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N. H. Christ

Publications and source records attributed to N. H. Christ.

At least 19 recordsLinked to original sources
arXiv2024

Workshop summary -- Kaons@CERN 2023

Kaon physics is at a turning point -- while the rare-kaon experiments NA62 and KOTO are in full swing, the end of their lifetime is approaching and the future experimental landscape needs to be defined. With HIKE, KOTO-II and LHCb-Phase-II on the table and under scrutiny, it is a very good moment in time to take stock and contemplate about the opportunities these experiments and theoretical developments provide for particle physics in the coming decade and beyond. This paper provides a compact summary of talks and discussions from the Kaons@CERN 2023 workshop.

hep-ph↗
arXiv2022

Lattice determination of $I= 0$ and 2 $ππ$ scattering phase shifts with a physical pion mass

Phase shifts for $s$-wave $ππ$ scattering in both the $I=0$ and $I=2$ channels are determined from a lattice QCD calculation performed on 741 gauge configurations obeying G-parity boundary conditions with a physical pion mass and lattice size of $32^3\times 64$. These results support our recent study of direct CP violation in $K\toππ$ decay \cite{Abbott:2020hxn}, improving our earlier 2015 calculation \cite{Bai:2015nea}. The phase shifts are determined for both stationary and moving $ππ$ systems, at three ($I=0$) and four ($I=2$) different total momenta. We implement several $ππ$ interpolating operators including a scalar bilinear "$σ$" operator and paired single-pion bilinear operators with the constituent pions carrying various relative momenta. Several techniques, including correlated fitting and a bootstrap determination of p-values have been used to refine the results and a comparison with the generalized eigenvalue problem (GEVP) method is given. A detailed systematic error analysis is performed which allows phase shift results to be presented at a fixed energy.

hep-lat↗
arXiv2016

Domain wall QCD with physical quark masses

We present results for several light hadronic quantities ($f_π$, $f_K$, $B_K$, $m_{ud}$, $m_s$, $t_0^{1/2}$, $w_0$) 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 $m_π$, $m_K$ and $m_Ω$ to determine the two quark masses and the scale - all other quantities are outputs from our simulations. We obtain results with sub-percent statistical errors and negligible chiral and finite-volume systematics for these light hadronic quantities, including: $f_π$ = 130.2(9) MeV; $f_K$ = 155.5(8) MeV; the average up/down quark mass and strange quark mass in the $\bar {\rm MS}$ scheme at 3 GeV, 2.997(49) and 81.64(1.17) MeV respectively; and the neutral kaon mixing parameter, $B_K$, in the RGI scheme, 0.750(15) and the $\bar{\rm MS}$ scheme at 3 GeV, 0.530(11).

hep-lat↗
arXiv2016

Erratum: Standard-model prediction for direct CP violation in $K\toππ$ decay

In this document we address an error discovered in the ensemble generation for our calculation of the $I=0$ $K\toππ$ amplitude (Phys. Rev. Lett. 115, 212001 (2015), arXiv:1505.07863) whereby the same random numbers were used for the two independent quark flavors, resulting in small but measurable correlations between gauge observables separated by 12 units in the y-direction. We conclude that the effects of this error are negligible compared to the overall errors on our calculation.

hep-lat↗
arXiv2016

Prospects for a lattice computation of rare kaon decay amplitudes: $K\toπ\ell^+\ell^-$ decays

The rare kaon decays $K\toπ\ell^+\ell^-$ and $K\toπν\barν$ are flavor changing neutral current (FCNC) processes and hence promising channels with which to probe the limits of the standard model and to look for signs of new physics. In this paper we demonstrate the feasibility of lattice calculations of $K\toπ\ell^+\ell^-$ decay amplitudes for which long-distance contributions are very significant. We show that the dominant finite-volume corrections (those decreasing as powers of the volume) are negligibly small and that, in the four-flavor theory, no new ultraviolet divergences appear as the electromagnetic current $J$ and the effective weak Hamiltonian $H_W$ approach each other. In addition, we demonstrate that one can remove the unphysical terms which grow exponentially with the range of the integration over the time separation between $J$ and $H_W$. We will now proceed to exploratory numerical studies with the aim of motivating further experimental measurements of these decays. Our work extends the earlier study by Isidori, Turchetti and Martinelli which focussed largely on the renormalization of ultraviolet divergences. In a companion paper we discuss the evaluation of the long-distance contributions to $K\toπν\barν$ decays; these contributions are expected to be at the level of a few percent for $K^+$ decays.

