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Flavour anomalies after the $R_{K^*}$ measurement
https://cds.cern.ch/record/2260350
The LHCb measurement of the $\mu/e$ ratio $R_{K^*}$ indicates a deficit with respect to the Standard Model prediction, supporting earlier hints of lepton universality violation observed in the $R_K$ ratio. We show that the $R_K$ and $R_{K^*}$ ratios alone constrain the chiralities of the states contributing to these anomalies, and we find deviations from the Standard Model at the $4\sigma$ level. This conclusion is further corroborated by hints in the theoretically challenging $b\to s\mu^+\mu^-$ distributions. Theoretical interpretations in terms of $Z'$, lepto-quarks, loop mediators, and composite dynamics are discussed. We highlight their distinctive features in terms of chiralities and flavour structure relevant for the observed anomalies.D'Amico, GuidoNardecchia, MarcoPanci, PaoloSannino, FrancescoStrumia, AlessandroTorre, RiccardoUrbano, AlfredoWed, 19 Apr 2017 06:09:15 GMT2017-04-18CERN-TH-2017-086https://cds.cern.ch/record/22603502017086Multi-loop calculations: numerical methods and applications
https://cds.cern.ch/record/2259753
We briefly review numerical methods for calculations beyond one loop and then describe new developments within the method of sector decomposition in more detail. We also discuss applications to two-loop integrals involving several mass scales.Borowka, S.Heinrich, G.Jahn, S.Jones, S.P.Kerner, M.Schlenk, J.Sat, 15 Apr 2017 06:30:26 GMT2017-04-12CERN-TH-2017-051https://cds.cern.ch/record/22597532017051Anomaly-Free Dark Matter Models are not so Simple
https://cds.cern.ch/record/2259752
We explore the anomaly-cancellation constraints on simplified dark matter (DM) models with an extra U(1)$^\prime$ gauge boson $Z'$. We show that, if the Standard Model (SM) fermions are supplemented by a single DM fermion $\chi$ that is a singlet of the SM gauge group, and the SM quarks have non-zero U(1)$^\prime$ charges, the SM leptons must also have non-zero U(1)$^\prime$ charges, in which case LHC searches impose strong constraints on the $Z'$ mass. Moreover, the DM fermion $\chi$ must have a vector-like U(1)$^\prime$ coupling. If one requires the DM particle to have a purely axial U(1)$^\prime$ coupling, which would be the case if $\chi$ were a Majorana fermion and would reduce the impact of direct DM searches, the simplest possibility is that it is accompanied by one other new singlet fermion, but in this case the U(1)$^\prime$ charges of the SM leptons still do not vanish. This is also true in a range of models with multiple new singlet fermions with identical charges. Searching for a leptophobic model, we then introduce extra fermions that transform non-trivially under the SM gauge group. We find several such models if the DM fermion is accompanied by two or more other new fermions with non-identical charges, which may have interesting experimental signatures. We present benchmark representatives of the various model classes we discuss.Ellis, JohnFairbairn, MalcolmTunney, PatrickSat, 15 Apr 2017 06:30:25 GMT2017-04-12KCL-PH-TH-2017-21https://cds.cern.ch/record/2259752201721Single top polarisation as a window to new physics
https://cds.cern.ch/record/2259607
We discuss the effect of heavy new physics, parameterised in terms of four-fermion operators, in the polarisation of single top (anti-)quarks in the $t$-channel process at the LHC. It is found that for operators involving a right-handed top quark field the relative effect on the longitudinal polarisation is twice larger than the relative effect on the total cross section. This enhanced dependence on possible four-fermion contributions makes the polarisation measurements specially interesting, in particular at high momenta.Aguilar-Saavedra, J.A.Degrande, C.Khatibi, S.Thu, 13 Apr 2017 06:29:24 GMT2017-01-20CERN-TH-2017-013https://cds.cern.ch/record/22596072017013Colorful Twisted Top Partners and Partnerium at the LHC
https://cds.cern.ch/record/2259465
