1
Computing the masses of hyperons and charmed baryons from lattice QCD C. Kallidonis 1 with C. Alexandrou 1,2 , V. Drach 3 , K. Hadjiyiannakou 2 , K. Jansen 3 , G. Koutsou 1 [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 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 Introduction Lattice Quantum Chromodynamics (LQCD) is the only method so far which solves the fundamental theory of strong interactions non-perturbatively Petascale computer resources available nowadays through PRACE make lattice QCD simulations at the physical pion mass possible Most of the simulations and our calculations were performed on HPC facilities such as the JUGENE, JUROPA and JUQUEEN at JSC Part of the analysis was performed on the Cy-Tera machine at The Cyprus Institute, provided through the project LinkSCEEM In this work: we present results on the hyperon and charmed baryon masses, including results from simulations at the physical pion mass we compare with the known spectrum and predict the mass of charmed baryons Hyperons and charmed baryons Baryons consist of three quarks. There is a total of 6 quarks and they come in three generations. According to the theory of Strong Interactions, known as Quantum Chromodynamics (QCD), quarks cannot be observed freely. Nuclear interactions confine them into bound states, the hadrons. The mediators of the strong force are the gluons. Hadrons can have half integer spin in which case they are called baryons, or integer spin and are known as mesons. In this work we focus on baryons consisting of up, down, strange and charm quarks. hadrons mesons baryons Light baryons are made of up and down quarks. Hyperons have at least one strange quark and charmed baryons at least one charm quark. s u d hyperon c d c charmed baryon u d u proton 4 4 4 = 20 20 20 ¯ 4 Baryons consisting of a combination of three of up, down strange and charm quarks are perceived as SU(3) subgroups of SU(4) flavor symmetry. They are grouped into two 20-plets, one with spin 1/2 baryons and one with spin 3/2 as shown below. QCD on the lattice Lattice QCD is a discrete formulation of QCD on a finite 4-dimensional space-time lattice that enables numerical simulation of QCD using Monte-Carlo methods. Lattice sites are separated by a lattice spacing, a. Quarks are defined on lattice sites while gluons are links connecting neighboring sites. m e(t) = log C (t) C (t + 1) tM At the large time limit, the two-point functions yield the energy of the low-lying hadrons. A constant fit on a plateau region is performed to extract the value. C (t f t i ) = Computer resources requirements As can be seen from the strong scaling plot of Fig. 1 the behavior of our inversion algorithm for the BlueGene/Q is most optimal when running on 1024 nodes. The inversion of the Dirac operator for the four quarks on a 48 3 x96 lattice requires 9600 JUQUEEN core-hours per gauge configuration Quark propagators are inverses of the Dirac operator. For a typical lattice size this operator is a sparse matrix of dimensions ~10 8 x10 8 . To invert the Dirac operator we use iterative methods such as the conjugate gradient method on high-performance computing facilities. The extraction of hadron masses requires the evaluation of correlators. We developed hybrid MPI-OpenMP codes to evaluate the correlators for the 40 low- lying baryons. These codes are imported on JUQUEEN, JUROPA and Cy-Tera and for a 48 3 x96 lattice they require 304 JUROPA core-hours per gauge configuration Recent algorithmic improvements include deflation methods that reduce the time required for inversions. This is particularly beneficial when multiple inversions are performed for a single gauge configuration. Masses of hyperons and charmed baryons The lattice results are in units of the lattice spacing. Before comparing with experiment, the lattice spacing needs to be fixed. This is done by using a physical quantity whose value is known from experiment. In our case we use the nucleon mass. Thus, an analysis with 1000 gauge configurations would require 9,600,000 JUQUEEN core-hours for quark propagators and 304,000 JUROPA core-hours for two-point functions. Conclusions Lattice QCD provides a method of calculating key observables using high- performance computing resources. In particular, Petascale computers enable simulations with physical pion mass which otherwise would not be possible. Thus, the results are more accurate and the systematic errors are reduced. Our results for the masses of the hyperons and charmed baryons produced at the physical pion mass are in very good agreement with experiment and other lattice calculations. We provide predictions for the masses of the charmed baryons which are sought experimentally. In Figs. 2, 3 and 4 we present our results extracted directly from simulations at the physical pion mass. Comparison with experiment [1] as well as with other lattice calculations [2-5] shows an overall agreement. Our prediction for the masses of the charmed baryons that have not yet been measured experimentally are also displayed. Fig. 1 Fig. 2 Fig. 3 Fig. 4 The Project GPUCW (ΤΠΕ/ΠΛΗΡΟ/0311(ΒΙΕ)/09) is co-financed by the European Regional Development Fund and the Republic of Cyprus through the Research Promotion Foundation. In order to calculate observables on the lattice, such as the mass of a baryon, one needs to obtain information on the probability of a quark to transport from one lattice site to the other. This is encompassed in objects called quark propagators, which in our calculations are the most computationally intensive objects to evaluate. These propagators are appropriately combined to form correlation functions and from those the various observables can be extracted. Baryon masses are obtained from two-point correlation functions. The blue lines in the figure represent the propagator for each quark.

