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Register a new userExploration of the electric spin polarizability of the neutron in lattice QCD
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Michael Engelhardt
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A scheme to calculate the electric spin polarizability of the neutron, based on a four-point function approach to the background field method, is presented. The connected contributions to this spin polarizability are evaluated within a mixed action calculation employing domain wall valence quarks on MILC asqtad sea quark ensembles. Results are reported for two pion masses, 759 MeV and 357 MeV.
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A calculational scheme for obtaining the electric polarizability of the neutron in lattice QCD with dynamical quarks is developed, using the background field approach. The scheme differs substantially from methods previously used in the quenched approximation, the physical reason being that the QCD ensemble is no longer independent of the external electromagnetic field in the dynamical quark case. One is led to compute (certain integrals over) four-point functions. Particular emphasis is also placed on the physical role of constant external gauge fields on a finite lattice; the presence of these fields complicates the extraction of polarizabilities, since it gives rise to an additional shift of the neutron mass unrelated to polarizability effects. The method is tested on a SU(3) flavor-symmetric ensemble furnished by the MILC Collaboration, corresponding to a pion mass of m_pi = 759 MeV. Disconnected diagrams are evaluated using stochastic estimation. A small negative electric polarizability of alpha =(-2.0 +/- 0.9) 10^(-4) fm^3 is found for the neutron at this rather large pion mass; this result does not seem implausible in view of the qualitative behavior of alpha as a function of m_pi suggested by Chiral Effective Theory.
We present a valence calculation of the electric polarizability of the neutron, neutral pion, and neutral kaon on two dynamically generated nHYP-clover ensembles. The pion masses for these ensembles are 227(2) MeV and 306(1) MeV, which are the lowest ones used in polarizability studies. This is part of a program geared towards determining these parameters at the physical point. We carry out a high statistics calculation that allows us to: (1) perform an extrapolation of the kaon polarizability to the physical point; we find $alpha_K =0.269(43)times10^{-4}$fm$^{3}$, (2) quantitatively compare our neutron polarizability results with predictions from $chi$PT, and (3) analyze the dependence on both the valence and sea quark masses. The kaon polarizability varies slowly with the light quark mass and the extrapolation can be done with high confidence.
The background field method for measuring the electric polarizability of the neutron is adapted to the dynamical quark case, resulting in the calculation of (certain space-time integrals over) three- and four-point functions. Particular care is taken to disentangle polarizability effects from the effects of subjecting the neutron to a constant background gauge field; such a field is not a pure gauge on a finite lattice and engenders a mass shift of its own. At a pion mass of m_pi = 759 MeV, a small, slightly negative electric polarizability is found for the neutron.
We extract the neutron electric dipole moment $vert vec{d}_Nvert$ within the lattice QCD formalism. We analyse one ensemble of $N_f=2+1+1$ twisted mass clover-improved fermions with lattice spacing of $a simeq 0.08 {rm fm}$ and physical values of the quark masses corresponding to a pion mass $m_{pi} simeq 139 {rm MeV}$. The neutron electric dipole moment is extracted by computing the $CP$-odd electromagnetic form factor $F_3(Q^2 to 0)$ through small $theta$-expansion of the action. This approach requires the calculation of the topological charge for which we employ a fermionic definition by means of spectral projectors while we also provide a comparison with the gluonic definition accompanied by the gradient flow. We show that using the topological charge from spectral projectors leads to absolute errors that are more than two times smaller than those provided when the field theoretic definition is employed. We find a value of $vert vec{d}_Nvert = 0.0009(24) theta e cdot {rm fm}$ when using the fermionic definition, which is statistically consistent with zero.
For a bound state internal wave function respecting parity symmetry, it can be rigorously argued that the mean electric dipole moment must be strictly zero. Thus, both the neutron, viewed as a bound state of three quarks, and the water molecule, viewed as a bound state of ten electrons two protons and an oxygen nucleus, both have zero mean electric dipole moments. Yet, the water molecule is said to have a nonzero dipole moment strength $d=eLambda $ with $Lambda_{H_2O} approx 0.385 dot{A}$. The neutron may also be said to have an electric dipole moment strength with $Lambda_{neutron} approx 0.612 fm$. The neutron analysis can be made experimentally consistent, if one employs a quark-diquark model of neutron structure.
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