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The S-matrix Bootstrap III: Higher Dimensional Amplitudes
http://cds.cern.ch/record/2285239
We consider constraints on the S-matrix of any gapped, Lorentz invariant quantum field theory in 3+1 dimensions due to crossing symmetry, analyticity and unitarity. We extremize cubic couplings, quartic couplings and scattering lengths relevant for the elastic scattering amplitude of two identical scalar particles. In the cases where our results can be compared with the older S-matrix literature they are in excellent agreement. We also extremize a cubic coupling in 2+1 dimensions which we can directly compare to a universal bound for a QFT in AdS. This paper generalizes our previous 1+1 dimensional results of arXiv:1607.06109 and arXiv:1607.06110.Paulos, Miguel F.Penedones, JoaoToledo, Jonathanvan Rees, Balt C.Vieira, PedroThu, 21 Sep 2017 12:21:25 GMT2017-08-22arXiv:1708.06765http://cds.cern.ch/record/2285239['arXiv:1708.06765']arXiv:1708.06765The Brother Higgs
http://cds.cern.ch/record/2284908
We present a version of the twin Higgs mechanism with minimal symmetry structure and particle content. The model is built upon a composite Higgs theory with global $SO(6)/SO(5)$ symmetry breaking. The leading contribution to the Higgs potential, from the top sector, is solely cancelled via the introduction of a Standard Model neutral top partner. We show that the inherent $Z_2$ breaking of this construction is under control and of the right size to achieve electroweak symmetry breaking, with a fine-tuning at the level of $5-10\%$, and compatibly with the observed Higgs mass. We briefly discuss the particular phenomenological features of this scenario.Serra, JaviTorre, RiccardoTue, 19 Sep 2017 09:15:36 GMT2017-09-15CERN-TH-2017-192http://cds.cern.ch/record/22849082017192Interpretation of quantum mechanics with indefinite norm
http://cds.cern.ch/record/2284572
The Born postulate can be reduced to its deterministic content that only applies to eigenvectors of observables: the standard probabilistic interpretation of generic states then follows from algebraic properties of repeated measurements and states. Extending this reasoning suggests an interpretation of quantum mechanics generalized with indefinite quantum norm.Strumia, AlessandroMon, 18 Sep 2017 08:35:38 GMT2017-09-14CERN-TH-2017-191http://cds.cern.ch/record/22845722017191Binary pulsars as probes of a Galactic dark matter disk
http://cds.cern.ch/record/2284138
As a binary pulsar moves through a wind of dark matter particles, the resulting dynamical friction modifies the binary's orbit. We study this effect for the double disk dark matter (DDDM) scenario, where a fraction of the dark matter is dissipative and settles into a thin disk. For binaries within the dark disk, this effect is enhanced due to the higher dark matter density and lower velocity dispersion of the dark disk, and due to its co-rotation with the baryonic disk.We estimate the effect and compare it with observations for two different limits in the Knudsen number ($Kn$). First, in the case where DDDM is effectively collisionless within the characteristic scale of the binary ($Kn\gg1$) and ignoring the possible interaction between the pair of dark matter wakes. Second, in the fully collisional case ($Kn\ll1$), where a fluid description can be adopted and the interaction of the pair of wakes is taken into account. We find that the change in the orbital period is of the same order of magnitude in both limits. A comparison with observations reveals good prospects to probe currently allowed DDDM models with timing data from binary pulsars in the near future. We finally comment on the possibility of extending the analysis to the intermediate (rarefied gas) case with $Kn\sim1$.Caputo, AndreaZavala, JesúsBlas, DiegoThu, 14 Sep 2017 08:14:03 GMT2017-09-12CERN-TH-2017-177http://cds.cern.ch/record/22841382017177Non-linear Realizations and Higher Curvature Supergravity
http://cds.cern.ch/record/2284134
We focus on non-linear realizations of local supersymmetry as obtained by using constrained superfields in supergravity. New constraints, beyond those of rigid supersymmetry, are obtained whenever curvature multiplets are affected as well as higher derivative interactions are introduced. In particular, a new constraint, which removes a very massive gravitino is introduced, and in the rigid limit it merely reduces to an explicit supersymmetry breaking. Higher curvature supergravities free of ghosts and instabilities are also obtained in this way. Finally, we consider direct coupling of the goldstino multiplet to the super Gauss--Bonnet multiplet and discuss the emergence of a new scalar degree of freedom.Farakos, F.Ferrara, S.Kehagias, A.Lust, D.Thu, 14 Sep 2017 08:13:54 GMT2017-07-21arXiv:1707.06991http://cds.cern.ch/record/2284134['arXiv:1707.06991']arXiv:1707.06991Highlights in Supergravity: CCJ 47 Years Later
