Nonperturbative Input Research Articles

Intrinsic mass scale in QCD factorization

We argue for existence of an intrinsic mass scale in QCD factorization and present a possible origin of it. Values of this scale are within the Non-Perturbative QCD mass range. This scale has nothing to do with the the factorization scales: their values are within the perturbative mass range and dependence on them vanishes in the factorization convolutions. We show that the intrinsic mass scale plays the key part in reduction of KT Factorization to Collinear Factorization: such a reduction can be done only if dependence of the non-perturbative inputs in KT Factorization on invariant energy has a sharp-peaked form, so the intrinsic mass scale is associated with location of the peak(s). We also present models where the intrinsic scale is generated by such peaks.

Dynamical parton distributions from DGLAP equations with nonlinear corrections**Supported by National Basic Research Program (973 Program 2014CB845406) and Century Program of Chinese Academy of Sciences (Y101020BR0)

Determination of proton parton distribution functions is presented under the dynamical parton model assumption by applying DGLAP equations with GLR-MQ-ZRS corrections. We provide two data sets, referred to as IMParton16, which are from two different nonperturbative inputs. One is the naive input of three valence quarks and the other is the input of three valence quarks with flavor-asymmetric sea components. Basically, both data sets are compatible with the experimental measurements at high scale (Q2 > 2 GeV2). Furthermore, our analysis shows that the input with flavor-asymmetric sea components better reproduces the structure functions at high Q2. Generally, the parton distribution functions obtained, especially the gluon distribution function, are good options for inputs to simulations of high energy scattering processes. The analysis is performed under the fixed-flavor number scheme for nf = 3, 4, 5. Both data sets start from very low scales, around 0.07 GeV2, where the nonperturbative input is directly connected to the simple picture of the quark model. These results may shed some lights on the origin of the parton distributions observed at high Q2.

ManeParse : A Mathematica reader for Parton Distribution Functions

Parton Distribution Functions (PDFs) are essential non-perturbative inputs for calculation of any observable with hadronic initial states. These PDFs are released by individual groups as discrete grids as a function of the Bjorken-x and energy scale Q. The LHAPDF project maintains a repository of PDFs from various groups in a new standardized LHAPDF6 format, additionally older formats such as the CTEQ PDS grid format are still in use. ManeParse is a package that provides access to PDFs within Mathematica to facilitate calculation and plotting. The program is self-contained so there are no external links to any FORTRAN, C or C++ programs. The package includes the option to use the built-in Mathematica interpolation or a custom cubic Lagrange interpolation routine which allows for flexibility in the extrapolation (particularly at small x-values). ManeParse is fast enough to enable simple calculations (involving even one or two integrations) in the Mathematica framework. Program summaryProgram Title:ManeParseProgram Files doi:http://dx.doi.org/10.17632/knbsccggg4.1Licensing provisions: MITProgramming language:MathematicaNature of problem: PDFs are currently read and interpolated via a FORTRAN or C++ interface. No method exist to read the LHAPDF6 or CTEQ PDFs directly in Mathematica.Solution method: A Mathematica package reads in LHAPDF6 and CTEQ PDF files. The PDFs are parsed into a three-dimensional array in Bjorken-x, scattering energy Q, and parton flavor, and are stored in memory. Provided functions give access to the PDF, the PDF uncertainty, the PDF correlations, and the parton–parton Luminosities. The LHAPDF6 info files are converted from YAML format into Mathematica rules.

Non-perturbative inputs for gluon distributions in the hadrons

Description of hadronic reactions at high energies is conventionally done in the framework of QCD factorization. All factorization convolutions comprise non-perturbative inputs mimicking non-perturbative contributions and perturbative evolution of those inputs. We construct inputs for the gluon–hadron scattering amplitudes in the forward kinematics and, using the optical theorem, convert them into inputs for gluon distributions in the hadrons, embracing the cases of polarized and unpolarized hadrons. In the first place, we formulate mathematical criteria which any model for the inputs should obey and then suggest a model satisfying those criteria. This model is based on a simple reasoning: after emitting an active parton off the hadron, the remaining set of spectators becomes unstable and therefore it can be described through factors of the resonance type, so we call it the resonance model. We use it to obtain non-perturbative inputs for gluon distributions in unpolarized and polarized hadrons for all available types of QCD factorization: basic, K_T-and collinear factorizations.

