Equation of state in ( 2 + 1 )-flavor QCD Bazavov, A.; Bhattacharya, Tanmoy; DeTar, C. ...
Physical review. D, Particles, fields, gravitation, and cosmology,
11/2014, Volume:
90, Issue:
9
Journal Article
Peer reviewed
Open access
We present results for the equation of state in (2 + 1)-flavor QCD using the highly improved staggered quark action and lattices with temporal extent N sub(tau) = 6, 8, 10, and 12. We show that these ...data can be reliably extrapolated to the continuum limit and obtain a number of thermodynamic quantities and the speed of sound in the temperature range 130-400 MeV. We compare our results with previous calculations and provide an analytic parameterization of the pressure, from which other thermodynamic quantities can be calculated, for use in phenomenology. We show that the energy density in the crossover region, 145 MeV < or = T < or = 163 MeV, defined by the chiral transition, is varepsilonc = (0.18-0.5) GeV /fm super(3), i.e., (1.2-3.1) varepsilon sub(nuclear). At high temperatures, we compare our results with resummed and dimensionally reduced perturbation theory calculations. As a byproduct of our analyses, we obtain the values of the scale parameters r sub(0) from the static quark potential and w sub(0) from the gradient flow.
FLAG Review 2019 Aoki, S; Aoki, Y; Bečirević, D ...
The European physical journal. C, Particles and fields,
02/2020, Volume:
80, Issue:
2
Journal Article
Peer reviewed
Open access
We review lattice results related to pion, kaon, D-meson, B-meson, and nucleon physics with the aim of making them easily accessible to the nuclear and particle physics communities. More ...specifically, we report on the determination of the light-quark masses, the form factor f+(0) arising in the semileptonic K→π transition at zero momentum transfer, as well as the decay constant ratio fK/fπ and its consequences for the CKM matrix elements Vus and Vud. Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of SU(2)L×SU(2)R and SU(3)L×SU(3)R Chiral Perturbation Theory. We review the determination of the BK parameter of neutral kaon mixing as well as the additional four B parameters that arise in theories of physics beyond the Standard Model. For the heavy-quark sector, we provide results for mc and mb as well as those for D- and B-meson decay constants, form factors, and mixing parameters. These are the heavy-quark quantities most relevant for the determination of CKM matrix elements and the global CKM unitarity-triangle fit. We review the status of lattice determinations of the strong coupling constant αs. Finally, in this review we have added a new section reviewing results for nucleon matrix elements of the axial, scalar and tensor bilinears, both isovector and flavor diagonal.
FLAG Review 2021 Aoki, Y.; Blum, T.; Colangelo, G. ...
The European physical journal. C, Particles and fields,
10/2022, Volume:
82, Issue:
10
Journal Article
Peer reviewed
Open access
We review lattice results related to pion, kaon,
D
-meson,
B
-meson, and nucleon physics with the aim of making them easily accessible to the nuclear and particle physics communities. More ...specifically, we report on the determination of the light-quark masses, the form factor
f
+
(
0
)
arising in the semileptonic
K
→
π
transition at zero momentum transfer, as well as the decay constant ratio
f
K
/
f
π
and its consequences for the CKM matrix elements
V
us
and
V
ud
. Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of
S
U
(
2
)
L
×
S
U
(
2
)
R
and
S
U
(
3
)
L
×
S
U
(
3
)
R
Chiral Perturbation Theory. We review the determination of the
B
K
parameter of neutral kaon mixing as well as the additional four
B
parameters that arise in theories of physics beyond the Standard Model. For the heavy-quark sector, we provide results for
m
c
and
m
b
as well as those for the decay constants, form factors, and mixing parameters of charmed and bottom mesons and baryons. These are the heavy-quark quantities most relevant for the determination of CKM matrix elements and the global CKM unitarity-triangle fit. We review the status of lattice determinations of the strong coupling constant
α
s
. We consider nucleon matrix elements, and review the determinations of the axial, scalar and tensor bilinears, both isovector and flavor diagonal. Finally, in this review we have added a new section reviewing determinations of scale-setting quantities.
