Small Pion Mass Research Articles

Amplitude’s positivity vs. subluminality: causality and unitarity constraints on dimension 6 & 8 gluonic operators in the SMEFT

We derive the causality and unitarity constraints on dimension 6 and dimension 8 Gluon field strength operators in the Standard Model Effective Field Theory (SMEFT). In the first part of the paper, we use the ‘amplitude analysis’ i.e. dispersion relation for 2 → 2 scattering in the forward limit, to put bounds on the Wilson coefficients. We show that the dimension 6 operators can exist only in the presence of certain dimension 8 operators. It is interesting that the square of the dimension 6 Wilson coefficients can be constrained in this case even at the tree level. In the second part of this work, we successfully rederive all these bounds using the classical causality argument that demands that the speed of fluctuations about any non-trivial background should not exceed the speed of light. We also point out some subtleties in the superluminality analysis regarding whether the low-frequency phase velocity can always be used as the relevant quantity for Causality violation: as an example, we show that, due to these subtleties, if a small pion mass is added in the chiral Lagrangian, it is unclear if any strict positivity bound can be derived on the dimension 8 Wilson coefficient. Finally, we mention an interesting non-relativistic example where the subluminality requirement produces a stronger bound than the ‘amplitude analysis’.

Holographic estimate of the meson cloud contribution to nucleon axial form factor

We use light-front Holography to estimate the valence quark and the meson cloud contributions to the nucleon axial form factor. The free couplings of the holographic model are determined by the empirical data and by the information extracted from lattice QCD. The holographic model provides a good description of the empirical data when we consider a meson cloud mixture of about 30\% in the physical nucleon state. The estimate of the valence quark contribution to the nucleon axial form factor compares well with the lattice QCD data for small pion masses. Our estimate of the meson cloud contribution to the nucleon axial form factor has a slower falloff with the square momentum transfer compared to typical estimates from quark models with meson cloud dressing.

The \u03c1-meson light-cone distribution amplitudes from lattice QCD

We present the results of a lattice study of the normalization constants and second moments of the light-cone distribution amplitudes of longitudinally and transversely polarized ρ mesons. The calculation is performed using two flavors of dynamical clover fermions at lattice spacings between 0.060 fm and 0.081 fm, different lattice volumes up to mπL = 6.7 and pion masses down to mπ = 150 MeV. Bare lattice results are renormalized non-perturbatively using a variant of the RI′-MOM scheme and converted to the overline{mathrm{MS}} scheme. The necessary conversion coefficients, which are not available in the literature, are calculated. The chiral extrapolation for the relevant decay constants is worked out in detail. We obtain for the ratio of the tensor and vector coupling constants fρT/fρ = 0.629(8) and the values of the second Gegenbauer moments a2‖ = 0.132(27) and a2⊥ = 0.101(22) at the scale μ = 2 GeV for the longitudinally and transversely polarized ρ mesons, respectively. The errors include the statistical uncertainty and estimates of the systematics arising from renormalization. Discretization errors cannot be estimated reliably and are not included. In this calculation the possibility of ρ → ππ decay at the smaller pion masses is not taken into account.

Charge-conjugation symmetric complete impulse approximation for the pion electromagnetic form factor in the covariant spectator theory

The pion form factor is calculated in the framework of the charge-conjugation invariant Covariant Spectator Theory. This formalism is established in Minkowski space and the calculation is set up in momentum space. In a previous calculation we included only the leading pole coming from the spectator quark (referred to as the relativistic impulse approximation). In this paper we also include the contributions from the poles of the quark which interacts with the photon and average over all poles in both the upper and lower half planes in order to preserve charge conjugation invariance (referred to as the $C$-symmetric complete impulse approximation). We find that for small pion mass these contributions are significant at all values of the four-momentum transfer $Q^2$ but, surprisingly, do not alter the shape obtained from the spectator poles alone.