Two-body non-leptonic heavy-to-heavy decays at NNLO in QCD factorization

We evaluate in the framework of QCD factorization the two-loop vertex corrections to the decays $\bar{B}_{(s)}\to D_{(s)}^{(\ast)+} \, L^-$ and $\Lambda_b \to \Lambda_c^+ \, L^-$, where $L$ is a light meson from the set $\{\pi,\rho,K^{(\ast)},a_1\}$. These decays are paradigms of the QCD factorization approach since only the colour-allowed tree amplitude contributes at leading power. Hence they are sensitive to the size of power corrections once their leading-power perturbative expansion is under control. Here we compute the two-loop ${\cal O}(\alpha_s^2)$ correction to the leading-power hard scattering kernels, and give the results for the convoluted kernels almost completely analytically. Our newly computed contribution amounts to a positive shift of the magnitude of the tree amplitude by $\sim 2$\%. We then perform an extensive phenomenological analysis to NNLO in QCD factorization, using the most recent values for non-perturbative input parameters. Given the fact that the NNLO perturbative correction and updated values for form factors increase the theory prediction for branching ratios, while experimental central values have at the same time decreased, we reanalyze the role and potential size of power corrections by means of appropriately chosen ratios of decay channels.

The leading twist light-cone distribution amplitudes for the S-wave and P-wave Bc mesons

The light-cone distribution amplitudes (LCDAs) serve as important non-perturbative inputs for the study of hard exclusive processes. In this paper, we calculate ten LCDAs at twist-2 for the S-wave and P-wave $B_c$ mesons up to the next-to-leading order (NLO) of the strong coupling $\alpha_s$ and leading order of the velocity expansion. Each one of these ten LCDAs is expressed as a product of a perturbatively calculable distribution and a universal NRQCD matrix-element. By use of the spin symmetry, only two NRQCD matrix-elements will be involved. The reduction of the number of non-perturbative inputs will improve the predictive power of collinear factorization.

Significance of nonperturbative input to the transverse momentum dependent gluon density for hard processes at the LHC

We study the role of the non-perturbative input to the transverse momentum dependent (TMD) gluon density in hard processes at the LHC. We derive the input TMD gluon distribution at low scale mu0^2 ~ 1 GeV^2 from the fit of the inclusive hadron spectra measured at low transverse momenta in pp collisions at the LHC and demonstrate that the best description of these spectra for larger hadron transverse momenta can be achieved by matching the derived TMD gluon distribution with the exact solution of the Balitsky-Fadin-Kuraev-Lipatov (BFKL) equation obtained at low x and small gluon transverse momenta outside the saturation region. Then, we extend the input TMD gluon density to higher mu^2 numerically using the Catani-Ciafoloni-Fiorani-Marchesini (CCFM) gluon evolution equation. A special attention is put to the phenomenological applications of obtained TMD gluon density to some LHC processes, which are sensitive to the gluon content of a proton.

Effect ofcc¯resonances in the branching ratio and forward-backward asymmetry of the decayB→K*μ+μ−

We compute the branching ratio and forward-backward asymmetry ($A_{FB}$) distribution for the rare dileptonic decay $B \to K^* \mu^+ \mu^-$ for the full range of $q^2$, the dimuon mass squared, region. For the required form factors, we use nonperturbative inputs as predicted by the anti-de Sitter (AdS)/QCD correspondence. When using the Breit-Wigner model with momentum-dependent decay constants to account for the $\psi$ and $\psi^\prime$ resonance effects in the nonresonance region of the spectrum, we find our predictions to be in better agreement with the experimental data for the branching ratio.

Three-body non-leptonic B decays and QCD factorization

We extend the framework of QCD factorization to non-leptonic B decays into three light mesons, taking as an example the decay B+→π+π+π−. We discuss the factorization properties of this decay in different regions of phase space. We argue that, in the limit of very large b-quark mass, the central region of the Dalitz plot can be described in terms of the B→π form factor and the B and π light-cone distribution amplitudes. The edges of the Dalitz plot, on the other hand, require different non-perturbative input: the B→ππ form factor and the two-pion distribution amplitude. We present the set-up for both regions to leading order in both αs and ΛQCD/mb and discuss how well the two descriptions merge. We argue that for realistic B-meson masses there is no perturbative center in the Dalitz plot, but that a systematic description might be possible in the context of two-pion states. As an example, we estimate the B→ρπ branching fraction beyond the quasi-particle approximation. We also discuss the prospects for studies of three-body and quasi-two-body non-leptonic B decays from QCD.

