Quark Mass Corrections Research Articles

Vortices and other topological solitons in dense quark matter

Abstract Dense quantum chromodynamic matter accommodates various kind of topological solitons such as vortices, domain walls, monopoles, kinks, boojums, and so on. In this review, we discuss various properties of topological solitons in dense quantum chromodynamics (QCD) and their phenomenological implications. Particular emphasis is placed on the topological solitons in the color–flavor-locked (CFL) phase, which exhibits both superfluidity and superconductivity. The properties of topological solitons are discussed in terms of effective field theories such as the Ginzburg–Landau theory, the chiral Lagrangian, or the Bogoliubov–de Gennes equation. The most fundamental string-like topological excitations in the CFL phase are non-Abelian vortices, which are 1/3 quantized superfluid vortices and color magnetic flux tubes. These vortices are created at a phase transition by the Kibble–Zurek mechanism or when the CFL phase is realized in compact stars, which rotate rapidly. The interaction between vortices is found to be repulsive and consequently a vortex lattice is formed in rotating CFL matter. Bosonic and fermionic zero-energy modes are trapped in the core of a non-Abelian vortex and propagate along it as gapless excitations. The former consists of translational zero modes (a Kelvin mode) with a quadratic dispersion and ${\mathbb {C}}P^2$ Nambu–Goldstone gapless modes with a linear dispersion, associated with the CFL symmetry spontaneously broken in the core of a vortex, while the latter is Majorana fermion zero modes belonging to the triplet of the symmetry remaining in the core of a vortex. The low-energy effective theory of the bosonic zero modes is constructed as a non-relativistic free complex scalar field and a relativistic ${\mathbb {C}}P^2$ model in 1+1 dimensions. The effects of strange quark mass, electromagnetic interactions, and non-perturbative quantum corrections are taken into account in the ${\mathbb {C}}P^2$ effective theory. Various topological objects associated with non-Abelian vortices are studied; colorful boojums at the CFL interface, the quantum color magnetic monopole confined by vortices, which supports the notion of quark–hadron duality, and Yang–Mills instantons inside a non-Abelian vortex as lumps are discussed. The interactions between a non-Abelian vortex and quasiparticles such as phonons, gluons, mesons, and photons are studied. As a consequence of the interaction with photons, a vortex lattice behaves as a cosmic polarizer. As a remarkable consequence of Majorana fermion zero modes, non-Abelian vortices are shown to behave as a novel kind of non-Abelian anyon. In the order parameters of chiral symmetry breaking, we discuss fractional and integer axial domain walls, Abelian and non-Abelian axial vortices, axial wall–vortex composites, and Skyrmions.

Corrections to the SU(3) × SU(3) Gell-Mann-Oakes-Renner relation and chiral couplings $ L_8^r $ and $ H_2^r $

Next to leading order corrections to the SU(3) × SU(3) Gell-Mann-Oakes-Renner relation (GMOR) are obtained using weighted QCD Finite Energy Sum Rules (FESR) involving the pseudoscalar current correlator. Two types of integration kernels in the FESR are used to suppress the contribution of the kaon radial excitations to the hadronic spectral function, one with local and the other with global constraints. The result for the pseudoscalar current correlator at zero momentum is ψ 5(0) = (2.8 ± 0.3) ×10-3 GeV4, leading to the chiral corrections to GMOR: δ K = (55 ± 5)%. The resulting uncertainties are mostly due to variations in the upper limit of integration in the FESR, within the stability regions, and to a much lesser extent due to the uncertainties in the strong coupling and the strange quark mass. Higher order quark mass corrections, vacuum condensates, and the hadronic resonance sector play a negligible role in this determination. These results confirm an independent determination from chiral perturbation theory giving also very large corrections, i.e. roughly an order of magnitude larger than the corresponding corrections in chiral SU(2) × SU(2). Combining these results with our previous determination of the corrections to GMOR in chiral SU(2) × SU(2), δ π , we are able to determine two low energy constants of chiral perturbation theory, i.e. $ L_8^r=\left( {1.0\pm 0.3} \right)\times {10^{-3 }} $ , and $ H_2^r=-\left( {4.7\pm 0.6} \right)\times {10^{-3 }} $ , both atthe scaleof the ρ-meson mass.

