QCD Factorization Formalism Research Articles

B→πℓνandBs→Kℓνform factors and|Vub|from2+1-flavor lattice QCD with domain-wall light quarks and relativistic heavy quarks

We calculate the $B \to\pi\ell\nu$ and $B_s \to K \ell\nu$ form factors in dynamical lattice QCD. We use the (2+1)-flavor RBC-UKQCD gauge-field ensembles generated with the domain-wall fermion and Iwasaki gauge actions. For the $b$ quarks we use the anisotropic clover action with a relativistic heavy-quark interpretation. We analyze two lattice spacings $a \approx 0.11, 0.086$ fm and unitary pion masses as light as $M_\pi \approx 290$ MeV. We simultaneously extrapolate our numerical results to the physical light-quark masses and to the continuum and interpolate in the pion/kaon energy using SU(2) "hard-pion" chiral perturbation theory. We provide complete error budgets for the form factors $f_+(q^2)$ and $f_0(q^2)$ at three momenta that span the $q^2$ range accessible in our numerical simulations. We extrapolate these results to $q^2 = 0$ using a model-independent $z$-parametrization and present our final form factors as the $z$-coefficients and the matrix of correlations between them. Our results agree with other lattice determinations using staggered light quarks and provide important independent cross-checks. Both $B \to\pi\ell\nu$ and $B_s \to K \ell\nu$ decays enable a determination of the CKM matrix element $|V_{ub}|$. To illustrate this, we perform a combined $z$-fit of our numerical $B\to\pi\ell\nu$ form-factor data with the experimental branching-fraction measurements leaving the relative normalization as a free parameter; we obtain $|V_{ub}| = 3.61(32) \times 10^{-3}$, where the error includes statistical and systematic uncertainties. This approach can be applied to $B_s\to K \ell\nu$ decay to determine $|V_{ub}|$ once the process has been measured experimentally. Finally, in anticipation of future measurements, we make predictions for $B \to \pi\ell\nu$ and $B_s\to K \ell\nu$ Standard-Model differential branching fractions and forward-backward asymmetries.

Exclusive radiative decays of W and Z bosons in QCD factorization

We present a detailed theoretical analysis of very rare, exclusive hadronic decays of the electroweak gauge bosons V=W, Z from first principles of QCD. Our main focus is on the radiative decays V->M+gamma, in which M is a pseudoscalar or vector meson. At leading order in an expansion in powers of Lambda_{QCD}/m_V the decay amplitudes can be factorized into convolutions of calculable hard-scattering coefficients with the leading-twist light-cone distribution amplitude of the meson M. Power corrections to the decay rates arise first at order (Lambda_{QCD}/m_V)^2. They can be estimated in terms of higher-twist distribution amplitudes and are predicted to be tiny. We include one-loop O(alpha_s) radiative corrections to the hard-scattering coefficients and perform the resummation of large logarithms [alpha_s log(m_V^2/mu_0^2)]^n (with mu_0=1 GeV a typical hadronic scale) to all orders in perturbation theory. Evolution effects have an important impact both numerically and conceptually, since they reduce the sensitivity to poorly determined hadronic parameters. We present detailed numerical predictions and error estimates, which can serve as benchmarks for future precision measurements. We also present an exploratory study of the weak radiative decays Z->M+W. Some of the decay modes studied here have branching ratios large enough to be accessible in the high-luminosity run of the LHC. Many of them can be measured with high accuracy at a future lepton collider. This will provide stringent tests of the QCD factorization formalism and enable novel searches for new physics.

Timelike pion form factor in lattice QCD

We perform a nonperturbative lattice calculation of the complex phase and modulus of the pion form factor in the timelike momentum region using the finite-volume technique. We use two ensembles of 2+1-flavor overlap fermion at pion masses m_pi = 380 and 290 MeV. By calculating the I = 1 correlators in the center-of-mass and three moving frames, we obtain the form factor at ten different values of the timelike momentum transfer around the vector resonance. We compare the results with the phenomenological model of Gounaris-Sakurai and its variant.

η(c) production at LHC and implications for the understanding of J/ψ production.

We present a complete evaluation for the prompt η_{c} production at the LHC at next-to-leading order in α_{s} in nonrelativistic QCD. By assuming heavy-quark spin symmetry, the recently observed η_{c} production data by LHCb results in a very strong constraint on the upper bound of the color-octet long-distance matrix element ⟨O^{J/ψ}(^{1}S_{0}^{[8]})⟩ of J/ψ. We find this upper bound is consistent with our previous study of the J/ψ yield and polarization and can give good descriptions for the measurements, but the upper bound is inconsistent with some other theoretical estimates. This may provide important information for understanding the nonrelativistic QCD factorization formalism.

