Twisted Mass QCD Research Articles

Logarithmic corrections to O(a) and O(a^2) effects in lattice QCD with Wilson or Ginsparg–Wilson quarks

We derive the asymptotic lattice spacing dependence a^n[2b_0bar{g}^2(1/a)]^{hat{Gamma }_i} relevant for spectral quantities of lattice QCD, when using Wilson, textrm{O}(a) improved Wilson or Ginsparg–Wilson quarks. We give some examples for the spectra encountered for hat{Gamma }_i including the partially quenched case, mixed actions and using two different discretisations for dynamical quarks. This also includes maximally twisted mass QCD relying on automatic textrm{O}(a) improvement. At textrm{O}(a^2), all cases considered have min _ihat{Gamma }_igtrsim -0.3 if N_{textrm{f}}le 4, which ensures that the leading order lattice artifacts are not severely logarithmically enhanced in contrast to the O(3) non-linear sigma model (Balog et al. in Nucl Phys B 824:563–615, 2010; Balog et al. in Phys Lett B 676:188–192, 2009). However, we find a very dense spectrum of these leading powers, which may result in major pile-ups and cancellations. We present in detail the computational strategy employed to obtain the 1-loop anomalous dimensions already used in Husung et al. (Phys Lett B 829:137069, 2022).

Non-leptonic kaon decays at large Nc

We study the scaling with the number of colors Nc of the weak amplitudes mediating kaon mixing and decay, in the limit of light charm masses (mu = md = ms = mc). The amplitudes are extracted directly on the lattice for Nc = 3 - 7 (with preliminar results for Nc = 8 and 17) using twisted mass QCD. It is shown that the (sub-leading) 1 /Nc corrections to [see formula in PDF] are small and that the naive Nc → ∞ limit, [see formula in PDF] = 3/4, seems to be recovered. On the other hand, the O (1/Nc) corrections in K → ππ amplitudes (derived from K → π matrix elements) are large and fully anti-correlated in the I = 0 and I = 2 channels. This may have some implications for the understanding of the ΔI = 1/2 rule.

Charmonia decay constants from the QCD lattice and QCD sum rules

Using lattice QCD and QCD sum rules we compute the lowest state charmonia JPC=0−+(ηc), 1−(J/ψ), and 1+−(hc) decay constants. For calculating the decay constant of J/ψ we use both the vector and tensor currents and compare the results. Lattice QCD results are obtained from the unquenched (Nf=2) simulations using twisted mass QCD at four lattice spacings and taking the continuum limit. In the QCD sum rule calculation we apply the moment sum rules. We also comment the phenomenological implications of calculated charmonia decay constants in ηc→γγ decay, and B→Xcc‾K decays.

Lattice QCD estimate of the η c (2S) → J/ψγ decay rate

We compute the hadronic matrix element relevant to the physical radiative decay $\eta_{c}(2S)\to J/\psi\gamma$ by means of lattice QCD. We use the (maximally) twisted mass QCD action with Nf=2 light dynamical quarks and from the computations made at four lattice spacings we were able to take the continuum limit. The value of the mass ratio $m_{\eta_c(2S)}/m_{\eta_c(1S)}$ we obtain is consistent with the experimental value, and our prediction for the form factor is $V^{\eta_{c}(2S)\to J/\psi\gamma}(0)\equiv V_{12}(0)=0.32(6)(2)$, leading to $\Gamma(\eta_c (2S) \to J/\psi\gamma) = (15.7\pm 5.7)$ keV, which is much larger than $\Gamma(\psi (2S) \to \eta_c\gamma)$ and within reach of modern experiments.

D0−D¯0mixing in the standard model and beyond fromNf=2twisted mass QCD

We present the first unquenched lattice QCD results for the bag parameters controlling the short distance contribution to D meson oscillations in the Standard Model and beyond. We have used the gauge configurations produced by the European Twisted Mass Collaboration with Nf = 2 dynamical quarks, at four lattice spacings and light meson masses in the range 280-500 MeV. Renormalization is carried out non-perturbatively with the RI-MOM method. The bag-parameter results have been used to constrain New Physics effects in D-Dbar mixing, to put a lower bound to the generic New Physics scale and to constrain off-diagonal squark mass terms for TeV-scale Supersymmetry.

High-loop perturbative renormalization constants for Lattice QCD (III): three-loop quark currents for Iwasaki gauge action and $$n_f=4$$ n f = 4 Wilson fermions

This is the third of a series of papers on three-loop computation of renormalization constants for Lattice QCD. Our main point of interest are results for the regularization defined by Iwasaki gauge action and n_f=4 Wilson fermions. Our results for quark bilinears renormalized according to the RI'-MOM scheme can be compared to non-perturbative results. The latter are available for Twisted Mass QCD: being defined in the chiral limit, renormalization constants must be the same. We also address more general problems. In particular, we discuss a few methodological issues connected to summing the perturbative series such as the effectiveness of Boosted Perturbation Theory and the disentanglement of irrelevant and finite volume contributions. Discussing these issues we consider ont only the new results of this paper, but also those for the regularization defined by tree-level Symanzik improved gauge action and n_f=2 Wilson fermions, which we presented in a recent paper of ours. We finally comment to which extent the techniques we put at work in the NSPT context can provide a fresher look into the lattice version of the RI'-MOM scheme.

