Short-distance QCD Research Articles

Is the Λc(2625)+ the heavy quark spin symmetry partner of the Λc(2595)+ ?

We use a $\mathcal{O}(\Lambda_\text{QCD}/m_c)$ heavy quark effective theory scheme, where only $\mathcal{O}(\Lambda_\text{QCD}/m_b)$ and perturbative QCD short distance corrections are neglected, to study the matrix elements of the scalar, pseudoscalar, vector, axial-vector and tensor currents between the $\Lambda_b$ ground state and the odd parity charm $\Lambda_c(2595)^+$ and $\Lambda_c(2625)^+$ resonances. We show that in the near-zero recoil regime, the scheme describes reasonably well, taking into account uncertainties, the results for the 24 form-factors obtained in lattice QCD (LQCD) just in terms of only 4 Isgur-Wise (IW) functions. We also find some support for the possibility that the $\Lambda_c(2595)^+$ and $\Lambda_c(2625)^+$ resonances might form a heavy-quark spin symmetry (HQSS) doublet. However, we argue that the available LQCD description of these two resonances is not accurate enough to disentangle the possible effects of the $\Sigma_c \pi$ and $\Sigma_c^*\pi$ thresholds, located only a few MeV above their position, and that it cannot be ruled out that these states are not HQSS partners. Finally, we study the ratio $\frac{d\Gamma[\Lambda_b\to \Lambda_{c,1/2^-}^* \ell \bar\nu_\ell]/dq^2}{d\Gamma[\Lambda_b\to \Lambda_{c,3/2^-}^*\ell \bar\nu_\ell]/dq^2}$ of the Standard Model differential semileptonic decay widths, with $q^\mu$ the momentum transferred between the initial and final hadrons. We provide a natural explanation for the existence of large deviations, near the zero recoil, of this ratio from 1/2 (value predicted in the infinite heavy quark mass limit, assuming that the $\Lambda_{c,1/2^-}^*$ and $\Lambda_{c,3/2^-}^*$ are the two members of a HQSS doublet) based on S-wave contributions to the $\Lambda_b\to \Lambda_{c,1/2^-}^*$ decay amplitude driven by a sub-leading IW function.

Standard-Model Prediction of ε_{K} with Manifest Quark-Mixing Unitarity.

The parameter ε_{K} describes CP violation in the neutral kaon system and is one of the most sensitive probes of new physics. The large uncertainties related to the charm-quark contribution to ε_{K} have so far prevented a reliable standard-model prediction. We show that Cabibbo-Kobayashi-Maskawa unitarity enforces a unique form of the |ΔS=2| weak effective Lagrangian in which the short-distance theory uncertainty of the imaginary part is dramatically reduced. The uncertainty related to the charm-quark contribution is now at the percent level. We present the updated standard-model prediction ε_{K}=2.16(6)(8)(15)×10^{-3}, where the errors in parentheses correspond to QCD short-distance, long-distance, and parametric uncertainties, respectively.

Direct CP violation in Cabibbo-favored charmed meson decays and \u03f5\u2032/\u03f5 in SU(2)L \xd7 SU(2)R \xd7 U(1)B\u2212L model

Since the standard model contribution is virtually absent, any observation of direct CP violation in the Cabibbo-favored charmed meson decays would be evidence of new physics. In this paper, we conduct a quantitative study on direct CP violation in D0 → K−π+, Ds+ → ηπ+ and Ds+ → η′π+ decays in the SU(2)L ×SU(2)R ×U(1)B−L gauge extension of the standard model. In the model, direct CP violation arises mainly from the interference between the decay amplitude coming from the SM left-left current operators and that from the right-right current operators induced by WR+ gauge boson exchange. Interestingly, the strong phase between the two amplitudes is evaluable, since it stems from difference in QCD corrections to the left-left and right-right current operators, which is a short-distance QCD effect given by sim left({alpha}_sleft({M}_{W_L}^2right)/4pi right) log left({M}_{W_R}^2/{M}_{W_L}^2right) . We assess the maximal direct CP violation in the above decays in the SU(2)L × SU(2)R × U(1)B−L model. Additionally, we present a correlation between direct CP violation in these modes and one in K → ππ decay parametrized by ϵ′, since WR+ gauge boson has a sizable impact on the latter.