hep-lat↗
arXiv2016

Standard-model prediction for direct CP violation in $K\toππ$ decay

We report the first lattice QCD calculation of the complex kaon decay amplitude $A_0$ with physical kinematics, using a $32^3\times 64$ lattice volume and a single lattice spacing $a$, with $1/a= 1.3784(68)$ GeV. We find Re$(A_0) = 4.66(1.00)(1.26) \times 10^{-7}$ GeV and Im$(A_0) = -1.90(1.23)(1.08) \times 10^{-11}$ GeV, where the first error is statistical and the second systematic. The first value is in approximate agreement with the experimental result: Re$(A_0) = 3.3201(18) \times 10^{-7}$ GeV while the second can be used to compute the direct CP violating ratio Re$(\varepsilon'/\varepsilon)=1.38(5.15)(4.59)\times 10^{-4}$, which is $2.1σ$ below the experimental value $16.6(2.3)\times 10^{-4}$. The real part of $A_0$ is CP conserving and serves as a test of our method while the result for Re$(\varepsilon'/\varepsilon)$ provides a new test of the standard-model theory of CP violation, one which can be made more accurate with increasing computer capability.

hep-lat↗
arXiv2015

The Low Energy Constants of $SU(2)$ Partially Quenched Chiral Perturbation Theory from $N_{f}=2+1$ Domain Wall QCD

We have performed fits of the pseudoscalar masses and decay constants, from a variety of RBC-UKQCD 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. We conclude that, for the range of pseudoscalar masses explored in this work, $115~\mathrm{MeV} \lesssim m_{\rm PS} \lesssim 430~\mathrm{MeV}$, the NNLO $SU(2)$ expansion is quite robust and can fit lattice data with percent-scale accuracy.

hep-lat↗
arXiv2015

$K \rightarrow ππ$ $ΔI=3/2$ decay amplitude in the continuum limit

We present new results for the amplitude $A_2$ for a kaon to decay into two pions with isospin $I=2$: Re$A_2 = 1.50(4)_\mathrm{stat}(14)_\mathrm{syst}\times 10^{-8}$ GeV; Im$A_2 = -6.99(20)_\mathrm{stat}(84)_\mathrm{syst}\times 10^{-13}$ GeV. These results were obtained from two ensembles generated at physical quark masses (in the isospin limit) with inverse lattice spacings $a^{-1}=1.728(4)$ GeV and $2.358(7)$ GeV. We are therefore able to perform a continuum extrapolation and hence largely to remove the dominant systematic uncertainty from our earlier results, that due to lattice artefacts. The only previous lattice computation of $K\toππ$ decays at physical kinematics was performed using an ensemble at a single, rather coarse, value of the lattice spacing ($a^{-1}\simeq 1.37(1)$ GeV). We confirm the observation that there is a significant cancellation between the two dominant contributions to Re$A_2$ which we suggest is an important ingredient in understanding the $ΔI=1/2$ rule, Re$A_0$/Re$A_2\simeq 22.5$, where the subscript denotes the total isospin of the two-pion final state. Our result for $A_2$ implies that the electroweak penguin contribution to $ε^\prime/ε$ is Re($ε^\prime/ε)_\textrm{EWP}=-(6.6\pm 1.0)\times 10^{-4}$.

hep-lat↗
arXiv2014

$K_L-K_S$ mass difference from lattice QCD

We report on the first complete calculation of the $K_L-K_S$ mass difference, $ΔM_K$, using lattice QCD. The calculation is performed on a 2+1 flavor, domain wall fermion ensemble with a 330MeV pion mass and a 575 MeV kaon mass. We use a quenched charm quark with a 949 MeV mass to implement Glashow-Iliopoulos-Maiani cancellation. For these heavier-than-physical particle masses, we obtain $ΔM_K =3.19(41)(96)\times 10^{-12}$ MeV, quite similar to the experimental value. Here the first error is statistical and the second is an estimate of the systematic discretization error. An interesting aspect of this calculation is the importance of the disconnected diagrams, a dramatic failure of the OZI rule.