http://cds.cern.ch/record/2283157
We consider an expression for the supercurrent in the superconformal formulation of N=1 supergravity. A chiral compensator provides the supersymmetric formulation of the Callan-Coleman-Jackiw (CCJ) improved stress energy tensor, when the conformal gauge is used. Superconformal and non-superconformal matter give different conservation laws of the supercurrent, when coupled to the curvature supermultiplets which underlie the local superspace geometry. This approach can be applied to any set of auxiliary fields and it is useful to classify rigid curved superspace geometries. Examples with four supersymmetries are briefly described.Ferrara, SergioSamsonyan, MarineTue, 12 Sep 2017 07:03:01 GMT2017-09-09CERN-TH-2017-189http://cds.cern.ch/record/22831572017189Conformal Window 2.0: The Large $N_f$ Safe Story
http://cds.cern.ch/record/2282816
We extend the phase diagram of SU(N) gauge-fermion theories as function of number of flavours and colours to the region in which asymptotic freedom is lost. We argue, using large $N_f$ results, for the existence of an ultraviolet interacting fixed point at sufficiently large number of flavours opening up to a second ultraviolet conformal window in the number of flavours vs colours phase diagram. We first review the state-of-the-art for the large $N_f$ beta function and then estimate the lower boundary of the ultraviolet window. The theories belonging to this new region are examples of safe non-abelian quantum electro dynamics, termed here {\it safe QCD}. Therefore, according to Wilson, they are fundamental. An important critical quantity is the fermion mass anomalous dimension at the ultraviolet fixed point that we determine at leading order in $1/N_f$. We discover that its value is comfortably below the bootstrap bound. We also investigate the abelian case and find that at the potential ultraviolet fixed point the related fermion mass anomalous dimension has a singular behaviour suggesting that a more careful investigation of its ultimate fate is needed.Antipin, OlegSannino, FrancescoSat, 09 Sep 2017 07:17:36 GMT2017-09-07CP3-ORIGINS-2017-033-DNRF90http://cds.cern.ch/record/2282816033DNRF90Conformal anomaly of generalized form factors and finite loop integrals
http://cds.cern.ch/record/2282717
We reveal a new mechanism of conformal symmetry breaking at Born level. It occurs in generalized form factors with several local operators and an on-shell state of massless particles. The effect is due to hidden singularities on collinear configurations of the momenta. This conformal anomaly is different from the holomorphic anomaly of amplitudes. We present a number of examples in four and six dimensions. We find an application of the new conformal anomaly to finite loop momentum integrals with one or more massless legs. The collinear region around a massless leg creates a contact anomaly, made visible by the loop integration. The anomalous conformal Ward identity for an $\ell-$loop integral is a 2nd-order differential equation whose right-hand side is an $(\ell-1)-$loop integral. We show several examples, in particular the four-dimensional scalar double box.Chicherin, DmitrySokatchev, EmeryFri, 08 Sep 2017 07:58:41 GMT08 Sep 2017CERN-TH-2017-190http://cds.cern.ch/record/22827172017190Loopedia, a Database for Loop Integrals
http://cds.cern.ch/record/2282523
Loopedia is a new database at loopedia.org for information on Feynman integrals, intended to provide both bibliographic information as well as results made available by the community. Its bibliometry is complementary to that of SPIRES or arXiv in the sense that it admits searching for integrals by graph-theoretical objects, e.g. its topology.Bogner, C.Borowka, S.Hahn, T.Heinrich, G.Jones, S.P.Kerner, M.von Manteuffel, A.Michel, M.Panzer, E.Papara, V.Wed, 06 Sep 2017 05:52:21 GMT2017-09-05CERN-TH-2017-175http://cds.cern.ch/record/22825232017175Spontaneous $CP$ breaking in QCD and the axion potential: an effective Lagrangian approach
http://cds.cern.ch/record/2282514