Short-distance QCD corrections to K 0 K ¯ 0 $$ {K}^0{\overline{K}}^0 $$ mixing at next-to-leading order in Left-Right models

Left-Right (LR) models are extensions of the Standard Model where left-right symmetry is restored at high energies, and which are strongly constrained by kaon mixing described in the framework of the $|\Delta S|=2$ effective Hamiltonian. We consider the short-distance QCD corrections to this Hamiltonian both in the Standard Model (SM) and in LR models. The leading logarithms occurring in these short-distance corrections can be resummed within a rigourous Effective Field Theory (EFT) approach integrating out heavy degrees of freedom progressively, or using an approximate simpler method of regions identifying the ranges of loop momentum generating large logarithms in the relevant two-loop diagrams. We compare the two approaches in the SM at next-to-leading order, finding a very good agreement when one scale dominates the problem, but only a fair agreement in the presence of a large logarithm at leading order. We compute the short-distance QCD corrections for LR models at next-to-leading order using the method of regions, and we compare the results with the EFT approach for the $WW'$ box with two charm quarks (together with additional diagrams forming a gauge-invariant combination), where a large logarithm occurs already at leading order. We conclude by providing next-to-leading-order estimates for $cc$, $ct$ and $tt$ boxes in LR models.

Renormalization group improved pQCD prediction for Υ(1S) leptonic decay

Abstract The complete next-to-next-to-next-to-leading order short-distance and bound-state QCD corrections to Υ(1S) leptonic decay rate Γ(Υ(1S) → ℓ+ℓ−) has been finished by Beneke et al. [8]. Based on those improvements, we present a renormalization group (RG) improved pQCD prediction for Γ(Υ(1S) → ℓ+ℓ−) by applying the principle of maximum conformality (PMC). The PMC is based on RG-invariance and is designed to solve the pQCD renormalization scheme and scale ambiguities. After applying the PMC, all known-type of β-terms at all orders, which are controlled by the RG-equation, are resummed to determine optimal renormalization scale for its strong running coupling at each order. We then achieve a more convergent pQCD series, a scheme- independent and more accurate pQCD prediction for Υ(1S) leptonic decay, i.e. $$ \varGamma {\left.{}_{Y(1S)\to {\mathrm{e}}^{+}{\mathrm{e}}^{-}}\right|}_{\mathrm{PMC}}=1.27{0}_{-0.187}^{+0.137} $$ Γ Υ 1 S → e + e − P M C = 1.27 0 − 0.187 + 0.137 keV, where the uncertainty is the squared average of the mentioned pQCD errors. This RG-improved pQCD prediction agrees with the experimental measurement within errors.

A change of perspective in quarkonium production: All data are equal, but some are more equal than others

Abstract Quarkonium polarization data, usually considered a difficult challenge for the QCD description of quarkonium production and relegated to an a posteriori test of predictions exclusively driven by cross-section measurements, with puzzling results, provide, in reality, the most fundamental, direct and model-independent connection to the production mechanisms. We have simultaneously fitted the ψ ( 2 S ) and ϒ ( 3 S ) differential cross sections and polarizations, reliably measured at the LHC up to higher transverse momentum p T values than ever before, as a superposition of colour-singlet and colour-octet contributions perturbatively calculated up to next-to-leading order. We show that, except for the lowest p T cross-section data, where factorization between short-distance and long-distance QCD effects is not expected to be applicable, all the measurements are very well reproduced. Besides providing a straightforward solution to the “quarkonium polarization puzzle”, our study shows that quarkonium production is dominated by the unpolarized S 0 [ 8 ] 1 octet term, an observation that opens new paths towards the understanding of bound-state formation in QCD.

Leptonic decay of the ϒ(1S) meson at third order in QCD.

