Constraints on U(1)Lμ−LτU(1)_{L_\mu-L_\tau} from LHC Data

In this study, we apply LHC data to constrain the extension of the Standard Model by an anomaly-free $U(1)_{L_\mu-L_\tau}$ gauge group; this model contains a new gauge boson ($Z^\prime$) and a scalar dark matter particle ($\phi_{\rm DM}$). We recast a large number of LHC analyses from ATLAS and CMS of multi-lepton final states. We find that for $10$ GeV $< m_{Z^\prime} < 60$ GeV the strongest constraint comes from a dedicated $Z^\prime$ search in the $4\mu$ final state by the CMS collaboration; for larger $Z^\prime$ masses, searches for final states with three leptons plus missing $E_T$ are more sensitive. Searches for final states with two leptons and missing $E_T$, which are sensitive to $Z^\prime$ decays into dark matter particles, can only probe regions of parameter space that are excluded by searches in the $3$ and $4$ lepton channels. The combination of LHC data excludes values of $Z^\prime$ mass and coupling constant that can explain the deficit in $g_\mu-2$ for $4$ GeV $\leq m_{Z^\prime} \leq 500$ GeV. However, for much of this range the LHC bound is weaker than the bound that can be derived from searches for trident events in neutrino-nucleus scattering.Comment: 15 pages, 4 figure

Two Piggybacking Codes with Flexible Sub-Packetization to Achieve Lower Repair Bandwidth

As a special class of array codes, $(n,k,m)$ piggybacking codes are MDS codes (i.e., any $k$ out of $n$ nodes can retrieve all data symbols) that can achieve low repair bandwidth for single-node failure with low sub-packetization $m$. In this paper, we propose two new piggybacking codes that have lower repair bandwidth than the existing piggybacking codes given the same parameters. Our first piggybacking codes can support flexible sub-packetization $m$ with $2\leq m\leq n-k$, where $n - k > 3$. We show that our first piggybacking codes have lower repair bandwidth for any single-node failure than the existing piggybacking codes when $n - k = 8,9$, $m = 6$ and $30\leq k \leq 100$. Moreover, we propose second piggybacking codes such that the sub-packetization is a multiple of the number of parity nodes (i.e., $(n-k)|m$), by jointly designing the piggyback function for data node repair and transformation function for parity node repair. We show that the proposed second piggybacking codes have lowest repair bandwidth for any single-node failure among all the existing piggybacking codes for the evaluated parameters $k/n = 0.75, 0.8, 0.9$ and $n-k\geq 4$

Generalized Simple Regenerating Codes: Trading Sub-packetization and Fault Tolerance

Maximum distance separable (MDS) codes have the optimal trade-off between storage efficiency and fault tolerance, which are widely used in distributed storage systems. As typical non-MDS codes, simple regenerating codes (SRCs) can achieve both smaller repair bandwidth and smaller repair locality than traditional MDS codes in repairing single-node erasure. In this paper, we propose {\em generalized simple regenerating codes} (GSRCs) that can support much more parameters than that of SRCs. We show that there is a trade-off between sub-packetization and fault tolerance in our GSRCs, and SRCs achieve a special point of the trade-off of GSRCs. We show that the fault tolerance of our GSRCs increases when the sub-packetization increases linearly. We also show that our GSRCs can locally repair any singe-symbol erasure and any single-node erasure, and the repair bandwidth of our GSRCs is smaller than that of the existing related codes