Large Quark Mass Research Articles

Comparison of different source calculations in two-nucleon channel at large quark mass

We investigate a systematic error coming from higher excited state contributions in the energy shift of light nucleus in the two-nucleon channel by comparing two different source calculations with the exponential and wall sources. Since it is hard to obtain a clear signal of the wall source correlation function in a plateau region, we employ a large quark mass as the pion mass is 0.8 GeV in quenched QCD. We discuss the systematic error in the spin-triplet channel of the two-nucleon system, and the volume dependence of the energy shift.

Dirac-mode analysis for quark number density and its application for deconfinement transition

The quark number density at finite imaginary chemical potential is investigated in the lattice QCD using the Dirac-mode expansion. We find the analytical formula of the quark number density in terms of the Polyakov loop in the large quark mass regime. On the other hand, in the small quark mass region, the quark number density is investigated by using the quenched lattice QCD simulation. The quark number density is found to strongly depend on the low-lying Dirac modes while its sign does not change. This result leads to that the quark number holonomy is not sensitive to the low-lying Dirac modes. We discuss the confinement-deconfinement transition from the property of the quark number density and the quark number holonomy.

Mapping the QCD phase diagram with susceptibilities of conserved charges within Nambu–Jona-Lasinio model

We evaluate the second to fourth-order baryon, charge and strangeness susceptibilities near a chiral critical point using the Nambu–Jona-Lasinio model under different temperatures and baryon chemical potential. Baryon number susceptibilities are found to be of the greatest magnitude, offering the strongest signal. Whereas the strangeness susceptibilities have the smallest divergence dominating area, owing to the large strange quark mass. We also make an attempt to compare our results with experiment data. The trend at high collision energy is found to be consistent between theory and experiment. The model calculation predicts more complex behavior at low collision energies, near the postulated critical end point.

Locations of Roberge-Weiss transition endpoints in lattice QCD with Nf=2 improved Kogut-Susskind quarks

Result on the locations of the tricritical points of $N_f=2$ lattice QCD with imaginary chemical potential is presented. Simulations are carried out with Symanzik improved gauge action and Asqtad fermion action. With imaginary chemical potential $i\mu_I=i\pi T$, previous studies show that the Roberge-Weiss (RW) transition endpoints are triple points at both large and small quark masses, and second order transition points at intermediate quark masses. The triple and second order endpoints are separated by two tricritical ones. Our simulations are carried out at 7 values of quark mass $am$ ranging from 0.024 to 0.070 on lattice volume $12^3\times 4, 16^3\times 4,\, 20^3\times4$. The susceptibility and Binder cumulant of the imaginary part of Polyakov loop are employed to determine the nature of RW transition endpoints. The simulations suggest that the two tricritical points are within the range $0.024-0.026$ and $0.040-0.050$, respectively.

Chiral phase transition of QCD with Nf = 2 + 1 flavors from holography

Chiral phase transition for three-flavor Nf = 2 + 1 QCD with mu = md ≠ ms is investigated in a modified soft-wall holographic QCD model. Solving temperature dependent chiral condensates from equations of motion of the modified soft-wall model, we extract the quark mass dependence of the order of chiral phase transition in the case of Nf = 2 + 1, and the result is in agreement with the “Columbia Plot”, which is summarized from lattice simulations and other non-perturbative methods. First order phase transition is observed around the three flavor chiral limit mu/d = 0, ms = 0, while at sufficient large quark masses it turns to be a crossover phase transition. The first order and crossover regions are separated by a second order phase transition line. The second order line is divided into two parts by the mu/d = ms line, and the ms dependence of the transition temperature in these two parts are totally contrast, which might indicate that the two parts are governed by different universality classes.

SU(2) low energy quark effective couplings in weak external magnetic field

In this work corrections to the usual flavor SU(2) Nambu-Jona-Lasinio coupling due to a weak external magnetic field are calculated by considering quark polarization in a (dressed) gluon exchange mechanism for quark interactions. The quark field is splitted into two components, one that condenses and another one that is a background field for interacting quarks, being the former integrated out. The resulting determinant is expanded for relatively large quark mass and small magnetic field, $(eB_0/{M^*}^2)<1$ by resolving magnetic field dependent low energy quark effective interactions. Besides the corrections for the NJL and vector NJL effective couplings, different $B_0-$dependent effective couplings that break isospin and chiral symmetry emerge.

