Short-distance Contribution Research Articles

Hadronic vacuum polarization in the muon g − 2: the short-distance contribution from lattice QCD

We present results for the short-distance window observable of the hadronic vacuum polarization contribution to the muon g – 2, computed via the time-momentum representation (TMR) in lattice QCD. A key novelty of our calculation is the reduction of discretization effects by a suitable subtraction applied to the TMR kernel function, which cancels the leading \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${x}_{0}^{4}$$\\end{document}-behaviour at short distances. To compensate for the subtraction, one must substitute a term that can be reliably computed in perturbative QCD. We apply this strategy to our data for the vector current collected on ensembles generated with 2 + 1 flavours of O(a)-improved Wilson quarks at six values of the lattice spacing and pion masses in the range 130 – 420 MeV. Our estimate at the physical point contains a full error budget and reads \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\left({a}_{\\mu }^{{\ ext{hvp}}}\\right)}^{{\ ext{SD}}}$$\\end{document} = 68.85(14)stat (42)syst·10−10, which corresponds to a relative precision of 0.7%. We discuss the implications of our result for the observed tensions between lattice and data-driven evaluations of the hadronic vacuum polarization.

Long-distance contribution to εK from lattice QCD

A lattice QCD approach to the calculation of the long-distance contributions to εK is presented. This parameter describes indirect CP violation in K→ππ decay. While the short-distance contribution to εK can be accurately calculated in terms of standard model parameters and a single hadronic matrix element, BK, there is a long-distance part which is estimated to be approximately 5% of the total and is more difficult to determine. A method for determining this small but phenomenologically important contribution to εK using lattice QCD is proposed and a complete exploratory calculation of the contribution is presented. This exploratory calculation uses an unphysical light quark mass corresponding to a 339 MeV pion mass and an unphysical charm quark mass of 968 MeV, expressed in the MS¯ scheme at 2 GeV. This calculation demonstrates that future work should be able to determine this long-distance contribution from first principles with a controlled error of 10% or less. Published by the American Physical Society 2024

Bounds on Species Scale and the Distance Conjecture

AbstractThe species scale serves as a UV cutoff in the gravitational sector of an EFT and can depend on the moduli of the theory as the spectrum of the theory varies. It is argued that the dependence of the species scale on massless (or light) modes satisfies . This bound is true at all points in moduli space including also its interior. The argument is based on the idea that the short distance contribution of massless modes to gravitational terms in the EFT cannot dramatically affect the black hole entropy. Based on string theory arguments the constant in this bound is expected to be equal to as the boundary of the moduli space is approached. However, it turns out that along trajectories going from interior points to the boundaries of moduli space the slope of the species scale can approach its asymptotic value from above, thereby implying that the constant in the bound must be larger than . The bound on the variation of the species scale also implies that the mass of towers of light modes cannot go to zero faster than exponential in field distance in accordance with the Distance Conjecture.

Impact of indirect CP violation on Br(KS→ μ+μ−)ℓ=0

The decay KS → (μ+μ−)ℓ=0, with the final muon pair in an angular-momentum zero state, is a sensitive probe of short-distance physics. It has recently been shown how to extract this branching ratio from neutral kaon decay data. We point out that the impact of indirect CP violation on the standard-model prediction of this mode, while nominally of order |ϵK| ∼ 10−3, is enhanced by a large amplitude ratio and leads to a shift of the branching ratio Br(KS → μ+μ−)ℓ=0 by a few percent, depending on the size of a relative phase that can be extracted from data. We also update the standard-model prediction of the short-distance contribution.

Neutrinoless double beta decay from lattice QCD: The short-distance π−→π+e−e− amplitude

This work presents a determination of potential short-distance contributions to the unphysical $\pi^-\rightarrow\pi^+ e^- e^-$ decay through lattice QCD calculations. The hadronic contributions to the transition amplitude are described by the pion matrix elements of five Standard Model Effective Field Theory operators, which are computed on five ensembles of domain-wall fermions with $N_f = 2 + 1$ quark flavors with a range of heavier-than-physical values of the light quark masses. The matrix elements are extrapolated to the continuum, physical light-quark mass, and infinite volume limit using a functional form derived in chiral Effective Field Theory ($\chi\mathrm{EFT}$). This extrapolation also yields the relevant low-energy constants of $\chi\mathrm{EFT}$, which are necessary input for $\chi\mathrm{EFT}$ calculations of neutrinoless double beta decay of nuclei.