The flavor universality of some mass splittings in hadrons

The approximate chiral invariance of the two-flavor (QCD) is known to be spontaneously broken. This effect explains the relatively small pion mass and, as is widely believed, the mass splittings of would-be chiral partners — the hadrons of equal spin but opposite parity lying in one multiplet of the chiral symmetry. We present experimental evidences that in reality such mass splittings in the meson sector seem to be approximately flavor-independent in all cases where they can be tested experimentally — the spin 0 and 1. In addition, a partial flavor independence holds for spin-1/2 baryons (namely among states in which at least one of the quark is not u or d one). This property allow to predict masses and quantum numbers for 10 new hadrons. The given flavor-independence, if confirmed for higher spins, hints at the existence of universal scale Λ strong ~300 MeV in the strong interactions which, in contrast to Λ QCD , is flavor and scheme independent. Some manifestations of Λ strong are discussed.

Background field approach to electromagnetic properties of baryons

We investigate the self-energies of particles in an external magnetic field $B$. The dependence is generally of the type $\sqrt{P(B)}$ with $P$ a polynomial in $B$ and the participating masses. The non-analytic point depends on the mass and charge constellations, is unproblematic for stable particles but constrains the linear energy shift approximation for resonances. We calculate the $B$ dependent self-energies of the nucleon and $\Delta(1232)$-isobar in the SU(2) covariant chiral perturbation theory and outline a way to obtain finite volume corrections to the nucleon anomalous magnetic moment without using the three point function method. We show that finite volume corrections might explain present discrepancies of lattice QCD and chiral perturbation theory results in the small pion mass region.

Towards a precise lattice determination of the leading hadronic contribution to (g − 2) μ

Abstract We report on our computation of the leading hadronic contribution to the anomalous magnetic moment of the muon using two dynamical flavours of non-perturbatively O(a) improved Wilson fermions. The strange quark is introduced in the quenched approximation. Partially twisted boundary conditions are applied to improve the momentum resolution in the relevant integral. Our results, obtained at three different values of the lattice spacing, allow for a preliminary study of discretization effects. We explore a wide range of lattice volumes, namely 2 fm ≤ L ≤ 3 fm, with pion masses from 600 to 280 MeV and discuss different chiral extrapolations to the physical point. We observe a non-trivial dependence of $a_\mu^{HLO}$ on m π especially for small pion masses. The final result, $a_\mu^{HLO} = 618\left( {64} \right) \times {10^{ - 10}}$ , is obtained by considering only the quark connected contribution to the vacuum polarization. We present a detailed analysis of systematic errors and discuss how they can be reduced in future simulations.

Meson and baryon spectrum for QCD with two light dynamical quarks

We present results of meson and baryon spectroscopy using the Chirally Improved Dirac operator on lattices of size 16**3 x 32 with two mass-degenerate light sea quarks. Three ensembles with pion masses of 322(5), 470(4) and 525(7) MeV and lattice spacings close to 0.15 fm are investigated. Results on ground and excited states for several channels are given, including spin two mesons and hadrons with strange valence quarks. The analysis of the states is done with the variational method, including two kinds of Gaussian sources and derivative sources. We obtain several ground states fairly precisely and find radial excitations in various channels. Excited baryon results seem to suffer from finite size effects, in particular at small pion masses. We discuss the possible appearance of scattering states in various channels, considering masses and eigenvectors. Partially quenched results in the scalar channel suggest the presence of a 2-particle state, however, in most channels we cannot identify them. Where available, we compare our results to results of quenched simulations using the same action.

