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.
We report on the first lattice calculation of the QCD phase transition using chiral fermions with physical quark masses. This calculation uses 2+1 quark flavors, spatial volumes between (4 fm)(3) and ...(11 fm)(3) and temperatures between 139 and 196 MeV. Each temperature is calculated at a single lattice spacing corresponding to a temporal Euclidean extent of N(t) = 8. The disconnected chiral susceptibility, χ(disc) shows a pronounced peak whose position and height depend sensitively on the quark mass. We find no metastability near the peak and a peak height which does not change when a 5 fm spatial extent is increased to 10 fm. Each result is strong evidence that the QCD "phase transition" is not first order but a continuous crossover for m(π) = 135 MeV. The peak location determines a pseudocritical temperature T(c) = 155(1)(8) MeV, in agreement with earlier staggered fermion results. However, the peak height is 50% greater than that suggested by previous staggered results. Chiral SU(2)(L) × SU(2)(R) symmetry is fully restored above 164 MeV, but anomalous U(1)(A) symmetry breaking is nonzero above T(c) and vanishes as T is increased to 196 MeV.
We present a lattice QCD calculation of the ΔI = 1/2, K → π π decay amplitude A 0 and ϵ ′, the measure of direct C P violation in K → π π decay, improving our 2015 calculation 1 of these quantities. ...Both calculations were performed with physical kinematics on a 323 × 64 lattice with an inverse lattice spacing of a−1 = 1.3784(68) GeV . However, the current calculation includes nearly 4 times the statistics and numerous technical improvements allowing us to more reliably isolate the π π ground state and more accurately relate the lattice operators to those defined in the standard model. We find Re(A0) = 2.99(0.32)(0.59) × 10−7 GeV and Im(A0) = − 6.98(0.62)(1.44) × 10−11 GeV, where the errors are statistical and systematic, respectively. The former agrees well with the experimental result Re(A0) = 3.3201(18) × 10−7 GeV . These results for A0 can be combined with our earlier lattice calculation of A2 2 to obtain Re(ϵ′/ϵ) = 21.7(2.6)(6.2)(5.0) × 10−4, where the third error represents omitted isospin breaking effects, and Re(A0) / Re(A2) = 19.9(2.3)(4.4). The first agrees well with the experimental result of Re(ϵ′/ϵ) = 16.6(2.3) × 10−4. A comparison of the second with the observed ratio Re(A0) / Re(A2) = 22.45(6), demonstrates the standard model origin of this " ΔI = 1/2 rule" enhancement.
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\.
We present results for several light hadronic quantities (f sub(pi), f sub(K), B sub(K), m sub(ud), m sub(s), t super(1/2) sub(0), w sub(0)) obtained from simulations of 2+1 flavor domain wall ...lattice QCD with large physical volumes and nearly physical pion masses at two lattice spacings. We perform a short, O(3)%, extrapolation in pion mass to the physical values by combining our new data in a simultaneous chiral/continuum "global fit" with a number of other ensembles with heavier pion masses. We use the physical values of m sub(pi), m sub(K) and m sub(Omega) to determine the two quark masses and the scale-all other quantities are outputs from our simulations. We obtain results with subpercent statistical errors and negligible chiral and finite-volume systematics for these light hadronic quantities, including f sub(pi)=130.2(9)MeV; f sub(K)=155.5(8)MeV; the average up/down quark mass and strange quark mass in the MS scheme at 3 GeV, 2.997(49) and 81.64(1.17) MeV respectively; and the neutral kaon mixing parameter, BK, in the renormalization group invariant scheme, 0.750(15) and the MS scheme at 3 GeV, 0.530(11).
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 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
.
We report the first lattice QCD calculation of the complex kaon decay amplitude A_{0} with physical kinematics, using a 32³×64 lattice volume and a single lattice spacing a, with 1/a=1.3784(68) GeV. ...We find Re(A_{0})=4.66(1.00)(1.26)×10(-7) GeV and Im(A_{0})=-1.90(1.23)(1.08)×10(-11) GeV, where the first error is statistical and the second systematic. The first value is in approximate agreement with the experimental result: Re(A_{0})=3.3201(18)×10(-7) GeV, while the second can be used to compute the direct CP-violating ratio Re(ϵ^{'}/ϵ)=1.38(5.15)(4.59)×10^{-4}, which is 2.1σ below the experimental value 16.6(2.3)×10(-4). The real part of A_{0} is CP conserving and serves as a test of our method while the result for Re(ϵ^{'}/ϵ) provides a new test of the standard model theory of CP violation, one which can be made more accurate with increasing computer capability.
Lattice QCD calculations including the effects of one or more nondegenerate sea quark flavors are conventionally performed using the rational hybrid Monte Carlo (RHMC) algorithm, which computes the ...square root of the determinant of D†D, where D is the Dirac operator. The special case of two degenerate quark flavors with the same mass is described directly by the determinant of D†D-in particular, no square root is necessary-enabling a variety of algorithmic developments, which have driven down the cost of simulating the light (up and down) quarks in the isospin-symmetric limit of equal masses. As a result, the relative cost of single quark flavors-such as the strange or charm-computed with RHMC has become more expensive. This problem is even more severe in the context of our measurements of the ΔI=1/2 K→ππ matrix elements on lattice ensembles with G-parity boundary conditions, since G-parity is associated with a doubling of the number of quark flavors described by D, and thus RHMC is needed for the isospin-symmetric light quarks as well. In this paper we report on our implementation of the exact one flavor algorithm (EOFA) introduced by the TWQCD Collaboration for simulations including single flavors of domain wall quarks. We have developed a new preconditioner for the EOFA Dirac equation, which both reduces the cost of solving the Dirac equation and allows us to reuse the bulk of our existing high-performance code. Coupling these improvements with careful tuning of our integrator, the time per accepted trajectory in the production of our 2+1 flavor G-parity ensembles with physical pion and kaon masses has been decreased by a factor of 4.2.
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