342 research outputs found

    Higher Loop Results for the Plaquette, Using the Clover and Overlap Actions

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    We calculate the perturbative value of the free energy in QCD on the lattice. This quantity is directly related to the average plaquette. Our calculation is done to 3 loops using the clover action for fermions; the results are presented for arbitrary values of the clover coefficient, and for a wide range of fermion masses. In addition, we calculate the 2 loop result for the same quantity, using the overlap action.Comment: 3 pages, 1 figure. Presented at Lattice2004(improved

    Lattice chiral fermions in the background of non-trivial topology

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    We address the problem of numerical simulations in the background non-trivial topology in the chiral Schwinger model. An effective fermionic action is derived which is in accord with established analytical results, and which satisfies the anomaly equation. We describe a numerical evaluation of baryon number violating amplitudes, specifically the 't Hooft vertex.Comment: LATTICE99(Chiral Gauge Theories

    A construction of the Glashow-Weinberg-Salam model on the lattice with exact gauge invariance

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    We present a gauge-invariant and non-perturbative construction of the Glashow-Weinberg-Salam model on the lattice, based on the lattice Dirac operator satisfying the Ginsparg-Wilson relation. Our construction covers all SU(2) topological sectors with vanishing U(1) magnetic flux and would be usable for a description of the baryon number non-conservation. In infinite volume, it provides a gauge-invariant regularization of the electroweak theory to all orders of perturbation theory. First we formulate the reconstruction theorem which asserts that if there exists a set of local currents satisfying cetain properties, it is possible to reconstruct the fermion measure which depends smoothly on the gauge fields and fulfills the fundamental requirements such as locality, gauge-invariance and lattice symmetries. Then we give a closed formula of the local currents required for the reconstruction theorem.Comment: 32 pages, uses JHEP3.cls, the version to appear in JHE

    A practical implementation of the Overlap-Dirac operator

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    A practical implementation of the Overlap-Dirac operator 1+γ5ϵ(H)2{{1+\gamma_5\epsilon(H)}\over 2} is presented. The implementation exploits the sparseness of HH and does not require full storage. A simple application to parity invariant three dimensional SU(2) gauge theory is carried out to establish that zero modes related to topology are exactly reproduced on the lattice.Comment: Y-axis label in figure correcte

    First-order restoration of SU(Nf) x SU(Nf) chiral symmetry with large Nf and Electroweak phase transition

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    It has been argued by Pisarski and Wilczek that finite temperature restoration of the chiral symmetry SU(Nf) x SU(Nf) is first-order for Nf >=3. This type of chiral symmetry with a large Nf may appear in the Higgs sector if one considers models such as walking technicolor theories. We examine the first-order restoration of the chiral symmetry from the point of view of the electroweak phase transition. The strength of the transition is estimated in SU(2) x U(1) gauged linear sigma model by means of the finite temperature effective potential at one-loop with the ring improvement. Even if the mass of the neutral scalar boson corresponding to the Higgs boson is larger than 114 GeV, the first-order transition can be strong enough for the electroweak baryogenesis, as long as the extra massive scalar bosons (required for the linear realization) are kept heavier than the neutral scalar boson. Explicit symmetry breaking terms reduce the strength of the first-order transition, but the transition can remain strongly first-order even when the masses of pseudo Nambu-Goldstone bosons become as large as the current lower bound of direct search experiments.Comment: 18 pages, 18 figures, minor corrections, references adde

