Leptons from heavy-quark semileptonic decay in pA collisions within the CGC framework

We study single lepton production from semileptonic decays of heavy flavor hadrons ($D,B\rightarrow~l$) in pp and p$A$ collisions at RHIC and the LHC within the saturation/Color-Glass-Condensate (CGC) framework. Using the gluon distribution function obtained with the dipole amplitude, whose energy dependence is described by the Balitsky-Kovchegov equation with running coupling effect, we compute the transverse-momentum ($p_\perp$) spectra of the lepton yields at mid and forward rapidities. We find that a large fraction of leptons at low $p_\perp$ stems from the saturation regime of the incoming gluons in the target, especially in p$A$ collisions at the LHC. The resultant $p_\perp$ spectra is slightly harder than the data, but the nuclear modification factor seems consistent with the data within some uncertainty. We also update the nuclear modification factors for J/$\psi$ and $D$ meson at the LHC energy.Comment: 19 pages, 11 figures; v2 Figure 5 replaced; v3 Figures 3,4,5,6,7,8,9 replaced; v4 typo in (1) correcte

Nuclear modification of forward DD production in pPb collisions at the LHC

We study nuclear modification factors for single $D$ meson and semileptonic decay lepton $l$ ($=e,\mu$) production in minimum bias proton-nucleus (p$A$) collisions at the LHC in the color-glass-condensate (CGC) framework at leading order in strong coupling. In our numerical computations, transverse momentum ($k_\perp$) dependent multi-point Wilson line correlators are employed for describing target nucleus for p$A$ and proton for pp. The projectile proton is treated with unintegrated gluon distribution function, which is also $k_\perp$-dependent. The rapidity evolutions of these functions in the small Bjorken $x$ region are taken into account by solving running coupling Balitsky-Kovchegov (BK) equation at leading logarithmic accuracy. For simplicity, we employ Kartvelishvili's type fragmentation function and a simple model for lepton energy distribution from seileptonic decay, respectively, to compute differential cross sections for $D$ and $l$ production. The gluon saturation scale inside the heavy nucleus is enhanced and dependent on $x$, which we take into account by replacing the initial saturation scale in the BK equation with a larger value for the heavy nucleus. We show that the saturation effect leads to perceptible nuclear suppression of $D$ production at forward rapidity. Our numerical results predict similar nuclear suppressions in p$A$ collisions for forward $l$ production at lower transverse momentum $p_\perp<2\;{\rm GeV}$. Numerical tables on the nuclear modifications of $D$ and $l$ are listed in this note.Comment: 12 pages, 3 figures; v2: typo in (3) correcte

Heavy quark pair production in high energy pA collisions: Open heavy flavors

We study open heavy flavor meson production in proton-nucleus (pA) collisions at RHIC and LHC energies within the Color Glass Condensate framework. We use the unintegrated gluon distribution at small Bjorken's x in the proton obtained by solving the Balitsky-Kovchegov equation with running coupling correction and constrained by global fitting of HERA data. We change the initial saturation scale of the gluon distribution for the heavy nucleus. The gluon distribution with McLerran-Venugopalan model initial condition is also used for comparison. We present transverse momentum spectra of single D and B productions in pA collisions, and the so-called nuclear modification factor. The azimuthal angle correlation of open heavy flavor meson pair is also computed to study the modification due to the gluon saturation in the heavy nucleus at the LHC.Comment: 20 pages, 10 figure

Magnetic screening in high-energy heavy-ion collisions

We show that classical chromomagnetic fields produced coherently in the initial stage of a heavy-ion collision exhibit screening. From the two-point field strength correlator we determine the magnetic mass for SU(2) to be m ~ 5 times the saturation scale. Magnetic screening leads to an intuitive understanding of the area law scaling of spatial Wilson loops observed previously. The presence of screening effects in the initial state provides a basis for defining kinetic processes in the early stage of heavy-ion collisions, with electric and magnetic masses of the same order

Chiral phase transition in a random matrix model with three flavors

The chiral phase transition in the conventional random matrix model is the second order in the chiral limit, irrespective of the number of flavors N_f, because it lacks the U_A(1)-breaking determinant interaction term. Furthermore, it predicts an unphysical value of zero for the topological susceptibility at finite temperatures. We propose a new chiral random matrix model which resolves these difficulties by incorporating the determinant interaction term within the instanton gas picture. The model produces a second-order transition for N_f=2 and a first-order transition for N_f=3, and recovers a physical temperature dependence of the topological susceptibility.Comment: 7 pages, 3 figures, Contribution to The XXVII International Symposium on Lattice Field Theor

Quantitative study of the violation of kt-factorization in hadroproduction of quarks at collider energies

