The axial coupling of the nucleon, g
, is the strength of its coupling to the weak axial current of the standard model of particle physics, in much the same way as the electric charge is the strength ...of the coupling to the electromagnetic current. This axial coupling dictates the rate at which neutrons decay to protons, the strength of the attractive long-range force between nucleons and other features of nuclear physics. Precision tests of the standard model in nuclear environments require a quantitative understanding of nuclear physics that is rooted in quantum chromodynamics, a pillar of the standard model. The importance of g
makes it a benchmark quantity to determine theoretically-a difficult task because quantum chromodynamics is non-perturbative, precluding known analytical methods. Lattice quantum chromodynamics provides a rigorous, non-perturbative definition of quantum chromodynamics that can be implemented numerically. It has been estimated that a precision of two per cent would be possible by 2020 if two challenges are overcome
: contamination of g
from excited states must be controlled in the calculations and statistical precision must be improved markedly
. Here we use an unconventional method
inspired by the Feynman-Hellmann theorem that overcomes these challenges. We calculate a g
value of 1.271 ± 0.013, which has a precision of about one per cent.
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.
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).
Observation of neutrinoless double beta decay, a lepton number violating process that has been proposed to clarify the nature of neutrino masses, has spawned an enormous world-wide experimental ...effort. Relating nuclear decay rates to high-energy, beyond the standard model (BSM) physics requires detailed knowledge of nonperturbative QCD effects. Using lattice QCD, we compute the necessary matrix elements of short-range operators, which arise due to heavy BSM mediators, that contribute to this decay via the leading order π^{-}→π^{+} exchange diagrams. Utilizing our result and taking advantage of effective field theory methods will allow for model-independent calculations of the relevant two-nucleon decay, which may then be used as input for nuclear many-body calculations of the relevant experimental decays. Contributions from short-range operators may prove to be equally important to, or even more important than, those from long-range Majorana neutrino exchange.
There has been much speculation as to the origin of the ΔI=1/2 rule (ReA0/ReA2≃22.5). We find that the two dominant contributions to the ΔI=3/2, K→ππ correlation functions have opposite signs, ...leading to a significant cancelation. This partial cancelation occurs in our computation of ReA2 with physical quark masses and kinematics (where we reproduce the experimental value of A2) and also for heavier pions at threshold. For ReA0, although we do not have results at physical kinematics, we do have results for pions at zero momentum with mπ≃420 MeV ReA0/ReA2=9.1(2.1) and mπ≃330 MeV ReA0/ReA2=12.0(1.7). The contributions which partially cancel in ReA2 are also the largest ones in ReA0, but now they have the same sign and so enhance this amplitude. The emerging explanation of the ΔI=1/2 rule is a combination of the perturbative running to scales of O(2 GeV), a relative suppression of ReA2 through the cancelation of the two dominant contributions, and the corresponding enhancement of ReA0. QCD and electroweak penguin operators make only very small contributions at such scales.
We report on the first realistic ab initio calculation of a hadronic weak decay, that of the amplitude A(2) for a kaon to decay into two π mesons with isospin 2. We find ...ReA(2)=(1.436±0.063(stat)±0.258(syst))10(-8) GeV in good agreement with the experimental result and for the hitherto unknown imaginary part we find ImA(2)=-(6.83±0.51(stat)±1.30(syst))10(-13) GeV. Moreover combining our result for ImA(2) with experimental values of ReA(2), ReA(0), and ε'/ε, we obtain the following value for the unknown ratio ImA(0)/ReA(0) within the standard model: ImA(0)/ReA(0)=-1.63(19)(stat)(20(syst)×10(-4). One consequence of these results is that the contribution from ImA(2) to the direct CP violation parameter ε' (the so-called Electroweak Penguin contribution) is Re(ε'/ε)(EWP)=-(6.52±0.49(stat)±1.24(syst))×10(-4). We explain why this calculation of A(2) represents a major milestone for lattice QCD and discuss the exciting prospects for a full quantitative understanding of CP violation in kaon decays.
A
bstract
We present a new calculation of the
K
→ π semileptonic form factor at zero momentum transfer in domain wall lattice QCD with
N
f
= 2+1 dynamical quark flavours. By using partially twisted ...boundary conditions we simulate directly at the phenomenologically relevant point of zero momentum transfer. We perform a joint analysis for all available ensembles which include three different lattice spacings (
a
= 0.09 – 0.14 fm), large physical volumes (
m
π
L >
3
.
9) and pion masses as low as 171 MeV. The comprehensive set of simulation points allows for a detailed study of systematic effects leading to the prediction
, where the first error is statistical and the second error systematic. The result allows us to extract the CKM-matrix element
and confirm first-row CKM-unitarity in the Standard Model at the sub per mille level.
Here, we have performed fits of the pseudoscalar masses and decay constants, from a variety of the RBC-UKQCD Collaboration’s domain wall fermion ensembles, to SU(2) partially quenched chiral ...perturbation theory at next-to-leading order (NLO) and next-to-next-to-leading order (NNLO). We report values for 9 NLO and 8 linearly independent combinations of NNLO partially quenched low-energy constants, which we compare to other lattice and phenomenological determinations. We discuss the size of successive terms in the chiral expansion and use our large set of low-energy constants to make predictions for mass splittings due to QCD isospin-breaking effects and the S-wave ππ scattering lengths. Lastly, we conclude that, for the range of pseudoscalar masses explored in this work, 115 MeV≲mPS≲430 MeV, the NNLO SU(2) expansion is quite robust and can fit lattice data with percent-scale accuracy.
We report on the first realistic ab initio calculation of a hadronic weak decay, that of the amplitude A2 for a kaon to decay into two π mesons with isospin 2. We find ...ReA2=(1.436±0.063stat±0.258syst)10-8 GeV in good agreement with the experimental result and for the hitherto unknown imaginary part we find ImA2=-(6.83±0.51stat±1.30syst)10-13 GeV. Moreover combining our result for ImA2 with experimental values of ReA2, ReA0, and ϵ'/ϵ, we obtain the following value for the unknown ratio ImA0/ReA0 within the standard model: ImA0/ReA0=-1.63(19)stat(20)syst×10-4. One consequence of these results is that the contribution from ImA2 to the direct CP violation parameter ϵ' (the so-called Electroweak Penguin contribution) is Re(ϵ'/ϵ)EWP=-(6.52±0.49stat±1.24syst)×10-4. We explain why this calculation of A2 represents a major milestone for lattice QCD and discuss the exciting prospects for a full quantitative understanding of CP violation in kaon decays.
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