Hadronic Matrix Elements Research Articles

Standard Model anatomy of WIMP dark matter direct detection. II. QCD analysis and hadronic matrix elements

Models of Weakly Interacting Massive Particles (WIMPs) specified at the electroweak scale are systematically matched to effective theories at hadronic scales where WIMP-nucleus scattering observables are evaluated. Anomalous dimensions and heavy quark threshold matching conditions are computed for the complete basis of lowest-dimension effective operators involving quarks and gluons. The resulting QCD renormalization group evolution equations are solved. The status of relevant hadronic matrix elements is reviewed and phenomenological illustrations are given, including details for the computation of the universal limit of nucleon scattering with heavy $SU(2)_W\times U(1)_Y$ charged WIMPs. Several cases of previously underestimated hadronic uncertainties are isolated. The results connect arbitrary models specified at the electroweak scale to a basis of $n_f=3$ flavor QCD operators. The complete basis of operators and Lorentz invariance constraints through order $v^2/c^2$ in the nonrelativistic nucleon effective theory are derived.

The Boer-Mulders Transverse Momentum Distribution in the Pion and its Evolution in Lattice QCD

Starting from a definition of transverse momentum-dependent parton distributions (TMDs) in terms of hadronic matrix elements of a quark bilocal operator containing a staple-shaped gauge link, selected TMD observables can be evaluated within Lattice QCD. A TMD ratio describing the Boer-Mulders effect in the pion is investigated, with a particular emphasis on its evolution as a function of a Collins-Soper-type parameter which quantifies the proximity of the staple-shaped gauge links to the light cone.

QCD Factorization and PDFs from Lattice QCD Calculation

In this talk, we review a QCD factorization based approach to extract parton distribution and correlation functions from lattice QCD calculation of single hadron matrix elements of quark-gluon operators. We argue that although the lattice QCD calculations are done in the Euclidean space, the nonperturbative collinear behavior of the matrix elements are the same as that in the Minkowski space, and could be systematically factorized into parton distribution functions with infrared safe matching coefficients. The matching coefficients can be calculated perturbatively by applying the factorization formalism on to asymptotic partonic states.

Study on theΥ(1S)→BcMWeak Decays

Motivated by the prospects of the potentialΥ(1S)particle at high-luminosity heavy-flavor experiments, we studied theΥ(1S)→BcMweak decays, whereM=π,ρ,K(∗). The nonfactorizable contributions to hadronic matrix elements are taken into consideration with the QCDF approach. It is found that the CKM-favoredΥ(1S)→Bcρdecay has branching ratio ofO(10-10), which might be measured promisingly by the future experiments.

Renormalization and mixing in lattice QCD: The case of the chromomagnetic operator

We study matrix elements of the "chromomagnetic" operator on the lattice. This operator is contained in the strangeness-changing effective Hamiltonian which describes electroweak effects in the Standard Model and beyond. Having dimension 5, the chromomagnetic operator is characterized by a rich pattern of mixing with other operators of equal and lower dimensionality, including also non gauge invariant quantities; it is thus quite a challenge to extract from lattice simulations a clear signal for the hadronic matrix elements of this operator. We compute all relevant mixing coefficients to one loop in lattice perturbation theory; this necessitates calculating both 2-point (quark-antiquark) and 3-point (gluon-quark-antiquark) Green's functions at nonzero quark masses. We use the twisted mass lattice formulation, with Symanzik improved gluon action. We also provide a nonperturbative method to compute mixing with lower dimensional operators; we use this method in numerical simulations, and extract the mixing with the 3-dimensional scalar density, finding good agreement with one-loop results.

Finite volume effects on the extraction of form factors at zero momentum

Hadronic matrix elements that depend on momentum are required for numerous phenomenological applications. Probing the low-momentum regime is often problematic for lattice QCD computations on account of the restriction to periodic momentum modes. Recently a novel method has been proposed to compute matrix elements at zero momentum, for which straightforward evaluation of the matrix elements would otherwise yield a vanishing result. We clarify an assumption underlying this method, and thereby establish the theoretical framework required to address the associated finite volume effects. Using the pion electromagnetic form factor as an example, we show how the charge radius and two higher moments can be calculated at zero momentum transfer, and determine the corresponding finite volume effects. These computations are performed using chiral perturbation theory to account for modified infrared physics, and can be generalized to ascertain finite volume effects for other hadronic matrix elements extracted at zero momentum.