We demonstrate the violation of kT-factorization for quark production in high energy hadronic collisions. This violation is quantified in the Color Glass Condensate framework and studied as a function of the quark mass, the quark transverse momentum, and the saturation scale Qsat, which is a measure of large parton densities. At x values where parton densities are large but leading twist shadowing effects are still small, violations of kT-factorization can be significant - especially for lighter quarks. At very small x, where leading twist shadowing is large, we show that violations of kT-factorization are relatively weaker.Comment: 4 pages, 6 figures, final version to appear in PR

Application of the Lefschetz thimble formulation to the (0+1) dim. Thirring model at finite density

Based on the Lefschetz thimble formulation of path-integration, we analyze the (0+1) dimensional Thirring model at finite chemical potentials and perform hybrid Monte Carlo (HMC) simulations. We adopt the lattice action defined with the staggered fermion and a compact link field for the auxiliary vector field. We firstly locate the critical points (saddle points) of the gradient flows within the subspace of time-independent (complex) link field, and study the thiemble structure and the Stokes phenomenon to identify the thimbles which contribute to the path-integral. Then, we perform HMC simulations on the single dominant thimble and compare the results to the exact solution. The numerical results are in agreement with the exact ones in small and large chemical potential regions, while they show some deviation in the crossover region in the chemical potential. We also comment on the necessity of the contributions from multiple thimbles in the crossover region.Comment: 7 pages, 7 figures, talk presented at the 33rd International Symposium on Lattice Field Theory - Lattice 2015, July 14-18, 2015, Kobe International Conference Center, Kobe, Japa

Monte Carlo study of Lefschetz thimble structure in one-dimensional Thirring model at finite density

We consider the one-dimensional massive Thirring model formulated on the lattice with staggered fermions and an auxiliary compact vector (link) field, which is exactly solvable and shows a phase transition with increasing the chemical potential of fermion number: the crossover at a finite temperature and the first order transition at zero temperature. We complexify its path-integration on Lefschetz thimbles and examine its phase transition by hybrid Monte Carlo simulations on the single dominant thimble. We observe a discrepancy between the numerical and exact results in the crossover region for small inverse coupling $\beta$ and/or large lattice size $L$, while they are in good agreement at the lower and higher density regions. We also observe that the discrepancy persists in the continuum limit keeping the temperature finite and it becomes more significant toward the low-temperature limit. This numerical result is consistent with our analytical study of the model's thimble structure. And these results imply that the contributions of subdominant thimbles should be summed up in order to reproduce the first order transition in the low-temperature limit.Comment: 15 pages, 10 figures. The revised version of the manuscript. v4: Corrected a simple bug in implementing the HMC algorithm and replaced fig.4-10. Our main conclusions remain unchanged. Erratum published in JHE

Performance of Complex Langevin Simulation in 0+1 dimensional massive Thirring model at finite density

Statistical sampling with the complex Langevin (CL) equation is applied to (0+1)-dimensional Thirring model, and its uniform-field variant, at finite fermion chemical potential $\mu$. The CL simulation reproduces a crossover behavior which is similar to but actually deviating from the exact solution in the transition region, where we confirm that the CL simulation becomes susceptible to the drift singularities, i.e., zeros of the fermion determinant. In order to simulate the transition region with the CL method correctly, we examine two approaches, a reweighting method and a model deformation, in both of which a single thimble with an attractive fixed point practically covers the integration domain and the CL sampling avoids the determinant zeros. It turns out that these methods can reproduce the correct crossover behavior of the original model with using reference ensembles in the complexified space. However, they need evaluation of the reweighting factor, which scales with the system size exponentially. We discuss feasibility of applying these methods to the Thirring model and to more realistic theories.Comment: 31 pages, 15 figure

Finite pulse effects on e+e−e^{+}e^{-} pair creation from strong electric fields

We investigate electron-positron pair creation from the vacuum in a pulsed electric background field. Employing the Sauter-type pulsed field $E(t)=E_0 {\rm sech}^2 (t/\tau)$ with height $E_0$ and width $\tau$, we demonstrate explicitly the interplay between the nonperturbative and perturbative aspects of pair creation in the background field. We analytically compute the number of produced pairs from the vacuum in the Sauter-type field, and the result reproduces Schwinger's nonperturbative formula in the long pulse limit (the constant field limit), while in the short pulse limit it coincides with the leading-order perturbative result. We show that two dimensionless parameters $\nu = |eE_0| \tau^2$ and $\gamma = |eE_0| \tau /m_e$ characterize the importance of multiple interactions with the fields and the transition from the perturbative to the nonperturbative regime. We also find that pair creation is enhanced compared to Schwinger's formula when the field strength is relativity weak $|eE_0|/m_e^2 \lesssim 1$ and the pulse duration is relatively short $m_e \tau \lesssim 1$, and reveal that the enhancement is predominantly described by the lowest order perturbation with a single photon.Comment: 12 pages, 8 figures; v2: discussion improved and some figures added; v3: PRD versio