Poster presented at the Electromagnetic Interactions on Nucleons and Nuclei 2013 (EINN2013) Conference, held in Paphos, Cyprus. We present results on the masses and axial charges of all forty light, strange and charm baryons, obtained from Lattice QCD simulations

1.
Hyperon and charmed baryon masses and axial charges from lattice QCD
C. Kallidonis1
[1] Computation-based Science and Technology Research Center, The Cyprus Institute
[2] Department of Physics, University of Cyprus
[3] Deutsches Elektronen-Synchrotron (DESY), Zeuthen, Germany
In this work we use Lattice Quantum Chromodynamics (LQCD)
simulations with the following two objectives:
• The study of the masses of the low-lying baryons, comparison of the
results with the experimental values and the evaluation of masses of
baryons not yet determined experimentally. The highlight of this work
are recent results using simulations with two dynamical quarks at the
physical pion mass.
• The calculation of the axial charges of baryons, that are fundamental
observables probing hadron structure. Reproducing the nucleon axial
charge, which is accurately measured from neutron β – decays, will
pave the way for a reliable evaluation of the axial charges of hyperons
and charmed baryons. We present results for a range of pion masses
from about 400 MeV to about 210 MeV.
References
[1] J. Beringer et al., (PDG), Phys.Rev. D86, 010001 (2012)
[2] H. Na and S. A. Gottlieb, PoS LAT2007, 124 (2007), 0710.1422
[3] H. Na and S. A. Gottlieb, PoS LATTICE2008, 119 (2008), 0812.1235
[4] R.A. Briceno et al., (2011), 1111.1028
[5] L. Liu et al., Phys. Rev. D81, 094505 (2010), 0909.3294
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
The first quantities one calculates before
proceeding with the evaluation of more
complex hadronic observables are the
hadron masses. In this case,
extrapolations are performed to obtain
the masses at the physical pion mass.
In the following figures we compare our
results obtained at the physical pion
mass with experiment [1] as well as
with other calculations [2-5]. Our
estimates for the masses of hadrons not
yet measured experimentally are also
displayed.
with C. Alexandrou1,2, V. Drach3, K. Hadjiyiannakou2, K. Jansen3, G. Koutsou1
The large time limit of two-point
functions yields the energy of the
low-lying hadrons:
We developed optimized codes to extract all the masses of the 40
particles, which are implemented and running on state-of-the-art
parallel computers, such as the JUQUEEN and the Cy-Tera facilities.
To evaluate the axial charges we need except for two-point functions, also three-
point functions, as the diagram below. Three-point functions are even more
computationally demanding to obtain and optimized codes to
evaluate them are also implemented on high performance
computing facilities.
The large Euclidean time limit of the
ratio of three- and two-point functions
directly yields the value of the axial
charge, as the figure to the right.
-0.05
0
0.05
0.1
0.15
0.2
0.25
-0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
SU(3)
x
Physical Point
Fit to TMF
Fit to all
TMF
Hybrid
Breaking ~ x2 leads to about 10% at
the physical point xphys=0.33
• Axial charges of hadrons
at the physical pion mass
We perform extrapolations of our
data to obtain the axial charge of the
baryons at the physical pion mass.
The Ansatz we used is of the form
• Study of the SU(3) flavour
symmetry breaking for the octet
gN
A = F + D
g⌃
A = 2F
g⌅
A = −D + F
⇒ gN
A − g⌃
A + g⌅
A = 0
SU(3) = gN
A − g⌃
A + g⌅
A
x = (m2
K − m2
⇡)4⇡2
f2
⇡
gN
A = F + D
g⌃
A = 2F
g⌅
A = −D + F
⇒ gN
A − g⌃
A + g⌅
A = 0
SU(3) = gN
A − g⌃
A + g⌅
A
x = (m2
K − m2
⇡)4⇡2
f2
⇡
gN
A = F + D
g⌃
A = 2F
g⌅
A = −D + F
⇒ gN
A − g⌃
A + g⌅
A = 0
SU(3) = gN
A − g⌃
A + g⌅
A
x = (m2
K − m2
⇡)4⇡2
f2
⇡
gN
A = F + D
g⌃
A = 2F
g⌅
A = −D + F
⇒ gN
A − g⌃
A + g⌅
A = 0
SU(3) = gN
A − g⌃
A + g⌅
A
x = (m2
K − m2
⇡)4⇡2
f2
⇡
if exact SU(3) symmetry:
gN
A = F + D
g⌃
A = 2F
g⌅
A = −D + F
⇒ gN
A − g⌃
A + g⌅
A = 0
SU(3) = gN
A − g⌃
A + g⌅
A
x = (m2
K − m2
⇡)4⇡2
f2
⇡
1
gN
A = F + D
g⌃
A = 2F
g⌅
A = −D + F
⇒ gN
A − g⌃
A + g⌅
A = 0
SU(3) = gN
A − g⌃
A + g⌅
A
x = (m2
K − m2
⇡)4⇡2
f2
⇡
1
vs.