Heavy quark spin symmetry partners of theX(3872)

We explore the consequences of heavy quark spin symmetry for the charmed meson-antimeson system in a contact-range (or pionless) effective field theory. As a trivial consequence, we theorize the existence of a heavy quark spin symmetry partner of the X(3872), with $J^{PC}=2^{++}$, which we call X(4012) in reference to its predicted mass. If we additionally assume that the X(3915) is a $0^{++}$ heavy spin symmetry partner of the X(3872), we end up predicting a total of six $D^{(*)}\bar{D}^{(*)}$ molecular states. We also discuss the error induced by higher order effects such as finite heavy quark mass corrections, pion exchanges and coupled channels, allowing us to estimate the expected theoretical uncertainties in the position of these new states.

NonleptonicB→D(*)DsJ(*)decays and the nature of the orbitally excited charmed-strange mesons

The Belle Collaboration has recently reported a study of the decays $B\ensuremath{\rightarrow}{D}_{s1}(2536{)}^{+}{\overline{D}}^{(*)}$ and has also given estimates of relevant ratios between branching fractions of decays $B\ensuremath{\rightarrow}{D}^{(*)}{D}_{sJ}^{(*)}$ providing important information to check the structure of the ${D}_{s0}^{*}(2317)$, ${D}_{s1}(2460)$, and ${D}_{s1}(2536)$ mesons. The disagreement between experimental data and heavy quark symmetry has been used as an indication that ${D}_{s0}^{*}(2317)$ and ${D}_{s1}(2460)$ mesons could have a more complex structure than the canonical $c\overline{s}$ one. We analyze these ratios within the framework of a constituent quark model, which allows us to incorporate the effects given by finite $c$-quark mass corrections. Our findings are that while the ${D}_{s1}(2460)$ meson could have a sizable non-$q\overline{q}$ component, the ${D}_{s0}^{*}(2317)$ and ${D}_{s1}(2536)$ mesons seem to be well described by a pure $q\overline{q}$ structure.

The effect of top quark mass on three jet rate and measurement of strong coupling constant

We present the calculation of top quark mass corrections to three-jet rates in electron-positron annihilation at center of mass energies of 60 and 206 GeV. Furthermore, we also calculate the effects of quark-antiquark interactions on QCD model for three-jet rates. We extract the strong coupling constant, αs, through our results from the massive three-jet rate and the massless one. We observe that the effect of t quark on three jet rate does not contribute significantly to the calculations of strong coupling constant and we can ignore this effect in higher energies.

Light quark mass dependence of the D and [formula omitted] decay constants

We study the light quark mass dependence of the D and Ds meson decay constants, fD and fDs, using a covariant formulation of chiral perturbation theory (χPT) at next-to-next-to-leading order (NNLO). Using the HPQCD lattice results for the D (Ds) decay constants as a benchmark we show that covariant χPT can describe the HPQCD results better than heavy meson χPT (HMχPT) at both NLO and NNLO. Within the same framework, taking into account sub-leading (1/mQ, with mQ the heavy quark mass) corrections to the values of the low-energy constants and employing the lattice QCD results for gBB⁎π, we estimate the ratio of fBs/fB to be 1.22−0.04+0.05, which agrees well with the HPQCD result 1.226(26).

Up- and down-quark masses from finite-energy QCD sum rules to five loops

The up- and down-quark masses are determined from an optimized QCD finite-energy sum rule involving the correlator of axial-vector divergences, to five-loop order in perturbative QCD, and including leading nonperturbative QCD and higher order quark-mass corrections. This finite-energy sum rule is designed to reduce considerably the systematic uncertainties arising from the (unmeasured) hadronic resonance sector, which in this framework contributes less than 3--4% to the quark mass. This is achieved by introducing an integration kernel in the form of a second degree polynomial, restricted to vanish at the peak of the two lowest lying resonances. The driving hadronic contribution is then the pion pole, with parameters well known from experiment. The determination is done in the framework of contour improved perturbation theory, which exhibits a very good convergence, leading to a remarkably stable result in the unusually wide window ${s}_{0}=1.0--4.0\text{ }\text{ }{\mathrm{GeV}}^{2}$, where ${s}_{0}$ is the radius of the integration contour in the complex energy (squared) plane. The results are ${m}_{u}(Q=2\text{ }\text{ }\mathrm{GeV})=2.9\ifmmode\pm\else\textpm\fi{}0.2\text{ }\text{ }\mathrm{MeV}$, ${m}_{d}(Q=2\text{ }\text{ }\mathrm{GeV})=5.3\ifmmode\pm\else\textpm\fi{}0.4\text{ }\text{ }\mathrm{MeV}$, and $({m}_{u}+{m}_{d})/2=4.1\ifmmode\pm\else\textpm\fi{}0.2\text{ }\text{ }\mathrm{MeV}$ (at a scale $Q=2\text{ }\text{ }\mathrm{GeV}$).

