Using clover fermions on CP-PACS dynamical configurations, we consider a number of ways of measuring hadronic electric polarizability, an $|\mathbf{E}|^{2}$ effect in hadron masses, using lattice techniques. We consider the effects of periodic and Dirichlet boundary conditions, the field linearization postulate as well as a quantized electric field. We also consider two ways of formulating the classical vector potential which describes a uniform electric field in combination with the other possibilities.
The electric polarizability of a hadron allows an external electric field to shift the hadron mass. We try to calculate the electric polarizability for several hadrons from their quadratic response to the field at a=0.17fm using an improved gauge field and the clover quark action. Results are compared to experiment where available.
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.
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.
By simulating a uniform electric field on a lattice and measuring the change in the rest mass, we calculate the electric polarizability of neutral mesons and baryons using the methods of quenched lattice QCD. Specifically, we measure the electric polarizability coefficient from the quadratic response to the electric field for 10 particles: the vector mesons $ρ^0$ and $K^{*0}$; the octet baryons n, $Σ^0$, $Λ_{o}^{0}$, $Λ_{s}^{0}$, and $Ξ^0$; and the decouplet baryons $Δ^0$, $Σ^{*0}$, and $Ξ^{*0}$. Independent calculations using two fermion actions were done for consistency and comparison purpos…
We present preliminary calculations for the electric polarizability of the neutral pion and neutron on three dynamically generated nHYP-Clover ensembles. We use two different pion masses ($m_π \simeq 300$ and 220 MeV) to gauge the chiral behavior. The effects of partial quenching are analyzed by computing a string of partial quenched valence masses for each ensemble. We also analyzed the volume dependence using elongated lattices, where the elongation is in the direction of the electric field.
The static electric polarizability of the neutron is evaluated using domain-wall valence quarks on a MILC asqtad sea quark ensemble corresponding to a pion mass of m_pi = 357 MeV. Both connected as well as disconnected contributions are included. The result is quantitatively compatible with the expectation from chiral effective theory.
Knowledge of the electric polarizability is crucial to understanding the interactions of hadrons with electromagnetic fields. The neutron polarizability is very sensitive to the quark mass and is expected to diverge in the chiral limit. Here we present results for the electric polarizability of the neutron, neutral pion, and neutral kaon on eight ensembles with nHYP-smeared clover dynamical fermions with two different pion masses (227 and 306 MeV). These are currently the lightest pion masses used in polarizability studies. For each pion mass we compute the polarizability at four different vol…
Electric polarizability is an important parameter for the internal structure of hadrons. Previous studies of polarizabilities have been done at relatively heavy pion masses, leaving the chiral region largely unexplored. In this report, we use overlap fermions which are known to be computationally demanding to properly capture the chiral dynamics. We present an implementation strategy to construct overlap on multi-GPUs. We find that our GPU code has an equivalent of \sim30 CPU cores to 1 GPU. We also present preliminary results for the polarizability of the neutral pion.
Electromagnetic polarizabilities are important parameters for understanding the interaction between photons and hadrons. For pions these quantities are poorly constrained experimentally since they can only be measured indirectly. New experiments at CERN and Jefferson Lab are planned that will measure the polarizabilities more precisely. Lattice QCD can be used to compute these quantities directly in terms of quark and gluons degrees of freedom, using the background field method. We present results for the electric polarizability for two different quark masses, light enough to connect to chiral…
We study the finite volume effects on the electric polarizability for the neutron, neutral pion, and neutral kaon using eight dynamically generated two-flavor nHYP-clover ensembles at two different pion masses: 306(1) and 227(2) MeV. An infinite volume extrapolation is performed for each hadron at both pion masses. For the neutral kaon, finite volume effects are relatively mild. The dependence on the quark mass is also mild and a reliable chiral extrapolation can be performed along with the infinite volume extrapolation. Our result is $α_{K^0}^\mbox{phys}=0.356(74) \times 10^{-4} \mbox{fm}^3$.…
We use the background field method to extract the "connected" piece of the neutron electric polarizability. We present results for quenched simulations using both clover and Wilson fermions and discuss our experience in extracting the mass shifts and the challenges we encountered when we lowered the quark mass. For the neutron we find that as the pion mass is lowered below $500\MeV$, the polarizability starts rising in agreement with predictions from chiral perturbation theory. For our lowest pion mass, $m_π=320\MeV$, we find that $α_n = 3.8(1.3)\times 10^{-4}\fm^3$, which is still only one th…
Direct evaluation of charged particle polarizabilities on the lattice is quite difficult. However, a short cut for charged pion polarizability - the Das, Mathur, Okubo Sum Rule - can readily be calculated using lattice techniques. A phenomenological model has been developed to fit the time behavior of the propagators in this expression. Numerical systematics are discussed and some preliminary results are presented.
