Talk presented at the Electromagnetic Interactions of Nucleons and Nuclei 2015 (EINN 2015) conference, Paphos, Cyprus. In this talk we present results on the axial charges of all forty light, strange and charm baryons from Lattice QCD calculations.

1. Hyperons and charmed baryons axial charges from lattice QCD
Christos Kallidonis
Computation-based Science and Technology Research Center
The Cyprus Institute
with
C. Alexandrou and K. Hadjiyiannakou
Electromagnetic Interactions with Nucleons and Nuclei, 2015
Paphos, Cyprus, 1-7 November 2015
C. Kallidonis (CyI) Axial charges EINN2015 1 / 10

2. Introduction
Motivation
Axial charges are important quantities probing hadron structure
low energy effective theories
chiral perturbation descriptions
intrinsic spin carried by the quarks
Nucleon gA (1.2695(29)) → benchmark calculation
Poor results available for hyperons and charmed baryons
Simulation details R. Baron et al. (ETMC) arXiv:1004.5284, A. Abdel-Rehim et al. (ETMC) 1507.05068
5 gauge ensembles produced by ETMC with Nf = 2 + 1 + 1 dynamical twisted mass fermions
a = 0.062 fm, L = 3.1 fm and a = 0.082 fm, L = 2.6 fm
pion masses ∼ 210 − 430 MeV
1 gauge ensemble with Nf = 2 at the physical pion mass by ETMC, a = 0.093 fm
C. Kallidonis (CyI) Axial charges EINN2015 2 / 10

3. Hyperons and charmed baryons - Spectrum
4 quark flavors
baryons (qqq)



SU(3) subgroups
of SU(4)
20plet of spin-1/2 baryons
20 = 8 ⊕ 6 ⊕ 3 ⊕ 3
20plet of spin-3/2 baryons
20 = 10 ⊕ 6 ⊕ 3 ⊕ 1
C. Kallidonis (CyI) Axial charges EINN2015 3 / 10

4. Hyperons and charmed baryons - 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 with CSW
ETMC Nf=2+1+1
BMW Nf=2+1
PACS-CS Nf=2+1
QCDSF-UKQCD Nf=2+1
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 with CSW
ETMC Nf=2+1+1
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
2.5
3
3.5
4
4.5
5
Σc
* Ξc
* Ωc
* Ξcc
* Ωcc
* Ωccc
M(GeV)
ETMC Nf=2 with CSW
ETMC Nf=2+1+1
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
C. Alexandrou et al. arXiV:1406.4310, S. Durr et al. arXiV:0906.3599, A. Aoki et al. arXiV:0807.1661, W. Bietenholz et al. arXiV:1102.5300,
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
C. Kallidonis (CyI) Axial charges EINN2015 4 / 10

5. Calculation of Axial matrix element
Axial matrix element B(pf , sf )|Aµ|B(pi, si)
– three-point functions, G(p = 0, tf − ti, Aµ(x)) with the axial vector current Aµ(x) = ¯q(x)γµγ5q(x) (using
the fixed current method)
– two-point functions, C(p = 0, tf − ti)
(neglect disconnected diagrams)
Flavor combinations:
Isovector, π-coupling: ¯uu − ¯dd
Isoscalar: ¯uu + ¯dd
η8-coupling: ¯uu + ¯dd − 2¯ss
η15-coupling: ¯uu + ¯dd + ¯ss − 3¯cc
Axial charge obtained directly as R(tf − ti)
(t−ti) 1
−−−−−−→
(tf −t) 1
gA
R(tf − ti) =
G(p = 0, tf − ti, Aµ)
C(p = 0, tf − ti)
0.6
0.8
1.0
1.2
g⌃+
⇡
-2.4
-2.2
-2.0
-1.8
g⌅0
⌘8
-3.2
-2.8
-2.4g
⌅+
c
⌘15
-4.8
-4.2
-3.6
0 1 2 3 4 5 6 7 8 9 10 11
g
⌦+
cc
⌘15
(tf t)/a
t/a = 5
t/a = 7
C. Kallidonis (CyI) Axial charges EINN2015 5 / 10

6. Results
mπ-dependence
Nucleon
0.9
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
0 0.05 0.1 0.15 0.2 0.25
gN
A
m2
⇡ (GeV2
)
Nf = 2 + 1 + 1 Fix Sink
Nf = 2 Fix Sink
Nf = 2 + 1 + 1 Fix Curr. (this work)
Experiment
0.2
0.4
0.6
0.8
1.0
1.2
gN
A
Nf = 2 + 1 + 1 Fix Sink
Nf = 2 Fix Sink
Nf = 2+CSW Fix Sink
Nf = 2 + 1 + 1 Fix Curr.
Experiment
C. Alexandrou et al. arXiV:1012.0857, C. Alexandrou et al.
arXiV:1303.5979, A. Abdel-Rehim et al. (ETMC) arXiv:1507.04936
(Talk by G. Koutsou on Thursday)
Σ, Ξ baryons
0.40
0.80
1.20
1.60
g⌃
⇡/gN
A
-0.26
-0.24
-0.22
-0.20
0 0.1 0.2 0.3 0.4 0.5 0.6g⌅
⇡/gN
A
m2
⇡ (GeV2
)
DWF Nf = 2 + 1
Clover Nf = 2 (QCDSF/UKQCD)
Clover Nf = 2 (CP-PACS)
TMF Nf = 2 + 1 + 1 (this work)
2.4
H. Lin et al. arXiV:0712.1214, G. Erkol et al. arXiV:0911.2447, M.
G¨ockeler et al. arXiv:1102.3407
C. Kallidonis (CyI) Axial charges EINN2015 6 / 10

