Formulation Of QCD Research Articles

The Sivers asymmetry in hadronic dijet production

We study the single spin asymmetry in the back-to-back dijet production in transversely polarized proton-proton collisions. Such an asymmetry is generated by the Sivers functions in the incoming polarized proton. We propose a QCD formalism in terms of the transverse momentum dependent parton distribution functions, which allow us to resum the large logarithms that arise in the perturbative calculations. We make predictions for the Sivers asymmetry of hadronic dijet production at the kinematic region that is relevant to the experiment at the Relativistic Heavy Ion Collider (RHIC). We further compute the spin asymmetries in the selected positive and negative jet charge bins, to separate the contributions from u- and d-quark Sivers functions. We find that both the sign and size of our numerical results are roughly consistent with the preliminary results from the STAR collaboration at the RHIC.

Global analysis of the Sivers functions at NLO+NNLL in QCD

We perform global fit to the quark Sivers function within the transverse momentum dependent (TMD) factorization formalism in QCD. We simultaneously fit Sivers asymmetry data from Semi-Inclusive Deep Inelastic Scattering (SIDIS) at COMPASS, HERMES, and JLab, from Drell-Yan lepton pair production at COMPASS, and from W/Z boson at RHIC. This extraction is performed at next-to-leading order (NLO) and next-to-next-to leading logarithmic (NNLL) accuracy. We find excellent agreement between our extracted asymmetry and the experimental data for SIDIS and Drell-Yan lepton pair production, while tension arises when trying to describe the spin asymmetries of W/Z bosons at RHIC. We carefully assess the situation, and we study in details the impact of the RHIC data and their implications through different ways of performing the fit. In addition, we find that the quality of the description of W/Z vector boson asymmetry data could be strongly sensitive to the DGLAP evolution of Qiu-Sterman function, besides the usual TMD evolution. We present discussion on this and the implications for measurements of the transverse-spin asymmetries at the future Electron Ion Collider.

Quarkonium Production in Heavy Ion Collisions: From Open Quantum System to Transport Equation

Using the open quantum system formalism and effective field theory of QCD, we derive the Boltzmann transport equation of quarkonium inside the quark-gluon plasma. Our derivation illuminates that the success of transport equations in quarkonium phenomenology is closely related to the separation of scales in the problem.

Chi _{c1} and chi _{c2} polarization as a probe of color octet channel

We analyze joint LHC data on the production of chi _{c1} and chi _{c2} mesons together with the polarization data obtained very recently by the CMS Collaboration at sqrt{s} = 8 TeV. Our consideration is based on the k_T-factorization approach and nonrelativistic QCD formalism for the formation of bound states. The observed polar anisotropy of chi _{c1} and chi _{c2} decays can be described as a combined effect of the color-singlet and color-octet contributions. We extract the corresponding long-distance matrix elements from the fits. Our fits point to unequal color singlet wave functions for chi _{c1} and chi _{c2} states.

Bottomonium spectroscopy motivated by general features of pNRQCD

The bottomonium mass spectra are computed in the framework of potential non-relativistic quantum chromodynamics. The potential consists of a static term incorporating the Coulomb plus confinement part along with a correction term added non-perturbatively from pNRQCD, which is classified in powers of the inverse of the heavy quark mass O(1/m). The masses of excited bottomonia are calculated by perturbatively adding spin–hyperfine, spin–orbit and tensor components of one-gluon exchange interactions in powers of O(1/m 2). Calculated masses are found to be consistent with other theoretical studies and experimental data. The Regge trajectories of the calculated mass spectra are also constructed. The values of the wave functions are extracted and employed to calculate the electromagnetic transition widths and γγ, e + e −, light hadron and γγγ decay widths of several states at various leading orders, within the non-relativistic QCD formalism. Some of the experimentally reported states of bottomonium family like ϒ(10 860), ϒ(11 020) and X(10 610) are identified as mixed S–D wave and P wave states.