Soft factor subtraction and transverse momentum dependent parton distributions on the lattice

We study the transverse momentum dependent (TMD) parton distributions in the newly proposed quasi-parton distribution function framework in Euclidean space. A soft factor subtraction is found to be essential to make the TMDs calculable on lattice. We show that the quasi-TMDs with the associated soft factor subtraction can be applied in hard QCD scattering processes such as Drell-Yan lepton pair production in hadronic collisions. This allows future lattice calculations to provide information on the non-perturbative inputs and energy evolutions for the TMDs. Extension to the generalized parton distributions and quantum phase space Wigner distributions will lead to a complete nucleon tomography on lattice.

Transverse single-spin asymmetries inp↑p→γXfrom quark-gluon-quark correlations in the proton

We analyze the transverse single-spin asymmetry in direct photon production from proton-proton collisions, denoted ${A}_{N}^{\ensuremath{\gamma}}$, within collinear twist-3 factorization. We provide a calculation of the contribution due to quark-gluon-quark correlations in the unpolarized proton as well as summarize previous studies on those effects in the polarized proton. Both soft-gluon poles and soft-fermion poles are considered. From this complete result we then estimate ${A}_{N}^{\ensuremath{\gamma}}$, including error bands due to uncertainties in the nonperturbative inputs, at kinematics relevant for planned measurements of this observable at the Relativistic Heavy Ion Collider. We find ${A}_{N}^{\ensuremath{\gamma}}$ can allow for a ``clean'' extraction of the Qiu-Sterman function, which could lead to a definitive solution to the so-called ``sign-mismatch'' crisis. Since we use the Sivers function extracted from semi-inclusive deep-inelastic scattering to develop our input for the Qiu-Sterman function, this reaction can also make a statement about the process dependence of the Sivers function.

Transverse Single-Spin Asymmetries in Proton-Proton Collisions Within Collinear Factorization

We provide a new analysis within collinear factorization of transverse single-spin asymmetries (TSSAs) in high transverse momentum charged and neutral pion production in pp collisions at the Relativistic Heavy Ion Collider (RHIC). This study incorporates the so-called twist-3 fragmentation term and shows that one can describe RHIC data through this mechanism. Moreover, by fixing other non-perturbative inputs through extractions of transverse momentum dependent functions in e+e- → h1h2X and semi-inclusive deep-inelastic scattering (SIDIS), we provide for the first time a consistency between certain spin/azimuthal asymmetries in all three reactions (i.e., pp, e+e-, and SIDIS).

ANin proton-proton collisions and the role of twist-3 fragmentation

We review and give an update on the current status of what causes transverse single-spin asymme- tries (TSSAs) in semi-inclusive processes where a single hadron is detected in the final state, especially those involving proton-proton (pp) collisions. In particular, we provide a new analysis within collinear factorization of TSSAs in high transverse momentum charged and neutral pion production in ppcollisions at the Relativistic Heavy Ion Collider (RHIC). This study incorporates the so-called twist-3 fragmentation term and shows that one can describe RHIC data through this mechanism. Moreover, by fixing other non-perturbative inputs through extractions of transverse momentum dependent functions in e + e − → h1h2X and semi-inclusive deep-inelastic scattering (SIDIS), we provide for the first time a consistency between certain spin/azimuthal asymmetries in all three reactions (i.e., pp, e + e − , and SIDIS).

Double Parton Interactions inp-Acollisions and Partonic Correlations

The Double Parton Scattering dynamics is different in p-p and in p-A collisions. Their joint study of DPS in p-p and in p-A collisions can therefore provide valuable information on the non-perturbative input to the process, namely multi-parton correlations, which cannot be obtained by studying DPS in p-p only. By studying WJJ production in p-Pb collisions, we estimate that the fraction of events due to DPS may be larger by a factor 3 or 4, as compared to p-p collisions, while the amount of the increased fraction can give information on the importance of different correlation terms.