hep-lat↗
arXiv2014

Domain Wall QCD with Near-Physical Pions

We present physical results for a variety of light hadronic quantities obtained via a combined analysis of three 2+1 flavour domain wall fermion ensemble sets. For two of our ensemble sets we used the Iwasaki gauge action with beta=2.13 (a^-1=1.75(4) GeV) and beta=2.25 (a^-1=2.31(4) GeV) and lattice sizes of 24^3 x 64 and 32^3 x 64 respectively, with unitary pion masses in the range 293(5)-417(10) MeV. The extent L_s for the 5^th dimension of the domain wall fermion formulation is L_s=16 in these ensembles. In this analysis we include a third ensemble set that makes use of the novel Iwasaki+DSDR (Dislocation Suppressing Determinant Ratio) gauge action at beta = 1.75 (a^-1=1.37(1) GeV) with a lattice size of 32^3 x 64 and L_s=32 to reach down to partially-quenched pion masses as low as 143(1) MeV and a unitary pion mass of 171(1) MeV, while retaining good chiral symmetry and topological tunneling. We demonstrate a significant improvement in our control over the chiral extrapolation, resulting in much improved continuum predictions for the above quantities. The main results of this analysis include the pion and kaon decay constants, f_π=127(3)_{stat}(3)_{sys} MeV and f_K = 152(3)_{stat}(2)_{sys} MeV respectively (f_K/f_π= 1.199(12)_{stat}(14)_{sys}); the average up/down quark mass and the strange-quark mass in the MSbar-scheme at 3 GeV, m_{ud}(MSbar, 3 GeV) = 3.05(8)_{stat}(6)_{sys} MeV and m_s(MSbar, 3 GeV) = 83.5(1.7)_{stat}(1.1)_{sys}; the neutral kaon mixing parameter in the MSbar-scheme at 3 GeV, B_K(MSbar,3 GeV) = 0.535(8)_{stat}(13)_{sys}, and in the RGI scheme, \hat B_K = 0.758(11)_{stat}(19)_{sys}; and the Sommer scales r_1 = 0.323(8)_{stat}(4)_{sys} fm and r_0 = 0.480(10)_{stat}(4)_{sys} (r_1/r_0 = 0.673(11)_{stat}(3)_{sys}). We also obtain values for the SU(2) ChPT effective couplings, \bar{l_3} = 2.91(23)_{stat}(7)_{sys}$ and \bar{l_4} = 3.99(16)_{stat}(9)_{sys}.

hep-lat↗
arXiv2014

Finite-volume effects in the evaluation of the K_L - K_S mass difference

The RBC and UKQCD collaborations have recently proposed a procedure for computing the K_L-K_S mass difference. A necessary ingredient of this procedure is the calculation of the (non-exponential) finite-volume corrections relating the results obtained on a finite lattice to the physical values. This requires a significant extension of the techniques which were used to obtain the Lellouch-Luscher factor, which contains the finite-volume corrections in the evaluation of non-leptonic kaon decay amplitudes. We review the status of our study of this issue and, although a complete proof is still being developed, suggest the form of these corrections for general volumes and a strategy for taking the infinite-volume limit. The general result reduces to the known corrections in the special case when the volume is tuned so that there is a two-pion state degenerate with the kaon.

hep-lat↗
arXiv2013

Long distance contribution to the $K_L-K_S$ mass difference

We develop and demonstrate techniques needed to compute the long distance contribution to the $K_{L}$-$K_{S}$ mass difference, $ΔM_K$, in lattice QCD and carry out a first, exploratory calculation of this fundamental quantity. The calculation is performed on 2+1 flavor, domain wall fermion, $16^3\times32$ configurations with a 421 MeV pion mass and an inverse lattice spacing $1/a=1.73$ GeV. We include only current-current operators and drop all disconnected and double penguin diagrams. The short distance part of the mass difference in a 2+1 flavor calculation contains a quadratic divergence cut off by the lattice spacing. Here, this quadratic divergence is eliminated through the GIM mechanism by introducing a valence charm quark. The inclusion of the charm quark makes the complete calculation accessible to lattice methods provided the discretization errors associated with the charm quark can be controlled. The long distance effects are discussed for each parity channel separately. While we can see a clear signal in the parity odd channel, the signal to noise ratio in the parity even channel is exponentially decreasing as the separation between the two weak operators increases. We obtain a mass difference $ΔM_K$ which ranges from $6.58(30)\times 10^{-12}$ MeV to $11.89(81)\times 10^{-12}$ MeV for kaon masses varying from 563 MeV to 839 MeV. Extensions of these methods are proposed which promise accurate results for both $ΔM_K$ and $ε_K$, including long distance effects.

hep-lat↗
arXiv2013

Determination of the $A_2$ amplitude of $K \rightarrow ππ$ decays

We review the status of recent calculations by the RBC-UKQCD collaboration of the complex amplitude $A_2$, corresponding to the decay of a kaon to a two pion state with total isospin 2. In particular, we present preliminary results from two new ensembles: $48^3 \times 96$ with $a^{-1}=1.73$ GeV and $64^3 \times 128$ with $a^{-1}=2.3$ GeV, both at physical kinematics. Both ensembles were generated Iwasaki gauge action and domain wall fermion action with 2+1 flavours. These results, in comparison to our earlier ones on a $32^3$ DSDR lattice with $a^{-1}=1.36$ GeV, enable us to significantly reduce the discretization errors. The partial cancellation between the two dominant contractions contributing to Re($A_2$) has been confirmed and we believe that this cancellation is a major contribution to the $ΔI=1/2$ rule.