In scenarios that stabilize the electroweak scale, the top quark is typically accompanied by partner particles. In this work, we demonstrate how extended stabilizing symmetries can yield scalar or fermionic top partners that transform as ordinary color triplets but carry exotic electric charges. We refer to these scenarios as "hypertwisted" since they involve modifications to hypercharge in the top sector. As proofs of principle, we construct two hypertwisted scenarios: a supersymmetric construction with spin-0 top partners, and a composite Higgs construction with spin-1/2 top partners. In both cases, the top partners are still phenomenologically compatible with the mass range motivated by weak-scale naturalness. The phenomenology of hypertwisted scenarios is diverse, since the lifetimes and decay modes of the top partners are model dependent. The novel coupling structure opens up search channels that do not typically arise in top-partner scenarios, such as pair production of top-plus-jet resonances. Furthermore, hypertwisted top partners are typically sufficiently long lived to form "top-partnerium" bound states that decay predominantly via annihilation, motivating searches for rare narrow resonances with diboson decay modes.Kats, YevgenyMcCullough, MatthewPerez, GiladSoreq, YotamThaler, JesseWed, 12 Apr 2017 05:18:53 GMT2017-04-11MIT-CTP-4897https://cds.cern.ch/record/2259465CTP4897Where is Particle Physics Going?
https://cds.cern.ch/record/2259332
The answer to the question in the title is: in search of new physics beyond the Standard Model, for which there are many motivations, including the likely instability of the electroweak vacuum, dark matter, the origin of matter, the masses of neutrinos, the naturalness of the hierarchy of mass scales, cosmological inflation and the search for quantum gravity. So far, however, there are no clear indications about the theoretical solutions to these problems, nor the experimental strategies to resolve them. It makes sense now to prepare various projects for possible future accelerators, so as to be ready for decisions when the physics outlook becomes clearer. Paraphrasing George Harrison, "If you don't yet know where you're going, any road may take you there."Ellis, JohnTue, 11 Apr 2017 06:06:11 GMT2017-04-10KCL-PH-TH-2017-18https://cds.cern.ch/record/2259332201718An Investigation of New Methods for Numerical Stochastic Perturbation Theory in $\varphi^4$ Theory
https://cds.cern.ch/record/2258997
Numerical stochastic perturbation theory is a powerful tool for estimating high-order perturbative expansions in lattice field theory. The standard algorithms based on the Langevin equation, however, suffer from several limitations which in practice restrict the potential of this technique. In this work we investigate some alternative methods which could in principle improve on the standard approach. In particular, we present a study of the recently proposed Instantaneous Stochastic Perturbation Theory, as well as a formulation of numerical stochastic perturbation theory based on Generalized Hybrid Molecular Dynamics algorithms. The viability of these methods is investigated in $\varphi^4$ theory.Dalla Brida, MattiaGarofalo, MarcoKennedy, A.D.Sat, 08 Apr 2017 05:18:59 GMT2017-03-13arXiv:1703.04406https://cds.cern.ch/record/2258997['arXiv:1703.04406']arXiv:1703.04406Long-range critical exponents near the short-range crossover
https://cds.cern.ch/record/2258840
The $d$-dimensional long-range Ising model, defined by spin-spin interactions decaying with the distance as the power $1/r^{d+s}$, admits a second order phase transition with continuously varying critical exponents. At $s = s_*$, the phase transition crosses over to the usual short-range universality class. The standard field-theoretic description of this family of models is strongly coupled at the crossover. We find a new description, which is instead weakly coupled near the crossover, and use it to compute critical exponents. The existence of two complementary UV descriptions of the same long-range fixed point provides a novel example of infrared duality.Behan, ConnorRastelli, LeonardoRychkov, SlavaZan, BernardoFri, 07 Apr 2017 05:44:29 GMT2017-03-09YITP-SB-17-12https://cds.cern.ch/record/22588401712Radiative symmetry breaking from interacting UV fixed points
https://cds.cern.ch/record/2258298