We present the complete next-to-next-to-next-to-leading order short-distance and bound-state QCD correction to the leptonic decay rate Γ(ϒ(1S)→ℓ+ℓ-) of the lowest-lying spin-1 bottomonium state. The perturbative QCD prediction is compared to the measurement Γ(ϒ(1S)→e+e-)=1.340(18) keV.

DirectCPviolation in two-body hadronic charmed meson decays

Motivated by the recent observation of $CP$ violation in the charm sector by LHCb, we study direct $CP$ asymmetries in the standard model (SM) for the singly Cabibbo-suppressed two-body hadronic decays of charmed mesons using the topological-diagram approach. In this approach, the magnitude and the phase of topological weak annihilation amplitudes, which arise mainly from final-state rescattering, can be extracted from the data. Consequently, direct $CP$ asymmetry ${a}_{\mathrm{dir}}^{(\mathrm{tree})}$ at tree level can be reliably estimated. In general, it lies in the range ${10}^{\ensuremath{-}4}<{a}_{\mathrm{dir}}^{(\mathrm{tree})}<{10}^{\ensuremath{-}3}$. Short-distance QCD penguins and penguin annihilation are calculated using QCD factorization. Their effects are generally small, especially for $D\ensuremath{\rightarrow}VP$ modes. Since weak penguin annihilation receives long-distance contributions from the color-allowed tree amplitude followed by final-state rescattering, it is expected to give the dominant contribution to the direct $CP$ violation in the decays ${D}^{0}\ensuremath{\rightarrow}{K}^{+}{K}^{\ensuremath{-}}$ and ${D}^{0}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$, in which ${a}_{\mathrm{dir}}^{(\mathrm{tree})}$ is absent. The maximal $\ensuremath{\Delta}{a}_{CP}^{\mathrm{dir}}$, the direct $CP$ asymmetry difference between the above-mentioned two modes, allowed in the SM is around $\ensuremath{-}0.25%$, more than $2\ensuremath{\sigma}$ away from the current world average of $\ensuremath{-}(0.645\ifmmode\pm\else\textpm\fi{}0.180)%$.

Hyperfine splittings in the system

Recent measurements of the $\eta_b(1S)$, the ground state of the $b\bar{b}$ system, show the splitting between it and the $\Up(1S)$ to be 69.5$\pm$3.2 MeV, considerably larger than lattice QCD and potential model predictions, including recent calculations published by us. The models are unable to incorporate such a large hyperfine splitting within the context of a consistent description of the energy spectrum and decays. We demonstrate that in our model, which incorporates a relativistic kinetic energy term, a linear confining term including its scalar-exchange relativistic corrections, and the complete one-loop QCD short distance potential, such a consistent description, including the measured hyperfine splitting, can be obtained by not softening the delta function terms in the hyperfine potential. We calculate the hyperfine splitting to be 67.5 MeV.

Hadronic light by light contribution to the(g−2)μwith holographic models of QCD

We study the anomalous electromagnetic pion form factor ${F}_{{\ensuremath{\pi}}^{0}{\ensuremath{\gamma}}^{*}{\ensuremath{\gamma}}^{*}}$ with a set of holographic models. By comparing with the measured value of the linear slope, some of these models can be ruled out. From the remaining models, we obtain predictions for the low-energy quadratic slope parameters of ${F}_{{\ensuremath{\pi}}^{0}{\ensuremath{\gamma}}^{*}{\ensuremath{\gamma}}^{*}}$, currently out of experimental reach but testable in the near future. We find it particularly useful to encode this low-energy information in a form factor able to satisfy also QCD short-distance constraints. We choose the form factor introduced by D'Ambrosio, Isidori, and Portoles in kaon decays, which has the right short distance for a particular value of the quadratic slope, which is later shown to be compatible with our holographic predictions. We then turn to a determination of the (dominant) pion exchange diagram in the hadronic light by light scattering contribution to the muon anomalous magnetic moment. We quantify the theoretical uncertainty in $(g\ensuremath{-}2{)}_{\ensuremath{\mu}}$ coming from the different input we use: QCD short distances, experimental input, and low-energy holographic predictions. We also test the pion-pole approximation. Our final result is ${a}_{\ensuremath{\mu}}^{{\ensuremath{\pi}}^{0}}=6.54(25)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$, where the error is driven by the linear slope of ${F}_{{\ensuremath{\pi}}^{0}{\ensuremath{\gamma}}^{*}{\ensuremath{\gamma}}^{*}}$, soon to be measured with precision at KLOE-2. Our numerical analysis also indicates that large values of the magnetic susceptibility ${\ensuremath{\chi}}_{0}$ are disfavored, therefore pointing at a mild effect from the pion off-shellness. However, in the absence of stronger bounds on ${\ensuremath{\chi}}_{0}$, an additional $(10--15)%$ systematic uncertainty on the previous value for ${a}_{\ensuremath{\mu}}^{{\ensuremath{\pi}}^{0}}$ cannot be excluded.

