Study of Rapidity Gap Events in Hadronic Z Decays with L3 detector

Rapidity gaps have been studied in well separated completely symmetric 3 jet events from hadronic Z decays to search for colour singlet exchange. Asymmetries in particle flow and angular separation, defined with respect to the inter-jet regions, are found to be sensitive to the exchange of a colour singlet object instead of a colour octet gluon. %Comparing data from the L3 experiment with Monte Carlo predictions, %a limit is obtained on the fraction %of colour singlet exchange in data. From a comparison of the distributions observed in the L3 experiment and Monte Carlo predictions, a limit is obtained on the fraction of colour singlet exchange in data.Comment: 4 pages, 7 figures (in eps) talk given at XXXI International Symposium on Multiparticle Dynamics, Sep. 1-7, 2001, Datong China. see http://ismd31.ccnu.edu.cn

Search for a Light Higgs Boson at BaBar

We search for evidence of a light Higgs boson (A0) in the radiative decays of the narrow Upsilon(3S) resonance: Upsilon(3S) -> gamma A0, where A0 -> invisible or A0 -> mu+mu-. Such an object appears in extensions of the Standard Model, where a light CP-odd Higgs boson naturally couples strongly to b-quarks. We find no evidence for such processes in a sample of 122 million Upsilon(3S) decays collected by the BaBar collaboration at the PEP II B-factory, and set 90% C.L. upper limits on the product of the corresponding branching fractions. We also set a limit on the di-muon branching fraction of the recently discovered eta_b meson.Comment: 8 pages, 4 figures. To appear in the proceedings of Les Rencontres de Physique de la Valle'e d'Aoste held at La Thuile, Italy from 1-7 March 200

Sub-linear Upper Bounds on Fourier dimension of Boolean Functions in terms of Fourier sparsity

We prove that the Fourier dimension of any Boolean function with Fourier sparsity $s$ is at most $O\left(s^{2/3}\right)$. Our proof method yields an improved bound of $\widetilde{O}(\sqrt{s})$ assuming a conjecture of Tsang~\etal~\cite{tsang}, that for every Boolean function of sparsity $s$ there is an affine subspace of $\mathbb{F}_2^n$ of co-dimension O(\poly\log s) restricted to which the function is constant. This conjectured bound is tight upto poly-logarithmic factors as the Fourier dimension and sparsity of the address function are quadratically separated. We obtain these bounds by observing that the Fourier dimension of a Boolean function is equivalent to its non-adaptive parity decision tree complexity, and then bounding the latter

Towards Better Separation between Deterministic and Randomized Query Complexity

We show that there exists a Boolean function $F$ which observes the following separations among deterministic query complexity $(D(F))$, randomized zero error query complexity $(R_0(F))$ and randomized one-sided error query complexity $(R_1(F))$: $R_1(F) = \widetilde{O}(\sqrt{D(F)})$ and $R_0(F)=\widetilde{O}(D(F))^{3/4}$. This refutes the conjecture made by Saks and Wigderson that for any Boolean function $f$, $R_0(f)=\Omega({D(f)})^{0.753..}$. This also shows widest separation between $R_1(f)$ and $D(f)$ for any Boolean function. The function $F$ was defined by G{\"{o}}{\"{o}}s, Pitassi and Watson who studied it for showing a separation between deterministic decision tree complexity and unambiguous non-deterministic decision tree complexity. Independently of us, Ambainis et al proved that different variants of the function $F$ certify optimal (quadratic) separation between $D(f)$ and $R_0(f)$, and polynomial separation between $R_0(f)$ and $R_1(f)$. Viewed as separation results, our results are subsumed by those of Ambainis et al. However, while the functions considerd in the work of Ambainis et al are different variants of $F$, we work with the original function $F$ itself.Comment: Reference adde

The zero-error randomized query complexity of the pointer function

The pointer function of G{\"{o}}{\"{o}}s, Pitassi and Watson \cite{DBLP:journals/eccc/GoosP015a} and its variants have recently been used to prove separation results among various measures of complexity such as deterministic, randomized and quantum query complexities, exact and approximate polynomial degrees, etc. In particular, the widest possible (quadratic) separations between deterministic and zero-error randomized query complexity, as well as between bounded-error and zero-error randomized query complexity, have been obtained by considering {\em variants}~\cite{DBLP:journals/corr/AmbainisBBL15} of this pointer function. However, as was pointed out in \cite{DBLP:journals/corr/AmbainisBBL15}, the precise zero-error complexity of the original pointer function was not known. We show a lower bound of $\widetilde{\Omega}(n^{3/4})$ on the zero-error randomized query complexity of the pointer function on $\Theta(n \log n)$ bits; since an $\widetilde{O}(n^{3/4})$ upper bound is already known \cite{DBLP:conf/fsttcs/MukhopadhyayS15}, our lower bound is optimal up to a factor of \polylog\, n