Formulas are developed for use in lattice studies of charged hadron polarizabilities. In particular, the valence quark different-flavor component of the charged pion polarizability is examined on a $16^{3}\times 24$ lattice at $β=6.0$ using Wilson fermions. Using the elastic limit results of Part I of this series, it is concluded that this represents a small negative component of the full charged polarizabilty.
We extract the magnetic polarizability from the quadratic response of a hadron's mass shift in progressively small static magnetic fields. The calculation is done on a 24x12x12x24 lattice at a = 0.17 fm with an improved gauge action and the clover quark action. The results are compared to those from experiments and models where available.
We present a lattice QCD calculation of the polarizability of the neutron and other neutral hadrons that includes the effects of the background field on the sea quarks. This is done by perturbatively reweighting the charges of the sea quarks to couple them to the background field. The main challenge in such a calculation is stochastic estimation of the weight factors, and we discuss the difficulties in this estimation. Here we use an extremely aggressive dilution scheme to reduce the stochastic noise to a manageable level. The pion mass in our calculation is 306 MeV and the lattice size is 3 f…
We explore the energy dependence of $π$ mesons off the background abelian magnetic field on the base of quenched SU(3) lattice gauge theory and calculate the magnetic dipole polarizability of charged and neutral pions for various lattice volumes and lattice spacings. The contribution of the magnetic hyperpolarizability to the neutral pion energy has been also found.
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 the…
The magnetic dipole polarizabilities of the vector $ρ^0$ and $ρ^{\pm}$ mesons in $SU(3)$ pure gauge theory are calculated in the article. Based on this the authors explore the contribution of the dipole magnetic polarizabilities to the tensor polarization of the vector mesons in external abelian magnetic field. The tensor polarization leads to the dilepton asymmetry observed in non-central heavy ion collisions and can be also estimated in lattice gauge 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 $α_K =0.269(43)\times10^{-4}$fm$^{3}$, (2) quantitatively compare our …
We use the background field method to extract the polarizability for the neutral "pion". In our previous study we found that the polarizability for this system is negative which is believed to be a finite volume artifact. To address this issue, we carry out simulations for different lattice sizes and we also look at the influence of the boundary conditions on these results. We find that for pion masses lower than 400 MeV the polarizability remains negative even on larger lattices. An infinite volume extrapolation is attempted, but the results are not conclusive due mainly to a lack of an analy…
We present a calculation of the charged pion electric polarizability using the background field method. To extract the mass-shift induced by the electric field for the accelerated charged particle we fit the lattice QCD correlators using correlators derived from an effective model. The methodology outlined in this study (boundary conditions, fitting procedure, etc.) is designed to ensure that the results are invariant under gauge transformations of the background field. We apply the method to four $N_f=2$ dynamical ensembles to extract $α_{π^\pm}$ at pion mass of $315$ MeV.