Lattice QCD and QCD sum rule determination of the decay constants of [formula omitted], [formula omitted] and [formula omitted] states

We compute the decay constants of the lowest cc¯-states with quantum numbers JPC=0−+ (ηc), 1−− (J/ψ), and 1+− (hc) by using lattice QCD and QCD sum rules. We consider the coupling of J/ψ to both the vector and tensor currents. Lattice QCD results are obtained from the unquenched (Nf=2) simulations using twisted mass QCD at four lattice spacings, allowing us to take the continuum limit. On the QCD sum rule side we use the moment sum rules. The results are then used to discuss the rate of ηc→γγ decay, and to comment on the factorization in B→Xcc¯K decays, with Xcc¯ being either ηc or J/ψ.

High-loop perturbative renormalization constants for Lattice QCD (II): three-loop quark currents for tree-level Symanzik improved gauge action and n f =2 Wilson fermions

Numerical Stochastic Perturbation Theory was able to get three- (and even four-) loop results for finite Lattice QCD renormalization constants. More recently, a conceptual and technical framework has been devised to tame finite size effects, which had been reported to be significant for (logarithmically) divergent renormalization constants. In this work we present three-loop results for fermion bilinears in the Lattice QCD regularization defined by tree-level Symanzik improved gauge action and n_f=2 Wilson fermions. We discuss both finite and divergent renormalization constants in the RI'-MOM scheme. Since renormalization conditions are defined in the chiral limit, our results also apply to Twisted Mass QCD, for which non-perturbative computations of the same quantities are available. We emphasize the importance of carefully accounting for both finite lattice space and finite volume effects. In our opinion the latter have in general not attracted the attention they would deserve.

On the significance of B-decays to the radially excited D

We discuss the possibilities of testing the recent claims of a relatively large B→D′ transition form factor through the non-leptonic B¯0→D′+π− and B−→D′0π− decay modes. To estimate the width of the latter we need the decay constant of the radially excited D-meson that we computed in lattice QCD with Nf=2 dynamical flavors and after taking the continuum limit we found fD′=117(25) MeV. We also provide an update for the values of the D-meson decay constants obtained by using maximally twisted mass QCD.

Theoretical estimate of the [formula omitted] decay rate

We present the results of our lattice QCD study of the gD⁎Dπ coupling, relevant to the D⁎→Dπ decay. Our computation is made on the gauge field configurations that include Nf=2 dynamical light quarks by using the twisted mass QCD action. From the results obtained at four different lattice spacings we were able to take for the first time the continuum limit of this quantity computed on the lattice. Our final value, gc=0.53(3)(3), leads to Γ(D⁎+→D¯0π+)=(50±5±6) keV, and is in good agreement with the experimental results for the width of the charged D⁎ meson.

Lattice QCD study of the radiative decays J/ψ → η c γ and h c → η c γ

Abstract We present the results of our lattice QCD study of the hadronic matrix elements relevant to the physical radiative J/ψ → η c γ and h c → η c γ decays. We used the twisted mass QCD action with N f = 2 light dynamical quarks and from the computations made at four lattice spacings we were able to take the continuum limit. Besides the form factors parameterizing the above decays we also computed: (i) the hyperfine splitting and obtained Δ = 112 ± 4 MeV, (ii) the annihilation constant f J/ψ which agrees with the one inferred from the measured Γ(J/ψ → e + e −).

Renormalization constants for 2-twist operators in twisted mass QCD

Perturbative and non-perturbative results on the renormalization constants of the fermion field and the twist-2 fermion bilinears are presented with emphasis on the non-perturbative evaluation of the one-derivative twist-2 vector and axial vector operators. Non-perturbative results are obtained using the twisted mass Wilson fermion formulation employing two degenerate dynamical quarks and the tree-level Symanzik improved gluon action. The simulations have been performed for pion masses in the range of about 450-260 MeV and at three values of the lattice spacing $a$ corresponding to $\beta=3.9, 4.05, 4.20$. Subtraction of ${\cal O}(a^2)$ terms is carried out by performing the perturbative evaluation of these operators at 1-loop and up to ${\cal O}(a^2)$. The renormalization conditions are defined in the RI$'$-MOM scheme, for both perturbative and non-perturbative results. The renormalization factors, obtained for different values of the renormalization scale, are evolved perturbatively to a reference scale set by the inverse of the lattice spacing. In addition, they are translated to ${\bar{\rm MS}}$ at 2 GeV using 3-loop perturbative results for the conversion factors.