Master-field simulations of O([formula omitted])-improved lattice QCD: Algorithms, stability and exactness

In master-field simulations of lattice QCD, the expectation values of interest are obtained from a single or at most a few representative gauge-field configurations on very large lattices. If the light quarks are included, the generation of these fields using standard techniques is however challenging in view of various algorithmic instabilities and precision issues. Ways to overcome these problems are described here for the case of the O(a)-improved Wilson formulation of lattice QCD and the viability of the proposed measures is then checked in extensive simulations of the theory with 2+1 flavours of quarks.

Bottomonia production and polarization in the NRQCD with k_T-factorization. II: Upsilon (2S) and chi _b(2P) mesons

The Upsilon (2S) production and polarization at high energies is studied in the framework of k_T-factorization approach. Our consideration is based on the non-relativistic QCD formalism for bound states formation and off-shell production amplitudes for hard partonic subprocesses. The direct production mechanism, feed-down contributions from radiative chi _b(3P) and chi _b(2P) decays and contributions from Upsilon (3S) decays are taken into account. The transverse momentum dependent gluon densities in a proton were derived from the Ciafaloni–Catani–Fiorani–Marchesini evolution equation, Kimber-Martin-Ryskin prescription and Parton Branching method. Treating the non-perturbative color octet transitions in terms of the mulitpole radiation theory, we extract the corresponding non-perturbative matrix elements for Upsilon (2S) and chi _b(2P) mesons from a combined fit to Upsilon (2S) transverse momenta distributions measured by the CMS and ATLAS Collaborations at the LHC energies sqrt{s} = 7 and 13 TeV and from the relative production rate R^{chi _b(2P)}_{Upsilon (2S)} measured by the LHCb Collaboration at sqrt{s} = 7 and 8 TeV. Then we apply the extracted values to investigate the polarization parameters lambda _theta , lambda _phi and lambda _{theta phi }, which determine the Upsilon (2S) spin density matrix. Our predictions have a good agreement with the currently available data within the theoretical and experimental uncertainties.

Ultrarelativistic quark-nucleus scattering in a light-front Hamiltonian approach

We investigate the scattering of a quark on a heavy nucleus at high energies using the time-dependent basis light-front quantization (tBLFQ) formalism, which is the first application of the tBLFQ formalism in QCD. We present the real-time evolution of the quark wave function in a strong classical color field of the relativistic nucleus, described as the Color Glass Condensate. The quark and the nucleus color field are simulated in the QCD SU(3) color space. We calculate the total and the differential cross sections, and the quark distribution in coordinate and color spaces using the tBLFQ approach. We recover the eikonal cross sections in the eikonal limit. We find that the differential cross section from the tBLFQ simulation is in agreement with a perturbative calculation at large $p_\perp$, and it deviates from the perturbative calculation at small $p_\perp$ due to higher-order contributions. In particular, we relax the eikonal limit by letting the quark carry realistic finite longitudinal momenta. We study the sub-eikonal effect on the quark through the transverse coordinate distribution of the quark with different longitudinal momentum, and we find the sub-eikonal effect to be sizable. Our results can significantly reduce the theoretical uncertainties in small $p_\perp$ region which has important implications to the phenomenology of the hadron-nucleus and deep inelastic scattering at high energies.

