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 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 x phys =0.33 • Axial charges of hadrons using Nf=2+1+1 simulations 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 g N A = F + D g ⌃ A = 2 F g ⌅ A = − D + F ⇒ g N A − g ⌃ A + g ⌅ A = 0 SU(3) = g N A − g ⌃ A + g ⌅ A x = ( m 2 K − m 2 ⇡ )4 ⇡ 2 f 2 ⇡ g N A = F + D g ⌃ A = 2 F g ⌅ A = − D + F ⇒ g N A − g ⌃ A + g ⌅ A = 0 SU(3) = g N A − g ⌃ A + g ⌅ A x = ( m 2 K − m 2 ⇡ )4 ⇡ 2 f 2 ⇡ g N A = F + D g ⌃ A = 2 F g ⌅ A = − D + F ⇒ g N A − g ⌃ A + g ⌅ A = 0 SU(3) = g N A − g ⌃ A + g ⌅ A x = ( m 2 K − m 2 ⇡ )4 ⇡ 2 f 2 ⇡ g N A = F + D g ⌃ A = 2 F g ⌅ A = − D + F ⇒ g N A − g ⌃ A + g ⌅ A = 0 SU(3) = g N A − g ⌃ A + g ⌅ A x = ( m 2 K − m 2 ⇡ )4 ⇡ 2 f 2 ⇡ if exact SU(3) symmetry: g N A = F + D g ⌃ A = 2 F g ⌅ A = − D + F ⇒ g N A − g ⌃ A + g ⌅ A = 0 SU(3) = g N A − g ⌃ A + g ⌅ A x = ( m 2 K − m 2 ⇡ )4 ⇡ 2 f 2 ⇡ 1 g N A = F + D g ⌃ A = 2 F g ⌅ A = − D + F ⇒ g N A − g ⌃ A + g ⌅ A = 0 SU(3) = g N A − g ⌃ A + g ⌅ A x = ( m 2 K − m 2 ⇡ )4 ⇡ 2 f 2 ⇡ 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: g N A = F + D g ⌃ A = 2F g ⌅ A = − D + F ⇒ g N A − g ⌃ A + g ⌅ A = 0 SU(3) = g N A − g ⌃ A + g ⌅ A x = ( m 2 K − m 2 ⇡ ) 4⇡ 2 f 2 ⇡ C ( tf − ti ) = me↵ ( t ) = log C ( t ) C ( t + 1 ) → t→∞ M G ( tf − ti,Aµ ( x,t )) = g N A = F + D g ⌃ A = 2F g ⌅ A = − D + F ⇒ g N A − g ⌃ A + g ⌅ A = 0 SU(3) = g N A − g ⌃ A + g ⌅ A x = ( m 2 K − m 2 ⇡ ) 4⇡ 2 f 2 ⇡ C ( tf − ti ) = me↵ ( t ) = log C ( t ) C ( t + 1 ) → t→∞ M g N A = F + D g ⌃ A = 2F g ⌅ A = − D + F ⇒ g N A − g ⌃ A + g ⌅ A = 0 SU(3) = g N A − g ⌃ A + g ⌅ A x = ( m 2 K − m 2 ⇡ ) 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 ⊕ ¯ 4 gA = lim tf −ti→∞ t−ti →∞ Gµ ( tf − ti,Aµ ) C ( tf − ti ) Axial current: g N A = F + D g ⌃ A = 2F g ⌅ A = − D + F ⇒ g N A − g ⌃ A + g ⌅ A = 0 SU(3) = g N A − g ⌃ A + g ⌅ A x = ( m 2 K − m 2 ⇡ ) 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 ⊕ ¯ 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 ( m 2 ⇡ )phys 0 0.04 0.08 0.12 0.16 g ⌦⇤+ cc A m 2 ⇡ (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 g N A = F + D g ⌃ A = 2F g ⌅ A = − D + F ⇒ g N A − g ⌃ A + g ⌅ A = 0 SU(3) = g N A − g ⌃ A + g ⌅ A x = ( m 2 K − m 2 ⇡ ) 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 ) = ¯ q ( x ) µ 5q ( x ) 1 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 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 g N A = F + D g ⌃ A = 2F g ⌅ A = − D + F ⇒ g N A − g ⌃ A + g ⌅ A = 0 SU(3) = g N A − g ⌃ A + g ⌅ A x = ( m 2 K − m 2 ⇡ ) 4⇡ 2 f 2 ⇡ 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 ⇒ g N A − g ⌃ A + g ⌅ A = 0 SU(3) = g N A − g ⌃ A + g ⌅ A x = ( m 2 K − m 2 ⇡ ) 4⇡ 2 f 2 ⇡ 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 + bm 2 ⇡ 1 5. Results on the axial charges 6. Conclusions and future work Cy-Tera The Project Cy-Tera (ΝΕΑ ΥΠΟ∆ΟΜΗ/ΣΤΡΑΤΗ/0308/31) is co-financed by the European Regional Development Fund and the Republic of Cyprus through the Research Promotion Foundation. g N A = F + D g ⌃ A = 2F g ⌅ A = − D + F ⇒ g N A − g ⌃ A + g ⌅ A = 0 SU(3) = g N A − g ⌃ A + g ⌅ A x = ( m 2 K − m 2 ⇡ ) 4⇡ 2 f 2 ⇡ 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 )