Using the well-known low-energy effective Lagrangian of QCD --valid for small (non-vanishing) quark masses and a large number of colors-- we study in detail the regions of parameter space where $CP$ is spontaneously broken/unbroken for a vacuum angle $\theta= \pi$. In the $CP$-broken region there are first order phase transitions as one crosses $\theta=\pi$, while on the (hyper)surface separating the two regions, there are second order phase transitions signaled by the vanishing of the mass of a pseudo Nambu-Goldstone boson and by a divergent QCD topological susceptibility. The second order point sits at the end of a first order line associated with the $CP$ spontaneous breaking, in the appropriate complex parameter plane. When the effective Lagrangian is extended by the inclusion of an axion these features of QCD imply that standard calculations of the axion potential have to be revised when the QCD parameters fall in the above mentioned $CP$-broken region, in spite of the fact that the axion solves the strong-$CP$ problem. These latter results could be of interest for axionic dark matter calculations if the topological susceptibility of pure Yang-Mills theory falls off sufficiently fast when temperature is increased towards the QCD deconfining transition.Di Vecchia, PaoloRossi, GiancarloVeneziano, GabrieleYankielowicz, ShimonWed, 06 Sep 2017 05:51:12 GMT2017-09-03CERN-TH-2017-186http://cds.cern.ch/record/22825142017186A tauberian theorem for the conformal bootstrap
http://cds.cern.ch/record/2282026
For expansions in one-dimensional conformal blocks, we provide a rigorous link between the asymptotics of the spectral density of exchanged primaries and the leading singularity in the crossed channel. Our result has a direct application to systems of SL(2,R)-invariant correlators (also known as 1d CFTs). It also puts on solid ground a part of the lightcone bootstrap analysis of the spectrum of operators of high spin and bounded twist in CFTs in d>2. In addition, a similar argument controls the spectral density asymptotics in large N gauge theories.Qiao, JiaxinRychkov, SlavaMon, 04 Sep 2017 05:21:09 GMT2017-08-31CERN-TH-2017-176http://cds.cern.ch/record/22820262017176Positivity of the real part of the forward scattering amplitude
http://cds.cern.ch/record/2281443
We prove the general theorem that the real part of the forward two-body scattering amplitude is positive at sufficiently high energies if, above a certain energy, the total cross section increases monotonically to infinity at infinite energy.Martin, AndréWu, Tai TsunWed, 30 Aug 2017 05:38:08 GMT2017-08-28CERN-TH-2017-182http://cds.cern.ch/record/22814432017182Observables for possible QGP signatures in central pp collisions
http://cds.cern.ch/record/2281442
Proton-proton (pp) data show collective effects, such as long-range azimuthal correlations and strangeness enhancement, which are similar to phenomenology observed in heavy ion collisions. Using simulations with and without explicit existing models of collective effects, we explore new ways to probe pp collisions at high multiplicity, in order to suggest measurements that could help identify the similarities and differences between large- and small-scale collective effects. In particular, we focus on the properties of jets produced in ultra-central pp collisions in association with a Z boson. We consider observables such as jet energy loss and jet shapes, which could point to the possible existence of an underlying quark-gluon plasma, or other new dynamical effects related to the presence of large hadronic densities.Mangano, Michelangelo L.Nachman, BenjaminWed, 30 Aug 2017 05:38:02 GMT2017-08-28CERN-TH-2017-184http://cds.cern.ch/record/22814422017184Collectivity from interference
http://cds.cern.ch/record/2281441
In hadronic collisions, interference between different production channels affects momentum distributions of multi-particle final states. As this QCD interference does not depend on the strong coupling constant, it is part of the no-interaction baseline that needs to be controlled prior to searching for other manifestations of collective dynamics. Here, we introduce a model that is based on the QCD theory of multi-parton interactions and that allows one to study interference effects in the production of $m$ particles in hadronic collisions with $N$ parton-parton interactions ("sources"). In an expansion in powers of $1/(N_c^2-1)$ and to leading order in the number of sources $N$, we calculate interference effects in the $m$-particle spectra and we determine from them the second and fourth order cumulant momentum anisotropies $v_n$. Without invoking any azimuthal asymmetry and any density dependent non-linear dynamics in the incoming state, and without invoking any interaction in the final state, we find that QCD interference alone can give rise to values for $v_n\lbrace 2\rbrace$ and $v_n\lbrace 4\rbrace$, $n$ even, that persist unattenuated for increasing