One-meson radiative tau decays

We have studied the one-meson radiative tau decays ${\ensuremath{\tau}}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\nu}}_{\ensuremath{\tau}}{\ensuremath{\pi}}^{\ensuremath{-}}({K}^{\ensuremath{-}})\ensuremath{\gamma}$, computing the structure-dependent contributions within a Lagrangian approach based on the large-${N}_{C}$ limit of QCD that ensures the proper low-energy limit dictated by chiral symmetry. Upon imposing the short-distance QCD constraints to the form factors, we are able to predict the structure-dependent radiation without any free parameter and, therefore, the relevant observables for the decay ${\ensuremath{\tau}}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\nu}}_{\ensuremath{\tau}}{\ensuremath{\pi}}^{\ensuremath{-}}\ensuremath{\gamma}$: the photon energy spectrum, the invariant mass spectrum of the meson-photon system, and the integrated decay rate. We also discuss the remaining uncertainties in these observables for the ${\ensuremath{\tau}}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\nu}}_{\ensuremath{\tau}}{K}^{\ensuremath{-}}\ensuremath{\gamma}$ decay. According to our results, the present facilities could detect these rare decays for the first time in the near future, allowing for a stringent test of our predictions.

Phenomenology of AdS/QCD and its gravity dual

We construct the dilaton potential in the gravity dual theory of AdS/QCD for the warp factor of Pirner and Galow [1] and Nian and Pirner [2]. Using this AdS 5 -metric with properties similar to QCD, we find that the gravity dual leads to a meaningful gauge coupling in the region between the charmonium and bottonium mass, but differs slightly from QCD in the extreme UV. When we fix the ultraviolet behavior in accord with the β-function, we can obtain good agreement with the overall heavy quark–antiquark potential. Although the leading order proportional to − α 4 / 3 r differs from perturbative QCD, the full potential agrees quite well with the short distance QCD potential in NNLO.

What can be learned from the Belle spectrum for the decay [formula omitted

A theoretical description of the differential decay spectrum for the decay τ−→ντKSπ−, which is based on the contributing Kπ vector and scalar form factors F+Kπ(s) and F0Kπ(s) being calculated in the framework of resonance chiral theory (RχT), additionally imposing constraints from dispersion relations as well as short distance QCD, provides a good representation of a recent measurement of the spectrum by the Belle Collaboration. Our fit allows to deduce the total branching fraction B[τ−→ντKSπ−]=0.427±0.024% by integrating the spectrum, as well as the K∗ resonance parameters MK∗=895.3±0.2 MeV and ΓK∗=47.5±0.4 MeV, where the last two errors are statistical only. From our fits, we confirm that the scalar form factor F0Kπ(s) is required to provide a good description, but we were unable to further constrain this contribution. Finally, from our results for the vector form factor F+Kπ(s), we update the corresponding slope and curvature parameters λ+′=(25.2±0.3)×10−3 and λ+″=(12.9±0.3)×10−4, respectively.