Renormalization of twist-two operators in covariant gauge to three loops in QCD

The leading short-distance contributions to hadronic hard-scattering cross sections in the operator product expansion are described by twist-two quark and gluon operators. The anomalous dimensions of these operators determine the splitting functions that govern the scale evolution of parton distribution functions. In massless QCD, these anomalous dimensions can be determined through the calculation of off-shell operator matrix elements, typically performed in a covariant gauge, where the physical operators mix with gauge-variant operators of the same quantum numbers. We derive a new method to systematically extract the counterterm Feynman rules resulting from these gauge-variant operators. As a first application of the new method, we rederive the unpolarized three-loop singlet anomalous dimensions, independently confirming previous results obtained with other methods. Employing a general covariant gauge, we observe the explicit cancellation of the gauge parameter dependence in these results.

Taming the long distance effects in the Ds+→π+ℓ−ℓ+ decay

The semileptonic decay ${D}_{s}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}{\ensuremath{\ell}}^{+}$, where $\ensuremath{\ell}=e$, $\ensuremath{\mu}$, is used as a reference channel when looking for suppressed or forbidden processes of the standard model of the form ${D}_{s}\ensuremath{\rightarrow}P{\ensuremath{\ell}}^{\ifmmode\pm\else\textpm\fi{}}{\ensuremath{\ell}}^{\ensuremath{'}+}$. The process is dominated by hadronic resonances from the $\ensuremath{\eta}$ to the $\ensuremath{\phi}$ meson region, usually excluded due to the large uncertainties associated. In this work, we explore the role of the parameters involved in the resonance region. We focus in the relative strong phase between the $\ensuremath{\rho}$ and the $\ensuremath{\phi}$ meson (${\ensuremath{\delta}}_{\ensuremath{\rho}\ensuremath{\phi}}$). We argue that this parameter can be bound from LHCb data of the dimuon invariant mass in the ${D}_{s}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}{\ensuremath{\mu}}^{+}$ decay and we perform a fit to provide a first approach to it. We obtain ${\ensuremath{\delta}}_{\ensuremath{\rho}\ensuremath{\phi}}=(0.44\ifmmode\pm\else\textpm\fi{}0.24)\ensuremath{\pi}$. In contradistinction, it would be useful to consider observables insensitive to this phase. We first compute the invariant mass of the lepton pair at a given angle of one of the leptons emission with respect to the pion, and then we compute the forward-backward distribution at such angle. We show that for the latter observable the resonance region is smeared, exhibiting no dependence on the ${\ensuremath{\delta}}_{\ensuremath{\rho}\ensuremath{\phi}}$ phase, although global effects are observed by comparing with the pure phase space approach. In order to consider this observable in more general scenarios, we analyze the behavior for the resonant background process ${D}_{s}^{+}\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi}\ensuremath{\pi}$, the short distance contribution in the standard model, and the charged Higgs mediated process as given by the two Higgs doublet model, which exhibit distinguishable features among themselves.

Disentangling long and short distances in momentum-space TMDs

The extraction of nonperturbative TMD physics is made challenging by prescriptions that shield the Landau pole, which entangle long- and short-distance contributions in momentum space. The use of different prescriptions then makes the comparison of fit results for underlying nonperturbative contributions not meaningful on their own. We propose a model-independent method to restrict momentum-space observables to the perturbative domain. This method is based on a set of integral functionals that act linearly on terms in the conventional position-space operator product expansion (OPE). Artifacts from the truncation of the integral can be systematically pushed to higher powers in ΛQCD/kT. We demonstrate that this method can be used to compute the cumulative integral of TMD PDFs over {k}_Tle {k}_T^{mathrm{cut}} in terms of collinear PDFs, accounting for both radiative corrections and evolution effects. This yields a systematic way of correcting the naive picture where the TMD PDF integrates to a collinear PDF, and for unpolarized quark distributions we find that when renormalization scales are chosen near {k}_T^{mathrm{cut}} , such corrections are a percent-level effect. We also show that, when supplemented with experimental data and improved perturbative inputs, our integral functionals will enable model-independent limits to be put on the non-perturbative OPE contributions to the Collins-Soper kernel and intrinsic TMD distributions.