Radius of convergence in lattice QCD at finite μB with rooted staggered fermions

In typical statistical mechanical systems the grand canonical partition function at finite volume is proportional to a polynomial of the fugacity $e^{\mu/T}$. The zero of this Lee-Yang polynomial closest to the origin determines the radius of convergence of the Taylor expansion of the pressure around $\mu=0$. The computationally cheapest formulation of lattice QCD, rooted staggered fermions, with the usual definition of the rooted determinant, does not admit such a Lee-Yang polynomial. We argue that the radius of convergence is then bounded by the spectral gap of the reduced matrix of the unrooted staggered operator. This is a cutoff effect that potentially affects all estimates of the radius of convergence with the standard staggered rooting. We suggest a new definition of the rooted staggered determinant at finite chemical potential that allows for a definition of a Lee-Yang polynomial, and, therefore of the numerical study of Lee-Yang zeros. We also describe an algorithm to determine the Lee-Yang zeros and apply it to configurations generated with the 2-stout improved staggered action at $N_t = 4$. We perform a finite-volume scaling study of the leading Lee-Yang zeros and estimate the radius of convergence of the Taylor expansion extrapolated to an infinite volume. We show that the limiting singularity is not on the real line, thus giving a lower bound on the location of any possible phase transitions at this lattice spacing. In the vicinity of the crossover temperature at zero chemical potential, the radius of convergence turns out to be $\mu_B/T \approx 2$ and roughly temperature independent. Our simulations are performed at strange quark chemical potential $\mu_s=0$, but the method can be straightforwardly extended to strangeness chemical potential $\mu_S=0$ or strangeness neutrality.

The transverse nucleon single-spin asymmetry for the semi-inclusive production of photons in lepton-nucleon scattering

We study the semi-inclusive production of real, high-pT, isolated photons in unpolarized and polarized lepton-proton collisions, ℓp→ℓγX. In particular we analyze the transverse nucleon single-spin asymmetry within the collinear twist-3 formalism in perturbative QCD to leading order (LO) accuracy. We find that this spin asymmetry is generated by twist-3 dynamical quark-gluon-quark (qgq) correlations in the nucleon through the so-called soft-fermion and hard pole contributions. Hence, this process unprecedentedly allows for a point-by-point scan of the support of the dynamical qgq twist-3 matrix elements FFT(x,x′) and GFT(x,x′) in lepton-nucleon scattering experiments.

Are there any challenges in the charmonia production and polarization at the LHC?

We analyze the inclusive prompt production of $\psi^\prime$, $\chi_c$, $J/\psi$ and $\eta_c$ mesons at the LHC using the $k_T$-factorization approach. Our consideration is based on the off-shell production amplitudes for hard partonic subprocesses, nonrelativistic QCD formalism for the formation of bound states and transverse momentum dependent (or unintegrated) gluon densities in a proton derived from Catani-Ciafaloni-Fiorani-Marchesini equation. The nonperturbative color octet transitions are treated in terms of the multipole radiation theory. We extract the corresponding long-distance matrix elements from a combined fit to transverse momentum distributions measured at various LHC experiments. We make predictions for the polarization parameters $\lambda_\theta$, $\lambda_\phi$, $\lambda_{\theta \phi}$ and the frame-independent parameter $\lambda^*$ and compare them to the available $\psi^\prime$ and $J/\psi$ data. Finally, we present a universal set of parameters that provides a reasonable simultaneous description for the whole body of the LHC data (on the $p_T$ distributions, relative production rates and polarization observables) for the whole charmonium family.

Jet fragmentation functions for Z-tagged jets

Recently the LHCb collaboration has measured both longitudinal and transverse momentum distribution of hadrons produced inside Z-tagged jets in proton-proton collisions at the Large Hadron Collider. These distributions are commonly referred to as jet fragmentation functions and are characterized by the longitudinal momentum fraction zh of the jet carried by the hadron and the transverse momentum j⊥ with respect to the jet direction. We derive a QCD formalism within Soft-Collinear Effective Theory to describe these distributions and find that the zh-dependence provides information on standard collinear fragmentation functions, while j⊥-dependence probes transverse momentum dependent (TMD) fragmentation functions. We perform theoretical calculations and compare our results with the LHCb data. We find good agreement for the intermediate zh region. For j⊥-dependence, we suggest binning in both zh and j⊥, which would lead to a more direct probing of TMD fragmentation functions.