Cold and dense perturbative Yukawa theory with massive fermions

Recent results for the two-loop thermodynamic potential of QCD at finite density have shown that nonzero quark mass corrections to the pressure are relevant and can dramatically affect the structure of compact stars. Motivated by these findings, we consider a simple toy model - cold and dense Yukawa theory - to study the effects of finite fermion masses on the pressure. The role of renormalization group running of the coupling and mass is also discussed. Results within this simple model might be useful in the description of condensates in the core of neutron stars.

Phase space and quark mass effects in neutrino emissions in a color superconductor

We study the phase space for neutrino emissions with massive quarks in direct Urca processes in normal and color superconducting quark matter. We derive in QCD and the NJL model the Fermi momentum reduction resulting from Fermi liquid properties which opens up the phase space for neutrino emissions. The relation between the Fermi momentum and chemical potential is found to be $p_{F}\approx\mu(1-\kappa)$ with $\kappa$ depending on coupling constants. We find in the weak coupling regime that $\kappa$ is a monotonously increasing function of the chemical potential. This implies quenched phase space for neutrino emissions at low baryon densities. We calculate neutrino emissivities with massive quarks in a spin-one color superconductor. The quark mass corrections are found to be of the same order as the contributions in the massless case, which will bring sizable effects on the cooling behavior of compact stars.

Radiative decays of decuplet to octet baryons in light cone QCD

The radiative decays of decuplet to octet baryons are analyzed within the light cone QCD sum rules framework. The electromagnetic transition form factors for these decays are calculated at q 2 = 0 up to twist-4 accuracy for photon wave functions and including first order strange quark mass corrections. A comparison of our results with predictions of lattice theory and existing experimental data is presented.

Quark mass effects in the soft-collinear effective theory andB¯→Xsγin the end point region

We consider the effects of a light quark mass in the soft-collinear effective theory (SCET) and we apply them to B -> X_s gamma in the endpoint region. We find that the reparameterization invariance can be extended by including the collinear quark mass in the SCET Lagrangian. This symmetry constrains the theory with the quark mass terms, and we present explicit results at one loop. It also relates the Wilson coefficients of some mass operators to those of the leading operators, which are useful in organizing the subleading effects due to the quark mass in B -> X_s gamma. We present strange quark mass corrections to B -> X_s gamma in the endpoint region as an application. The forward scattering amplitude from the mass corrections is factorized, and it can be expressed as a convolution of the m_s^2/p_X^2-suppressed jet function and the leading-order shape function of the B meson. This contribution should be added to the existing subleading contributions from the B meson shape functions to obtain complete subleading corrections.

Strange-Quark Mass from Tau-Lepton Decays withO(αs3)Accuracy

The first complete calculation of the quadratic quark mass correction to the correlator of the two currents relevant for the strangeness-changing semihadronic tau-decay rate is presented including its real part at the four-loop level. This allows us to perform the extraction of the strange-quark mass m(s) from the decay width of the tau-lepton with full O(alpha3s) accuracy. In agreement with previous estimates, the newly computed alpha3s term proves to be rather large. This justifies inclusion of the similarly estimated alpha4s term in phenomenological analysis. Combined with an updated value of V us and an "improved" version of the renormalization group improvement of the perturbative series, this leads to an increase of the central value of m(s) by about 20% and a partial reduction of the theoretical uncertainty by about 50%.

Perturbative QCD and tau-decays

The current status of the higher order QCD corrections to the width of the tau is discussed. We report on the result of the first complete calculation of the quadratic quark mass correction to the correlator of the two currents relevant for the strangeness-changing semihadronic tau-decay rate including its real part at the four-loop level. We discuss phenomenological implications for determination of m s .