hep-lat↗
arXiv2013

Emerging understanding of the ΔI = 1/2 Rule from Lattice QCD

There has been much speculation as to the origin of the ΔI = 1/2 rule (Re A_0/Re A_2 \simeq 22.5). We find that the two dominant contributions to the ΔI=3/2, K \to ππ correlation functions have opposite signs leading to a significant cancellation. This partial cancellation occurs in our computation of Re A_2 with physical quark masses and kinematics (where we reproduce the experimental value of A_2) and also for heavier pions at threshold. For Re A_0, although we do not have results at physical kinematics, we do have results for pions at zero-momentum with m_π \simeq 420 MeV (Re A_0/Re A_2=9.1(2.1)) and m_π \simeq 330 MeV (Re A_0/Re A_2=12.0(1.7)). The contributions which partially cancel in Re A_2 are also the largest ones in Re A_0, 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 Re A_2 through the cancellation of the two dominant contributions and the corresponding enhancement of Re A_0. QCD and EWP penguin operators make only very small contributions at such scales.

hep-lat↗
arXiv2012

Lattice determination of the $K \to (ππ)_{I=2}$ Decay Amplitude $A_2$

We describe the computation of the amplitude A_2 for a kaon to decay into two pions with isospin I=2. The results presented in the letter Phys.Rev.Lett. 108 (2012) 141601 from an analysis of 63 gluon configurations are updated to 146 configurations giving Re$A_2=1.381(46)_{\textrm{stat}}(258)_{\textrm{syst}} 10^{-8}$ GeV and Im$A_2=-6.54(46)_{\textrm{stat}}(120)_{\textrm{syst}}10^{-13}$ GeV. Re$A_2$ is in good agreement with the experimental result, whereas the value of Im$A_2$ was hitherto unknown. We are also working towards a direct computation of the $K\to(ππ)_{I=0}$ amplitude $A_0$ but, within the standard model, our result for Im$A_2$ can be combined with the experimental results for Re$A_0$, Re$A_2$ and $ε^\prime/ε$ to give Im$A_0/$Re$A_0= -1.61(28)\times 10^{-4}$ . Our result for Im\,$A_2$ implies that the electroweak penguin (EWP) contribution to $ε^\prime/ε$ is Re$(ε^\prime/ε)_{\mathrm{EWP}} = -(6.25 \pm 0.44_{\textrm{stat}} \pm 1.19_{\textrm{syst}}) \times 10^{-4}$.

hep-lat↗
arXiv2012

The chiral transition and U(1)_A symmetry restoration from lattice QCD using Domain Wall Fermions

We present results on both the restoration of the spontaneously broken chiral symmetry and the effective restoration of the anomalously broken U(1)_A symmetry in finite temperature QCD at zero chemical potential using lattice QCD. We employ domain wall fermions on lattices with fixed temporal extent N_τ= 8 and spatial extent N_σ= 16 in a temperature range of T = 139 - 195 MeV, corresponding to lattice spacings of a \approx 0.12 - 0.18 fm. In these calculations, we include two degenerate light quarks and a strange quark at fixed pion mass m_π= 200 MeV. The strange quark mass is set near its physical value. We also present results from a second set of finite temperature gauge configurations at the same volume and temporal extent with slightly heavier pion mass. To study chiral symmetry restoration, we calculate the chiral condensate, the disconnected chiral susceptibility, and susceptibilities in several meson channels of different quantum numbers. To study U(1)_A restoration, we calculate spatial correlators in the scalar and pseudo-scalar channels, as well as the corresponding susceptibilities. Furthermore, we also show results for the eigenvalue spectrum of the Dirac operator as a function of temperature, which can be connected to both U(1)_A and chiral symmetry restoration via Banks-Casher relations.

hep-lat↗
arXiv2012

Fundamental Physics at the Intensity Frontier

The Proceedings of the 2011 workshop on Fundamental Physics at the Intensity Frontier. Science opportunities at the intensity frontier are identified and described in the areas of heavy quarks, charged leptons, neutrinos, proton decay, new light weakly-coupled particles, and nucleons, nuclei, and atoms.

hep-ex↗