SU(2) Higher-order effective quark interactions from polarization

Higher order quark effective interactions are found for SU(2) flavor by departing from a non local quark-quark interaction. By integrating out a component of the quark field, the determinant is expanded in chirally symmetric and symmetry breaking effective interactions up to the fifh order in the quark bilinears. The resulting coupling constants are resolved in the leading order of the longwavelength limit and exact numerical ratios between several of these coupling constants are obtained in the large quark mass limit. In this level, chiral invariant interactions only show up in even powers of the quark bilinears, i.e. ${\cal O}(\bar{\psi} \psi)^{2 n}$ ($n=1,2,3,..$), whereas (explicit) chiral symmetry breaking terms emerge as ${\cal O}(\bar{\psi} \psi)^{n}$ being always proportional to some power of the Lagrangian quark mass.

Electroweak baryogenesis in a scalar-assisted vectorlike fermion model

We extend the standard model to a scalar-assisted vector-like fermion model to realize electroweak baryogenesis. The extended Cabbibo-Kobayashi-Maskawa matrix, due to the mixing among the vector-like quark and the standard model quarks, provides additional sources of the CP violation. Together with the enhancement from large vector-like quark mass, a large enough baryon-to-photon ratio could be obtained. The strongly first-order phase transition could be realized via the potential barrier which separate the broken minimum and the symmetric minimum in the scalar potential. We investigate in detail the one-loop temperature-dependent effective potential, and perform a random parameter scan to study the allowed parameter region that satisfies the strongly first order phase transition criteria $v_c \ge T_c$. Several distinct patterns of phase transition are classified and discussed. Among these patterns, large trilinear mass term between the Higgs boson and the scalar is preferred, for it controls the width of the potential barrier. Our results indicate large quartic scalar couplings, and moderate mixing angle between the Higgs boson and the new scalar. This parameter region could be further explored at the Run 2 LHC.

Test for a universal behavior of Dirac eigenvalues in the complex Langevin method

We apply the complex Langevin (CL) method to a chiral random matrix theory (ChRMT) at non-zero chemical potential and study the nearest neighbor spacing (NNS) distribution of the Dirac eigenvalues. The NNS distribution is extracted using an unfolding procedure for the Dirac eigenvalues obtained in the CL method. For large quark mass, we find that the NNS distribution obeys the Ginibre ensemble as expected. For small quark mass, the NNS distribution follows the Wigner surmise for correct convergence case, while it follows the Ginibre ensemble for wrong convergence case. The Wigner surmise is physically reasonable from the chemical potential independence of the ChRMT. The Ginibre ensemble is known to be favored in a phase quenched QCD at finite chemical potential. Our result suggests a possibility that the originally universal behavior of the NNS distribution is preserved even in the CL method for correct convergence case.

Quark and pion effective couplings from polarization effects

A flavor SU(2) effective model for pions and quarks is derived by considering polarization effects departing from the usual quark-quark effective interaction induced by dressed gluon exchange, i.e. a global color model for QCD. For that, the quark field is decomposed into a component that yields light mesons and the quark-antiquark condensate, being integrated out by means of the auxiliary field method, and another component which yields constituent quarks, which is basically a background quark field. Within a longwavelength and weak quark field expansion (or large quark effective mass expansion) of a quark determinant, the leading terms are found up to the second order in a zero order derivative expansion, by neglecting vector mesons that are considerably heavier than the pion. Pions are considered in the structureless limit and, besides the chiral invariant terms that reproduce previously derived expressions, symmetry breaking terms are also presented. The leading chiral quark-quark effective couplings are also found corresponding to a NJL and a vector-NJL couplings. All the resulting effective coupling constants and parameters are expressed in terms of the current and constituent quark masses and of the coupling $g$.

Chiral phase transition in the soft-wall model of AdS/QCD

We investigate the chiral phase transition in the soft-wall model of AdS/QCD at zero chemical potential for two-flavor and three-flavor cases, respectively. We show that there is no spontaneous chiral symmetry breaking in the original soft-wall model. After detailed analysis, we find that in order to realize chiral symmetry breaking and restoration, both profiles for the scalar potential and the dilaton field are essential. The scalar potential determines the possible solution structure of the chiral condensate, except the mass term, it takes another quartic term for the two-flavor case, and for the three-flavor case, one has to take into account an extra cubic term due to the t'Hooft determinant interaction. The profile of the dilaton field reflects the gluodynamics, which is negative at a certain ultraviolet scale and approaches positive quadratic behavior at far infrared region. With this set-up, the spontaneous chiral symmetry breaking in the vacuum and its restoration at finite temperature can be realized perfectly. In the two-flavor case, it gives a second order chiral phase transition in the chiral limit, while the transition turns to be a crossover for any finite quark mass. In the case of three-flavor, the phase transition becomes a first order one in the chiral limit, while above sufficient large quark mass it turns to be a crossover again. This scenario agrees exactly with the current understanding on chiral phase transition from lattice QCD and other effective model studies.