We calculate the up-, down-, strange-, charm-, and bottom-quark masses using the MILC highly improved staggered-quark ensembles with four flavors of dynamical quarks. We use ensembles at six lattice ...spacings ranging from a≈0.15 to 0.03 fm and with both physical and unphysical values of the two light and the strange sea-quark masses. We use a new method based on heavy-quark effective theory (HQET) to extract quark masses from heavy-light pseudoscalar meson masses. Combining our analysis with our separate determination of ratios of light-quark masses we present masses of the up, down, strange, charm, and bottom quarks. Our results for the MS¯-renormalized masses are mu(2 GeV)=2.130(41) MeV, md(2 GeV)=4.675(56) MeV, ms(2 GeV)=92.47(69) MeV, mc(3 GeV)=983.7(5.6) MeV, and mc(mc)=1273(10) MeV, with four active flavors; and mb(mb)=4195(14) MeV with five active flavors. We also obtain ratios of quark masses mc/ms=11.783(25), mb/ms=53.94(12), and mb/mc=4.578(8). The result for mc matches the precision of the most precise calculation to date, and the other masses and all quoted ratios are the most precise to date. Moreover, these results are the first with a perturbative accuracy of αs4. As byproducts of our method, we obtain the matrix elements of HQET operators with dimension 4 and 5: Λ¯MRS=555(31) MeV in the minimal renormalon-subtracted (MRS) scheme, μπ2=0.05(22) GeV2, and μG2(mb)=0.38(2) GeV2. The MRS scheme Phys. Rev. D 97, 034503 (2018) is the key new aspect of our method.
We review lattice results related to pion, kaon, D- and B-meson physics with the aim of making them easily accessible to the particle-physics community. More specifically, we report on the ...determination of the light-quark masses, the form factor \f_+(0)\, arising in the semileptonic \K \rightarrow \pi \ transition at zero momentum transfer, as well as the decay constant ratio \f_K/f_\pi \ and its consequences for the CKM matrix elements \V_{us}\ and \V_{ud}\. Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of \SU(2)_L\times SU(2)_R\ and \SU(3)_L\times SU(3)_R\ Chiral Perturbation Theory. We review the determination of the \B_K\ parameter of neutral kaon mixing as well as the additional four B parameters that arise in theories of physics beyond the Standard Model. The latter quantities are an addition compared to the previous review. For the heavy-quark sector, we provide results for \m_c\ and \m_b\ (also new compared to the previous review), as well as those for D- and B-meson-decay constants, form factors, and mixing parameters. These are the heavy-quark quantities most relevant for the determination of CKM matrix elements and the global CKM unitarity-triangle fit. Finally, we review the status of lattice determinations of the strong coupling constant \\alpha _s\.
FLAG Review 2019 Aoki, S.; Aoki, Y.; Bečirević, D. ...
The European physical journal. C, Particles and fields,
02/2020, Volume:
80, Issue:
2
Journal Article
Peer reviewed
Open access
We review lattice results related to pion, kaon,
D
-meson,
B
-meson, and nucleon physics with the aim of making them easily accessible to the nuclear and particle physics communities. More ...specifically, we report on the determination of the light-quark masses, the form factor
f
+
(
0
)
arising in the semileptonic
K
→
π
transition at zero momentum transfer, as well as the decay constant ratio
f
K
/
f
π
and its consequences for the CKM matrix elements
V
us
and
V
ud
. Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of
S
U
(
2
)
L
×
S
U
(
2
)
R
and
S
U
(
3
)
L
×
S
U
(
3
)
R
Chiral Perturbation Theory. We review the determination of the
B
K
parameter of neutral kaon mixing as well as the additional four
B
parameters that arise in theories of physics beyond the Standard Model. For the heavy-quark sector, we provide results for
m
c
and
m
b
as well as those for
D
- and
B
-meson decay constants, form factors, and mixing parameters. These are the heavy-quark quantities most relevant for the determination of CKM matrix elements and the global CKM unitarity-triangle fit. We review the status of lattice determinations of the strong coupling constant
α
s
. Finally, in this review we have added a new section reviewing results for nucleon matrix elements of the axial, scalar and tensor bilinears, both isovector and flavor diagonal.
