Constraint on the branching ratio of B_c \to tau nu from LEP1 and consequences for R(D(*)) anomaly

Recently there has been interest in the correlation between R(D*) and the branching ratio (BR) of $B_c \to \tau \nu$ in models with a charged scalar H^\pm. Any enhancement of R(D*) by $H^\pm$ alone (in order to agree with current data) also enhances $BR(B_c \to \tau \nu$), for which there has been no direct search at hadron colliders. We show that LEP data taken at the Z peak requires BR($B_c \to \tau \nu$) < 10%, and this constraint is significantly stronger than the recent constraint BR($B_c \to \tau \nu$) < 30% from considering the lifetime of B_c. In order to respect this new constraint, any explanation of the R(D) and R(D*) anomaly in terms of $H^\pm$ alone would require the future measurements of R(D*) to be even closer to the Standard Model prediction. A stronger limit on BR($B_c \to \tau \nu$) (or its first measurement) would be obtained if the L3 collaboration used all its data taken at the Z peak.Comment: 14 pages, 4 figures, a reference and two sentences adde

Three-particle bound states in a finite volume: unequal masses and higher partial waves

An explicit expression for the finite-volume energy shift of shallow three-body bound states for non-identical particles is obtained in the unitary limit. The inclusion of the higher partial waves is considered. To this end, the method of arXiv:1412.4969 (Mei{\ss}ner et al.) is generalized for the case of unequal masses and arbitrary angular momenta. It is shown that in the S-wave and in the equal mass limit, the result from arXiv:1412.4969 is reproduced.Comment: 17 pages, 1 figur

A bounded degree SOS hierarchy for polynomial optimization

We consider a new hierarchy of semidefinite relaxations for the general polynomial optimization problem $(P):\:f^{\ast}=\min \{\,f(x):x\in K\,\}$ on a compact basic semi-algebraic set $K\subset\R^n$. This hierarchy combines some advantages of the standard LP-relaxations associated with Krivine's positivity certificate and some advantages of the standard SOS-hierarchy. In particular it has the following attractive features: (a) In contrast to the standard SOS-hierarchy, for each relaxation in the hierarchy, the size of the matrix associated with the semidefinite constraint is the same and fixed in advance by the user. (b) In contrast to the LP-hierarchy, finite convergence occurs at the first step of the hierarchy for an important class of convex problems. Finally (c) some important techniques related to the use of point evaluations for declaring a polynomial to be zero and to the use of rank-one matrices make an efficient implementation possible. Preliminary results on a sample of non convex problems are encouraging

Long-distance entanglement generation with scalable and robust two-dimensional quantum network

We present a protocol for generating entanglement over long distances in a two-dimensional quantum network based on the surface error-correction code. This protocol requires a fixed number of quantum memories at each node of the network and tolerates error rates of up to 1.67% in the quantum channels.Comment: 5 pags, 4 figs. V2: text corrected, discussion on channel losses added. Accepted by PR

A Pure Test for the Elasticity of Yield Spreads

The correlation between interest rates and corporate bond yield spreads is a well-known feature of structural bond pricing models. Duffee (1998) argues that this correlation is weak once the effects of call options are removed from the data; a conclusion that contradicts the negative correlation expected by Longstaff and Schwartz (1995). However, Elton et al. (2001) point out that Duffee's analysis ignores the effects of the tax differential between U.S. Treasury and corporate bonds. Canadian bonds have no such tax differential, yet, after controlling for callability, we find that the correlation between interest rates and corporate bond spreads remains negligible. We also find a significant negative relationship for callable bonds with this relationship increasing with the moneyness of the call provision. These results are robust under alternate empirical specifications.Bond Yield Spread, Default Risk, Callable Bonds, Corporate Bonds