From strange to charmed baryons using two-flavour QCD

We compute the mass spectrum for strange and charmed baryons in the partially quenched approach using N f = 2 twisted mass QCD configurations. We investigate two main issues: the size of lattice artefacts using three values of the lattice spacing (the smallest of which is approximately 0.05 fm) and the dependence of baryon masses on meson masses. We thus perform a global fit in order to extrapolate simultaneously to the continuum limit and to the physical point. We obtain predictions for the Ω s s s , Ξ d s s , Λ u d s , Ω c c c , Ξ d c c , Λ u d c masses.

QuenchedBK-parameter from Osterwalder-Seiler tmQCD quarks and mass-splitting discretization effects

We apply an Osterwalder-Seiler version of twisted mass QCD to a study of the $B_K$ parameter, in which three of the four quark fields making up the relevant $\Delta S =2$ operator are maximally twisted with the same twist angle, while the fourth one has a twist angle of opposite sign. It is known that this setup ensures automatic improvement of the bare $K^0$-$\overline K^0$ operator matrix element and multiplicative renormalization of the $\Delta S =2$ operator, at the price of breaking the $K^0$-$\overline K^0$ mass degeneracy by discretization effects. As a result, two dominant systematic errors of the $B_ K$ determination with Wilson fermions are kept under control. With the Clover term included in the fermion action, we perform a feasibility study and find, in the quenched approximation, a significant improvement of the scaling behaviour of $B_K$, compared to earlier standard tmQCD determinations. Moreover, we study in detail the $K^0$-$\overline K^0$ mass splitting that characterizes this approach and confirm that, in the presence of the Clover term, it is greatly reduced in a maximally twisted theory.

Flavour symmetry restoration and kaon weak matrix elements in quenched twisted mass QCD

We simulate two variants of quenched twisted mass QCD (tmQCD), with degenerate Wilson quarks of masses equal to or heavier than half the strange quark mass. We use Ward identities in order to measure the twist angles of the theory and thus check the quality of the tuning of mass parameters to a physics condition which stays constant as the lattice spacing is varied. Flavour symmetry breaking in tmQCD is studied in a framework of two fully twisted and two standard Wilson quark flavours, tuned to be degenerate in the continuum. Comparing pseudoscalar masses, obtained from connected quark diagrams made of tmQCD and/or standard Wilson quark propagators, we confirm that flavour symmetry breaking effects, which are at most 5%, decrease as we approach the continuum limit. We also compute the pseudoscalar decay constant in the continuum limit, with reduced systematics. As a consequence of improved tuning of the mass parameters at β = 6.1 , we reanalyze our previous B K results. Our main phenomenological findings are r 0 f K = 0.421 ( 7 ) and B ˆ K = 0.735 ( 71 ) .

Twisted mass QCD for the pion electromagnetic form factor

The pion form factor is computed using quenched twisted mass QCD and the GMRES-DR matrix inverter. The momentum averaging procedure of Frezzotti and Rossi is used to remove leading lattice spacing artifacts, and numerical results for the form factor show the expected improvement with respect to the standard Wilson action. Although some matrix inverters are known to fail when applied to twisted mass QCD, GMRES-DR is found to be a viable and powerful option. Results obtained for the pion form factor are consistent with the published results from other $O(a)$ improved actions and are also consistent with the available experimental data.

Pion form factor with twisted mass QCD

The pion form factor is calculated using quenched twisted mass QCD with beta=6.0 and maximal twisting angle omega=pi/2. Two pion masses and several values of momentum transfer are considered. The momentum averaging procedure of Frezzotti and Rossi is used to reduce lattice spacing errors, and numerical results are consistent with the expected O(a) improvement.

Wilson twisted mass towards the chiral limit

We present a scaling test of twisted mass QCD with pure Wilson quarks for a twisting angle of π / 2 for a range of pseudoscalar masses 250 MeV ≲ m PS ≲ 1 GeV . We have computed the vector meson mass and the pseudoscalar decay constant f PS for different values of β at fixed value of r 0 m PS . Our results from Wilson twisted mass QCD seems to indicate that the lattice spacing errors are consistent with O( a ) improvement, without the need of any improvement terms added, with an increase of the scaling violation going towards the chiral limit.

Precision computation of BK in quenched lattice QCD

We present the results of a precision computation of BK with Wilson fermions. Simulations are performed at different lattice spacings, enabling continuum limit extrapolations. Two different twisted mass QCD (tmQCD) regularisations are considered for the computation of bare matrix elements. In both cases the relevant four-fermion operator renormalises multiplicatively. In one regularisation it is possible to perform the computation directly at the physical kaon mass value, thus avoiding extrapolations in the mass. Nonperturbative renormalisation is carried out using available Schrodinger Functional results.

Chiral perturbation theory for twisted mass QCD

Quantum Chromodynamics on a lattice with Wilson fermions and a chirally twisted mass term for two degenerate quark flavours is considered in the framework of chiral perturbation theory. The pion masses and decay constants are calculated in next-to-leading order including terms linear in the lattice spacing a. We treat both unquenched and partially quenched QCD. We also discuss the phase structure of twisted mass lattice QCD.