Computing the masses of hyperons and charmed baryons from Lattice QCD

Embed Size (px)

Citation preview

Page 1: Computing the masses of hyperons and charmed baryons from Lattice QCD

Computing the masses of hyperons and charmed baryons from lattice QCD C. Kallidonis1

with C. Alexandrou1,2, V. Drach3, K. Hadjiyiannakou2, K. Jansen3, G. Koutsou1

[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

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

Introduction

•  Lattice Quantum Chromodynamics (LQCD) is the only method so far which solves the fundamental theory of strong interactions non-perturbatively

•  Petascale computer resources available nowadays through PRACE make lattice QCD simulations at the physical pion mass possible

• Most of the simulations and our calculations were performed on HPC facilities such as the JUGENE, JUROPA and JUQUEEN at JSC

•  Part of the analysis was performed on the Cy-Tera machine at The Cyprus Institute, provided through the project LinkSCEEM

In this work: • we present results on the hyperon and charmed baryon masses, including results from simulations at the physical pion mass • we compare with the known spectrum and predict the mass of charmed baryons

Hyperons and charmed baryons

Baryons consist of three quarks. There is a total of 6 quarks and they come in three generations. According to the theory of Strong Interactions, known as Quantum Chromodynamics (QCD), quarks cannot be observed freely. Nuclear interactions confine them into bound states, the hadrons. The mediators of the strong force are the gluons. Hadrons can have half integer spin in which case they are called baryons, or integer spin and are known as mesons. In this work we focus on baryons consisting of up, down, strange and charm quarks.

hadrons  

mesons   baryons  

Light baryons are made of up and down quarks. Hyperons have at least one strange quark and charmed baryons at least one charm quark.

s  u  

d  

hyperon  

c  d  

c  

charmed  baryon  

u  d  

u  

proton  

g

NA = F +D

g

⌃A = 2F

g

⌅A = −D + F

⇒ g

NA − g⌃A + g⌅A = 0

�SU(3) = gNA − g⌃A + g⌅Ax = (m2

K −m2⇡)�4⇡2

f

2⇡

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) = q̄(x)�µ�5q(x)

1

Baryons consisting of a combination of three of up, down strange and charm quarks are perceived as SU(3) subgroups of SU(4) flavor symmetry. They are grouped into two 20-plets, one with spin 1/2 baryons and one with spin 3/2 as shown below.

QCD on the lattice

Lattice QCD is a discrete formulation of QCD on a finite 4-dimensional space-time lattice that enables numerical simulation of QCD using Monte-Carlo methods. Lattice sites are separated by a lattice spacing, a. Quarks are defined on lattice sites while gluons are links connecting neighboring sites.