Feynman-Hellmann approach to the spin structure of hadrons

We perform a Nf = 2 + 1 lattice QCD simulation to determine the quark spin fractions of hadrons using the Feynman-Hellmann theorem. By introducing an external spin operator to the fermion action, the matrix elements relevant for quark spin fractions are extracted from the linear response of the hadron energies. Simulations indicate that the Feynman-Hellmann method offers statistical precision that is comparable to the standard three-point function approach, with the added benefit that it is less susceptible to excited state contamination. This suggests that the Feynman-Hellmann technique offers a promising alternative for calculations of quark line disconnected contributions to hadronic matrix elements. At the SU(3)-flavour symmetry point, we find that the connected quark spin fractions are universally in the range 55-70% for vector mesons and octet and decuplet baryons. There is an indication that the amount of spin suppression is quite sensitive to the strength of SU(3) breaking.

Form factors for B meson weak decays in QCD light cone sum rules with a chiral current correlator

We report some applications of QCD light cone sum rules (LCSR) to \(B\) meson weak decays. Special emphasis is on estimates of the form factors for \(B\) decays into a pseudoscalar (\(P\))/vector (\(V\)) meson, with a certain chiral current correlator. The main new ingredient, as compared with the case of the standard correlators, is that in the operator product expansion calculations, the contributions due to the twist-3 distribution amplitudes of the related light mesons, which are less known and would bring a larger uncertainty to the calculations with the standard correlators, cancel out fully in the \(B\rightarrow P\) case and do out partially in the \(B\rightarrow V\) one. An important observation, which is similar to that in soft collinear effective theory, is made in twist-3 approximation: whereas only one independent form factor is needed for parameterizing the hadronic matrix elements for a \(B\rightarrow P\) transition induced by all the relevant heavy-light quark currents, there exist two independent form factors under the condition of neglecting the terms suppressed by a factor of \(m_V^2\), for the \(B\rightarrow V\) transition. Therefore, the improved LCSR approach could be of stronger predictive power for the weak form factors. Also, this approach is employed to understand the \(B\rightarrow D\) transitions by introducing a leading twist-2 DA for an energetic \(D\) meson, combined with some of other QCD-based approaches. A detailed QCD next-to-leading order calculation of the \(B\rightarrow \pi \) form factors is presented for an illustrative purpose, and the sum rule results are used to extract the Cabibbo–Kobayashi–Maskawa matrix element \(|V_{ub}|\) from the latest BaBar data.

Decay constants of B-mesons from non-perturbative HQET with two light dynamical quarks

We present a computation of B-meson decay constants from lattice QCD simulations within the framework of Heavy Quark Effective Theory for the b-quark. The next-to-leading order corrections in the HQET expansion are included non-perturbatively. Based on Nf=2 gauge field ensembles, covering three lattice spacings a≈(0.08–0.05) fm and pion masses down to 190 MeV, a variational method for extracting hadronic matrix elements is used to keep systematic errors under control. In addition we perform a careful autocorrelation analysis in the extrapolation to the continuum and to the physical pion mass limits. Our final results read fB=186(13) MeV, fBs=224(14) MeV and fBs/fB=1.203(65). A comparison with other results in the literature does not reveal a dependence on the number of dynamical quarks, and effects from truncating HQET appear to be negligible.

Cross-channel analysis of quark and gluon generalized parton distributions with helicity flip

Quark and gluon helicity flip generalized parton distributions (GPDs) address the transversity quark and gluon structure of the nucleon. In order to construct a theoretically consistent parametrization of these hadronic matrix elements, we work out the set of combinations of those GPDs suitable for the ${\rm SO}(3)$ partial wave (PW) expansion in the cross-channel. This universal result will help to build up a flexible parametrization of these important hadronic non-perturbative quantities, using for instance the approaches based on the conformal PW expansion of GPDs such as the Mellin-Barnes integral or the dual parametrization techniques.

RPV SUSY effects in $\tau^- \to e^-(\mu^-) K\bar{K}$ decays

In this paper, we investigate [Formula: see text] decays in the framework of the RPV SUSY model. We discuss the tree-level contribution of the sparticles [Formula: see text] and [Formula: see text] to these decay branching ratios. In the two channels, the [Formula: see text]-mediated channel is more sensitive to the parameter product [Formula: see text] than the [Formula: see text]-mediated channel to [Formula: see text]. And the parameter product [Formula: see text] is severely constrained to the order of [Formula: see text] by the experiment data with [Formula: see text], which is one order of magnitude more stringent than before. In the calculation of hadronic matrix elements, the resonant effects are large than those of nonresonant terms. Especially, the resonant contribution of scalar meson f(980) plays a dominate role in [Formula: see text]-mediated channel.

