Perturbative and non-perturbative renormalization results of the Chromomagnetic Operator on the Lattice

The Chromomagnetic operator (CMO) mixes with a large number of operators under renormalization. We identify which operators can mix with the CMO, at the quantum level. Even in dimensional regularization (DR), which has the simplest mixing pattern, the CMO mixes with a total of 9 other operators, forming a basis of dimension-five, Lorentz scalar operators with the same flavor content as the CMO. Among them, there are also gauge noninvariant operators; these are BRST invariant and vanish by the equations of motion, as required by renormalization theory. On the other hand using a lattice regularization further operators with $d \leq 5$ will mix; choosing the lattice action in a manner as to preserve certain discrete symmetries, a minimul set of 3 additional operators (all with $d<5$) will appear. In order to compute all relevant mixing coefficients, we calculate the quark-antiquark (2-pt) and the quark-antiquark-gluon (3-pt) Green's functions of the CMO at nonzero quark masses. These calculations were performed in the continuum (dimensional regularization) and on the lattice using the maximally twisted mass fermion action and the Symanzik improved gluon action. In parallel, non-perturbative measurements of the $K-\pi$ matrix element are being performed in simulations with 4 dynamical ($N_f = 2+1+1$) twisted mass fermions and the Iwasaki improved gluon action.Comment: 7 pages, 1 figure, 3 tables, LATTICE2014 proceeding

D→K,lνD \rightarrow K, l \nu Semileptonic Decay Scalar Form Factor and ∣Vcs∣|V_{cs}| from Lattice QCD

We present a new study of D semileptonic decays on the lattice which employs the Highly Improved Staggered Quark (HISQ) action for both the charm and the light valence quarks. We work with MILC unquenched $N_f = 2 + 1$ lattices and determine the scalar form factor $f_0(q^2)$ for $D \rightarrow K, l \nu$ semileptonic decays. The form factor is obtained from a scalar current matrix element that does not require any operator matching. We develop a new approach to carrying out chiral/continuum extrapolations of $f_0(q^2)$. The method uses the kinematic "$z$" variable instead of $q^2$ or the kaon energy $E_K$ and is applicable over the entire physical $q^2$ range. We find $f^{D \rightarrow K}_0(0) \equiv f^{D \rightarrow K}_+(0) = 0.747(19)$ in the chiral plus continuum limit and hereby improve the theory error on this quantity by a factor of $\sim$4 compared to previous lattice determinations. Combining the new theory result with recent experimental measurements of the product $f^{D \rightarrow K}_+(0) * |V_{cs}|$ from BaBar and CLEO-c leads to the most precise direct determination of the CKM matrix element $|V_{cs}|$ to date, $|V_{cs}| = 0.961(11)(24)$, where the first error comes from experiment and the second is the lattice QCD theory error. We calculate the ratio $f^{D \rightarrow K}_+(0)/f_{D_s}$ and find $2.986 \pm 0.087$ GeV$^{-1}$ and show that this agrees with experiment.Comment: 23 pages, 31 figures, 11 tables. Added a paragraph in sction VII, and updated with PDG 2010 instead of PDG 200

The chromomagnetic operator on the lattice

We study matrix elements of the "chromomagnetic" operator on the lattice. This operator is contained in the strangeness-changing effective Hamiltonian which describes electroweak effects in the Standard Model and beyond. Having dimension 5, the chromomagnetic operator is characterized by a rich pattern of mixing with other operators of equal and lower dimensionality, including also non gauge invariant quantities; it is thus quite a challenge to extract from lattice simulations a clear signal for the hadronic matrix elements of this operator. We compute all relevant mixing coefficients to one loop in lattice perturbation theory; this necessitates calculating both 2-point (quark-antiquark) and 3-point (gluon-quark-antiquark) Green's functions at nonzero quark masses. We use the twisted mass lattice formulation, with Symanzik improved gluon action. For a comprehensive presentation of our results, along with detailed explanations and a more complete list of references, we refer to our forthcoming publication [1].Comment: 7 pages, 1 figure. Talk presented at the 31st International Symposium on Lattice Field Theory (Lattice 2013), 29 July - 3 August 2013, Mainz, German

K→πK \to \pi matrix elements of the chromomagnetic operator on the lattice

We present the results of the first lattice QCD calculation of the $K \to \pi$ matrix elements of the chromomagnetic operator $O_{CM} = g\, \bar s\, \sigma_{\mu\nu} G_{\mu\nu} d$, which appears in the effective Hamiltonian describing $\Delta S = 1$ transitions in and beyond the Standard Model. Having dimension 5, the chromomagnetic operator is characterized by a rich pattern of mixing with operators of equal and lower dimensionality. The multiplicative renormalization factor as well as the mixing coefficients with the operators of equal dimension have been computed at one loop in perturbation theory. The power divergent coefficients controlling the mixing with operators of lower dimension have been determined non-perturbatively, by imposing suitable subtraction conditions. The numerical simulations have been carried out using the gauge field configurations produced by the European Twisted Mass Collaboration with $N_f = 2+1+1$ dynamical quarks at three values of the lattice spacing. Our result for the B-parameter of the chromomagnetic operator at the physical pion and kaon point is $B_{CMO}^{K \pi} = 0.273 ~ (70)$, while in the SU(3) chiral limit we obtain $B_{CMO} = 0.072 ~ (22)$. Our findings are significantly smaller than the model-dependent estimate $B_{CMO} \sim 1 - 4$, currently used in phenomenological analyses, and improve the uncertainty on this important phenomenological quantity.Comment: 20 pages, 4 figures, 2 table. Refined SU(3) ChPT analysis with no changes in the final result. Version to appear in PR

