

Δm

(G

eV)

a2 (fm2)

Ξcc*++ - Ξcc

*+

very small effects for spin-1/2 charmed baryons

no isospin symmetry breaking for spin-3/2 charmed baryons


ComparisonLattice results from other schemes

0.6

0.8

1

1.2

1.4

1.6

0 0.05 0.1 0.15 0.2 0.25

mN

(G

eV)

mπ2 (GeV2)

ETMC Nf=2+1+1ETMC Nf=2 with CSW

BMWLHPC

QCDSF-UKQCDMILC

PACS-CS 0.9

1

1.1

1.2

1.3

1.4

1.5

0 0.05 0.1 0.15 0.2 0.25

mΛ (

GeV

)

mπ2 (GeV2)

ETMCETMC Nf=2 with CSW

BMWPACS-CS

LHPC

BMW: Nf = 2 + 1 clover fermions S. Durr et al. arXiV:0906.3599

PACS-CS: Nf = 2 + 1 O(a) improved clover fermions A. Aoki et al. arXiV:0807.1661

LHPC: domain wall valence quarks on a staggered fermions sea (hybrid) A. Walker-Loud et al. arXiV:0806.4549

MILC: Nf = 2 + 1 + 1 Kogut-Susskind fermion action C.W. Bernard et al. hep/lat 0104002

QCDSF-UKQCD: Nf = 2 Wilson fermions G. Bali et al. arXiV:1206.7034


ComparisonExperiment

Octet - Decuplet spectrum

0.9

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

N Λ Σ Ξ Δ Σ* Ξ* Ω

M (

GeV

)ETMC Nf=2+1+1

ETMC Nf=2 with CSW

BMW Nf=2+1

PACS-CS Nf=2+1

QCDSF-UKQCD Nf=2+1

S. Durr et al. arXiV:0906.3599, A. Aoki et al. arXiV:0807.1661, W. Bietenholz et al. arXiV:1102.5300, Particle Data Group



Charm baryons, spin-1/2 spectrum

2.2

2.4

2.6

2.8

3

3.2

3.4

3.6

3.8

Λc Σc Ξc Ξ'c Ωc Ξcc Ωcc

M (

GeV

)ETMC Nf=2+1+1

ETMC Nf=2 with CSW

PACS-CS Nf=2+1

Na et al. Nf=2+1

Briceno et al. Nf=2+1+1

Liu et al. Nf=2+1

G. Bali et al. Nf=2+1

R. A. Briceno et al. arXiV:1207.3536, H. Na et al. arXiV:0812.1235, H. Na et al. arXiV:0710.1422, L. Liu et al.

arXiV:0909.3294, G. Bali et al. arXiv:1503.08440, Particle Data Group



Charm baryons, spin-3/2 spectrum

2.5

3

3.5

4

4.5

5

Σc* Ξc

* Ωc* Ξcc

* Ωcc* Ωccc

M (

GeV

)ETMC Nf=2+1+1

ETMC Nf=2 with CSW

PACS-CS Nf=2+1

Na et al. Nf=2+1

Briceno et al. Nf=2+1+1

G. Bali et al. Nf=2+1

R. A. Briceno et al. arXiV:1207.3536, H. Na et al. arXiV:0812.1235, H. Na et al. arXiV:0710.1422, G. Bali et al.

arXiv:1503.08440, Particle Data Group


Ongoing - Future work

I finalize work on baryon spectrum for the Nf = 2 plus clover ensemble

I proceed with calculation of other observables (gA,...)

I new implementation in twisted mass CG inverter to accelerate inversions using deflation leads tolarge speed-up! (might become even larger...) - Arnoldi algorithm and ARPACK package

I more gauge ensembles from ETMC at the physical pion mass / with Nf = 2 plus clover action (?)


Conclusions

I twisted mass formulation with Nf = 2 + 1 + 1 flavors provides a good framework to study baryonspectrum

I promising results from Nf = 2 plus clover ensemble at the physical pion mass

I physical nucleon mass appropriate to fix lattice spacing when studying baryon masses

I isospin symmetry breaking effects are small and vanish as the continuum limit is approached

I cut-off effects are small and under control

I good agreement with other lattice calculations and with experiment - reliable predictions of theΞ∗cc, Ωcc, Ω∗cc and Ωccc masses

Thank you

The Project Cy-Tera (NEA YΠO∆OMH/ΣTPATH/0308/31) is co-financed by the European Regional Development Fund and theRepublic of Cyprus through the Research Promotion Foundation


Conclusions

I twisted mass formulation with Nf = 2 + 1 + 1 flavors provides a good framework to study baryonspectrum

I promising results from Nf = 2 plus clover ensemble at the physical pion mass

I physical nucleon mass appropriate to fix lattice spacing when studying baryon masses

I isospin symmetry breaking effects are small and vanish as the continuum limit is approached

I cut-off effects are small and under control

I good agreement with other lattice calculations and with experiment - reliable predictions of theΞ∗cc, Ωcc, Ω∗cc and Ωccc masses

Thank you

The Project Cy-Tera (NEA YΠO∆OMH/ΣTPATH/0308/31) is co-financed by the European Regional Development Fund and theRepublic of Cyprus through the Research Promotion Foundation



mBeff(t) = log

(CB(t)

CB(t+ 1)

)= mB + log

(1 +

∑∞i=1 cie

−∆it

1 +∑∞

i=1 cie−∆i(t+1)

)−→t→∞

mB , ∆i = mi −mB

mBeff(t) ≈ me

B + log

(1 + c1e

−∆1t

1 + c1e−∆1(t+1)

)

criterion for plateau selection

∣∣∣∣∣ mcB −me

B12(mc

B +meB)

∣∣∣∣∣ ≤ 1

2σmcB

0.3

0.4

0.5

0.6

0.7

0 4 8 12 16 20

amef

f

t/a

Ξ0

Exponential fitConstant fit


Backup slidesNucleon σ-term

20 30 40 50 60 70 80 90 100

σπN (MeV)

ETMC Nf = 2 + 1 + 1 (this work)

C. Alexandrou et al. (ETMC) arXiv:0910.2419

G. Bali et al. (QCDSF) arXiv:1111.1600

L. Alvarez-Ruso et al. arXiv:1304.0483

X.-L. Ren et al. arXiv:1404.4799

M.F.M. Lutz et al. arXiv:1401.7805

S. Durr et al. (BMW) arXiv:1109.4265

R. Horsley et al. (QCDSF-UKQCD) arXiv:1110.4971


Backup slidesHyperon σ-terms

20 40 60 80

Λ

20 40 60 80

σπB (MeV)

Σ

0 10 20 30

Ξ

ETMC Nf = 2 + 1 + 1 (this work)

C. Alexandrou et al. (ETMC) [1]

X.-L. Ren et al. [2]

M.F.M. Lutz et al. [3]

S. Durr et al. (BMW) [4]

R. Horsley et al. (QCDSF-UKQCD) [5]

[1] C. Alexandrou et al. (ETMC) arXiv:0910.2419

[2] X.-L. Ren et al. arXiv:1404.4799

[3] M.F.M. Lutz et al. arXiv:1401.7805

[4] S. Durr et al. (BMW) arXiv:1109.4265

[5] R. Horsley et al. (QCDSF-UKQCD) arXiv:1110.4971


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