- Email: [email protected]
Light hadron spectrum from the CP-PACS
~ ~
~
ELSEVIER
II!IIIA Nuclear Physics A663&664 (2000) 969c-972c www.elsevier.nl/locate/npe
Light hadron spectrum from the CP-PACS T. Yoshie" for the CP-PACS Collaboration' Institute of Physics and Center for Computational Physics, University of Tsukuba, Tsukuba, Ibaraki 305-8577, Japan
a
We present results of the light hadron spectrum derived from large-scale simulations in lattice QCD on the CP-PACS computer. The spectrum calculated in the quenched approximation systematically deviates from the experiment. We find indications that the discrepancy is significantly reduced by introduction of two flavors of light dynamical quarks. The strange quark mass in full QCD turns out to be ~ 85 MeV in the MS scheme at If = 2 GeV, which is significantly smaller than previous phenomenological estimates. 1. INTRODUCTION
Deriving the light hadron spectrum from first principles of QCD has been a fundamental issue in lattice QCD, because it demonstrates the validity of QCD for strong interactions in the low energy non-perturbative region. In order to step forward toward this goal, we have carried out two large-scale simulations. The first simulation [1) employed the quenched approximation of ignoring sea quark effects. We tried to control all other systematic errors with high statistics and establish the quenched spectrum. The second simulation [2], still in progress, is made in full QCD with two light dynamical quarks. We also determine the values of light quark masses and investigate the U(I) problem. Results presented here have been obtained from two and a half years running of the CPPACS computer, a massively parallel system with a peak speed of 614 GFlops. It is one of the fastest computers devoted to lattice QCD simulations so far, and this computing power has made our systematic studies possible.
2. QUENCHED QCD SPECTRUM A very important step in calculating the quenched spectrum was made by the GFll Collaboration [3] in 1991-92. Making the chiral and continuum extrapolations and correcting for finite-size effects, they obtained results for the quenched spectrum in agreement with experiment within one standard deviation, which is 1-9 % depending on the particle. We reproduce their result in Fig.l with filled square symbols. In spite of this encouraging result, there has been no further work to give results with errors convincingly better than 5 %. thereby answering the question of how the quenched spectrum deviates from exper'CP-PACS Collaboration: A. Ali Khan, S. Aoki, G. Boyd. R. Burkhalter, S. Ejiri, M. Fukugita, S. Hashimoto, N. Ishizuka, Y. Iwasaki, K. Kanaya, T. Kaneko, Y. Kuramashi, T. Manke, K. Nagai, M. Okawa. H. P. Shanahan, A. Ukawa. T. Yoshie 0375-9474/00/$ - see front matter © 2000 Elsevier Science B.Y. All rights reserved. PI! S0375-9474(99)00740-X
T. Yoshie/Nuclear Physics A663&664 (2000) 969c-972c
970c
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Figure 1. Quenched QCD spectrum compared with GFll's [3] and experiment.
0.85
~------9-~-Q.--&
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0.0
0.2
0.4
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Figure 2. Continuum extrapolations of meson masses in full and quenched QCD.
iment. To this end, one has to reduce both statistical errors and systematic ones arising from extrapolations. In our work we therefore pushed the calculation closer to the continuum limit, the infinite-volume limit and the chirallimit. We took four lattice spacings covering the range a = 0.1-0.05 fm, which was closer toward the continuum limit than the range a = 0.140.07 fm used by GFll. The systematic error arising from the continuum extrapolation is estimated to be 1% or less with our result. We employed lattices with a physical size of La >::; 3 fm, which is known to be large enough to avoid size effects beyond a few % level, as compared to La >::; 2.3 fm of GFll. We selected five quark masses ranging over 125 ;:::: m q ;:::: 23 MeV, reducing the smallest quark mass by a factor 2 from m q >::; 40 MeV of GFl1. The data at the smallest quark mass were important for reliable chiral extrapolations: Clear negative curvatures of the nucleon and A masses as functions of the quark mass were observed, which were not seen in the data of GFll. We found our pseudo-scalar meson mass data to be consistent with the presence of chiral logarithms predicted by quenched chiral perturbation theory (QxPT). This led us to employ the QxPT mass formulae for chiral extrapolations. In the continuum limit we obtain results with errors of 1-2 % for meson masses and 2-3 % for baryon masses. We present our results in Fig.1. Those for m.; and m p are omitted; they are used as inputs to set the scale and fix the up and down quark masses, taken to be degenerate in our work. In Fig.l, we see a statistically significant and systematic deviation of the quenched spectrum from experiment, amounting to 7a for some particles. The pattern of the deviation is summarized as follows. If one uses mK as input to fix the strange quark mass, 1) masses of vector mesons mK" and m1> are smaller than experiment, 2) octet baryon masses are systematically smaller than experiment and 3) decuplet baryon mass splitting is smaller than experiment. If one uses m1> instead of m tc as input, tn tc- appears consistent with experiment and the discrepancies for baryon masses are much reduced. However, mK turns out to be much higher. In other words, the meson hyperfine splitting remains smaller than experiment. In summary, we conclude that the strange quark mass cannot be tuned in quenched
T. Yoshie/Nuclear Physics A663&664 (2000) 969c-972c
I
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Figure 3. up and down quark mass
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Figure 4. strange quark mass
QCD so that all strange hadron masses are in agreement with experiment.