Nucleon electromagnetic form factors from lattice QCD using2+1flavor domain wall fermions on fine lattices and chiral perturbation theory

We present a high-statistics calculation of nucleon electromagnetic form factors in $N_f=2+1$ lattice QCD using domain wall quarks on fine lattices, to attain a new level of precision in systematic and statistical errors. Our calculations use $32^3 \times 64$ lattices with lattice spacing a=0.084 fm for pion masses of 297, 355, and 403 MeV, and we perform an overdetermined analysis using on the order of 3600 to 7000 measurements to calculate nucleon electric and magnetic form factors up to $Q^2 \approx$ 1.05 GeV$^2$. Results are shown to be consistent with those obtained using valence domain wall quarks with improved staggered sea quarks, and using coarse domain wall lattices. We determine the isovector Dirac radius $r_1^v$, Pauli radius $r_2^v$ and anomalous magnetic moment $\kappa_v$. We also determine connected contributions to the corresponding isoscalar observables. We extrapolate these observables to the physical pion mass using two different formulations of two-flavor chiral effective field theory at one loop: the heavy baryon Small Scale Expansion (SSE) and covariant baryon chiral perturbation theory. The isovector results and the connected contributions to the isoscalar results are compared with experiment, and the need for calculations at smaller pion masses is discussed.

Lattice study of light scalar tetraquarks

The observed mass pattern of scalar resonances below 1 GeV suggests a tetraquark assignment over the conventional $\overline{q}q$ assignment for these states. We present a search for tetraquarks with isospins 0, $1/2$, 1 in lattice QCD, where the isospin channels $1/2$ and 1 have not been studied before. We determine three energy levels in each isospin channel using the variational method. The scattering states and possible tetraquark states are distinguished by considering the volume dependence of spectral weights and by considering the time dependence of correlators near $t\ensuremath{\simeq}T/2$. We find no indication for light tetraquarks at our range of pion masses, $344--576\text{ }\text{ }\mathrm{MeV}$. However, our simulation does not exclude a possibility of finding tetraquarks in a simulation with smaller pion masses or a different interpolator basis.

On the two-loop contributions to the pion mass

We derive a simplified representation for the pion mass to two loops in three-flavour chiral perturbation theory. For this purpose, we first determine the reduced expressions for the tensorial two-loop 2-point sunset integrals arising in chiral perturbation theory calculations. Making use of those relations, we obtain the expression for the pion mass in terms of the minimal set of master integrals. On the basis of known results for these, we arrive at an explicit analytic representation, up to the contribution from KKη intermediate states where a closed-form expression for the corresponding sunset integral is missing. However, the expansion of this function for a small pion mass leads to a simple representation which yields a very accurate approximation of this contribution. Finally, we also give a discussion of the numerical implications of our results.

Light quarks with twisted mass fermions

We investigate Wilson twisted mass fermions in the quenched approximation using different definitions of the critical bare quark mass mc to realize maximal twist and, correspondingly, automatic O(a) improvement for physical observables. A particular definition of mc is given by extrapolating the value of mc obtained from the PCAC relation at non-vanishing bare twisted quark mass μ to μ=0. Employing this improved definition of the critical mass the Wilson twisted mass formulation provides the possibility to perform reliable simulations down to very small quark masses with correspondingly small pion masses of mπ≃250 MeV, while keeping the cutoff effects of O(a2) under control.

PCAC and shadowing of low energy neutrinos

The Adler relation between reactions initiated by neutrinos and pions is easy to misinterpret as a manifestation of the pion pole dominance. An axial current, however, cannot fluctuate into a pion, but only to heavy axial-vector states, since the lepton current is transverse. This is the miracle of the PCAC hypothesis which dictates a specific conspiracy between the heavy fluctuations, so that all together they mock the pion pole. Indeed, the observed Q^2 dependence of the axial form factor is controlled by the effective mass m_A \sim 1 GeV, rather than the pion mass. On the contrary, the onset of nuclear shadowing is governed by the small pion mass, rather than by the large axial mass scale. This is in variance with the conventional wisdom which equates the fluctuation lifetime and the coherence time. For the case of axial current they are different by almost two orders of magnitude. As a result, neutrino interactions are shadowed at very low energies of few hundred MeV, while energy of about 10 GeV is needed to access nuclear shadowing for the vector current. On the contrary to naive expectations, nuclear absorption enhances, rather than suppresses the cross section of coherent neutrino-production of pions which is the strongest channel (half of the total cross section) in the black disc limit.