We present the results of a reweighting calculation to compute the contribution of the charged quark sea to the neutron electric polarizability. The chief difficulty is the stochastic estimation of weight factors, and we present a hopping parameter expansion-based technique for reducing the stochastic noise, along with a discussion of why this particular reweighting is so difficult. We used this technique to estimate weight factors for 300 configurations of nHYP-clover fermions and compute the neutron polarizability, but the reweighting greatly inflates the overall statistical error, driven by…
The background field method has been used successfully to determine hadron electromagnetic polarizabilities. Recently questions have been raised regarding the proper way to deal with the electric field on the lattice. In this paper, we show how the presence of a background electric field affects the quark hopping matrix. We use this formulation to carry out simulations on quenched configurations, and we present the results for neutron electric polarizability for pion masses as low as $500\MeV$. We find that the polarizability is roughly constant for the quark masses considered, $α\sim 1.5 \tim…
An evaluation of charged pion polarizability using correlation functions measured on a 16^{3}\times 24 lattice in the context of the Das, Mathur, Okubo (DMO) sum rule is carried out. The calculation is limited to the so-called intrinsic part of the polarizability. This contribution, equivalent to a Euclidean time integral over vector and axial vector momentum-differentiated propagators, is evaluated in both a continuous and discrete sense. In the continuous case, the time behavior of the correlation functions is fit to the continuum quark model; the discrete case is handled by a straightforwar…
The magnetic polarizability of the neutral pion has been calculated in the background magnetic-field formalism of Lattice QCD. In this investigation, the chiral extrapolation of these lattice results is considered in a formalism preserving the exact leading nonanalytic terms of chiral perturbation theory. The $n_f = 2 + 1$ numerical simulations are electro-quenched, such that the virtual sea-quarks of the QCD vacuum do not interact with the background field. To understand the impact of this, we draw on partially quenched chiral perturbation theory and identify the leading contributions of quar…
The proton-polarizability contribution to the muonic-hydrogen Lamb shift is a major source of theoretical uncertainty in the extraction of the proton charge radius. An empirical evaluation of this effect, based on the proton structure functions, requires a systematically improvable calculation of the "subtraction function", possibly using lattice QCD. We consider a different subtraction point, with the aim of accessing the subtraction function directly in lattice calculations. A useful feature of this subtraction point is that the corresponding contribution of the structure functions to the La…
We present a calculation of hadron magnetic polarizability using the techniques of lattice QCD. This is carried out by introducing a uniform external magnetic field on the lattice and measuring the quadratic part of a hadron's mass shift. The calculation is performed on a $24^4$ lattice with standard Wilson actions at beta=6.0 (spacing $a=0.1$ fm) and pion mass down to about 500 MeV. Results are obtained for 30 particles covering the entire baryon octet ($n$, $p$, $Σ^0$, $Σ^-$, $Σ^+$, $Ξ^-$, $Ξ^0$, $Λ$) and decuplet ($Δ^0$, $Δ^-$, $Δ^+$, $Δ^{++}$, $Σ^{*0}$, $Σ^{*-}$, $Σ^{*+}$, $Ξ^{*0}$, $Ξ^{*-…
The background magnetic-field formalism of Lattice QCD has been used recently to calculate the magnetic polarizability of the charged pion. These $n_f = 2 + 1$ numerical simulations are electro-quenched, such that the virtual sea-quarks of the QCD vacuum do not interact with the background field. To understand the impact of this, we draw on partially quenched chiral perturbation theory. In this case, the leading term proportional to $1/M_π$ arises at tree level from $\mathcal{L}_4$. To describe the results from lattice QCD, while maintaining the exact leading terms of chiral perturbation theor…
There has been much progress in the experimental measurement of the electric and magnetic polarizabilities of the nucleon. Similarly, lattice QCD simulations have recently produced dynamical QCD results for the magnetic polarizability of the neutron approaching the chiral regime. In order to compare the lattice simulations with experiment, calculation of partial quenching and finite-volume effects is required prior to an extrapolation in quark mass to the physical point. These dependencies are described using chiral effective field theory. Corrections to the partial quenching effects associate…