Significance of gluon density at soft and hard processes at LHC

We study the role of the non-perturbative input to the transverse momentum dependent (TMD) gluon density in hard processes at the LHC. We derive the TMD gluon distribution from the fit of the inclusive hadron spectra measured at low transverse momenta in [Formula: see text] collisions at the LHC and demonstrate that the best description of these spectra for larger hadron transverse momenta can be achieved by matching the derived TMD gluon distribution with the exact solution of the Balitsky-Fadin-Kuraev-Lipatov (BFKL) equation obtained at small transverse momenta outside the saturation region. A special attention is put to the phenomenological applications of presented TMD parton densities to some LHC processes, which are sensitive to the quark and gluon content of a proton.

Isospin asymmetry inB→K*μ+μ−using AdS/QCD

We compute the isospin asymmetry distribution in the rare dileptonic decay $B \to K^* \mu^+ \mu^-$, in the dimuon mass squared ($q^2$) region below the $J/\Psi$ resonance, using non-perturbative inputs as predicted by the anti-de Sitter/Quantum Chromodynamics (AdS/QCD) correspondence and by Sum Rules. We predict a positive asymmetry at $q^2=0$ which flips sign in the region $q^2 \in [1,2]~\mbox{GeV}^2$ to remain small ($\le 2\%$) and negative for larger $q^2$. While our predictions are distinct as $q^2 \to 0$, they become hardly model-dependent $q^2 \ge 4~\mbox{GeV}^2$. We compare our predictions to the most recent LHCb data.

Perturbative QCD correlations in multi-parton collisions

We examine the role played in double parton interactions (DPI) by the parton--parton correlations originating from perturbative QCD parton splittings. Also presented are the results of the numerical analysis of the integrated DPI cross sections at Tevatron and LHC energies. To obtain the numerical results the knowledge of the single-parton GPDs gained by the HERA experiments was used to construct the non-perturbative input for generalized double parton distributions. The perturbative two-parton correlations induced by three-parton interactions contribute significantly to resolution of the longstanding puzzle of an excess of multi-jet production events in the back-to-back kinematics observed at the Tevatron.

DirectCPasymmetries of three-bodyBdecays in perturbative QCD

We propose a theoretical framework for analyzing three-body hadronic $B$ meson decays based on the perturbative QCD approach. The crucial nonperturbative input is a two-hadron distribution amplitude for final states, whose involved time-like form factor and rescattering phase are fit to relevant experimental data. Together with the short-distance strong phase from the $b$-quark decay kernel, we are able to make predictions for direct CP asymmetries in, for example, the $B^\pm \to \pi^+ \pi^- \pi^\pm$ and $\pi^+\pi^-K^\pm$ modes, which are consistent with the LHCb data in various localized regions of phase space. Applications of our formalism to other three-body hadronic and radiative $B$ meson decays are mentioned.

Higher twist in electroproduction: Flavor nonsinglet QCD evolution

We present results for the one loop anomalous dimension matrix of flavor non-singlet twist-4 operators of lowest spin that contribute to the leading moment of the $F_2$ structure function in deep inelastic electron-nucleon scattering. We analyze the flavor structure of the anomalous dimension matrix and decompose the leading moment of $F_2$ into separate flavor channels. In addition to building on previous work with higher-twist operators, these results can provide a benchmark for future work that generalizes to include the higher moments as well. We include non-perturbative input from the lattice and phenomenological estimates of the twist-4 matrix elements and estimate the twist-4 contributions to the leading moment of $F_2$. The results suggest that the overall twist-4 contribution may be suppressed due to either cancellations among the twist-4 terms or inherently small twist-4 matrix elements.

Mass of thebquark from lattice NRQCD and lattice perturbation theory

We present a determination of the b-quark mass accurate through O(\alpha_s^2) in perturbation theory and including partial contributions at O(\alpha_s^3). Nonperturbative input comes from the calculation of the Upsilon and B_s energies in lattice QCD including the effect of u, d and s sea quarks. We use an improved NRQCD action for the b-quark. This is combined with the heavy quark energy shift in NRQCD determined using a mixed approach of high-beta simulation and automated lattice perturbation theory. Comparison with experiment enables the quark mass to be extracted: in the MS bar scheme we find m_b(m_b) = 4.166(43) GeV.