The Hb b ¯ $$ Hb\overline{b} $$ form factor to three loops in QCD

We compute the three-loop QCD corrections to the vertex function for the Yukawa coupling of a Higgs boson to a pair of bottom quarks in the limit of vanishing quark masses. This QCD form factor is a crucial ingredient to third-order QCD corrections for the production of Higgs bosons in bottom quark fusion, and for the fully differential decay rate of Higgs bosons to bottom quarks. The infrared pole structure of the form factors agrees with the prediction from infrared factorization in QCD.

Computation of the electromagnetic pion form factor from lattice QCD in theεregime

We calculate the electromagnetic pion form factor in lattice QCD with 2+1 flavors of the dynamical overlap quarks. Up and down quark masses are set below their physical values so that the system is in the so-called epsilon regime with the small size of our lattice ~ 1.8 fm. The finite volume corrections are generally expected to be ~ 100% in the epsilon regime. We, however, find a way to automatically cancel the dominant part of them. Inserting non-zero momenta and taking appropriate ratios of the two and three point functions, we can eliminate the contribution from the zero-momentum pion mode. Then the remaining finite volume effect is a small perturbation from the non-zero modes. Our lattice data agree with this theoretical prediction and the extracted pion charge radius is consistent with the experiment.

Transverse charge and magnetization densities in holographic QCD

We present a study of flavor structures of transverse charge and anomalous magnetization densities for both unpolarized and transversely polarized nucleons. We consider two different models for the electromagnetic form factors in holographic QCD. The flavor form factors are obtained by decomposing the Dirac and Pauli form factors for nucleons using the charge and isospin symmetry. The results are compared with two standard phenomenological parametrizations.

Heavy quarkonium fragmentation functions from a heavy quark pair. I.Swave

A QCD factorization formalism was recently proposed for evaluating heavy quarkonium production at large $p_T$ at collider energies. With systematically calculated short-distance partonic hard parts and evolution kernels of fragmentation functions (FFs), the predictive power of this factorization approach relies on our knowledge of a large number of universal FFs at an input factorization scale $\mu_0\gtrsim 2m_Q$ with heavy quark mass $m_Q$. With the large heavy quark mass, the relative motion of the heavy quark pair inside a heavy quarkonium is effectively non-relativistic. We evaluate these universal input FFs using non-relativistic QCD (NRQCD) factorization, and express the large number of FFs in terms of a few universal NRQCD long-distance matrix elements (LDMEs) with perturbatively calculated coefficients. We derive complete contributions to the single-parton FFs at both ${\cal O}(\alpha_s)$ and ${\cal O}(\alpha_s^2)$, and the heavy quark pair FFs at ${\cal O}(\alpha_s)$. We present detailed derivation for all contributions involving LDMEs of $S$-wave NRQCD $Q\bar{Q}$-states ($P$-wave contributions in a companion paper). Our results bridge the gap between the QCD factorization formalism and its phenomenological applications.

Heavy quarkonium fragmentation functions from a heavy quark pair. II.Pwave

Recently, a new perturbative QCD factorization formalism for heavy quarkonium production at a large transverse momentum was proposed. Phenomenological application of this new approach relies on our knowledge of a large number of universal fragmentation functions (FFs) at an input factorization scale $\mu_0\gtrsim 2m_Q$ with heavy quark mass $m_Q$, which are nonperturbative, and in principle, should be extracted from data. With heavy quark mass $m_Q\gg \Lambda_{\rm QCD}$, we calculate these input FFs in terms of non-relativistic QCD (NRQCD) factorization. In a companion paper, we calculated these input FFs in NRQCD factorization approach including all contributions from $S$-wave NRQCD $Q\bar{Q}$-states. In this paper, we calculate contributions to the heavy quark-pair FFs from all $P$-wave NRQCD $Q\bar{Q}$-states.

Scalar pion form factor in two-flavor lattice QCD

We calculate the scalar form factor of the pion using two dynamical flavors of non-perturbatively $\mathcal{O}(a)$-improved Wilson fermions, including both the connected and the disconnected contribution to the relevant correlation functions. We employ the calculation of all-to-all propagators using stochastic sources and a generalized hopping parameter expansion. From the form factor data at vanishing momentum transfer, $Q^2=0$, and two non-vanishing $Q^2$ we obtain an estimate for the scalar radius $\left<r^2\right>^\pi_{_{\rm S}}$ of the pion at one value of the lattice spacing and for five different pion masses. Using Chiral Perturbation Theory at next-to-leading order, we find $\left<r^2\right>^\pi_{_{\rm S}}=0.635\pm0.016$ fm$^2$ at the physical pion mass (statistical error only). This is in good agreement with the phenomenological estimate from $\pi\pi$-scattering. The inclusion of the disconnected contribution is essential for achieving this level of agreement.