We calculate the leptonic decay constants of heavy-light pseudoscalar mesons with charm and bottom quarks in lattice quantum chromodynamics on four-flavor QCD gauge-field configurations with ...dynamical u, d, s, and c quarks. We analyze over twenty isospin-symmetric ensembles with six lattice spacings down to a≈0.03 fm and several values of the light-quark mass down to the physical value 12(mu+md). We employ the highly-improved staggered-quark (HISQ) action for the sea and valence quarks; on the finest lattice spacings, discretization errors are sufficiently small that we can calculate the B-meson decay constants with the HISQ action for the first time directly at the physical b-quark mass. We obtain the most precise determinations to-date of the D- and B-meson decay constants and their ratios, fD+=212.7(0.6) MeV, fDs=249.9(0.4) MeV, fDs/fD+=1.1749(16), fB+=189.4(1.4) MeV, fBs=230.7(1.3) MeV, fBs/fB+=1.2180(47), where the errors include statistical and all systematic uncertainties. Our results for the B-meson decay constants are three times more precise than the previous best lattice-QCD calculations, and bring the QCD errors in the standard model predictions for the rare leptonic decays B¯(Bs→μ+μ−)=3.64(11)×10−9, B¯(B0→μ+μ−)=1.00(3)×10−11, and B¯(B0→μ+μ−)/B¯(Bs→μ+μ−)=0.00264(8) to well below other sources of uncertainty. As a byproduct of our analysis, we also update our previously published results for the light-quark-mass ratios and the scale-setting quantities fp4s, Mp4s, and Rp4s. We obtain the most precise lattice-QCD determination to date of the ratio fK+/fπ+=1.1950( −23+16) MeV.
We report on a scale determination with gradient-flow techniques on the N sub(functionof)=2+1+1 highly improved staggered quark ensembles generated by the MILC Collaboration. The ensembles include ...four lattice spacings, ranging from approximately 0.15 to 0.06 fm, and both physical and unphysical values of the quark masses. The scales radicalt sub(0)/a and w sub(0)/a and their tree-level improvements, radicalt sub(0,imp) and w sub(0,imp), are computed on each ensemble using Symanzik flow and the cloverleaf definition of the energy density E. Using a combination of continuum chiral-perturbation theory and a Taylor-series ansatz for the lattice-spacing and strong-coupling dependence, the results are simultaneously extrapolated to the continuum and interpolated to physical quark masses. We determine the scales (ProQuest: Formulae and/or non-USASCII text omitted)and (ProQuest: Formulae and/or non-USASCII text omitted), where the errors are sums, in quadrature, of statistical and all systematic errors. The precision of w sub(0) and radicalt sub(0) is comparable to or more precise than the best previous estimates, respectively. We then find the continuum mass dependence of radicalt sub(0) and w sub(0), which will be useful for estimating the scales of new ensembles. We also estimate the integrated autocorrelation length of left angle bracketE(t)right angle bracket. For long flow times, the autocorrelation length of left angle bracketEright angle bracket appears to be comparable to that of the topological charge.
We present a lattice calculation of the electromagnetic (EM) effects on the masses of light pseudoscalar mesons. The simulations employ 2+1 dynamical flavors of asqtad QCD quarks and quenched ...photons. Lattice spacings vary from ≈0.12 fm to ≈0.045 fm. We compute the quantity ε, which parametrizes the corrections to Dashen’s theorem for the K+–K0 EM mass splitting, as well as εK0, which parametrizes the EM contribution to the mass of the K0 itself. An extension of the nonperturbative EM renormalization scheme introduced by the BMW group is used in separating EM effects from isospin-violating quark mass effects. We correct for leading finite-volume effects in our realization of lattice electrodynamics in chiral perturbation theory, and remaining finite-volume errors are relatively small. While electroquenched effects are under control for ε, they are estimated only qualitatively for εK0 and constitute one of the largest sources of uncertainty for that quantity. We find ε=0.78(1)stat(+8−11)syst and εK0=0.035(3)stat(20)syst. We then use these results on 2+1+1 flavor pure QCD highly improved staggered quark (HISQ) ensembles and find mu/md=0.4529(48)stat(+150−67)syst.
We review lattice results related to pion, kaon,
D
- and
B
-meson physics with the aim of making them easily accessible to the particle-physics community. More specifically, we report on the ...determination of the light-quark masses, the form factor
f
+
(
0
)
, arising in the semileptonic
K
→
π
transition at zero momentum transfer, as well as the decay constant ratio
f
K
/
f
π
and its consequences for the CKM matrix elements
V
u
s
and
V
u
d
. Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of
S
U
(
2
)
L
×
S
U
(
2
)
R
and
S
U
(
3
)
L
×
S
U
(
3
)
R
Chiral Perturbation Theory. We review the determination of the
B
K
parameter of neutral kaon mixing as well as the additional four
B
parameters that arise in theories of physics beyond the Standard Model. The latter quantities are an addition compared to the previous review. For the heavy-quark sector, we provide results for
m
c
and
m
b
(also new compared to the previous review), as well as those for
D
- and
B
-meson-decay constants, form factors, and mixing parameters. These are the heavy-quark quantities most relevant for the determination of CKM matrix elements and the global CKM unitarity-triangle fit. Finally, we review the status of lattice determinations of the strong coupling constant
α
s
.
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