    Neutron electric dipole moment from lattice QCD

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    We carry out a feasibility study for the lattice QCD calculation of the neutron electric dipole moment (NEDM) in the presence of the θ\theta term. We develop the strategy to obtain the nucleon EDM from the CP-odd electromagnetic form factor F3F_3 at small θ\theta, in which NEDM is given by limq20θF3(q2)/(2mN)\lim_{q^2\to 0}\theta F_3(q^2)/(2m_N) where qq is the momentum transfer and mNm_N is the nucleon mass. We first derive a formula which relates F3F_3, a matrix element of the electromagnetic current between nucleon states, with vacuum expectation values of nucleons and/or the current. In the expansion of θ\theta, the parity-odd part of the nucleon-current-nucleon three-point function contains contributions not only from the parity-odd form factors but also from the parity-even form factors multiplied by the parity-odd part of the nucleon two-point function, and therefore the latter contribution must be subtracted to extract F3F_3. We then perform an explicit lattice calculation employing the domain-wall quark action with the RG improved gauge action in quenched QCD at a12a^{-1}\simeq 2 GeV on a 163×32×1616^3\times 32\times 16 lattice. At the quark mass mfa=0.03m_f a =0.03, corresponding to mπ/mρ0.63m_\pi/m_\rho \simeq 0.63, we accumulate 730 configurations, which allow us to extract the parity-odd part in both two- and three-point functions. Employing two different Dirac γ\gamma matrix projections, we show that a consistent value for F3F_3 cannot be obtained without the subtraction described above. We obtain F3(q20.58GeV2)/(2mN)=F_3(q^2\simeq 0.58 \textrm{GeV}^2)/(2m_N) = -0.024(5) ee\cdotfm for the neutron and F3(q20.58GeV2)/(2mN)=F_3(q^2\simeq 0.58 \textrm{GeV}^2)/(2m_N) = 0.021(6) ee\cdotfm for the proton.Comment: LaTeX2e, 43 pages, 42 eps figures, uses revtex4 and graphicx, comments added and typos corrected, final version to appear in Phys. Rev.

    Domain wall fermion and CP symmetry breaking

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    We examine the CP properties of chiral gauge theory defined by a formulation of the domain wall fermion, where the light field variables qq and qˉ\bar q together with Pauli-Villars fields QQ and Qˉ\bar Q are utilized. It is shown that this domain wall representation in the infinite flavor limit N=N=\infty is valid only in the topologically trivial sector, and that the conflict among lattice chiral symmetry, strict locality and CP symmetry still persists for finite lattice spacing aa. The CP transformation generally sends one representation of lattice chiral gauge theory into another representation of lattice chiral gauge theory, resulting in the inevitable change of propagators. A modified form of lattice CP transformation motivated by the domain wall fermion, which keeps the chiral action in terms of the Ginsparg-Wilson fermion invariant, is analyzed in detail; this provides an alternative way to understand the breaking of CP symmetry at least in the topologically trivial sector. We note that the conflict with CP symmetry could be regarded as a topological obstruction. We also discuss the issues related to the definition of Majorana fermions in connection with the supersymmetric Wess-Zumino model on the lattice.Comment: 33 pages. Note added and a new reference were added. Phys. Rev.D (in press

    Neutron electric dipole moment with external electric field method in lattice QCD

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    We discuss a possibility that the Neutron Electric Dipole Moment (NEDM) can be calculated in lattice QCD simulations in the presence of the CP violating θ\theta term. In this paper we measure the energy difference between spin-up and spin-down states of the neutron in the presence of an uniform and static external electric field. We first test this method in quenched QCD with the RG improved gauge action on a 163×3216^3\times 32 lattice at a1a^{-1}\simeq 2 GeV, employing two different lattice fermion formulations, the domain-wall fermion and the clover fermion for quarks, at relatively heavy quark mass (mPS/mV0.85)(m_{PS}/m_V \simeq 0.85). We obtain non-zero values of NEDM from calculations with both fermion formulations. We next consider some systematic uncertainties of our method for NEDM, using 243×3224^3\times 32 lattice at the same lattice spacing only with the clover fermion. We finally investigate the quark mass dependence of NEDM and observe a non-vanishing behavior of NEDM toward the chiral limit. We interpret this behavior as a manifestation of the pathology in the quenched approximation.Comment: LaTeX2e, 51 pages, 43 figures, uses revtex4 and graphicx, References and comments added, typos corrected, accepted by PR
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