7. Results
mπ-dependence
Decuplet
1.2
1.6
2.0
2.4
g
++
⇡
-0.3
-0.2
-0.1
0.0
g⌃⇤+
⌘8
-2.4
-2.2
-2.0
-1.8
g⌅⇤0
⌘8
-4.8
-4.4
-4.0
-3.6
0 0.05 0.1 0.15 0.2
g⌦
⌘8
m2
⇡ (GeV2
)
Charm sector
-2.90
-2.80
-2.70
g
⇤+
c
⌘15
1.50
1.80
2.10
g
⌃++
c
⌘15
-1.36
-1.28
-1.20
g
⌦⇤+
cc
⌘8
-4.95
-4.80
-4.65
g
⌅⇤++
cc
⌘15
-8.40
-8.00
-7.60
0 0.05 0.1 0.15 0.2
g
⌦++
ccc
⌘15
m2
⇡ (GeV2
)
1.2
1.4
1.6
g⌃+
⌘8
weak pion mass dependence
no noticeable cut-off effects
C. Kallidonis (CyI) Axial charges EINN2015 7 / 10

8. Results
SU(3) symmetry breaking
Octet
exact SU(3) symmetry:
gN
π = F + D
gΣ
π = 2F
gΞ
π = F − D



gN
π − gΣ
π + gΞ
π = 0
δ
SU(3)
π = gN
π − gΣ
π + gΞ
π = x cnxn
, x =
m2
K −m2
π
4π2f2
π
0
0.1
0.2
0.3
0 0.1 0.2 0.3 0.4
SU(3)
⇡
x
Physical Point
Fit to ETMC
ETMC
Lin et al. 0712.1214
0.3
breaking ∼ 14% at xphys = 0.33
Decuplet
g∆
π = H
gΣ∗
π = 2
3 H
gΞ∗
π = 1
3 H



g∆
π − 3
2 gΣ∗
π = 0
g∆
π − 3gΞ∗
π = 0
g∆
π − gΣ∗
π − gΞ∗
π = 0
-0.4
-0.2
0
0.2
0 0.1 0.2 0.3 0.4
SU(3)
x
Physical Point
SU(3) = g⇡ g⇡⌃⇤⌃⇤ g⇡⌅⇤⌅⇤
-0.4
-0.2
0
0.2
0.4
0 0.1 0.2 0.3 0.4
SU(3)
x
Physical Point
g⇡
3
2
g⇡⌃⇤⌃⇤
g⇡ 3g⇡⌅⇤⌅⇤
g⇡ g⇡⌃⇤⌃⇤ g⇡⌅⇤⌅⇤
breaking consistent with zero ∀ x
C. Kallidonis (CyI) Axial charges EINN2015 8 / 10

9. Results
Contributions to spin
Sum rule Jq
= 1
2 ∆Σq
+ Lq
, ∆Σq
= gq
proton
0.0
0.2
0.4
0.6
0 0.05 0.1 0.15 0.2 0.25
1
2 ⌃u+d
Contributionstoprotonspin
m2
⇡ (GeV2
)
Nf = 2
Nf = 2 + 1 + 1 (this work)
Experiment
0.28
0.32
0.36
0.40
1
2 ⌃u+d+s
⇤
0.60
0.80
1.00
1
2 ⌃u
0.80
1.00
1.20
0 0.05 0.1 0.15 0.2
1
2 ⌃s
⌦
Contributionstospin
Λ, ∆ baryons
0.16
⌃++
c
0.24
0.26
0.28
0.30 1
2 ⌃s+c
⌦0
c
0.96
1.02
1.08
1.14 1
2 ⌃u+s+c
⌅⇤+
c
1.12
1.16
1.20
1.24
0 0.05 0.1 0.15 0.2
1
2 ⌃u+c
⌅⇤++
cc
Contributionstospin
m2
⇡ (GeV2
)
0.28
0.32
0.36
0.40
1
2 ⌃u+d+s
⇤
0.60
0.80
1.00
0 0.05 0.1 0.15 0.2
1
2 ⌃u
Contributionstospin
m2
⇡ (GeV2
)
Charm baryons
0.16
0.20
0.24
0.28 1
2 ⌃u+c
⌃++
c
0.24
0.26
0.28
0.30 1
2 ⌃s+c
⌦0
c
0.96
1.02
1.08
1.14 1
2 ⌃u+s+c
⌅⇤+
c
1.12
1.16
1.20
1.24
0 0.05 0.1 0.15 0.2
1
2 ⌃u+c
⌅⇤++
cc
Contributionstospin
m2
⇡ (GeV2
)
weak mπ-dependence
intrinsic spin carried by quarks ∼ 40 − 60%
of total particle spin
C. Kallidonis (CyI) Axial charges EINN2015 9 / 10

10. Conclusions
good agreement with existing results for the nucleon and the octet hyperons axial charges
weak mπ-dependence of the axial charges → estimates for decuplet baryons and charmed baryons
small SU(3) breaking effects for the octet - consistent with zero for decuplet
estimates on intrinsic spin carried by quarks for hyperons and charmed baryons
Future Work
finalize results for Nf = 2 at the physical pion mass
calculate baryon spectrum, axial charges,(etc...) for Nf = 2 + 1 + 1 at the physical pion mass
Thank you
C. Kallidonis (CyI) Axial charges EINN2015 10 / 10