Production of heavy meson pairs in pp̄ collisions within a double handbag approach

We study the pair-production of heavy mesons in proton-antiproton annihilations within a perturbative QCD-motivated framework. In particular we investigate pp̄ → D0 within a double handbag approach, where a hard subprocess factorizes from soft hadronic matrix elements. The soft matrix elements can be parametrized by transition distribution amplitudes, which are off-diagonal in flavor space. The transition distribution amplitudes are modelled as overlaps of light-cone wave functions. We obtain rather robust model results for pp̄ → D0 cross sections, which are expected to be measured at the future detector at GSI-FAIR.

Branching ratios and directCPasymmetries inD→PVdecays

We study the two-body hadronic $D\to PV$ decays, where $P$ ($V$) denotes a pseudoscalar (vector) meson, in the factorization-assisted topological-amplitude approach proposed in our previous work. This approach is based on the factorization of short-distance and long-distance dynamics into Wilson coefficients and hadronic matrix elements of four-fermion operators, respectively, with the latter being parametrized in terms of several nonperturbative quantities. We further take into account the $\rho$-$\omega$ mixing effect, which improves the global fit to the branching ratios involving the $\rho^0$ and $\omega$ mesons. Combining short-distance dynamics associated with penguin operators and the hadronic parameters determined from the global fit to branching ratios, we predict direct $CP$ asymmetries. In particular, the direct $CP$ asymmetries in the $D^0\to K^0\overline{K}^{*0},~\overline{K}^0K^{*0}$, $D^+\to\pi^+\rho^0$, and $D_s^+\to K^+\omega,~K^+\phi$ decays are found to be of ${\cal O}(10^{-3})$, which can be observed at the LHCb or future Belle II experiment. We also predict the $CP$ asymmetry observables of some neutral $D$ meson decays.

Isospin Breaking in the Nucleon Mass and the Sensitivity ofβDecays to New Physics

We discuss the consequences of the approximate conservation of the vector and axial currents for the hadronic matrix elements appearing in β decay if nonstandard interactions are present. In particular, the isovector (pseudo)scalar charge gS(P) of the nucleon can be related to the difference (sum) of the nucleon masses in the absence of electromagnetic effects. Using recent determinations of these quantities from phenomenological and lattice QCD studies we obtain the accurate values gS=1.02(11) and gP=349(9) in the modified minimal subtraction scheme at μ=2 GeV. The consequences for searches of nonstandard scalar interactions in nuclear β decays are studied, finding for the corresponding Wilson coefficient εS=0.0012(24) at 90%C.L., which is significantly more stringent than current LHC bounds and previous low-energy bounds using less precise gS values. We argue that our results could be rapidly improved with updated computations and the direct calculation of certain ratios in lattice QCD. Finally, we discuss the pion-pole enhancement of gP, which makes β decays much more sensitive to nonstandard pseudoscalar interactions than previously thought.

Lepton flavor violation in the Higgs sector and the role of hadronicτ-lepton decays

It has been pointed out recently that current low-energy constraints still allow for sizable flavor-changing decay rates of the 125 GeV boson into leptons, $h\ensuremath{\rightarrow}\ensuremath{\tau}\ensuremath{\ell}$ ($\ensuremath{\ell}=e$, $\ensuremath{\mu}$). In this work we discuss the role of hadronic $\ensuremath{\tau}$-lepton decays in probing lepton flavor violating couplings in the Higgs sector. At low energy, the effective Higgs coupling to gluons induced by heavy quarks contributes to hadronic $\ensuremath{\tau}$ decays, establishing a direct connection with the relevant process at the LHC, $pp(gg)\ensuremath{\rightarrow}h\ensuremath{\rightarrow}\ensuremath{\tau}\ensuremath{\ell}$. Semileptonic transitions like $\ensuremath{\tau}\ensuremath{\rightarrow}\ensuremath{\ell}\ensuremath{\pi}\ensuremath{\pi}$ are sensitive to flavor-changing scalar couplings, while decays such as $\ensuremath{\tau}\ensuremath{\rightarrow}\ensuremath{\ell}{\ensuremath{\eta}}^{(\ensuremath{'})}$ probe pseudoscalar couplings, thus providing a useful low-energy handle to disentangle possible Higgs flavor violating signals at the LHC. As part of our analysis, we provide an appropriate description of all the relevant hadronic matrix elements needed to describe Higgs mediated $\ensuremath{\tau}\ensuremath{\rightarrow}\ensuremath{\ell}\ensuremath{\pi}\ensuremath{\pi}$ transitions, improving over previous treatments in the literature.