Short-distance analysis of [formula omitted] mixing

We study the Standard Model short-distance prediction for the mass and lifetime differences between the two neutral D meson mass eigenstates. We find that, despite α s / 4 π suppression, next-to-leading order (NLO) short-distance QCD corrections exceed the corresponding leading order (LO) amplitudes. For the lifetime difference, this stems from the lifting of helicity suppression of a light-quark intermediate state. We find y D is given by y NLO to a reasonable approximation but x D is greatly affected by destructive interference between x LO and x NLO . The net effect is to render y D ∼ x D ≃ 6 × 10 −7 . Our NLO short-distance results, still smaller than most long-distance estimates, depend on the same two nonperturbative matrix elements of four-quark operators as in leading order.

Hadronic light-by-light scattering contribution to the muon anomalous magnetic moment reexamined

We discuss hadronic light-by-light scattering contribution to the muon anomalous magnetic moment a_\mu^{\rm lbl}, paying particular attention to the consistent matching between the short- and the long-distance behavior of the light-by-light scattering amplitude. We argue that the short-distance QCD imposes strong constraints on this amplitude overlooked in previous analyses. We find that accounting for these constraints leads to approximately 50 per cent increase in the central value of a_\mu^{\rm lbl}, compared to existing estimates. The hadronic light-by-light scattering contribution becomes a_\mu^{\rm lbl}=136(25) \times 10^{-11}, thereby shifting the Standard Model prediction closer to the experimental value.

CP violation in the decays [formula omitted] in the presence of [formula omitted] mixing

We have recently shown that the large direct CP violation observed in the decay B0→π+π−, and the enhanced branching ratio for B0→π0π0, can be understood by invoking a small mixing of the ππ system with the dominant DD¯ channel. We examine here the analogous effect of DD¯↔KK¯ mixing on the rare decays B0→K0K¯0, B−→K−K0 and B0→K+K−. We find (a) significant values for the asymmetry parameters C and S in B0/B¯0→K0K¯0, (b) a possible enhancement of the suppressed mode B0→K+K−, (c) a correlation between the three decay channels following from a triangle relation between amplitudes AK0K¯0−AK+K−=AK−K0. The pattern of asymmetries and branching ratios is compared with that derived from the short-distance QCD penguin interaction.

Partons and jets at the LHC

I review some issues related to short distance QCD and its relation to the experimental program of the large hadron collider (LHC) now under construction in Geneva.

QCD Short-distance constraints and hadronic approximations

This paper discusses a general class of ladder resummation inspired hadronic approximations. It is found that this approach naturally reproduces many successes of single meson per channel saturation models (e.g. VMD) and NJL based models. In particular the existence of a constituent quark mass and a gap equation follows naturally. We construct an approximation that satisfies a large set of QCD short-distance and large $N_c$ constraints and reproduces many hadronic observables. We show how there exists in general a problem between QCD short-distance constraints for Green Functions and those for form factors and cross-sections following from the quark-counting rule. This problem while expected for Green functions that do not vanish in purely perturbative QCD also persists for many Green functions that are order parameters.

Electroweak Hadronic Contributions to the muong−2

We reanalyze the two-loop electroweak hadronic contributions to the muon g-2 that may be enhanced by large logarithms. The present evaluation is improved over those already existing in the literature by the implementation of the current algebra Ward identities and the inclusion of the correct short-distance QCD behaviour of the relevant hadronic Green's function.

Helicity conservation and factorization-suppressed charmlessBdecays

Toward the goal of extracting the weak angle alpha, the decay B^0/B^0-bar to a_0^{+/-}pi^{-/+} was recently measured. The decay B^0 to a_0^+pi^- is not only forbidden in the factorization limit of the tree interaction, but also strongly suppressed for the penguin interaction if short-distance QCD dominates. This makes extraction of alpha very difficult from a^{+/-}\pi^{-/+}. We examine the simlar factorization-suppressed decays, in particular, B^0\to b_1^+pi^-. The prospect of obtaining alpha is even less promising with b_1^{+/-}pi^{-/+}. To probe how well the short-distance dominance works, we emphasize importance of testing helicity conservation in the charmless B decays with spins.