Covariances of density probability distribution functions. Lessons from hierarchical models

Context. Statistical properties of the cosmic density fields are to a large extent encoded in the shape of the one-point density probability distribution functions (PDF) as measured in surveys. In order to successfully exploit such observables, a detailed functional form of the covariance matrix of the one-point PDF is needed.Aims. The objectives are to model the properties of this covariance for general stochastic density fields and for stochastic fields that reproduce the properties expected in cosmology. The accuracy of the proposed forms is evaluated in specific cases.Methods. The study was conducted in a cosmological context and determined whether the density is defined absolutely or relatively to the sample mean density. Leading and subleading contributions were identified within a large class of models, the so-called hierarchical models. They come from either large or short separation contributions. The validity of the proposed forms for the covariance matrix was assessed with the help of a toy model, the minimum tree model, for which a corpus of exact results could be obtained (forms of the one- and two-point PDF, large-scale density-bias functions, and full covariance matrix of the one-point PDF).Results. It is first shown that the covariance matrix elements are directly related to the spatial average of the two-point density PDF within the sample. The dominant contribution to this average is explicitly given for hierarchical models (coming from large scale contribution), which leads to the construction of specific density-bias functions. However, this contribution alone cannot be used to construct an operational likelihood function. Subdominant large-scale effects are found to provide corrective terms, but also a priori lead to limited information on the covariance matrix. Short distance effects are found to be more important but more difficult to derive as they depend more on the details of the model. However, a simple and generic form of these contributions is proposed. Detailed comparisons in the context of the Rayleigh-Levy flight model show that the large-scale effects capture the bulk of the supersample effects and that, by adding the short-distance contributions, a qualitatively correct model of the likelihood function can be obtained.

New physics in s → d semileptonic transitions: rare hyperon vs. kaon decays

We investigate the potential of rare hyperon decays to probe the short distance structure in the sto dvoverline{v} and s → dℓ+ℓ− transitions. Hyperon decays into neutrinos left({B}_1to {B}_2voverline{v}right) can be reliably predicted by using form factors determined in baryon chiral perturbation theory. Their decay rates are sensitive to different short-distance operators, as compared to their kaon counterparts, and the corresponding branching fractions are in the range of 10−14 ∼ 10−13 in the standard model. In the context of the low-energy effective theory, we find that the anticipated BESIII measurements of the {B}_1to {B}_2voverline{v} decays would lead to constraints on new physics in the purely axial vector overline{d}{gamma}_{mu }{gamma}_5s current that are stronger than the present limits from their kaon siblings Kto pi pi voverline{v} . On the other hand, although hyperon decays into charged leptons are dominated by long-distance hadronic contributions, angular observable such as the leptonic forward-backward asymmetry is sensitive to the interference between long- and short-distance contributions. We discuss the sensitivity to new physics of a potential measurement of this observable in comparison with observables in the kaon decays KL→ μ+μ− and K+→ π+μ+μ−. We conclude that the current kaon bounds are a few orders of magnitude better than those that could be obtained from Σ+→ pμ+μ− except for two scenarios with new physics in the left(overline{d}{gamma}^{mu }sright)left(overline{mathrm{ell}}{gamma}_{mu }{gamma}_5mathrm{ell}right) and left(overline{d}{gamma}^{mu }{gamma}_5sright)left(overline{mathrm{ell}}{gamma}_{mu}mathrm{ell}right) currents. Finally, we point out that the loop effects from renormalization group evolution are important in this context, when relating the low-energy effective field theory to new physics models in the UV.

Short-distance HLbL contributions to the muon g-2

The current 3.7σ discrepancy between the Standard Model prediction and the experimental value of the muon anomalous magnetic moment could be a hint for the existence of new physics. The hadronic light-by-light contribution is one of the pieces requiring improved precision on the theory side, and an important step is to derive short-distance constraints for this quantity containing four electromagnetic currents. Here, we derive such short-distance constraints for three large photon loop virtualities and the external fourth photon in the static limit. The static photon is considered as a background field and we construct a systematic operator product expansion in the presence of this field. We show that the massless quark loop, i.e. the leading term, is numerically dominant over non-perturbative contributions up to next-to-next-to leading order, both those suppressed by quark masses and those that are not.

Weak decays of bottom-charm baryons: mathcal {B}_{bc}rightarrow mathcal {B}_bP

After the discovery of the double-charm baryon Xi _{cc}^{++} by LHCb, one of the most important topics is to search for the bottom-charm baryons which contain a b quark, a c quark and a light quark. In this work, we study the two-body non-leptonic weak decays of a bottom-charm baryon into a spin-1/2 bottomed baryon and a light pseudoscalar meson with the short-distance contributions calculated under the factorization hypothesis and the long-distance contributions considering the final-state-interaction effects. The branching fractions of all fifty-seven decay channels are estimated. The results indicate that Xi _{bc}^+rightarrow Xi _b^0pi ^+, Xi _{bc}^{0}rightarrow Xi _{b}^{-}pi ^+ and Omega _{bc}^0rightarrow Omega _b^-pi ^+ decay modes have relatively large decay rates and thus could be used to experimentally search for the bottom-charm baryons. The topological diagrams and the SU(3) symmetry of bottom-charm baryon decays are discussed.