It is shown that the addition of positive mass-squared terms to asymptotically safe gauge-Yukawa theories with perturbative UV fixed points leads to calculable radiative symmetry breaking in the IR. This phenomenon, and the multiplicative running of the operators that lies behind it, is akin to the radiative symmetry breaking that occurs in the Supersymmetric Standard Model.Abel, StevenSannino, FrancescoWed, 05 Apr 2017 05:33:27 GMT2017-04-03CERN-TH-2017-066https://cds.cern.ch/record/22582982017066Wilson lines and UV sensitivity in magnetic compactifications
https://cds.cern.ch/record/2257664
We investigate the ultraviolet (UV) behaviour of 6D N=1 supersymmetric effective (Abelian) gauge theories compactified on a two-torus ($T_2$) with magnetic flux. To this purpose we compute offshell the one-loop correction to the Wilson line state self-energy. The offshell calculation is actually necessary to capture the usual effective field theory expansion in powers of $(\partial/\Lambda)$. Particular care is paid to the regularization of the (divergent) momentum integrals, which is relevant for identifying the corresponding counterterm(s). We find a counterterm which is a new higher dimensional effective operator of dimension d=6, that is enhanced for a larger compactification area (where the effective theory applies) and is consistent with the symmetries of the theory. Its consequences are briefly discussed and comparison is made with orbifold compactifications without flux. We investigate the ultraviolet (UV) behaviour of 6D N=1 supersymmetric effective (Abelian) gauge theories compactified on a two-torus (T$_{2}$) with magnetic flux. To this purpose we compute offshell the one-loop correction to the Wilson line state self-energy. The offshell calculation is actually necessary to capture the usual effective field theory expansion in powers of (∂/Λ). Particular care is paid to the regularization of the (divergent) momentum integrals, which is relevant for identifying the corresponding counterterm(s). We find a counterterm which is a new higher dimensional effective operator of dimension d=6, that is enhanced for a larger compactification area (where the effective theory applies) and is consistent with the symmetries of the theory. Its consequences are briefly discussed and comparison is made with orbifold compactifications without flux.Ghilencea, D.M.Lee, Hyun MinFri, 31 Mar 2017 05:54:57 GMT2017-03-30CERN-TH-2017-072https://cds.cern.ch/record/22576642017072Continuum limit and universality of the Columbia plot
https://cds.cern.ch/record/2257659
Results on the thermal transition of QCD with 3 degenerate flavors, in the lower-left corner of the Columbia plot, are puzzling. The transition is expected to be first-order for massless quarks, and to remain so for a range of quark masses until it turns second-order at a critical quark mass. But this critical quark mass and resulting "pion" mass disagree violently between Wilson and staggered fermions at finite lattice spacing, and decrease sharply with the lattice spacing, for staggered fermions at least. To clarify this puzzle and eliminate potential systematic effects from rooting, we study the 4-flavor theory with staggered fermions, on lattices with 4 to 10 time-slices. Our results are qualitatively similar to the 3-flavor case, so that rooting is not an issue. However, dramatic cutoff effects are visible, even on our finest lattices. Universality implies that cutoff effects for Wilson fermions are even more dramatic. In order to obtain a first-order thermal transition in the continuum theory, extremely light quarks are needed.de Forcrand, PhilippeD'Elia, MassimoFri, 31 Mar 2017 05:54:46 GMT2017-02-01arXiv:1702.00330https://cds.cern.ch/record/2257659['arXiv:1702.00330']arXiv:1702.00330Higher order perturbations of Anti-de Sitter space and time-periodic solutions of vacuum Einstein equations
https://cds.cern.ch/record/2257658