3. FULL QeD SPECTRUM Before we start a full-scale full QCD simulation, we made a pilot study to investigate effects of improving lattice actions using four possible types of action combinations, the standard plaquette or a renormalization-group (RG) improved action for gluons, and the standard Wilson or the clover action for quarks. We find that the magnitude of scaling violation, or discretization errors, in the full QCD spectrum is significantly smaller for the combination of the RG action and the clover action. Therefore this action combination is employed for our systematic full QCD study. Our simulation is carried out for two flavors of dynamical quarks, to be identified with degenerate up and down quarks, with the mass in the range mq;c, 45 MeV. The strange quark is treated in the quenched approximation. We employ four lattice spacings in the range a = 0.22-0.09 fm and lattices with La ~ 2.5 fm, except 2.1 fm for the finest lattice. We observe effects of introducing dynamical quarks in the meson sector. In Fig.2, we compare meson masses. The most interesting feature is that mK* and m.p for full QCD extrapolate to values significantly closer to experiment than for quenched QCD. The remaining discrepancy might be due to the quenching effect of the strange quark. Results for baryon masses are less clear. The central values are in general closer to the experimental values. However, the errors are large so that we need much higher statistics. The lattice size La ~ 2.5 fm used may also be too small for baryons. In Fig.2, we cannot directly compare the quenched and full QCD data at finite lattice spacings since the lattice actions employed are different. We have started a study of the quenched spectrum using the same improved action as for full QCD, in order to make a point-by-point comparison. For preliminary results, see Ref.[4].
4. LIGHT QUARK MASSES In lattice QCD, quark mass can be defined from vector Ward identity(VWI) or axialvector Ward identity (AWl). As we show in Fig.3, values of quark mass in the two def-
972c
T. Yoshie/Nuclear Physics A663&664 (2000) 969c-972c
initions differ at finite lattice spacings, but they converge to a common value in the continuum limit. In full QCD, one can define the VWI quark mass either from the sea quark or from the valence quark in the presence of dynamical quarks. These quark masses also converge to a common value in the continuum limit. The fact that various definitions give a common value strengthens reliability of our analysis. The strange quark mass in quenched QCD depends on whether we choose ui« or m
5. U(l) PROBLEM IN FULL QCD In the course of our full QCD simulations, the U(1) problem is also investigated [5]. We measure the mass of "I = (U'Y5U + d'Y5d), ignoring mixing with "Is = 81'58. We find m'l = 863(86) MeV in the chiral and continuum limit, which lies close to the experimental value of m'l" Work to incorporate the mixing is in progress.
6. CONCLUSIONS In summary, we have observed a clear deviation of the quenched spectrum from experiment beyond 10% accuracy and indications that the discrepancy is reduced by introducing two light dynamical quarks. A small value of the strange quark mass rs 85 MeV we find in full QCD may have a significant implication for phenomenology of CP violation. All the results encourage us to perform works to unquench the strange quarks in the new future, which would lead us to first principles determinations of the spectrum and quark masses. I thank members of CP-PACS group for their collaboration. I am grateful to K.Kanaya and A.Ukawa for valuable suggestions on the manuscript. This work is supported in part by the Grant-in-Aid Nos. 08NPOl01 and 09304029 of Ministry of Education.
REFERENCES 1. 2. 3. 4. 5.
CP-PACS Collaboration, hep-Iat/9904012. CP-PACS Collaboration, hep-Iat/9902018; ibid. 9904003 and references theirin. GFll Collaboration, Nue!. Phys. B430 (1994) 179. CP-PACS Collaboration, talk presented by T. Kaneko at Lattice99. CP-PACS Collaboration, talk presented by R. Burkhalter at Lattice99.