Long distance chiral corrections in B meson amplitudes

We discuss the chiral corrections to fB and BB with particular emphasis on determining the portion of the correction that arises from long distance physics. For very small pion and kaon masses all of the usual corrections are truly long distance, while for larger masses the long distance portion decreases. These chiral corrections have been used to extrapolate lattice calculations towards the physical region of lighter masses. We show in particular that the chiral extrapolation is better behaved if only the long distance portion of the correction is used. We also display the long distance portions of the infrared enhanced chiral logarithms that appear in partially quenched chiral perturbation theory.

Twisted mass QCD and theΔ I =½ rule

We show that the application of twisted mass QCD (tmQCD) with four (Wilson) quark flavours to the computation of lattice weak matrix elements relevant toΔ I =½ transitions has important advantages: the renormalisation of K → π matrix elements does not require the subtraction of other dimension six operators, the divergence arising from the subtraction of lower dimensional operators is softened by one power of the lattice spacing and quenched simulations do not suffer from exceptional configurations at small pion mass. This last feature is also retained in the tmQCD computation of K → ππ matrix elements, which, as far as renormalisation and power subtractions axe concerned, has properties analogous to the standard Wilson case.

Dynamical vertex mass generation and chiral symmetry breaking on the light front

Naively, helicity flip amplitudes for fermions seem to vanish in the chiral limit of light-front QCD, which would make it nearly impossible to generate a small pion mass in this framework. Using a simple model, it is illustrated how a large helicity flip amplitude is generated dynamically by summing over an infinite number of Fock space components. While the kinetic mass is basically generated by a zero-mode induced counter-term, the vertex mass is generated dynamically by infinitesimally small, but nonzero, momenta. Implications for the renormalization of light-front Hamiltonians for fermions are discussed.

The QCD spectrum and phase diagram on the lattice - 1991

Recent numerical computations of the hadron spectrum and phase diagram in lattice QCD are summarized. Incremental improvements in the quality of spectrum calculations give increasing credibility to the claim that lattice calculations reproduce the physical hadron spectrum as the quark mass is lowered. A transition to high temperature behavior is clear, both for Kogut-Susskind and Wilson fermions. For four flavors of Kogut-Susskind fermions the transition appears to be first order. However, for two flavors no indications of metastability are seen. Hints of new phenomena with many flavors of quarks are seen with both Kogut-Susskind and Wilson quarks. Observations of the masses and spatial structure of screening propagators give information about the nature of high temperature QCD. For Wilson fermions it remains difficult to simulate with small pion mass, both for the zero temperature and high temperature simulations.

Limitations of a semiclassical treatment of the Skyrme soliton.

We discuss a semiclassical approach to the Skyrme model in which the effects from the diagonalization of the collective coordinates are treated in a self-consistent way. We obtain an upper bound on the nucleon-\ensuremath{\Delta} mass difference which is valid if the semiclassical limit is taken with the pion mass parameter held fixed, but is inconsistent with the experimental values of the masses. Because of the interplay of the semiclassical and chiral limits, the approximations break down for sufficiently small pion mass.

Chiral estimate of the electric dipole moment of the neutron in quantum chromodynamics

Current algebra for CP violating strong interactions is investigated. In particular, the neutron electric dipole moment D n is shown to behave as θm π 21n m π 2 for small pion mass m π and CP violating parameter θ. This logarithm is explicitly calculable: it contributes 5.2×10 −16θ cm to D n. This result is somewhat larger than a previous O( m π 2) estimate based on the bag model.

Pion Radius and Isovector Nucleon Radii in the Limit of Small Pion Mass

We study the pion radius and the isovector nucleon radii in the limit in which the pion mass approaches zero. The leading terms in this limit are calculated.