Robust characteristics of non-Gaussian fluctuations from the NJL model

We evaluate the third- and fourth-order baryon, charge and strangeness susceptibilities near a chiral critical point using the Nambu-Jona-Lasinio model. We identify robust qualitative behaviours of the susceptibilities along hypothetical freeze-out lines that agree with previous model studies. Quantitatively, baryon number fluctuations are the largest in magnitude and thus offer the strongest signal when freeze-out occurs farther away from a critical point. Charge and strangeness susceptibilities also diverge at a critical point, but the area where the divergence dominates is smaller, meaning freeze-out must occur closer to a critical point for a signal to be visible in these observables. In case of strangeness, this is attributable to the relatively large strange quark mass. Plotting the third- and fourth-order susceptibilities against each other along the freeze-out line exhibits clearly their non-montonicity and robust features.

Heavy-quark-mass expansion of vector and tensor currents and intrinsic charm in nucleon form factors

The framework of the expansion by subgraphs is used to compute asymptotic expansions for the vector and the tensor currents in the limit of large quark masses. We use the results to obtain an estimate for the influence of heavy quarks on the nucleon electromagnetic and tensor form factors.

Spin-dependent fragmentation functions of gluon splitting into heavy quarkonia considering three different scenarios

Heavy quarkonium production is a powerful implement to study the strong interaction dynamics and QCD theory. Fragmentation is the dominant production mechanism for heavy quarkonia with large transverse momentum. With the large heavy quark mass, the relative motion of the heavy quark pair inside a heavy quarkonium is effectively nonrelativistic and it is also well known that their fragmentation functions can be calculated in the perturbative QCD framework. Here, we analytically calculate the process-independent fragmentation functions for a gluon to split into the spin-singlet and spin-triplet [Formula: see text]-wave heavy quarkonia using three different scenarios. We will show that the fragmentation probability of the gluon into the spin-triplet bound-state is the biggest one.

Axion cosmology, lattice QCD and the dilute instanton gas

Axions are one of the most attractive dark matter candidates. The evolution of their number density in the early universe can be determined by calculating the topological susceptibility χ(T) of QCD as a function of the temperature. Lattice QCD provides an ab initio technique to carry out such a calculation. A full result needs two ingredients: physical quark masses and a controlled continuum extrapolation from non-vanishing to zero lattice spacings. We determine χ(T) in the quenched framework (infinitely large quark masses) and extrapolate its values to the continuum limit. The results are compared with the prediction of the dilute instanton gas approximation (DIGA). A nice agreement is found for the temperature dependence, whereas the overall normalization of the DIGA result still differs from the non-perturbative continuum extrapolated lattice results by a factor of order ten. We discuss the consequences of our findings for the prediction of the amount of axion dark matter.

Pseudo-scalar form factors at three loops in QCD

The coupling of a pseudo-scalar Higgs boson to gluons is mediated through a heavy quark loop. In the limit of large quark mass, it is described by an effective Lagrangian that only admits light degrees of freedom. In this effective theory, we compute the three-loop massless QCD corrections to the form factor that describes the coupling of a pseudo-scalar Higgs boson to gluons. Due to the axial anomaly, the pseudo-scalar operator for the gluonic field strength mixes with the divergence of the axial vector current. Working in dimensional regularization and using the 't~Hooft-Veltman prescription for the axial vector current, we compute the three-loop pseudo-scalar form factors for massless quarks and gluons. Using the universal infrared factorization properties, we independently derive the three-loop operator mixing and finite operator renormalisation from the renormalisation group equation for the form factors, thereby confirming recent results in the operator product expansion. The finite part of the three-loop form factor is an important ingredient to the precise prediction of the pseudo-scalar Higgs boson production cross section at hadron colliders. We discuss potential applications and derive the hard matching coefficient in soft-collinear effective theory.