Matching of heavy-light flavour currents between HQET at order 1/m and QCD: I. Strategy and tree-level study

We present a strategy how to match the full set of components of the heavy-light axial and vector currents in Heavy Quark Effective Theory (HQET), up to and including 1/m h -corrections, to QCD. While the ultimate goal is to apply these matching conditions non-perturbatively, in this study we first have implemented them at tree-level, in order to find good choices of the matching observables with small $ \mathcal{O}\left( {{1 \left/ {{m_{\mathrm{h}}^2}} \right.}} \right) $ contributions. They can later be employed in the non-perturbative matching procedure which is a crucial part of precision HQET computations of semileptonic decay form factors in lattice QCD.

Quarkonium production in high energy proton-nucleus collisions: CGC meets NRQCD

We study the production of heavy quarkonium states in high energy proton-nucleus collisions. Following earlier work of Blaizot, Fujii, Gelis, and Venugopalan, we systematically include both small $x$ evolution and multiple scattering effects on heavy quark pair production within the Color Glass Condensate (CGC) framework. We obtain for the first time expressions in the Non-Relativistic QCD (NRQCD) factorization formalism for heavy quarkonium differential cross sections as a function of transverse momentum and rapidity. We observe that the production of color singlet heavy quark pairs is sensitive to both "quadrupole" and "dipole" Wilson line correlators, whose energy evolution is described by the Balitsky-JIMWLK equations. In contrast, the color octet channel is sensitive to dipole correlators alone. In a quasi-classical approximation, our results for the color singlet channel reduce to those of Dominguez et. al. [1]. We compare our results to those obtained combining the CGC with the color evaporation model and point to qualitative differences in the two approaches.

DOUBLE PARTON FRAGMENTATION FUNCTION AND ITS EVOLUTION IN QUARKONIUM PRODUCTION

We summarize the results of a recent study on a new perturbative QCD factorization formalism for the production of heavy quarkonia of large transverse momentum pT at collider energies. Such a new factorization formalism includes both the leading power (LP) and next-to-leading power (NLP) contributions to the cross section in the [Formula: see text] expansion for heavy quark mass mQ. For the NLP contribution, the so-called double parton fragmentation functions are involved, whose evolution equations have been derived. We estimate fragmentation functions in the non-relativistic QCD formalism, and found that their contribution reproduce the bulk of the large enhancement found in explicit NLO calculations in the color singlet model. Heavy quarkonia produced from NLP channels prefer longitudinal polarization, in contrast to the single parton fragmentation function. This might shed some light on the heavy quarkonium polarization puzzle.

Standard Model Predictions forB→Kℓ+ℓ−with Form Factors from Lattice QCD

We calculate, for the first time using unquenched lattice QCD form factors, the standard model differential branching fractions dB/dq2(B→Kℓ(+)ℓ(-)) for ℓ=e, μ, τ and compare with experimental measurements by Belle, BABAR, CDF, and LHCb. We report on B(B→Kℓ(+)ℓ(-)) in q2 bins used by experiment and predict B(B→Kτ(+)τ(-))=(1.41±0.15)×10(-7). We also calculate the ratio of branching fractions R(e)(μ)=1.00029(69) and predict R(ℓ)(τ)=1.176(40), for ℓ=e, μ. Finally, we calculate the "flat term" in the angular distribution of the differential decay rate F(H)(e,μ,τ) in experimentally motivated q2 bins.

γ*N→N(1535)transition form factors in QCD

The form factors, as well as the helicity amplitudes for the ${\ensuremath{\gamma}}^{*}N\ensuremath{\rightarrow}N(1535)$ transition, are calculated in the framework of the QCD light-cone sum rules. The contamination coming from diagonal transition is eliminated by considering combinations of the sum rules corresponding to different Lorentz structures. A similar procedure is applied for the determination of the residue and mass of the negative-parity baryon. A comparison of our predictions on the helicity amplitudes with the existing theoretical and experimental results is also presented.