Motivated by the problem of stability of Anti-de Sitter (AdS) spacetime, we discuss nonlinear gravitational perturbations of maximally symmetric solutions of vacuum Einstein equations in general and the case of AdS in particular. We present the evidence that, similarly to the self-gravitating scalar field at spherical symmetry, the negative cosmological constant allows for the existence of globally regular, asymptotically AdS, time-periodic solutions of vacuum Einstein equations whose frequencies bifurcate from linear eigenfrequencies of AdS. Interestingly, our preliminary results indicate that the number of one parameter families of time-periodic solutions bifurcating from a given eigenfrequency equals the multiplicity of this eigenfrequency. Motivated by the problem of stability of anti–de Sitter (AdS) spacetime, we discuss nonlinear gravitational perturbations of maximally symmetric solutions of vacuum Einstein equations in general and the case of AdS in particular. We present the evidence that, similarly to the self-gravitating scalar field at spherical symmetry, the negative cosmological constant allows for the existence of globally regular asymptotically AdS, time-periodic solutions of vacuum Einstein equations whose frequencies bifurcate from linear eigenfrequencies of AdS. Interestingly, our preliminary results indicate that the number of one-parameter families of time-periodic solutions bifurcating from a given eigenfrequency equals the multiplicity of this eigenfrequency.Rostworowski, AndrzejFri, 31 Mar 2017 05:54:44 GMT2017-01-26CERN-TH-2017-023https://cds.cern.ch/record/22576582017023pySecDec: a toolbox for the numerical evaluation of multi-scale integrals
https://cds.cern.ch/record/2257527
We present pySecDec, a new version of the program SecDec, which performs the factorisation of dimensionally regulated poles in parametric integrals, and the subsequent numerical evaluation of the finite coefficients. The algebraic part of the program is now written in the form of python modules, which allow a very flexible usage. The optimization of the C++ code, generated using FORM, is improved, leading to a faster numerical convergence. The new version also creates a library of the integrand functions, such that it can be linked to user-specific codes for the evaluation of matrix elements in a way similar to analytic integral libraries.Borowka, S.Heinrich, G.Jahn, S.Jones, S.P.Kerner, M.Schlenk, J.Zirke, T.Thu, 30 Mar 2017 05:25:16 GMT2017-03-28MPP-2017-42https://cds.cern.ch/record/2257527201742NLO predictions for Higgs boson pair production with full top quark mass dependence matched to parton showers
https://cds.cern.ch/record/2257526
We present the first combination of NLO QCD matrix elements for di-Higgs production, retaining the full top quark mass dependence, with a parton shower. Results are provided within both the POWHEG-BOX and MadGraph5_aMC@NLO Monte Carlo frameworks. We assess in detail the theoretical uncertainties and provide differential results. We find that, as expected, the shower effects are relatively large for observables like the transverse momentum of the Higgs boson pair, which are sensitive to extra radiation. However, these shower effects are still much smaller than the differences between the Born-improved HEFT approximation and the full NLO calculation in the tails of the distributions.Heinrich, G.Jones, S.P.Kerner, M.Luisoni, G.Vryonidou, E.Thu, 30 Mar 2017 05:25:03 GMT2017-03-27CERN-TH-2017-069https://cds.cern.ch/record/22575262017069A Worm Algorithm for the Lattice CP(N-1) Model
https://cds.cern.ch/record/2257524
The CP(N-1) model in 2D is an interesting toy model for 4D QCD as it possesses confinement, asymptotic freedom and a non-trivial vacuum structure. Due to the lower dimensionality and the absence of fermions, the computational cost for simulating 2D CP(N-1) on the lattice is much lower than the one for simulating 4D QCD. However to our knowledge, no efficient algorithm for simulating the lattice CP(N-1) model has been tested so far, which also works at finite density. To this end we propose and test a new type of worm algorithm which is appropriate to simulate the lattice CP(N-1) model in a dual, flux-variables based representation, in which the introduction of a chemical potential does not give rise to any complications.Rindlisbacher, Tobiasde Forcrand, PhilippeThu, 30 Mar 2017 05:25:02 GMT2017-03-15CERN-TH-2017-060https://cds.cern.ch/record/22575242017060$W^\pm Z$ production at the LHC: fiducial cross sections and distributions in NNLO QCD
