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S. Hassani

Publications and source records attributed to S. Hassani.

At least 37 records · Page 2Linked to original sources
arXiv2020

First combined measurement of the muon neutrino and antineutrino charged-current cross section without pions in the final state at T2K

This paper presents the first combined measurement of the double-differential muon neutrino and antineutrino charged-current cross sections with no pions in the final state on hydrocarbon at the off-axis near detector of the T2K experiment. The data analyzed in this work comprise 5.8$\times$10$^{20}$ and 6.3$\times$10$^{20}$ protons on target in neutrino and antineutrino mode respectively, at a beam energy peak of 0.6 GeV. Using the two measured cross sections, the sum, difference and asymmetry were calculated with the aim of better understanding the nuclear effects involved in such interactions. The extracted measurements have been compared with the prediction from different Monte Carlo generators and theoretical models showing that the difference between the two cross sections have interesting sensitivity to nuclear effects.

hep-ex↗
arXiv2020

Measurements of $\barν_μ$ and $\barν_μ + ν_μ$ charged-current cross-sections without detected pions nor protons on water and hydrocarbon at mean antineutrino energy of 0.86 GeV

We report measurements of the flux-integrated $\barν_μ$ and $\barν_μ+ν_μ$ charged-current cross-sections on water and hydrocarbon targets using the T2K anti-neutrino beam, with a mean neutrino energy of 0.86 GeV. The signal is defined as the (anti-)neutrino charged-current interaction with one induced $μ^\pm$ and no detected charged pion nor proton. These measurements are performed using a new WAGASCI module recently added to the T2K setup in combination with the INGRID Proton module. The phase space of muons is restricted to the high-detection efficiency region, $p_μ>400~{\rm MeV}/c$ and $θ_μ<30^{\circ}$, in the laboratory frame. Absence of pions and protons in the detectable phase space of "$p_π>200~{\rm MeV}/c$ and $θ_π<70^{\circ}$", and "$p_{\rm p}>600~{\rm MeV}/c$ and $θ_{\rm p}<70^{\circ}$" is required. In this paper, both of the $\barν_μ$ cross-sections and $\barν_μ+ν_μ$ cross-sections on water and hydrocarbon targets, and their ratios are provided by using D'Agostini unfolding method. The results of the integrated $\barν_μ$ cross-section measurements over this phase space are $σ_{\rm H_{2}O}\,=\,(1.082\pm0.068(\rm stat.)^{+0.145}_{-0.128}(\rm syst.)) \times 10^{-39}~{\rm cm^{2}/nucleon}$, $σ_{\rm CH}\,=\,(1.096\pm0.054(\rm stat.)^{+0.132}_{-0.117}(\rm syst.)) \times 10^{-39}~{\rm cm^{2}/nucleon}$, and $σ_{\rm H_{2}O}/σ_{\rm CH} = 0.987\pm0.078(\rm stat.)^{+0.093}_{-0.090}(\rm syst.)$. The $\barν_μ+ν_μ$ cross-section is $σ_{\rm H_{2}O} = (1.155\pm0.064(\rm stat.)^{+0.148}_{-0.129}(\rm syst.)) \times 10^{-39}~{\rm cm^{2}/nucleon}$, $σ_{\rm CH}\,=\,(1.159\pm0.049(\rm stat.)^{+0.129}_{-0.115}(\rm syst.)) \times 10^{-39}~{\rm cm^{2}/nucleon}$, and $σ_{\rm H_{2}O}/σ_{\rm CH}\,=\,0.996\pm0.069(\rm stat.)^{+0.083}_{-0.078}(\rm syst.)$.

hep-ex↗
arXiv2019

Extending the constraint for axion-like particles as resonances at the LHC and laser beam experiments

We study the discovery potential of axion-like particles (ALP), pseudo-scalars weakly coupled to Standard Model fields, at the Large Hadron Collider (LHC). Our focus is on ALPs coupled to the electromagnetic field, which would induce anomalous scattering of light-by-light. This can be directly probed in central exclusive production of photon pairs in ultra-peripheral collisions at the LHC in proton and heavy ion collisions. We consider non-standard collision modes of the LHC, such as argon-argon collisions at $\sqrt{s_{NN}} = 7$ TeV and proton-lead collisions at $\sqrt{s_{NN}} = 8.16$ TeV to access regions in the parameter space complementary to the ones previously considered for lead-lead or proton-proton collisions. In addition, we show that, using laser beam interactions, we can constrain ALPs as resonant deviations in the refractive index, induced by anomalous light-by-light scattering effects. If we combine the aforementioned approaches, ALPs can be probed in a wide range of masses from the eV scale up to the TeV scale.

hep-ph↗
arXiv2019

Future physics opportunities for high-density QCD at the LHC with heavy-ion and proton beams

The future opportunities for high-density QCD studies with ion and proton beams at the LHC are presented. Four major scientific goals are identified: the characterisation of the macroscopic long wavelength Quark-Gluon Plasma (QGP) properties with unprecedented precision, the investigation of the microscopic parton dynamics underlying QGP properties, the development of a unified picture of particle production and QCD dynamics from small (pp) to large (nucleus--nucleus) systems, the exploration of parton densities in nuclei in a broad ($x$, $Q^2$) kinematic range and the search for the possible onset of parton saturation. In order to address these scientific goals, high-luminosity Pb-Pb and p-Pb programmes are considered as priorities for Runs 3 and 4, complemented by high-multiplicity studies in pp collisions and a short run with oxygen ions. High-luminosity runs with intermediate-mass nuclei, for example Ar or Kr, are considered as an appealing case for extending the heavy-ion programme at the LHC beyond Run 4. The potential of the High-Energy LHC to probe QCD matter with newly-available observables, at twice larger center-of-mass energies than the LHC, is investigated.