Low x physics as an infinite twist (G)TMD framework: unravelling the origins of saturation

We show how the formulations of low x physics involving Wilson line operators can be fully rewritten into an infinite twist TMD or GTMD framework, respectively for inclusive and exclusive observables. This leads to a perfect match between low x physics and moderate x formulations of QCD in terms of GTMDs, TMDs, GPDs or PDFs. We derive the BFKL limit as a kinematic limit and argue that beyond the Wandzura-Wilczek approximation, 3-body and 4-body unintegrated PFDs should be taken into account even in this regime. Finally we analyse how saturation should be understood as 3 distinct effects: saturation through non-linearities in the evolution equations at small x, saturation through multiple interactions with slow gluons as TMD gauge links, and saturation as the enhancement of genuine twist corrections.

Bottomonia production and polarization in the NRQCD with k_T-factorization. I: Upsilon (3S) and chi _b(3P) mesons

The Upsilon (3S) production and polarization at high energies is studied in the framework of k_T-factorization approach. Our consideration is based on the non-relativistic QCD formalism for bound states formation and off-shell production amplitudes for hard partonic subprocesses. The transverse momentum dependent (TMD, or unintegrated) gluon densities in a proton were derived from the Ciafaloni-Catani-Fiorani-Marchesini (CCFM) evolution equation as well as from the Kimber–Martin–Ryskin (KMR) prescription. Treating the non-perturbative color octet transitions in terms of the multipole radiation theory and taking into account feed-down contributions from radiative chi _b(3P) decays, we extract the corresponding non-perturbative matrix elements for Upsilon (3S) and chi _b(3P) mesons from a combined fit to Upsilon (3S) transverse momenta distributions measured by the CMS and ATLAS Collaborations at the LHC energies sqrt{s} = 7 and 13 TeV and central rapidities. Then we apply the extracted values to describe the CDF and LHCb data on Upsilon (3S) production and to investigate the polarization parameters lambda _theta , lambda _phi and lambda _{theta phi }, which determine the Upsilon (3S) spin density matrix. Our predictions have a good agreement with the currently available data within the theoretical and experimental uncertainties.

Phenomenological studies on the Bd,s0→J/ψf0(500)[f0(980)] decays

Encouraged by the global agreement between theoretical predictions and experimental measurements for $B \to J/\psi V$ decays, we extend that perturbative QCD formalism to $B_{d,s}^0 \to J/\psi f_0(500) [f_0(980)]$ decays at the presently known next-to-leading order in the quark-antiquark description of $f_0(500)$ and $f_0(980)$. With the angle $\phi_f \approx 25^\circ$ of the $f_0(500)-f_0(980)$ mixing in the quark-flavor basis, we find that the branching ratios of the $B_d^0 \to J/\psi f_0(500) (\to \pi^+ \pi^-)$ and $B_{d,s}^0 \to J/\psi f_0(980) (\to \pi^+ \pi^-)$ modes generally agree with the current data or the upper limits within uncertainties, except for the seemingly challenging $B_s^0 \to J/\psi f_0(500) (\to \pi^+\pi^-)$ one. Then, we further explore the relevant observables of the $B_{d,s}^0 \to J/\psi f_0(500) [f_0(980)]$ decays, which could provide further constraints on the mixing angle $\phi_f$ and/or SU(3) flavor symmetry breaking effects. As a byproduct, we predict ${\rm BR}(B_{d}^0 \to J/\psi f_0(980)(\to K^+ K^-))=5.8^{+3.1}_{-2.9} \times 10^{-7}$ and ${\rm BR}(B_{s}^0 \to J/\psi f_0(980)(\to K^+ K^-)) =4.6^{+2.6}_{-2.3} \times 10^{-5}$. All theoretical predictions await the future examinations with high precision.

Deciphering the X(3872) via its Polarization in Prompt Production at the CERN LHC.

Based on the hypothesis that the X(3872) exotic hadron is a mixture of χ_{c1}(2P) and other states and that its prompt hadroproduction predominately proceeds via its χ_{c1}(2P) component, we calculate the prompt-X(3872) polarization at the CERN LHC through next-to-leading order in α_{s} within the factorization formalism of nonrelativistic QCD, including both the color-singlet ^{3}P_{1}^{[1]} and color-octet ^{3}S_{1}^{[8]} cc[over ¯] Fock states. We also consider the polarization of the J/ψ produced by the subsequent X(3872) decay. We predict that, under ATLAS, CMS, and LHCb experimental conditions, the X(3872) is largely longitudinally polarized, while the J/ψ is largely transversely polarized. We propose that the LHC experiments perform such polarization measurements to pin down the nature of the X(3872) and other X, Y, Z exotic states with nonzero spin.