• Our results on hyperons and charmed baryon masses are consistent with results
from other lattice calculations, as well as with the known experimental values.
This enables us to give predictions on the masses that are not yet measured.
• We provide results on the axial charges of hyperons and charmed baryons and
examine the validity of SU(3) flavour symmetry. We find an SU(3) symmetry
breaking of about 10% for the octet.
• Future work will concentrate on further studies of the baryon spectrum and
hadron structure at the physical pion mass. This includes the evaluation of the
axial charge as well as other observables concerning the low-lying strange and
charmed baryons using recently developed noise reduction techniques.
check
deviation:
SU(4) representations: baryons are grouped into two 20-plets, one with
spin 1/2 baryons and one with spin 3/2 as shown below:
gN
A = F + D
g⌃
A = 2F
g⌅
A = −D + F
⇒ gN
A − g⌃
A + g⌅
A = 0
SU(3) = gN
A − g⌃
A + g⌅
A
x = (m2
K − m2
⇡)4⇡2
f2
⇡
C(tf − ti) =
me↵(t) = log
C(t)
C(t + 1)
→
t→∞
M
G(tf − ti,Aµ(x,t)) =
gN
A = F + D
g⌃
A = 2F
g⌅
A = −D + F
⇒ gN
A − g⌃
A + g⌅
A = 0
SU(3) = gN
A − g⌃
A + g⌅
A
x = (m2
K − m2
⇡)4⇡2
f2
⇡
C(tf − ti) =
me↵(t) = log
C(t)
C(t + 1)
→
t→∞
M
gN
A = F + D
g⌃
A = 2F
g⌅
A = −D + F
⇒ gN
A − g⌃
A + g⌅
A = 0
SU(3) = gN
A − g⌃
A + g⌅
A
x = (m2
K − m2
⇡)4⇡2
f2
⇡
C(tf − ti) =
me↵(t) = log
C(t)
C(t + 1)
→
t→∞
M
Gµ(tf − ti,Aµ(x,t)) =
4 ⊗ 4 ⊗ 4 = 20 ⊕ 20 ⊕ ¯4
gA = lim
tf −ti→∞
t−ti→∞
Gµ(tf − ti,Aµ)
C(tf − ti)
Axial current:
gN
A = F + D
g⌃
A = 2F
g⌅
A = −D + F
⇒ gN
A − g⌃
A + g⌅
A = 0
SU(3) = gN
A − g⌃
A + g⌅
A
x = (m2
K − m2
⇡)4⇡2
f2
⇡
C(tf − ti) =
me↵(t) = log
C(t)
C(t + 1)
→
t→∞
M
Gµ(tf − ti,Aµ(x,t)) =
4 ⊗ 4 ⊗ 4 = 20 ⊕ 20 ⊕ ¯4
gA = lim
tf −ti→∞
t−ti→∞
Gµ(tf − ti,Aµ)
C(tf − ti)
Aµ(x,t) = ¯q(x) µ 5q(x)
1.8
2
g⌦
A
¯ss
0
0.008
g
⌅0
c
A
¯ss
2.2
(m2
⇡)phys0 0.04 0.08 0.12 0.16
g
⌦⇤+
cc
A
m2
⇡(GeV2
)
¯cc
1.05
1.2
gN
A
¯uu ¯dd
0.4
0.8
g
+
A
¯uu ¯dd
1.3
1.4
1.5
g⌃0
A
¯uu + ¯dd 2¯ss
gN
A = F + D
g⌃
A = 2F
g⌅
A = −D + F
⇒ gN
A − g⌃
A + g⌅
A = 0
SU(3) = gN
A − g⌃
