We correct a statement in our original paper and add anomaly-free charge assignments for SMν
            
              R
             with 7 ≤ Q
            max ≤ 10.</jats:p

Allanach, BC

Davighi, J

Melville, S

English

Apollo (Cambridge)

JHEP08(2019)064Published for SISSA by SpringerReceived: July 30, 2019Accepted: August 1, 2019Published: August 12, 2019Erratum: An anomaly-free atlas: charting the spaceof flavour-dependent gauged U(1) extensions of theStandard ModelB.C. Allanach,a Joe Davighia,1 and Scott Melvillea,baDAMTP, University of Cambridge,Wilberforce Road, Cambridge, CB3 0WA, U.K.bEmmanuel College, University of Cambridge,St Andrew’s Street, Cambridge, CB2 3AP, U.K.E-mail: B.C.Allanach@damtp.cam.ac.uk, jed60@cam.ac.uk,scott.melville@damtp.cam.ac.ukErratum to: JHEP02(2019)082Abstract: We correct a statement in our original paper and add anomaly-free chargeassignments for SMνR with 7 ≤ Qmax ≤ 10.ArXiv ePrint: 1812.04602We correct a statement in the Examples paragraph of section 3.1, page 8, of ref. [1]. Wewrote: “Alternatively, if we set Fν = −1, the solution in eq. (3.2) reduces to gaugingB − L, baryon number minus lepton number within that family, as has appeared in refs.[36, 61]”. The correct condition is actually Fν = −3FQ.We also take this opportunity to augment the results of the SMνR scan to include 7 ≤Qmax ≤ 10. These new solutions, which (together with the previous ones) can be obtainedfrom http://doi.org/10.5281/zenodo.3345889 [2], are summarised in table 1. Figure 1 showsthe number of anomaly-free solutions including 7 ≤ Qmax ≤ 10. We see that the previouslyproposed [1] “fit-by-eye” function of 12e7Qmax/4 − 11, while providing a good rough fit forQmax ≤ 6, significantly overestimates the number of solutions for higher Qmax. We provideupdated versions of both plots that were in figure 1 of ref. [1] in figure 2 of this erratum,where we also propose a new fit to the true curve for the number of solutions in the SMνR.1Corresponding author.Open Access, c© The Authors.Article funded by SCOAP3.https://doi.org/10.1007/JHEP08(2019)064JHEP08(2019)064Qmax Solutions Symmetry Quadratics Cubics Time/sec7 1358388 2332 24616693253 241368652 3128 3612734 3514 127878976089 978792750 15599 9587085 5648 558403872034 3432486128 658410 21546920 7540 2117256832910 10687426240 24748Table 1. Number of inequivalent solutions to the anomaly equations for SMνR fermion content anddifferent maximum U(1)F charges 7 ≤ Qmax ≤ 10. Each row contains the all-zero charge solution,as well as the solutions indicated in the rows above. The column marked “Symmetry” shows howmany of the solutions are charge inversion symmetric. We also list the number of quadratic andcubic anomaly equations checked by the program, as well as the real time taken for computation inseconds on a modern DELLTM XPS 13-9350 laptop. 0 1 2 3 4 5 6 7 8 9 0  2  4  6  8  10log 10(# solutions)Qmaxdata12e7Qmax/4-11Figure 1. Number of anomaly-free solutions as a function of Qmax ≤ 10 for the SMνR. Forcomparison, we show the “fit-by-eye” 12e7x/4 − 11 originally suggested [1] to fit the growth of thenumber of solutions. 0 2 4 6 8 10 0  2  4  6  8  10log 10(# solutions)QmaxSMνRSM-12-11-10-9-8-7-6-5-4-3-2 1  2  3  4  5  6  7  8  9  10log 10(fraction)QmaxFigure 2. Left : the total number of inequivalent anomaly-free solutions with a given Qmax, togetherwith the functions 1+a exp(bQmax+cQ2max)−a which are fit the growth of the number of solutions:a = 22.5, b = 2.0, c = −0.062 for the SMνR and a = 2.50, b = 1.34, c = −0.043 for the SM. Right :the fraction of all inequivalent charge assignments which is anomaly free for a given Qmax, showingthat imposing anomaly-freedom can lead to a drastic reduction in the available parameter space.– 2 –JHEP08(2019)064AcknowledgmentsWe thank other members of the Cambridge SUSY Working Group, as well as D. Gvirtz,N. Dorey, and D. Tong for their helpful advice and comments. SM is supported by anEmmanuel College Research Fellowship, and JD is supported by The Cambridge Trust.This work has been partially supported by STFC consolidated grant ST/P000681/1.Open Access. This article is distributed under the terms of the Creative CommonsAttribution License (CC-BY 4.0), which permits any use, distribution and reproduction inany medium, provided the original author(s) and source are credited.References[1] B.C. Allanach, J. Davighi and S. Melville, An anomaly-free atlas: charting the space offlavour-dependent gauged U(1) extensions of the Standard Model, JHEP 02 (2019) 082[arXiv:1812.04602] [INSPIRE].[2] B. Allanach, J. Davighi and S. Melville, Anomaly-free, flavour-dependent U(1) chargeassignments for Standard Model/Standard Model plus three right-handed neutrino fermioniccontent, http://doi.org/10.5281/zenodo.3345889.– 3 –

Erratum: An anomaly-free atlas: charting the space of flavour-dependent gauged U(1) extensions of the Standard Model (Journal of High Energy Physics, (2019), 2019, 2, (82), 10.1007/JHEP02(2019)082)

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Erratum: An anomaly-free atlas: charting the space of flavour-dependent gauged U(1) extensions of the Standard Model (Journal of High Energy Physics, (2019), 2019, 2, (82), 10.1007/JHEP02(2019)082)

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