Proton decay matrix elements on the lattice

Hadronic matrix elements of proton decays are essential ingredients for bridging the grand unification theory to low-energy observables like the proton lifetime. In this paper we nonperturbatively calculate the matrix elements, relevant for the process of a nucleon decaying into a pseudoscalar meson and an antilepton through generic baryon-number-violating four-fermi operators. Lattice QCD with $2+1$ flavor dynamical domain-wall fermions with the direct method---which is the direct measurement of the matrix elements from the three-point function without using chiral perturbation theory---is used for this study in order to have good control over the errors due to lattice discretization effects, operator renormalization, and chiral extrapolation. The relevant form factors for possible transition processes from an initial proton or neutron to a final pion or kaon induced by all types of three-quark operators are obtained through three-point functions of the (nucleon)-(three-quark operator)-(meson) with physical kinematics. In this study all the relevant systematic uncertainties of the form factors are taken into account for the first time, and the total error is found to be in the range 30%--40% for the $\ensuremath{\pi}$ and 20%--40% for the $K$ final states.

Study on branching ratios and direct CP asymmetries of D → PV decays

We study the non-leptonic two-body decays of D mesons decaying into one pseudoscalar meson (P) and one vector meson (V) in the factorization-asisted topological-amplitude approach. In this approach, the decay amplitudes are factorized into two parts, the short-distance contribution (Wilson coefficients) and the long-distance contribution (hadronic matrix elements). We predict the branching ratios of D → PV decays using a global fit with the non-perturbative parameters. Our results agree well with the experimental data. We also predict the direct CP asymmetries by combining short-distance dynamics associated with penguin operators and long-distance hadronic matrix elements determined by branching ratios. The large asymmetries in D+ → π+ρ0 and [Formula: see text] may be measurable in the LHCb and future Belle II experiments.

A stochastic method for computing hadronic matrix elements

We present a stochastic method for the calculation of baryon three-point functions that is more versatile compared to the typically used sequential method. We analyze the scaling of the error of the stochastically evaluated three-point function with the lattice volume and find a favorable signal-to-noise ratio suggesting that our stochastic method can be used efficiently at large volumes to compute hadronic matrix elements.

∆I= 1/2 Rule andB̂K: 2014

I summarize the status of the ∆I = 1/2 rule in K → ππ decays within an analytic approach based on the dual representation of QCD as a theory of weakly interacting mesons for large N , where N is the number of colours. This approximate approach, developed in the 1980s by William Bardeen, Jean-Marc Gerard and myself, allowed us already 28 years ago to identify the dominant dynamics behind the ∆I = 1/2 rule. However, the recent inclusion of lowest-lying vector meson contributions in addition to the pseudoscalar ones to hadronic matrix elements of current-current operators and the calculation of the corresponding Wilson coefficients in a momentum scheme at the NLO improved significantly the matching between quark-gluon short distance contributions and meson long distance contributions over our results in 1986. We obtain satisfactory description of the ReA 2 amplitude and ReA 0 /ReA 2 = 16.0 ± 1.5 to be compared with its experimental value of 22.3. While this difference could be the result of present theoretical uncertainties in our approach, it cannot be excluded that New Physics (NP) is here at work. The analysis by Fulvia De Fazio, Jennifer Girrbach-Noe and myself shows that indeed a tree-level Z ′ or G ′ exchanges with masses in the reach of the LHC and special couplings to quarks can significantly improve the theoretical status of the ∆I = 1/2 rule while satisfying constraints from e K , e ′/e , ∆MK , LEP-II and the LHC. The ratio e ′/e plays an important role in these considerations. I stress that our approach allows to understand the physics behind recent numerical results obtained in lattice QCD not only for the ∆I = 1/2 rule but also for the parameter B K that enters the evaluation of e K . In contrast to the ∆I = 1/2 rule and e ′/e the chapter on B K in QCD appears to be basically closed.

WHY X(3915) IS SO NARROW AS A χc0(2P) STATE?

New resonance X(3915) was identified as the charmonium χc0(2P) by BaBar Collaboration, but there still seems an open question of this assignment: why its full width is so narrow? To answer this question, we calculate the Okubo–Zweig–Iizuka (OZI)-allowed strong decays [Formula: see text], where X(3915) is assigned as a χc0(2P) state, and estimate its full width in the cooperating framework of 3P0 model and the Bethe–Salpeter (BS) method using the Mandelstam formalism, during which nonperturbative quantum chromodynamics (QCD) effects of the hadronic matrix elements are well-considered by overlapping integral over the relativistic Salpeter wave functions of the initial and final states. We find the node structure of χc0(2P) wave function resulting in the narrow width of X(3915) and show the dependence of the decay width on the variation of the initial mass of X(3915). We point out that the rate of [Formula: see text] is crucial to confirm whether X(3915) is the χc0(2P) state or not.