Associated production of Υ(1S)W at LHC in next-to-leading order QCD

We investigate the complete next-to-leading order (NLO) QCD corrections to Υ(1S) + W production at the LHC, and predict theoretically the distribution of the Υ(1S) transverse momentum. We analyse the contributions from different components up to the QCD NLO in the pp → Υ(1S) + W + X process. Our results show that the pp → Υ(1S)+W +X process has a large production rate and could be potentially detected at the LHC. We see that the differential cross section for the Υ(1S) direct-production at the LO is significantly enhanced by the QCD corrections, and the $ b\overline{b}\left[ {^3S_1^{(8) }} \right] $ contribution component dominates in the whole plotted $ p{{_T^{\varUpsilon}}^{{\left( {1S} \right)}}} $ region. We have also calculated the Υ(1S) meson indirect-productions via feed-down decays of Υ(2S), Υ(3S), χ b1(1P), χ b2(1P), χ b1(2P), and χ b2(2P) mesons. We find that the Υ(1S) indirect-productions can give important contributions to the distribution of $ p_T^{{\varUpsilon \left( {1S} \right)}} $ for the pp → Υ(1S) + W + X process at the NLO. We conclude that the studying the Υ(1S) + W production at the LHC could provide an interesting opportunity in testing the nonrelativistic QCD factorization formalism.

Quarkonium+γ production in coherent hadron–hadron interactions at LHC energies

In this paper we study the $H + \gamma$ ($H = J/\Psi$ and $\Upsilon$) production in coherent hadron - hadron interactions at LHC energies. Considering the ultrarelativistic protons as a source of photons, we estimate the $\gamma + p \rightarrow H + \gamma + X$ cross section using the non-relativistic QCD (NRQCD) factorization formalism and considering different sets of values for the matrix elements. Our results for the total $ p + p \rightarrow p + H + \gamma + X$ cross sections and rapidity distributions at $\sqrt{s} = 7$ and 14 TeV demonstrate that the experimental analysis of the $J/\Psi + \gamma$ production at LHC is feasible.

Space- and time-like kaon electromagnetic form factors in perturbative QCD

We present a phenomenological analysis of the space- and time-like charged kaon electromagnetic form factors in factorized perturbative QCD (pQCD) by employing an analytic model for αs(Q2) and an infrared (IR) finite gluon propagator. In the space-like region, due to the lack of available experimental data above Q2 ∼ 0.2 GeV2, we only give our results for intermediate energies and make no comparison. In the time-like region, our results agree reasonably well with the available experimental data at moderate energies, including the CLEO data and the J/ψ result.

Comparative analysis of the semileptonic Λ b → Λℓ+ℓ− transition in SM and different SUSY scenarios using form factors from full QCD

We work out the semileptonic $\Lambda_b\rightarrow \Lambda \ell^+ \ell^-$ transition in standard as well as different supersymmetric models. In particular, considering the parametrization of the matrix elements entered the low energy effective Hamiltonian in terms of form factors in full QCD, we calculate the amplitude and differential decay rate responsible for this decay channel in supersymmetric models. We then use the form factors calculated via light cone QCD sum rules in full theory to analyze the differential branching ratio and lepton forward-backward asymmetry of this decay channel in different supersymmetric models and compare the obtained results with those of the standard model. We also discuss how the results of different supersymmetric models deviate from the standard model predictions and which SUSY scenarios are favored.

Prompt heavy quarkonium production in association with a massive (anti)bottom quark at the LHC

In this work, we investigate the associated production of prompt heavy quarkonium and a massive (anti)bottom quark to leading order in the nonrelativistic QCD factorization formalism at the LHC. We present numerical results for the processes involving $J/\ensuremath{\psi}$, ${\ensuremath{\chi}}_{cJ}$, $\ensuremath{\Upsilon}$ and ${\ensuremath{\chi}}_{bJ}$. From our work, we find that the production rates of these processes are quite large, and these processes have the potential to be detected at the LHC. When ${p}_{T}$ is smaller than about 10 GeV, the $c\overline{c}[^{1}S_{0}^{(8)}]$ states give the main contribution to the ${p}_{T}$ distribution of prompt $J/\ensuremath{\psi}$ with a massive (anti)bottom quark production. For the process $pp\ensuremath{\rightarrow}\ensuremath{\Upsilon}+b(\overline{b})$, the contribution of the color-singlet mechanism is larger than that in the color-octet mechanism at low ${p}_{T}$ region. We also investigate the processes $pp\ensuremath{\rightarrow}{\ensuremath{\chi}}_{cJ}+b(\overline{b})$ and $pp\ensuremath{\rightarrow}{\ensuremath{\chi}}_{bJ}+b(\overline{b})$; the ${p}_{T}$ distributions are dominated by the color-octet Fock-state contribution at large ${p}_{T}$. These processes provide an interesting signature that could be studied at the LHC, and the measurement of these processes is useful to test the color-singlet mechanism and color-octet mechanism.