����

����

����

����

����

� � �� �� ��� �� �� ��� ��� �� �

� �

���

��������������������������� ����

g

NA = F +D

g

⌃A = 2F

g

⌅A = −D + F

⇒ g

NA − g⌃A + g⌅A = 0

�SU(3) = gNA − g⌃A + g⌅Ax = (m2

K −m2⇡)�4⇡2

f

2⇡

C(tf − ti) =

me↵(t) = log� C(t)C(t + 1)��→t→∞M

G(tf − ti,Aµ(�x, t)) =

4⊗ 4⊗ 4 = 20⊕ 20⊕ ¯

4

1

At the large time limit, the two-point functions yield the energy of the low-lying hadrons. A constant fit on a plateau region is performed to extract the value.

g

NA = F +D

g

⌃A = 2F

g

⌅A = −D + F

⇒ g

NA − g⌃A + g⌅A = 0

�SU(3) = gNA − g⌃A + g⌅Ax = (m2

K −m2⇡)�4⇡2

f

2⇡

C(tf − ti) =

me↵(t) = log� C(t)C(t + 1)��→t→∞M

G(tf − ti,Aµ(�x, t)) =

4⊗ 4⊗ 4 = 20⊕ 20⊕ ¯

4

1

Computer resources requirements

As can be seen from the strong scaling plot of Fig. 1 the behavior of our inversion algorithm for the BlueGene/Q is most optimal when running on 1024 nodes. The inversion of the Dirac operator for the four quarks on a 483x96 lattice requires

9600 JUQUEEN core-hours per gauge configuration

Quark propagators are inverses of the Dirac operator. For a typical lattice size this operator is a sparse matrix of dimensions ~108x108. To invert the Dirac operator we use iterative methods such as the conjugate gradient method on high-performance computing facilities.

The extraction of hadron masses requires the evaluation of correlators. We developed hybrid MPI-OpenMP codes to evaluate the correlators for the 40 low-lying baryons. These codes are imported on JUQUEEN, JUROPA and Cy-Tera and for a 483x96 lattice they require

304 JUROPA core-hours per gauge configuration

Recent algorithmic improvements include deflation methods that reduce the time required for inversions. This is particularly beneficial when multiple inversions are performed for a single gauge configuration.

Masses of hyperons and charmed baryons

����

��

����

����

����

����

��

����

� � �� �� �

���

����������

���� ����������

����

����

����

����

��

����

����

����

����

� � �� �

����

���

����������������

��� ������������������������

����

��

����

��

����

��

�� �

�� ��

��� ����

�� �

���

������������� �������

����������������

The lattice results are in units of the lattice spacing. Before comparing with experiment, the lattice spacing needs to be fixed. This is done by using a physical quantity whose value is known from experiment. In our case we use the nucleon mass.

Thus, an analysis with 1000 gauge configurations would require 9,600,000 JUQUEEN core-hours for quark propagators and 304,000 JUROPA core-hours for two-point functions.

Conclusions

•  Lattice QCD provides a method of calculating key observables using high-performance computing resources. In particular, Petascale computers enable simulations with physical pion mass which otherwise would not be possible. Thus, the results are more accurate and the systematic errors are reduced.

•  Our results for the masses of the hyperons and charmed baryons produced at the physical pion mass are in very good agreement with experiment and other lattice calculations.

• We provide predictions for the masses of the charmed baryons which are sought experimentally.

In Figs. 2, 3 and 4 we present our results extracted directly from simulations at the physical pion mass. Comparison with experiment [1] as well as with other lattice calculations [2-5] shows an overall agreement. Our prediction for the masses of the charmed baryons that have not yet been measured experimentally are also displayed.

Fig. 1

Fig. 2

Fig. 3 Fig. 4

The Project GPUCW (ΤΠΕ/ΠΛΗΡΟ/0311(ΒΙΕ)/09) is co-financed by the European Regional Development Fund and the Republic of Cyprus through the Research Promotion Foundation.

In order to calculate observables on the lattice, such as the mass of a baryon, one needs to obtain information on the probability of a quark to transport from one lattice site to the other. This is encompassed in objects called quark propagators, which in our calculations are the most computationally intensive objects to evaluate. These propagators are appropriately combined to form correlation functions and from those the various observables can be extracted. Baryon masses are obtained from two-point correlation functions. The blue lines in the figure represent the propagator for each quark.