https://cds.cern.ch/record/2257523
We report on the first fully differential calculation for $W^\pm Z$ production in hadron collisions up to next-to-next-to-leading order (NNLO) in QCD perturbation theory. Leptonic decays of the $W$ and $Z$ bosons are consistently taken into account, i.e. we include all resonant and non-resonant diagrams that contribute to the process $pp\to \ell^{'\pm} \nu_{\ell^{'}} \ell^+\ell^-+X$ both in the same-flavour ($\ell'=\ell$) and the different-flavour ($\ell'\neq \ell$) channel. Fiducial cross sections and distributions are presented in the presence of standard selection cuts applied in the experimental $W^\pm Z$ analyses by ATLAS and CMS at centre-of-mass energies of 8 and 13\,TeV. As previously shown for the inclusive cross section, NNLO corrections increase the NLO result by about $10\%$, thereby leading to an improved agreement with experimental data. The importance of NNLO accurate predictions is also shown in the case of new-physics scenarios, where, especially in high-$p_T$ categories, their impact can reach ${\cal O}(20\%)$. The availability of differential NNLO predictions will play a crucial role in the rich physics programme that is based on precision studies of $W^\pm Z$ signatures at the LHC.Grazzini, MassimilianoKallweit, StefanRathlev, DirkWiesemann, MariusThu, 30 Mar 2017 05:24:44 GMT2017-03-27ZU-TH-06-17https://cds.cern.ch/record/22575230617Standard Model Parton Distributions at Very High Energies
https://cds.cern.ch/record/2257521
We compute the leading-order evolution of parton distribution functions for all the Standard Model fermions and bosons up to energy scales far above the electroweak scale, where electroweak symmetry is restored. Our results include the 52 PDFs of the unpolarized proton, evolving according to the SU(3), SU(2), U(1), mixed SU(2) x U(1) and Yukawa interactions. We illustrate the numerical effects on parton distributions at large energies, and show that this can lead to important corrections to parton luminosities at a future 100 TeV collider.Bauer, Christian W.Ferland, NicolasWebber, Bryan R.Thu, 30 Mar 2017 05:24:42 GMT2017-03-24CAVENDISH-HEP-17-03https://cds.cern.ch/record/22575211703Spontaneous symmetry breaking in three-Higgs-doublet $S_3$-symmetric models
https://cds.cern.ch/record/2257519
The talk summarises work done by the authors consisting of a detailed study of the possible vacua in models with three Higgs doublets with $S_3$ symmetry and without explicit CP violation. Different vacua require special regions of the parameter space which were analysed in our work. We establish the possibility of spontaneous CP violation in this framework and we also show which complex vacua conserve CP. In our work we discussed constraints from vacuum stability. The results presented here are relevant for model building.Emmanuel-Costa, D.Ogreid, O.M.Osland, P.Rebelo, M.N.Thu, 30 Mar 2017 05:24:39 GMT2017-03-24CERN-TH-2017-070https://cds.cern.ch/record/22575192017070Inflationary Perturbations in No-Scale Theories
https://cds.cern.ch/record/2257516
We study the inflationary perturbations in general (classically) scale-invariant theories. Such scenario is motivated by the hierarchy problem and provides natural inflationary potentials and dark matter candidates. We analyse in detail all sectors (the scalar, vector and tensor perturbations) giving general formul$\ae$ for the potentially observable power spectra, as well as for the curvature spectral index $n_s$ and the tensor-to-scalar ratio $r$. We show that the conserved Hamiltonian for all perturbations does not feature negative energies even in the presence of the Weyl-squared term if the appropriate quantization is performed and argue that this term does not lead to phenomenological problems at least in some relevant setups. The general formul$\ae$ are then applied to a concrete no-scale model, which includes the higgs and a scalar, "the planckion", whose vacuum expectation value generates the Planck mass. Inflation can be triggered by a combination of the planckion and the Starobinsky scalar and we show that no tension with observations is present even in the case of pure planckion-inflation, if the coefficient of the Weyl-squared term is large enough. In general, even quadratic inflation is allowed in this case. Moreover, the Weyl-squared term leads to an isocurvature mode, which currently satisfies the observational bounds, but may be detectable with future experiments.Salvio, AlbertoThu, 30 Mar 2017 05:23:04 GMT2017-03-23CERN-TH-2017-068https://cds.cern.ch/record/22575162017068Heat kernel methods for Lifshitz theories