number of sources, that may increase with increasing multiplicity and that agree with measurements in proton-proton (pp) collisions in terms of the order of magnitude of the signal and the approximate shape of the transverse momentum dependence. We further find that the non-abelian features of QCD interference can give rise to odd harmonic anisotropies. These findings indicate that the no-interaction baseline including QCD interference effects can make a sizeable if not dominant contribution to the measured $v_n$ coefficients in pp collisions. Prospects for analyzing QCD interference contributions further and their possible relevance for proton-nucleus and nucleus-nucleus collisions are discussed shortly.Blok, BorisJäkel, Christian D.Strikman, MarkWiedemann, Urs AchimWed, 30 Aug 2017 05:37:57 GMT2017-08-28CERN-TH-2017-179http://cds.cern.ch/record/22814412017179Diboson Interference Resurrection
http://cds.cern.ch/record/2281126
High-energy diboson processes at the LHC are potentially powerful indirect probes of heavy new physics, whose effects can be encapsulated in higher-dimensional operators or in modified Standard Model couplings. An obstruction however comes from the fact that leading new physics effects often emerge in diboson helicity amplitudes that are anomalously small in the Standard Model. As such, the formally leading Standard Model/New Physics interference contribution cancels in inclusive measurements. This paper describes a solution to this problem.Panico, GiulianoRiva, FrancescoWulzer, AndreaMon, 28 Aug 2017 09:27:12 GMT2017-08-25CERN-TH-2017-185http://cds.cern.ch/record/22811262017185Determination of the strong coupling constant $\alpha_s(m_Z)$ from measurements of the total cross section for top-antitop quark production
http://cds.cern.ch/record/2281037
We present a determination of the strong coupling constant $\alpha_s(m_Z)$ using inclusive top-quark pair production cross section measurements performed at the LHC and at the Tevatron. Following a procedure first applied by the CMS collaboration, we extract individual values of $\alpha_s(m_Z)$ from measurements by different experiments at several centre-of-mass energies, using QCD predictions complete in NNLO perturbation theory, supplemented with NNLL approximations to all orders, and suitable sets of parton distribution functions. The determinations are then combined using a likelihood-based approach, where special emphasis is put on a consistent treatment of theoretical uncertainties and of correlations between various sources of systematic uncertainties. Our final combined result is $\alpha_s(m_Z) = 0.1177^{+0.0034}_{-0.0036}$.Klijnsma, ThomasBethke, SiegfriedDissertori, GüntherSalam, Gavin P.Sat, 26 Aug 2017 05:28:56 GMT2017-08-24arXiv:1708.07495http://cds.cern.ch/record/2281037['arXiv:1708.07495']arXiv:1708.07495Direct determination of Wilson coefficients using $B^0\to K^{*0}\mu^+\mu^-$ decays
http://cds.cern.ch/record/2279143
A method to directly determine the Wilson coefficients for rare $b\to s$ transitions using $B^0\to K^{*0}\mu^+\mu^-$ decays in an unbinned maximum likelihood fit is presented. The method has several advantages compared to the conventional determination of the Wilson coefficients from angular observables that are determined in bins of $q^2$, the square of the mass of the dimuon system. The method uses all experimental information in an optimal way and automatically accounts for experimental correlations. Performing pseudoexperiments, we show the improved sensitivity of the proposed method for the Wilson coefficients. We also demonstrate that it will be possible to use the method with the combined Run 1 and 2 data sample taken by the LHCb experiment.Hurth, T.Langenbruch, C.Mahmoudi, F.Wed, 16 Aug 2017 05:46:49 GMT2017-08-15CERN-TH-2017-178http://cds.cern.ch/record/22791432017178Improving the Simulation of Quark and Gluon Jets with Herwig 7
http://cds.cern.ch/record/2277686
The properties of quark and gluon jets, and the differences between them, are increasingly important at the LHC. However, Monte Carlo event generators are normally tuned to data from $e^+e^-$ collisions which are primarily sensitive to quark-initiated jets. In order to improve the description of gluon jets we make improvements to the perturbative and the non-perturbative modelling of gluon jets and include data with gluon-initiated jets in the tuning for the first time. The resultant tunes significantly improve the description of gluon jets and are now the default in Herwig 7.1.Reichelt, DanielRichardson, PeterSiodmok, AndrzejWed, 09 Aug 2017 05:44:49 GMT2017-08-04CERN-TH-2017-174http://cds.cern.ch/record/22776862017174Gluon-fusion Higgs production in the Standard Model Effective Field Theory