~
ELSEVIER
II!IIIA Nuclear Physics A663&664 (2000) 969c-972c www.elsevier.nl/locate/npe
Light hadron spectrum from the CP-PACS T. Yoshie" for the CP-PACS Collaboration' Institute of Physics and Center for Computational Physics, University of Tsukuba, Tsukuba, Ibaraki 305-8577, Japan
a
We present results of the light hadron spectrum derived from large-scale simulations in lattice QCD on the CP-PACS computer. The spectrum calculated in the quenched approximation systematically deviates from the experiment. We find indications that the discrepancy is significantly reduced by introduction of two flavors of light dynamical quarks. The strange quark mass in full QCD turns out to be ~ 85 MeV in the MS scheme at If = 2 GeV, which is significantly smaller than previous phenomenological estimates. 1. INTRODUCTION
Deriving the light hadron spectrum from first principles of QCD has been a fundamental issue in lattice QCD, because it demonstrates the validity of QCD for strong interactions in the low energy non-perturbative region. In order to step forward toward this goal, we have carried out two large-scale simulations. The first simulation [1) employed the quenched approximation of ignoring sea quark effects. We tried to control all other systematic errors with high statistics and establish the quenched spectrum. The second simulation [2], still in progress, is made in full QCD with two light dynamical quarks. We also determine the values of light quark masses and investigate the U(I) problem. Results presented here have been obtained from two and a half years running of the CPPACS computer, a massively parallel system with a peak speed of 614 GFlops. It is one of the fastest computers devoted to lattice QCD simulations so far, and this computing power has made our systematic studies possible.
2. QUENCHED QCD SPECTRUM A very important step in calculating the quenched spectrum was made by the GFll Collaboration [3] in 1991-92. Making the chiral and continuum extrapolations and correcting for finite-size effects, they obtained results for the quenched spectrum in agreement with experiment within one standard deviation, which is 1-9 % depending on the particle. We reproduce their result in Fig.l with filled square symbols. In spite of this encouraging result, there has been no further work to give results with errors convincingly better than 5 %. thereby answering the question of how the quenched spectrum deviates from exper'CP-PACS Collaboration: A. Ali Khan, S. Aoki, G. Boyd. R. Burkhalter, S. Ejiri, M. Fukugita, S. Hashimoto, N. Ishizuka, Y. Iwasaki, K. Kanaya, T. Kaneko, Y. Kuramashi, T. Manke, K. Nagai, M. Okawa. H. P. Shanahan, A. Ukawa. T. Yoshie 0375-9474/00/$ - see front matter © 2000 Elsevier Science B.Y. All rights reserved. PI! S0375-9474(99)00740-X
T. Yoshie/Nuclear Physics A663&664 (2000) 969c-972c
970c
1.8
1.05
e
1.6 1.00
1.4
~ 095
%12
f------l44--~
.
--- -
K'
0.90
E 1.0
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0.8
0.6
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Q.
e experiment e!uIlOCD D quenched OCD
$
K
-o
e CP-PACS K input o CP-PACS ~ input experiment e GFll K input
0.4 ' - - - - - - - - - - - - - - - - - '
Figure 1. Quenched QCD spectrum compared with GFll's [3] and experiment.
0.85
~------9-~-Q.--&
--Kinpul
0.0
0.2
0.4
0.6 a [Gevr']
0.8
1.0
1.2
Figure 2. Continuum extrapolations of meson masses in full and quenched QCD.
iment. To this end, one has to reduce both statistical errors and systematic ones arising from extrapolations. In our work we therefore pushed the calculation closer to the continuum limit, the infinite-volume limit and the chirallimit. We took four lattice spacings covering the range a = 0.1-0.05 fm, which was closer toward the continuum limit than the range a = 0.140.07 fm used by GFll. The systematic error arising from the continuum extrapolation is estimated to be 1% or less with our result. We employed lattices with a physical size of La >::; 3 fm, which is known to be large enough to avoid size effects beyond a few % level, as compared to La >::; 2.3 fm of GFll. We selected five quark masses ranging over 125 ;:::: m q ;:::: 23 MeV, reducing the smallest quark mass by a factor 2 from m q >::; 40 MeV of GFl1. The data at the smallest quark mass were important for reliable chiral extrapolations: Clear negative curvatures of the nucleon and A masses as functions of the quark mass were observed, which were not seen in the data of GFll. We found our pseudo-scalar meson mass data to be consistent with the presence of chiral logarithms predicted by quenched chiral perturbation theory (QxPT). This led us to employ the QxPT mass formulae for chiral extrapolations. In the continuum limit we obtain results with errors of 1-2 % for meson masses and 2-3 % for baryon masses. We present our results in Fig.1. Those for m.; and m p are omitted; they are used as inputs to set the scale and fix the up and down quark masses, taken to be degenerate in our work. In Fig.l, we see a statistically significant and systematic deviation of the quenched spectrum from experiment, amounting to 7a for some particles. The pattern of the deviation is summarized as follows. If one uses mK as input to fix the strange quark mass, 1) masses of vector mesons mK" and m1> are smaller than experiment, 2) octet baryon masses are systematically smaller than experiment and 3) decuplet baryon mass splitting is smaller than experiment. If one uses m1> instead of m tc as input, tn tc- appears consistent with experiment and the discrepancies for baryon masses are much reduced. However, mK turns out to be much higher. In other words, the meson hyperfine splitting remains smaller than experiment. In summary, we conclude that the strange quark mass cannot be tuned in quenched
T. Yoshie/Nuclear Physics A663&664 (2000) 969c-972c
I
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-
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6~ %
3.5
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3 .0
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.