https://cds.cern.ch/record/2257513
We study the one-loop covariant effective action of Lifshitz theories using the heat kernel technique. The characteristic feature of Lifshitz theories is an anisotropic scaling between space and time. This is enforced by the existence of a preferred foliation of space-time, which breaks Lorentz invariance. In contrast to the relativistic case, covariant Lifshitz theories are only invariant under diffeomorphisms preserving the foliation structure. We develop a systematic method to reduce the calculation of the effective action for a generic Lifshitz operator to an algorithm acting on known results for relativistic operators. In addition, we present techniques that drastically simplify the calculation for operators with special properties. We demonstrate the efficiency of these methods by explicit applications.Barvinsky, Andrei O.Blas, DiegoHerrero-Valea, MarioNesterov, Dmitry V.Pérez-Nadal, GuillemSteinwachs, Christian F.Thu, 30 Mar 2017 05:22:57 GMT2017-03-14CERN-TH-2017-055https://cds.cern.ch/record/22575132017055Space-time CFTs from the Riemann sphere
https://cds.cern.ch/record/2257512
We consider two-dimensional chiral, first-order conformal field theories governing maps from the Riemann sphere to the projective light cone inside Minkowski space -- the natural setting for describing conformal field theories in two fewer dimensions. These theories have a SL(2,R) algebra of local bosonic constraints which can be supplemented by additional fermionic constraints depending on the matter content of the theory. By computing the BRST charge associated with gauge fixing these constraints, we find anomalies which vanish for specific target space dimensions. These critical dimensions coincide precisely with those for which (biadjoint) cubic scalar theory, gauge theory and gravity are classically conformally invariant. Furthermore, the BRST cohomology of each theory contains vertex operators for the full conformal multiplets of single field insertions in each of these space-time CFTs. We give a prescription for the computation of three-point functions, and compare our formalism with the scattering equations approach to on-shell amplitudes.Adamo, TimMonteiro, RicardoPaulos, Miguel F.Thu, 30 Mar 2017 05:22:55 GMT2017-03-14IMPERIAL-TP-TA-2017-01https://cds.cern.ch/record/2257512201701Right-handed charged currents in the era of the Large Hadron Collider
https://cds.cern.ch/record/2257511
We discuss the phenomenology of right-handed charged currents in the framework of the Standard Model Effective Field Theory, in which they arise due to a single gauge-invariant dimension-six operator. We study the manifestations of the nine complex couplings of the $W$ to right-handed quarks in collider physics, flavor physics, and low-energy precision measurements. We first obtain constraints on the couplings under the assumption that the right-handed operator is the dominant correction to the Standard Model at observable energies. We subsequently study the impact of degeneracies with other Beyond-the-Standard-Model effective interactions and identify observables, both at colliders and low-energy experiments, that would uniquely point to right-handed charged currents.Alioli, S.Cirigliano, V.Dekens, W.de Vries, J.Mereghetti, E.Thu, 30 Mar 2017 05:22:48 GMT2017-03-14CERN-TH-2017-043https://cds.cern.ch/record/22575112017043Testing Invisible Momentum Ansatze in Missing Energy Events at the LHC
https://cds.cern.ch/record/2256461