Path from Lattice QCD to the Short-Distance Contribution to 0νββ Decay with a Light Majorana Neutrino.

Neutrinoless double-β (0νββ) decay of certain atomic isotopes, if observed, will have significant implications for physics of neutrinos and models of physics beyond the standard model. In the simplest scenario, if the mass of the light neutrino of the standard model has a Majorana component, it can mediate the decay. Systematic theoretical studies of the decay rate in this scenario, through effective field theories matched to abinitio nuclear many-body calculations, are needed to draw conclusions about the hierarchy of neutrino masses, and to plan the design of future experiments. However, a recently identified short-distance contribution at leading order in the effective field theory amplitude of the subprocess nn→pp(ee) remains unknown, and only lattice quantum chromodynamics (QCD) can directly and reliably determine the associated low-energy constant. While the numerical computations of the correlation function for this process are underway with lattice QCD, the connection to the physical amplitude, and hence this short-distance contribution, is missing. A complete framework that enables this complex matching is developed in this Letter. The complications arising from the Euclidean and finite-volume nature of the corresponding correlation function are fully resolved, and the value of the formalism is demonstrated through a simple example. The result of this work, therefore, fills the gap between first-principles studies of the nn→pp(ee) amplitude from lattice QCD and those from effective field theory, and can be readily employed in the ongoing lattice-QCD studies of this process.

Rescattering mechanism of weak decays of double-charm baryons * *Supported by the National Natural Science Foundation of China (11775117, U1732101, 11975112), and National Key Research and Development Program of China (2020YFA0406400)

The doubly charmed baryon was recently observed by LHCb via the decay processes of and . These discovery channels were successfully predicted in a framework in which the short-distance contributions are calculated under the factorization hypothesis and the long-distance contributions are estimated using the rescattering mechanism for the final-state-interaction effects. In this paper, we illustrate the above framework in detail by systematic studies on the two-body baryonic decays involving the doubly charmed baryons , the singly charmed baryons and the light pseudoscalar mesons .

Analysis of the tetraquark and hexaquark molecular states with the QCD sum rules

In this article, we construct the color-singlet-color-singlet type currents and the color-singlet-color-singlet-color-singlet type currents to study the scalar , tetraquark molecular states and the vector , hexaquark molecular states with the QCD sum rules in details. In calculations, we choose the pertinent energy scales of the QCD spectral densities with the energy scale formula and for the tetraquark and hexaquark molecular states respectively in a consistent way. We obtain stable QCD sum rules for the scalar , tetraquark molecular states and the vector hexaquark molecular state, but cannot obtain stable QCD sum rules for the vector hexaquark molecular state. The connected (nonfactorizable) Feynman diagrams at the tree level (or the lowest order) and their induced diagrams via substituting the quark lines make positive contributions for the scalar tetraquark molecular state, but make negative or destructive contributions for the vector hexaquark molecular state. It is of no use or meaningless to distinguish the factorizable and nonfactorizable properties of the Feynman diagrams in the color space in the operator product expansion so as to interpret them in terms of the hadronic observables, we can only obtain information about the short-distance and long-distance contributions.

Weak decays of doubly heavy baryons: * *Supported by the National Natural Science Foundation of China (11765012, 12075126)

The discovery of has inspired new interest in studying doubly heavy baryons. In this study, the weak decays of a doubly charmed baryon to a light baryon and a charm meson (either a pseudoscalar or a vector one) are calculated. Following our previous work, we calculate the short distance contributions under the factorization hypothesis, whereas the long distance contributions are modeled as the final state interactions, which are calculated with the one particle exchange model. We find that the decays' branching ratios are obviously larger, as they receive contributions of more polarization states. Among the decays that we investigate, the following have the largest branching fractions: estimated with fs; and with fs; and , , and with fs. By comparing the decay widths of pure color commensurate channels with those of pure bow-tie ones, we find that the bow-tie mechanism plays an important role in charm decays.

Stopping power of hot dense deuterium-tritium plasmas mixed with impurities to charged particles.