Exclusive decay of the upsilon intohc, theX(3940)andX(4160)

In this paper, we study double charmonia production in Upsilon peaks, especially, a S-wave charmonium $\eta_c$ and a P-wave charmonium $h_c(^1P_1)$, or a S-wave charmonium $J/\psi$ and the $X(3940)$ and $X(4160)$ within the nonrelativistic QCD (NRQCD) approach which is a powerful tool to realize the factorization of double charmonia production in electron-positron annihilation. The $J^{PC}=1^{--}$ state $\Upsilon(nS)$ can provide an ideal laboratory for studying the properties of double-heavy quarkonium and also can separate the perturbative and nonperturbative parts due to the large heavy quark mass compared with the typical hadron scale $\Lambda_{QCD}$. Explanation of the $X(3940)$ and $X(4160)$ as the $3 ^1S_0$ and $4 ^1S_0$ states, respectively, are compatible with the observed upper limits for the branching fractions of $\Upsilon(1S,2S)\to J/\psi+X$, where $X=X(3940)$, $X(4160)$ by the Belle Collaboration. The branching fractions of $\Upsilon(1S,2S,3S)\to \eta_c+h_c(^1P_1)$ are predicted to be around $10^{-6}$, which shall be tested in Belle-II experiments.

Meson mass decomposition from lattice QCD

Hadron masses can be decomposed as a sum of quark and glue components which are defined through hadronic matrix elements of QCD operators. The components consist of the quark mass term, the quark energy term, the glue energy term, and the trace anomaly term. We calculate these components for mesons with lattice QCD for the first time. The calculation is carried out with overlap fermion on $2+1$ flavor domain-wall fermion gauge configurations. We confirm that $\sim 50\%$ of the light pion mass comes from the quark mass term and $\sim 10\%$ comes from the quark energy; whereas, while for the $\rho$ meson, the quark energy contributes roughly half of its mass but the quark mass term contributes little. The combined glue components contribute $\sim 40 - 50\%$ for both mesons. It is interesting to observe that the quark mass contribution to the mass of the vector meson is almost linear in quark mass over a large quark mass region below the charm quark mass. For heavy mesons, the quark mass term dominates the masses, while the contribution from the glue components is about $200$ MeV (a bare value around 2GeV) for the heavy pseudoscalar and vector mesons. The charmonium hyperfine splitting is found to be dominated by the quark energy term which is consistent with the picture of the quark potential model.

SU(3)and isospin breaking effects onB→PPPamplitudes

Several modes of $B$ decays into three pseudoscalar octet mesons $PPP$ are measured. These decays provide useful information for $B$ decays in the standard model (SM). Some powerful tools in analyzing $B$ decays are flavor $SU(3)$ and isospin symmetries. Such analyses are usually hampered by $SU(3)$ breaking effects due to a relatively large strange quark mass which breaks $SU(3)$ symmetry down to isospin symmetry. The isospin symmetry also breaks down when the up and down quark mass difference is nonzero. It is, therefore, interesting to find relations which are not sensitive to $SU(3)$ and isospin breaking effects. We find that the relations among several fully symmetric $B\ensuremath{\rightarrow}PPP$ decay amplitudes are not affected by first-order $SU(3)$ breaking effects due to a nonzero strange quark mass, and also some of them are not affected by first isospin breaking effects. These relations, therefore, hold to good precisions. The measurements for these relations can provide important information about $B$ decays in the SM.

Nature of Roberge-Weiss transition endpoints for heavy quarks inNf=2lattice QCD with Wilson fermions

The phase structure of QCD with imaginary chemical potential provides information on the phase diagram of QCD with real chemical potential. With imaginary chemical potential $i{\ensuremath{\mu}}_{I}=i\ensuremath{\pi}T$, previous studies show that the Roberge-Weiss (RW) transition endpoints are triple points at both large and small quark masses, and second order transition points at intermediate quark masses. The triple and second order endpoints are separated by two tricritical ones. We present simulations with ${N}_{f}=2$ Wilson fermions to investigate the nature of RW transition endpoints. The simulations are carried out at 8 values of the hopping parameter $\ensuremath{\kappa}$ ranging from 0.020 to 0.140 on different lattice volumes. The Binder cumulant, susceptibility, and reweighted distribution of the imaginary part of the Polyakov loop are employed to determine the nature of RW transition endpoints. The simulations show that the two tricritical points are within the ranges 0.070--0.080 and 0.120--0.140, respectively.