New observables in longitudinal single-spin asymmetries in semi-inclusive DIS

We analyze longitudinal beam and target single-spin asymmetries in semi-inclusive deep inelastic scattering and in jet deep inelastic scattering, including all possible twist-3 contributions as well as quark mass corrections. We take into account the path-ordered exponential in the soft correlators and show that it leads to the introduction of a new distribution and a new fragmentation function contributing to the asymmetries.

Nuclear shadowing in neutrino–nucleus deeply inelastic scattering

In the framework of the collinear factorized pQCD approach we calculate the small-xB process-dependent nuclear modification to the structure functions measured in neutrino–nucleus deeply inelastic scattering. We include both heavy quark mass corrections (M2/Q2) and resummed nuclear-enhanced dynamical power corrections in the quantity (ξ2/Q2)(A1/3−1) with ξ2 evaluated to leading order in αs. Our formalism predicts a measurable difference in the shadowing pattern of the structure functions F2A(xB,Q2) and F3A(xB,Q2) and a significant low- and moderate-Q2 modification of the QCD sum rules. We also comment on the relevance of our results to the NuTeV extraction of sin2θW.

DsJ+(2317):What can the lattice say?

We present lattice results on the scalar ${D}_{s}$ meson and comment on the ${D}_{\mathrm{sJ}}^{+}(2317)$ state recently discovered by BaBar and confirmed by CLEO, in view of a series of theoretical claims and counterclaims. Lattice predictions in the static limit indicate larger masses than observed for a scalar quark model state. Finite c quark mass corrections seem to further enlarge this discrepancy, in support of a non-quark-antiquark-state interpretation of experiment.

Revisiting top–bottom-tau Yukawa unification in supersymmetric grand unified theories

Third family Yukawa unification, as suggested by minimal SO(10) unification, is revisited in light of recent experimental measurements and theoretical progress. We characterize unification in a semi-model-independent fashion, and conclude that finite b quark mass corrections from superpartners must be non-zero, but much smaller than naively would be expected. We show that a solution that does not require cancellations of dangerously large tan β effects in observables implies that scalar superpartner masses should be substantially heavier than the Z scale, and perhaps inaccessible to all currently approved colliders. On the other hand, gauginos must be significantly lighter than the scalars. We demonstrate that a spectrum of anomaly-mediated gaugino masses and heavy scalars works well as a theory compatible with third family Yukawa unification and dark matter observations.

Λ hyperon as helicity analyser of s quark in B decay

We explore how well one can probe the s quark chirality of the fundamental weak interaction of nonleptonic B decay using the spin-analysing property of the Λ hyperon. We present the prediction of the standard model as quantitatively as possible in a perturbative QCD picture avoiding detailed form-factor calculation involving quark mass corrections. A clean test of chirality will be possible with B̄ → ΛX when X is an antibaryon or its excited state.

Helicity-dependent twist-two and twist-three generalized parton distributions in light-front QCD

We investigate the helicity dependent twist-two and twist-three generalized parton distributions in light-front Hamiltonian QCD for a massive dressed quark target. Working in the kinematical region $\xi< x <1$, we obtain the splitting functions for the evolutions of twist-two quark and gluon distributions in a straightforward way. For the twist-three distribution, we find that all contributions are proportional to the quark mass and thus the twist-three distribution is directly related to the chiral symmetry breaking dynamics in light-front QCD. We also show that the off-forward Wandzura-Wilczek relation is violated in perturbative QCD for a massive dressed quark.We calculate the quark mass correction to the WW relation in the off-forward case and show that it is related to $h_1(x)$ in the forward limit. We extract the 'genuine twist three' part of the matrix element in the forward case and verify the Burkhardt Cottingham and Efremov-Leader-Teryaev sum rules.

Towards orderαs4accuracy inτdecays

Recently computed terms of orders O(\alpha_s^4 n_f^2) in the perturbative series for the tau decay rate, and similar (new) strange quark mass corrections, are used to discuss the validity of various optimization schemes. The results are then employed to arrive at improved predictions for the complete terms order O(\alpha_s^4) and O(\alpha_s^5) in the massless limit as well as for terms due to the strange quark mass. Phenomenological implications are presented.