Probing space-time structure of new physics with polarized beams at the ILC

At the International Linear Collider large beam polarization of both the electron and positron beams will enhance the signature of physics due to interactions that are beyond the Standard Model. Here we review our recently obtained results on a general model independent method of determining for an arbitary one-particle inclusive state the space-time structure of such new physics through the beam polarization dependence and angular distribution of the final state particle.Comment: 6 pages, plain latex, Talk given at LCWS06, Linear Collider Workshop, 9-13 March 2006, Bangalore, Indi

Squeezing in Multivariate Spin Systems

In contrast to the canonically conjugate variates $q$,$p$ representing the position and momentum of a particle in the phase space distributions, the three Cartesian components, $J_{x}$,$J_{y}$, $J_{z}$ of a spin-$j$ system constitute the mutually non-commuting variates in the quasi-probabilistic spin distributions. It can be shown that a univariate spin distribution is never squeezed and one needs to look into either bivariate or trivariate distributions for signatures of squeezing. Several such distributions result if one considers different characteristic functions or moments based on various correspondence rules. As an example, discrete probability distribution for an arbitrary spin-1 assembly is constructed using Wigner-Weyl and Margenau-Hill correspondence rules. It is also shown that a trivariate spin-1 assembly resulting from the exposure of nucleus with non-zero quadrupole moment to combined electric quadrupole field and dipole magnetic field exhibits squeezing in cerain cases.Comment: 13 pages, 1 Table, Presented at ICSSUR-05, Franc

Construction of m-Repeated Burst Error Detecting and Correcting Non-binary Linear Codes

Error correcting codes are required to ensure reliable communication of digitally encoded information. One of the areas of practical importance in which a parallel growth of the subject error correcting codes took place is that of burst error detecting and correcting codes. The nature of burst errors differs from channel to channel depending upon the behavior of channels or the kind of errors which occur during the process of transmission. The rate of transmission is efficient if the number of parity-check digits are as minimum as possible. It is usually not possible to give the exact number of parity-check digits required for a given code. However, bounds can be obtained over the number of parity-check digits. An upper bound for a linear code capable of detecting/ correcting burst errors or its variants is many a times established by the technique used to establish Varsharmov-Gilbert-Sacks bound by constructing a parity-check matrix for the requisite code. This technique not only ensures the existence of such a code but also gives a method for constructing such a code. The synthesis method using this technique is cumbersome and to the best of our knowledge, there is no systematic way to construct a parity-check matrix for a burst error correcting non-binary linear code. Extending the algorithm for binary linear codes given by the authors to non-binary codes, the paper proposes a new algorithm for constructing a parity-check matrix for any linear code over GF(q) capable of detecting and correcting a new kind of burst error called `m-repeated burst error of length b or less\u27. Codes based on the proposed algorithm have been illustrated

Repeated Burst Error Detecting Linear Codes

This paper presents lower bounds on the number of parity-check digits required for a linear code that is capable of detecting errors which are ‘m-repeated burst errors’. Further, codes capable of detecting and simultaneously correcting such errors have also been studied

On 2-Repeated Burst Codes

There are several kinds of burst errors for which error detecting and error correcting codes have been constructed. In this paper, we consider a new kind of burst error which will be termed as ‘2-repeated burst error of length b(fixed)’. Linear codes capable of detecting such errors have been studied. Further, codes capable of detecting and simultaneously correcting such errors have also been dealt with. The paper obtains lower and upper bounds on the number of parity-check digits required for such codes. An example of such a code has also been provided

Testing the ΔS=ΔQ\Delta S=\Delta Q Rule with Exclusive Semi-Leptonic Kaon Decays

We consider the possibility of violations of the selection rule $\Delta S=\Delta Q$ at an appreciable level in {\it exclusive} semi-leptonic decays of Kaons. At $\Phi$-Factories, intense Kaon beams will be available and will probe among others, the semi-leptonic decays $K_{l4}$ and $K_{l3\gamma}$ in addition to $K_{l3}$ and could provide novel testing grounds for the $\Delta S=\Delta Q$ rule. In particular, the branching ratio of $K_{l3\gamma}$ is non-negligible and could be used to probe new phenomena associated with the violation of this selection rule. Furthermore, we modify certain di-lepton event rate ratios and asymmetries and time asymmetries that have been constructed by Dass and Sarma for di-lepton events from Beon decays to test the $\Delta B=\Delta Q$ at the $\Upsilon (4S)$, to the Kaon system at the $\phi(1020)$. We find that the large width of the $K_S$ relative to that of $K_L$ plays an important role in enhancing some of the time asymmetries.Comment: 10 pages, Plain Latex, To be run twice

On Walsh Spectrum of Cryptographic Boolean Function

Walsh transformation of a Boolean function ascertains a number of cryptographic properties of the Boolean function viz, non-linearity, bentness, regularity, correlation immunity and many more. The functions, for which the numerical value of Walsh spectrum is fixed, constitute a class of Boolean functions known as bent functions. Bent functions possess maximum possible non-linearity and therefore have a significant role in design of cryptographic systems. A number of generalisations of bent function in different domains have been proposed in the literature. General expression for Walsh transformation of generalised bent function (GBF) is derived. Using this condition, a set of Diophantine equations whose solvability is a necessary condition for the existence of GBF is also derived. Examples to demonstrate how these equations can be utilised to establish non-existence and regularity of GBFs is presented

Effects of Possible ΔB=−ΔQ\Delta B =- \Delta Q Transitions in Neutral BB Meson Decays}

We explore the possibility that the existing data on like-sign dileptons at the $\Upsilon (4S)$ resonance consist of events arising from $B_{d}^0 -\bar B_{d}^0$ mixing and also from $\Delta B = - \Delta Q$ transitions. The consequences of these nonstandard transitions for certain time-asymmetries which are likely to be measured at the $B$ factories are studied.Comment: {\LARGE \bf 10 pages, no figures, process using latex, TIFR/TH/93-5

Transverse beam polarization and CP-violating triple-gauge-boson couplings in e+e- -> gamma Z

We show that an anomalous CP-violating gamma-gamma-Z vertex gives rise to a novel asymmetry with transversely polarized electron and positron beams in the process e+e- -> gamma Z. This asymmetry, which is odd under naive time reversal, is proportional to the real part of the gamma-gamma-Z CP-violating coupling. This is in contrast to the simple forward-backward asymmetry of the gamma (or Z) with unpolarized or longitudinally polarized beams studied earlier, which is even under naive time reversal, and is proportional to the imaginary part. We estimate the sensitivity of future experiments to the determination of CP-odd gamma-gamma-Z and gamma-Z-Z couplings using these asymmetries and transversely polarized beams.Comment: 13 pages, latex, 7 figures included as postscrip