Prompt eta _c meson production at the LHC in the NRQCD with k_T-factorization

In the framework of the k_T-factorization approach, the prompt production of eta _c mesons at the LHC conditions is studied. Our consideration is based on the off-shell amplitudes for hard partonic subprocesses and on the nonrelativistic QCD (NRQCD) formalism for the formation of bound states. We try two latest parametrizations for noncollinear, or transverse momentum dependent (TMD) gluon densities derived from the Catani–Ciafaloni–Fiorani–Marchesini (CCFM) equation. We use the values of the nonperturbative matrix elements obtained from a combined fit of the eta _c and J/psi differential cross sections. Finally, we show an universal set of parameters that provides a reasonable simultaneous description for all of the available data on the prompt J/psi and eta _c production at the LHC.

Induced QCD II: numerical results

We numerically explore an alternative discretization of continuum SU(Nc) Yang-Mills theory on a Euclidean spacetime lattice, originally introduced by Budzcies and Zirnbauer for gauge group U(Nc). This discretization can be reformulated such that the self-interactions of the gauge field are induced by a path integral over Nb auxiliary bosonic fields, which couple linearly to the gauge field. In the first paper of the series we have shown that the theory reproduces continuum SU(Nc) Yang-Mills theory in d = 2 dimensions if Nb is larger than Nc − frac{3}{4} and conjectured, following the argument of Budzcies and Zirnbauer, that this remains true for d > 2. In the present paper, we test this conjecture by performing lattice simulations of the simplest nontrivial case, i.e., gauge group SU(2) in three dimensions. We show that observables computed in the induced theory, such as the static q overline{q} potential and the deconfinement transition temperature, agree with the same observables computed from the ordinary plaquette action up to lattice artifacts. We also find evidence that the bound for Nb can be relaxed to Nc − frac{5}{4} as conjectured in our earlier paper. Studies of how the new discretization can be used to change the order of integration in the path integral to arrive at dual formulations of QCD are left for future work.

Studies on the decays in the perturbative QCD approach**Research exercises for excellent undergraduate students.

The decays are investigated for the first time in the perturbative QCD formalism based on the kT factorization theorem, where the light scalar κ is assumed as a two-quark state. Our numerical results and phenomenological analyses on the CP-averaged branching ratios and CP-violating asymmetries show that: (a) the and decays have large decay rates around , which could be examined by the upgraded large hadron collider beauty and/or Belle-II experiments in the near future; (b) a large decay rate of about appears in the pure annihilation channel, which could provide more evidence to help distinguish different QCD-inspired factorization approaches, even understand the annihilation decay mechanism; (c) the pure penguin modes and would provide a promising ground to search for the possible new physics because of their zero direct and mixing-induced CP violations in the standard model. The examinations with good precision from the future experiments will help to further study the perturbative and/or nonperturbative QCD dynamics involved in these considered decay modes.

Dual models of QCD and their implications

Some of the dual formulations of QCD are reviewed and analyzed for their possible implications especially in non-perturbative sector of QCD at zero temperature. Starting from the Nambu-Mandelstam idea and the ’t Hooft Abelian Projection technique, the effective formulations of QCD like the dual GinzburgLandau formulation and magnetic symmetry based dual QCD formulation have been analyzed in which dual magnetic potentials coupled with monopole field act as fundamental variables. The dual dynamics associated with these models is discussed in the quenched approximation and the analysis of symmetry breaking , flux tube configurations, confinement potential and nature of dual QCD vacuum is presented which establishes magnetic symmetry based dual QCD formulation as a more effective topological viable formulation for analysing the non-perturbative aspects of QCD.