http://cds.cern.ch/record/2276908
We provide the complete set of predictions needed to achieve NLO accuracy in the Standard Model Effective Field Theory at dimension six for Higgs production in gluon fusion. In particular, we compute for the first time the contribution of the chromomagnetic operator $ \bar Q_L \Phi \sigma q_R G$ at NLO in QCD, which entails two-loop virtual and one-loop real contributions, as well as renormalisation and mixing with the Yukawa operator $\Phi^\dagger \Phi\, \bar Q_L \Phi q_R$ and the gluon-fusion operator $\Phi^\dagger \Phi\, GG$. Focusing on the top-quark-Higgs couplings, we consider the phenomenological impact of the NLO corrections in constraining the three relevant operators by implementing the results into the MadGraph5_aMC@NLO framework. This allows us to compute total cross sections as well as to perform event generation at NLO that can be directly employed in experimental analyses.Deutschmann, NicolasDuhr, ClaudeMaltoni, FabioVryonidou, EleniFri, 04 Aug 2017 05:48:12 GMT2017-08-01CP3-17-24http://cds.cern.ch/record/22769081724Higgs amplitudes from $\mathcal{N}=4$ super Yang-Mills theory
http://cds.cern.ch/record/2276638
Higgs plus multi-gluon amplitudes in QCD can be computed in an effective Lagrangian description. In the infinite top-mass limit, an amplitude with a Higgs and $n$ gluons is computed by the form factor of the operator ${\rm Tr}\, F^2$. Up to two loops and for three gluons, its maximally transcendental part is captured entirely by the form factor of the protected stress tensor multiplet operator $\mathcal{T}_2$ in $\mathcal{N}=4$ supersymmetric Yang-Mills theory. The next order correction involves the calculation of the form factor of the higher-dimensional, trilinear operator ${\rm Tr}\, F^3$. We present explicit results at two loops for three gluons, including the subleading transcendental terms derived from a particular descendant of the Konishi operator that contains ${\rm Tr}\, F^3$. These are expressed in terms of a few universal building blocks already identified in earlier calculations. We show that the maximally transcendental part of this quantity, computed in non-supersymmetric Yang-Mills theory, is identical to the form factor of another protected operator, $\mathcal{T}_3$, in the maximally supersymmetric theory. Our results suggest that the maximally transcendental part of Higgs amplitudes in QCD can be entirely computed through $\mathcal{N}=4$ super Yang-Mills.Brandhuber, AndreasKostacinska, MartynaPenante, BrendaTravaglini, GabrieleWed, 02 Aug 2017 05:42:00 GMT2017-07-31QMUL-PH-17-12http://cds.cern.ch/record/22766381712Stochastic locality and master-field simulations of very large lattices
http://cds.cern.ch/record/2276637
In lattice QCD and other field theories with a mass gap, the field variables in distant regions of a physically large lattice are only weakly correlated. Accurate stochastic estimates of the expectation values of local observables may therefore be obtained from a single representative field. Such master-field simulations potentially allow very large lattices to be simulated, but require various conceptual and technical issues to be addressed. In this talk, an introduction to the subject is provided and some encouraging results of master-field simulations of the SU(3) gauge theory are reported.Lüscher, MartinWed, 02 Aug 2017 05:42:00 GMT2017-07-31CERN-TH-2017-171http://cds.cern.ch/record/22766372017171Anomalous non-conservation of fermion/chiral number in Abelian gauge theories at finite temperature
http://cds.cern.ch/record/2276636
We discuss the non-conservation of fermion number (or chirality breaking, depending on the fermionic charge assignment) in Abelian gauge theories at finite temperature. We study different mechanisms of fermionic charge disappearance in the high temperature plasma, with the use of both analytical estimates and real-time classical numerical simulations. We investigate the random walk of the Chern-Simons number $N_{\rm CS} \propto \int d^4x F_{\mu\nu}{\tilde F}^{\mu\nu}$, and show that it has a diffusive behaviour in the presence of an external magnetic field $B$. This indicates that the mechanism for fermionic number non-conservation for $B \neq 0$, is due to fluctuations of the gauge fields, similarly as in the case of non-Abelian gauge theories. We determine numerically the rate of chirality non-conservation associated with this diffusion, finding it larger by a factor $\sim 60$ compared to previous theoretical estimates. We also perform numerical simulations for the system which contains a chemical potential $\mu$ representing a fermionic charge density, again both with and without an external magnetic field. When $B=0$, we observe clearly the expected instability of the system for $\mu \neq 0$, as long as the chemical potential exceeds a critical value $\mu > \mu_c(L)$, which depends on the size $L$ of the system. When $B \neq 0$, the fluctuations of bosonic fields lead to the transfer of chemical potential into Chern-Simons number for arbitrary $\mu$.Figueroa, Daniel G.Shaposhnikov, MikhailWed, 02 Aug 2017 05:41:26 GMT2017-07-31CERN-TH-2017-172http://cds.cern.ch/record/22766362017172Comments on Nonlinear Sigma Models Coupled to Supergravity