Deterministic Walks in Quenched Random Environments of Chaotic Maps

This paper concerns the propagation of particles through a quenched random medium. In the one- and two-dimensional models considered, the local dynamics is given by expanding circle maps and hyperbolic toral automorphisms, respectively. The particle motion in both models is chaotic and found to fluctuate about a linear drift. In the proper scaling limit, the cumulative distribution function of the fluctuations converges to a Gaussian one with system dependent variance while the density function shows no convergence to any function. We have verified our analytical results using extreme precision numerical computations.Comment: 18 pages, 9 figure

Electromagnetic meson form factor from a relativistic coupled-channel approach

Point-form relativistic quantum mechanics is used to derive an expression for the electromagnetic form factor of a pseudoscalar meson for space-like momentum transfers. The elastic scattering of an electron by a confined quark-antiquark pair is treated as a relativistic two-channel problem for the $q\bar{q}e$ and $q\bar{q}e\gamma$ states. With the approximation that the total velocity of the $q\bar{q}e$ system is conserved at (electromagnetic) interaction vertices this simplifies to an eigenvalue problem for a Bakamjian-Thomas type mass operator. After elimination of the $q\bar{q}e\gamma$ channel the electromagnetic meson current and form factor can be directly read off from the one-photon-exchange optical potential. By choosing the invariant mass of the electron-meson system large enough, cluster separability violations become negligible. An equivalence with the usual front-form expression, resulting from a spectator current in the $q^+=0$ reference frame, is established. The generalization of this multichannel approach to electroweak form factors for an arbitrary bound few-body system is quite obvious. By an appropriate extension of the Hilbert space this approach is also able to accommodate exchange-current effects.Comment: 30 pages, 5 figure

Improved Semileptonic Form Factor Calculations in Lattice QCD

We investigate the computational efficiency of two stochastic based alternatives to the Sequential Propagator Method used in Lattice QCD calculations of heavy-light semileptonic form factors. In the first method, we replace the sequential propagator, which couples the calculation of two of the three propagators required for the calculation, with a stochastic propagator so that the calculations of all three propagators are independent. This method is more flexible than the Sequential Propagator Method but introduces stochastic noise. We study the noise to determine when this method becomes competitive with the Sequential Propagator Method, and find that for any practical calculation it is competitive with or superior to the Sequential Propagator Method. We also examine a second stochastic method, the so-called ``one-end trick", concluding it is relatively inefficient in this context. The investigation is carried out on two gauge field ensembles, using the non-perturbatively improved Wilson-Sheikholeslami-Wohlert action with N_f=2 mass-degenerate sea quarks. The two ensembles have similar lattice spacings but different sea quark masses. We use the first stochastic method to extract ${\mathcal O}(a)$-improved, matched lattice results for the semileptonic form factors on the ensemble with lighter sea quarks, extracting f_+(0)

Electroexcitation of the P33(1232), P11(1440), D13(1520), S11(1535) at Q^2=0.4 and 0.65(GeV/c)^2

Using two approaches: dispersion relations and isobar model, we have analyzed recent high precision CLAS data on cross sections of \pi^0, \pi^+, and \eta electroproduction on protons, and the longitudinally polarized electron beam asymmetry for p(\vec{e},e'p)\pi^0 and p(\vec{e},e'n)\pi^+. The contributions of the resonances P33(1232), P11(1440), D13(1520), S11(1535) to \pi electroproduction and S11(1535) to \eta electroproduction are found. The results obtained in the two approaches are in good agreement with each other. There is also good agreement between amplitudes of the \gamma^* N \to S11(1535) transition found in \pi and \eta electroproduction. For the first time accurate results are obtained for the longitudinal amplitudes of the P11(1440), D13(1520) and S11(1535) electroexcitation on protons.Comment: 9 pages, 9 figure

Global Analysis of Data on the Proton Structure Function g1 and Extraction of its Moments

Inspired by recent measurements with the CLAS detector at Jefferson Lab, we perform a self-consistent analysis of world data on the proton structure function g1 in the range 0.17 < Q2 < 30 (GeV/c)**2. We compute for the first time low-order moments of g1 and study their evolution from small to large values of Q2. The analysis includes the latest data on both the unpolarized inclusive cross sections and the ratio R = sigmaL / sigmaT from Jefferson Lab, as well as a new model for the transverse asymmetry A2 in the resonance region. The contributions of both leading and higher twists are extracted, taking into account effects from radiative corrections beyond the next-to-leading order by means of soft-gluon resummation techniques. The leading twist is determined with remarkably good accuracy and is compared with the predictions obtained using various polarized parton distribution sets available in the literature. The contribution of higher twists to the g1 moments is found to be significantly larger than in the case of the unpolarized structure function F2.Comment: 18 pages, 13 figures, to appear in Phys. Rev.

Theory of the optical absorption of light carrying orbital angular momentum by semiconductors

We develop a free-carrier theory of the optical absorption of light carrying orbital angular momentum (twisted light) by bulk semiconductors. We obtain the optical transition matrix elements for Bessel-mode twisted light and use them to calculate the wave function of photo-excited electrons to first-order in the vector potential of the laser. The associated net electric currents of first and second-order on the field are obtained. It is shown that the magnetic field produced at the center of the beam for the $\ell=1$ mode is of the order of a millitesla, and could therefore be detected experimentally using, for example, the technique of time-resolved Faraday rotation.Comment: Submitted to Phys. Rev. Lett. (23 Jan 2008