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Figure 3. up and down quark mass
----
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0.0
0.2
0.4
0.6 0.8 a [GeV-'j
1.0
1.2
Figure 4. strange quark mass
QCD so that all strange hadron masses are in agreement with experiment.
3. FULL QeD SPECTRUM Before we start a full-scale full QCD simulation, we made a pilot study to investigate effects of improving lattice actions using four possible types of action combinations, the standard plaquette or a renormalization-group (RG) improved action for gluons, and the standard Wilson or the clover action for quarks. We find that the magnitude of scaling violation, or discretization errors, in the full QCD spectrum is significantly smaller for the combination of the RG action and the clover action. Therefore this action combination is employed for our systematic full QCD study. Our simulation is carried out for two flavors of dynamical quarks, to be identified with degenerate up and down quarks, with the mass in the range mq;c, 45 MeV. The strange quark is treated in the quenched approximation. We employ four lattice spacings in the range a = 0.22-0.09 fm and lattices with La ~ 2.5 fm, except 2.1 fm for the finest lattice. We observe effects of introducing dynamical quarks in the meson sector. In Fig.2, we compare meson masses. The most interesting feature is that mK* and m.p for full QCD extrapolate to values significantly closer to experiment than for quenched QCD. The remaining discrepancy might be due to the quenching effect of the strange quark. Results for baryon masses are less clear. The central values are in general closer to the experimental values. However, the errors are large so that we need much higher statistics. The lattice size La ~ 2.5 fm used may also be too small for baryons. In Fig.2, we cannot directly compare the quenched and full QCD data at finite lattice spacings since the lattice actions employed are different. We have started a study of the quenched spectrum using the same improved action as for full QCD, in order to make a point-by-point comparison. For preliminary results, see Ref.[4].
4. LIGHT QUARK MASSES In lattice QCD, quark mass can be defined from vector Ward identity(VWI) or axialvector Ward identity (AWl). As we show in Fig.3, values of quark mass in the two def-
972c
T. Yoshie/Nuclear Physics A663&664 (2000) 969c-972c
initions differ at finite lattice spacings, but they converge to a common value in the continuum limit. In full QCD, one can define the VWI quark mass either from the sea quark or from the valence quark in the presence of dynamical quarks. These quark masses also converge to a common value in the continuum limit. The fact that various definitions give a common value strengthens reliability of our analysis. The strange quark mass in quenched QCD depends on whether we choose ui« or m
5. U(l) PROBLEM IN FULL QCD In the course of our full QCD simulations, the U(1) problem is also investigated [5]. We measure the mass of "I = (U'Y5U + d'Y5d), ignoring mixing with "Is = 81'58. We find m'l = 863(86) MeV in the chiral and continuum limit, which lies close to the experimental value of m'l" Work to incorporate the mixing is in progress.
6. CONCLUSIONS In summary, we have observed a clear deviation of the quenched spectrum from experiment beyond 10% accuracy and indications that the discrepancy is reduced by introducing two light dynamical quarks. A small value of the strange quark mass rs 85 MeV we find in full QCD may have a significant implication for phenomenology of CP violation. All the results encourage us to perform works to unquench the strange quarks in the new future, which would lead us to first principles determinations of the spectrum and quark masses. I thank members of CP-PACS group for their collaboration. I am grateful to K.Kanaya and A.Ukawa for valuable suggestions on the manuscript. This work is supported in part by the Grant-in-Aid Nos. 08NPOl01 and 09304029 of Ministry of Education.
REFERENCES 1. 2. 3. 4. 5.
CP-PACS Collaboration, hep-Iat/9904012. CP-PACS Collaboration, hep-Iat/9902018; ibid. 9904003 and references theirin. GFll Collaboration, Nue!. Phys. B430 (1994) 179. CP-PACS Collaboration, talk presented by T. Kaneko at Lattice99. CP-PACS Collaboration, talk presented by R. Burkhalter at Lattice99.