A + g⌅
A
x = (m2
K − m2
⇡)4⇡2
f2
⇡
C(tf − ti) =
me↵(t) = log
C(t)
C(t + 1)
→
t→∞
M
Gµ(tf − ti,Aµ(x,t)) =
4 ⊗ 4 ⊗ 4 = 20 ⊕ 20 ⊕ 20 ⊕ ¯4
gA = lim
tf −ti→∞
t−ti→∞
Gµ(tf − ti,Aµ)
C(tf − ti)
Aµ(x,t) = ¯q(x) µ 5q(x)
1
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2. Hyperons and charmed baryons
1. Introduction – Motivation 3. Masses of hyperons and charmed baryons
• Results using simulations with Nf=2+1+1 quark flavours with pion masses
from about 210 MeV to about 475 MeV
• Results using simulations at the physical pion mass
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  
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 
 
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

4. Evaluation of axial charges
0
2
4
¯uu ¯dd+
1.2
1.4
1.6 ¯uu + ¯dd 2¯ss⌃0
-0.24
-0.2
Ratio
¯uu⌅0
0
0.8 ¯uu + ¯dd 2¯ss⌃⇤0
1.8
2
2.2
0 2 4 6 8 10 12 14 16
time
¯ss⌅⇤0
gN
A = F + D
g⌃
A = 2F
g⌅
A = −D + F
⇒ gN
A − g⌃
A + g⌅
A = 0
SU(3) = gN
A − g⌃
A + g⌅
A
x = (m2
K − m2
⇡)4⇡2
f2
⇡
C(tf − ti) =
me↵(t) = log
C(t)
C(t + 1)
→
t→∞
M
Gµ(t,Aµ) =
4 ⊗ 4 ⊗ 4 = 20 ⊕ 20 ⊕ 20 ⊕ ¯4
R(tf − ti) =
Gµ(tf − ti,Aµ(x,t))
C(tf − ti)
gA = lim
tf −ti→∞
t−ti→∞
R(tf − ti)
A (x,t) = ¯q(x) q(x)
g⌃
A = 2F
g⌅
A = −D + F
⇒ gN
A − g⌃
A + g⌅
A = 0
SU(3) = gN
A − g⌃
A + g⌅
A
x = (m2
K − m2
⇡)4⇡2
f2
⇡
C(tf − ti) =
me↵(t) = log
C(t)
C(t + 1)
→
t→∞
M
Gµ(t, Aµ) =
4 ⊗ 4 ⊗ 4 = 20 ⊕ 20 ⊕ 20 ⊕ ¯4
R(tf − ti) =
Gµ(tf − ti, Aµ(x, t))
C(tf − ti)
gA = lim
tf −ti→∞
t−ti→∞
R(tf − ti)
Aµ(x, t) = ¯q(x) µ 5q(x)
gA(m⇡) = a + bm2
⇡
1
5. Results on the axial charges
6. Conclusions and future work
Cy-Tera
The Project Cy-Tera (ΝΕΑ ΥΠΟΔΟΜΗ/ΣΤΡΑΤΗ/0308/31) is co-financed by the European Regional
Development Fund and the Republic of Cyprus through the Research Promotion Foundation.
gN
A = F + D
g⌃
A = 2F
g⌅
A = −D + F
⇒ gN
A − g⌃
A + g⌅
A = 0
SU(3) = gN
A − g⌃
A + g⌅
A
x = (m2
K − m2
⇡)4⇡2
f2
⇡
C(tf − ti) =
me↵(t) = log
C(t)
C(t + 1)
→
t→∞
M
Gµ(t,Aµ) =
4 ⊗ 4 ⊗ 4 = 20 ⊕ 20 ⊕ 20 ⊕ ¯4
R(tf − ti) =
Gµ(tf − ti,Aµ(x,t))
C(tf − ti)
gA = lim
tf −ti→∞
R(tf − ti)
Aµ(x,t) = ¯q(x) µ 5q(x)