We consider SUSY-like events with two decay chains, each terminating in an invisible particle, whose true energy and momentum are not measured in the detector. Nevertheless, a useful educated guess about the invisible momenta can still be obtained by optimizing a suitable invariant mass function. We review and contrast several proposals in the literature for such ansatze: four versions of the M_T2-assisted on-shell reconstruction (MAOS), as well as several variants of the on-shell constrained M_2 variables. We compare the performance of these methods with regards to the mass determination of a new particle resonance along the decay chain from the peak of the reconstructed invariant mass distribution. For concreteness, we consider the event topology of dilepton ttbar events and study each of the three possible subsystems, in both a ttbar and a SUSY example. We find that the M_2 variables generally provide sharper peaks and therefore better ansatze for the invisible momenta. We show that the performance can be further improved by preselecting events near the kinematic endpoint of the corresponding variable from which the momentum ansatz originates.Kim, DoojinMatchev, Konstantin T.Moortgat, FilipPape, LucWed, 22 Mar 2017 06:51:39 GMT2017-03-20CERN-TH-2017-061https://cds.cern.ch/record/22564612017061SMD-based numerical stochastic perturbation theory
https://cds.cern.ch/record/2255663
The viability of a variant of numerical stochastic perturbation theory, where the Langevin equation is replaced by the SMD algorithm, is examined. In particular, the convergence of the process to a unique stationary state is rigorously established and the use of higher-order symplectic integration schemes is shown to be highly profitable in this context. For illustration, the gradient-flow coupling in finite volume with Schr\"odinger functional boundary conditions is computed to two-loop (i.e. NNL) order in the SU(3) gauge theory. The scaling behaviour of the algorithm turns out to be rather favourable in this case, which allows the computations to be driven close to the continuum limit.Dalla Brida, MattiaLüscher, MartinTue, 14 Mar 2017 15:44:46 GMT2017-03-13CERN-TH-2017-057https://cds.cern.ch/record/22556632017057Dispersion relation for hadronic light-by-light scattering: two-pion contributions
https://cds.cern.ch/record/2255659
In this third paper of a series dedicated to a dispersive treatment of the hadronic light-by-light (HLbL) tensor, we derive a partial-wave formulation for two-pion intermediate states in the HLbL contribution to the anomalous magnetic moment of the muon $(g-2)_\mu$, including a detailed discussion of the unitarity relation for arbitrary partial waves. We show that obtaining a final expression free from unphysical helicity partial waves is a subtle issue, which we thoroughly clarify. As a by-product, we obtain a set of sum rules that could be used to constrain future calculations of $\gamma^*\gamma^*\to\pi\pi$. We validate the formalism extensively using the pion-box contribution, defined by two-pion intermediate states with a pion-pole left-hand cut, and demonstrate how the full known result is reproduced when resumming the partial waves. Using dispersive fits to high-statistics data for the pion vector form factor, we provide an evaluation of the full pion box, $a_\mu^{\pi\text{-box}}=-15.9(2)\times 10^{-11}$. As an application of the partial-wave formalism, we present a first calculation of $\pi\pi$-rescattering effects in HLbL scattering, with $\gamma^*\gamma^*\to\pi\pi$ helicity partial waves constructed dispersively using $\pi\pi$ phase shifts derived from the inverse-amplitude method. In this way, the isospin-$0$ part of our calculation can be interpreted as the contribution of the $f_0(500)$ to HLbL scattering in $(g-2)_\mu$. We argue that the contribution due to charged-pion rescattering implements corrections related to the corresponding pion polarizability and show that these are moderate. Our final result for the sum of pion-box contribution and its $S$-wave rescattering corrections reads $a_\mu^{\pi\text{-box}} + a_{\mu,J=0}^{\pi\pi,\pi\text{-pole LHC}}=-24(1)\times 10^{-11}$.Colangelo, GilbertoHoferichter, MartinProcura, MassimilianoStoffer, PeterTue, 14 Mar 2017 15:44:22 GMT2017-02-23INT-PUB-17-009https://cds.cern.ch/record/225565917009