http://cds.cern.ch/record/2276204
N=1, D=4 non linear sigma models, parametrized by chiral superfields, usually describe Kaehlerian geometries, provided that Einstein frame supergravity is used. The sigma model metric is no longer Kaehler when local supersymmetry becomes nonlinearly realized through the nilpotency of the supergravity auxiliary fields. In some cases the nonlinear realization eliminates one scalar propagating degree of freedom. This happens when the sigma model conformal-frame metric has co-rank 2. In the geometry of the inflaton, this effect eliminates its scalar superpartner. We show that the sigma model metric remains semidefinite positive in all cases, due the to positivity properties of the conformal-frame sigma model metric.Ferrara, SergioPorrati, MassimoMon, 31 Jul 2017 06:15:30 GMT2017-07-28CERN-TH-2017-164http://cds.cern.ch/record/22762042017164Quenching of high-$p_T$ jet spectra
http://cds.cern.ch/record/2275716
We compute modifications to the jet spectrum in the presence of a dense medium. We show that in the large-$N_c$ approximation and at leading logarithmic accuracy the jet nuclear modification factor factorizes into a quenching factor associated to the total jet color charge and a Sudakov suppression factor which accounts for the energy loss of jet substructure fluctuations. This factor, called the jet collimator, implements the fact that subjets, that are not resolved by the medium, lose energy coherently as a single color charge, whereas resolved large angle fluctuations suffer more quenching. For comparison, we show that neglecting color coherence results in a stronger suppression of the jet nuclear modification factor.Mehtar-Tani, YacineTywoniuk, KonradTue, 25 Jul 2017 05:27:55 GMT2017-07-23INT-PUB-17-025http://cds.cern.ch/record/227571617025Unified Halo-Independent Formalism Derived From Convex Hulls
http://cds.cern.ch/record/2275715
Using the Fenchel-Eggleston theorem for convex hulls (an extension of the Caratheodory theorem), we prove that any likelihood can be maximized by either a dark matter 1- speed distribution $F(v)$ in Earth's frame or 2- Galactic velocity distribution $f^{\rm gal}(\vec{u})$, consisting of a sum of delta functions. The former case applies only to time-averaged rate measurements and the maximum number of delta functions is $({\mathcal N}-1)$, where ${\mathcal N}$ is the total number of data entries. The second case applies to any harmonic expansion coefficient of the time-dependent rate and the maximum number of terms is ${\mathcal N}$. Using time-averaged rates, the aforementioned form of $F(v)$ results in a piecewise constant unmodulated halo function $\tilde\eta^0_{BF}(v_{\rm min})$ (which is an integral of the speed distribution) with at most $({\mathcal N}-1)$ downward steps. The authors had previously proven this result for likelihoods comprised of at least one extended likelihood, and found the best-fit halo function to be unique. This uniqueness, however, cannot be guaranteed in the more general analysis applied to arbitrary likelihoods. Thus we introduce a method for determining whether there exists a unique best-fit halo function, and provide a procedure for constructing either a pointwise confidence band, if the best-fit halo function is unique, or a degeneracy band, if it is not. Using measurements of modulation amplitudes, the aforementioned form of $f^{\rm gal}(\vec{u})$, which is a sum of Galactic streams, yields a periodic time-dependent halo function $\tilde\eta_{BF}(v_{\rm min}, t)$ which at any fixed time is a piecewise constant function of $v_{\rm min}$ with at most ${\mathcal N}$ downward steps. In this case, we explain how to construct pointwise confidence and degeneracy bands from the time-averaged halo function. Finally, we show that requiring an isotropic ...Gelmini, Graciela B.Huh, Ji-HaengWitte, Samuel J.Tue, 25 Jul 2017 05:27:53 GMT2017-07-21CERN-TH-2017-159http://cds.cern.ch/record/22757152017159