In this work, we studied the stopping power of deuterium-tritium (DT) plasmas mixed with impurities to the injected charged particles. Based on the Brown-Preston-Singleton model, the analytical expression for the change ratio of stopping power (denoted by η) induced by impurities in DT plasmas is developed, in which both classical short-distance collision part and quantum correction contribution are purely linear response to the impurity concentration ξ_{X}, while the classical long-range collision brings about higher-order nonlinear response to ξ_{X}. Furthermore, the expression for change ratio of deposition depth (denoted by χ) of charged particles induced by impurities in DT plasmas is also derived. As applications, we systemically investigated the energy loss of α particles deposited into a hot dense DT plasma mixed with impurity X(X=C, Si, Ge), where the temperature and density of DT are smaller than 10 keV and 500 g/cm^{3} and the concentration of Xξ_{X} is less than 5%. The numerical results suggest that (i) for the case of C mixed into DT, both change ratios of stopping power and deposition depth of α particles (i.e., η and χ) are linear response to the concentration of C ξ_{C}; (ii) for the case of Si mixed into DT, the second-order nonlinear response of η and χ to ξ_{Si} cannot be ignored when the densities of DT are larger than 200 g/cm^{3}; and (iii) for the case of Ge mixed into DT, the second- and third-order nonlinear response of η and χ to ξ_{Ge} are very remarkable because of the higher ionization degree and heavier atomic mass of Ge. The formulas and findings in this work may be helpful to the research of internal confinement fusion (ICF) related implosion physics and may provide useful theoretical guidance and data for the design of ICF target.

The Optimal Strategy for ε ′/ε in the SM: 2019

Following the recent analysis done in collaboration with Jason Aebischer and Christoph Bobeth, I summarize the optimal, in our view, strategy for the present evaluation of the ratio ε ′/ε in the Standard Model. In particular, I emphasize the importance of the correct matching of the long-distance and short-distance contributions to ε ′/ε, which presently is only achieved by RBC-UKQCD lattice QCD collaboration and by the analytical Dual QCD approach. An important role play also the isospin-breaking and QED effects, which presently are best known from chiral perturbation theory, albeit still with a significant error. Finally, it is essential to include NNLO QCD corrections in order to reduce unphysical renormalization scheme and scale dependences present at the NLO level. Here µ c in m c (µ c ) in the case of QCD penguin contributions and µ t in m t (µ t ) in the case of electroweak penguin contributions play the most important roles. Presently the error on ε ′/ε is dominated by the uncertainties in the QCDP parameter and the isospin-breaking parameter . We present a table illustrating this.

S-factor and scattering-parameter extractions from

Previous studies of the reaction have mainly focused on providing the best central value and error bar for the S factor at solar energies. Experimental measurements of this capture reaction at higher energies, the – scattering phase shifts, as well as properties of and its excited state, have been used to constrain the theoretical models employed for this purpose. Here we show that much more information than was previously appreciated can be extracted from angle-integrated capture data alone. We use the next-to-leading-order (NLO) amplitude in an effective field theory (EFT) for to perform the extrapolation. At this order the EFT describes the capture process using an s-wave scattering length and effective range, the asymptotic properties of and its excited state, and short-distance contributions to the E1 capture amplitude. We extract the multi-dimensional posterior of all these parameters via a Bayesian analysis that uses capture data below 2 MeV. We find that properties of the ground and excited states are well constrained. The total S factor keV b, while the branching ratio for excited- to ground-state capture at zero energy, , both at 68% degree of belief. This S(0) is broadly consistent with other recent evaluations, and agrees with the previously recommended value b, but has a smaller error bar. We also find significant constraints on – scattering parameters, and we obtain constraints on the angular distribution of capture gamma rays, which is important for interpreting experiments. The path forward for this reaction seems to lie with better measurements of the scattering phase shifts and S(E)'s angular dependence away from zero energy, together with better understanding of the asymptotic normalization coefficients of the Be bound states’ wave functions. Data on these could further reduce the uncertainty on S(0).

Probing dark-axionlike particle portals at future e+e− colliders

We study portal interactions connecting visible and dark sectors, and involving local interactions of a photon, a dark photon and a axion-like particle (ALP) at future $e^+e^-$ colliders. These interactions, mediated by higher-dimensional effective operators, may arise at one-loop by kinetic mixing between dark and ordinary photons, or, for massless dark photons, by direct short-distance contributions. We explore these portal interactions for a heavy ALP with masses between about 10 GeV and 230 GeV by investigating the sensitivity of the production $e^+e^- \to \gamma \gamma \bar{\gamma}$ to the effective couplings, where the dark photon $\bar\gamma$ gives rise to missing momentum in the final state. We will show how an appropriate choice of missing-energy and missing-mass cuts can optimize the signal to standard-model background ratio. Exclusion regions for the effective photon-dark-photon-ALP couplings versus the ALP mass are worked out for a few representative values of the collision energy and integrated luminosity, as presently envisaged by future $e^+e^-$ projects.