hep-ph↗
arXiv2016

Lattice Green Functions: the d-dimensional face-centred cubic lattice, d=8, 9, 10, 11, 12

We previously reported on a recursive method to generate the expansion of the lattice Green function of the $d$-dimensional face-centred cubic lattice (fcc). The method was used to generate many coefficients for d=7 and the corresponding linear differential equation has been obtained. In this paper, we show the strength and the limit of the method by producing the series and the corresponding linear differential equations for d=8, 9, 10, 11, 12. The differential Galois groups of these linear differential equations are shown to be symplectic for d=8, 10, 12 and orthogonal for d= 9, 11. The recursion relation naturally provides a 2-dimensional array $ T_d(n,j)$ where only the coefficients $ t_d(n,0)$ correspond to the coefficients of the lattice Green function of the d-dimensional fcc. The coefficients $ t_d(n,j)$ are associated to D-finite bivariate series annihilated by linear partial differential equations that we analyze.

math-ph↗
arXiv2014

Scaling functions in the square Ising model

We show and give the linear differential operators ${\cal L}^{scal}_q$ of order q= n^2/4+n+7/8+(-1)^n/8, for the integrals $I_n(r)$ which appear in the two-point correlation scaling function of Ising model $ F_{\pm}(r)= \lim_{scaling} {\cal M}_{\pm}^{-2} < σ_{0,0} \, σ_{M,N}> = \sum_{n} I_{n}(r)$. The integrals $ I_{n}(r)$ are given in expansion around r= 0 in the basis of the formal solutions of $\, {\cal L}^{scal}_q$ with transcendental combination coefficients. We find that the expression $ r^{1/4}\,\exp(r^2/8)$ is a solution of the Painlevé VI equation in the scaling limit. Combinations of the (analytic at $ r= 0$) solutions of $ {\cal L}^{scal}_q$ sum to $ \exp(r^2/8)$. We show that the expression $ r^{1/4} \exp(r^2/8)$ is the scaling limit of the correlation function $ C(N, N)$ and $ C(N, N+1)$. The differential Galois groups of the factors occurring in the operators $ {\cal L}^{scal}_q$ are given.

math-ph↗
arXiv2014

Canonical decomposition of linear differential operators with selected differential Galois groups

We revisit an order-six linear differential operator having a solution which is a diagonal of a rational function of three variables. Its exterior square has a rational solution, indicating that it has a selected differential Galois group, and is actually homomorphic to its adjoint. We obtain the two corresponding intertwiners giving this homomorphism to the adjoint. We show that these intertwiners are also homomorphic to their adjoint and have a simple decomposition, already underlined in a previous paper, in terms of order-two self-adjoint operators. From these results, we deduce a new form of decomposition of operators for this selected order-six linear differential operator in terms of three order-two self-adjoint operators. We then generalize the previous decomposition to decompositions in terms of an arbitrary number of self-adjoint operators of the same parity order. This yields an infinite family of linear differential operators homomorphic to their adjoint, and, thus, with a selected differential Galois group. We show that the equivalence of such operators is compatible with these canonical decompositions. The rational solutions of the symmetric, or exterior, squares of these selected operators are, noticeably, seen to depend only on the rightmost self-adjoint operator in the decomposition. These results, and tools, are applied on operators of large orders. For instance, it is seen that a large set of (quite massive) operators, associated with reflexive 4-polytopes defining Calabi-Yau 3-folds, obtained recently by P. Lairez, correspond to a particular form of the decomposition detailed in this paper.

math-ph↗
arXiv2014

The Ising model and Special Geometries

We show that the globally nilpotent G-operators corresponding to the factors of the linear differential operators annihilating the multifold integrals $χ^{(n)}$ of the magnetic susceptibility of the Ising model ($n \le 6$) are homomorphic to their adjoint. This property of being self-adjoint up to operator homomorphisms, is equivalent to the fact that their symmetric square, or their exterior square, have rational solutions. The differential Galois groups are in the special orthogonal, or symplectic, groups. This self-adjoint (up to operator equivalence) property means that the factor operators we already know to be Derived from Geometry, are special globally nilpotent operators: they correspond to "Special Geometries". Beyond the small order factor operators (occurring in the linear differential operators associated with $ χ^{(5)}$ and $ χ^{(6)}$), and, in particular, those associated with modular forms, we focus on the quite large order-twelve and order-23 operators. We show that the order-twelve operator has an exterior square which annihilates a rational solution. Then, its differential Galois group is in the symplectic group $ Sp(12, \mathbb{C})$. The order-23 operator is shown to factorize in an order-two operator and an order-21 operator. The symmetric square of this order-21 operator has a rational solution. Its differential Galois group is, thus, in the orthogonal group $ SO(21, \mathbb{C})$.

math-ph↗
arXiv2013

Ising n-fold integrals as diagonals of rational functions and integrality of series expansions

We show that the n-fold integrals $χ^{(n)}$ of the magnetic susceptibility of the Ising model, as well as various other n-fold integrals of the "Ising class", or n-fold integrals from enumerative combinatorics, like lattice Green functions, correspond to a distinguished class of function generalising algebraic functions: they are actually diagonals of rational functions. As a consequence, the power series expansions of the, analytic at x=0, solutions of these linear differential equations "Derived From Geometry" are globally bounded, which means that, after just one rescaling of the expansion variable, they can be cast into series expansions with integer coefficients. We also give several results showing that the unique analytical solution of Calabi-Yau ODEs, and, more generally, Picard-Fuchs linear ODEs, with solutions of maximal weights, are always diagonal of rational functions. Besides, in a more enumerative combinatorics context, generating functions whose coefficients are expressed in terms of nested sums of products of binomial terms can also be shown to be diagonals of rational functions. We finally address the question of the relations between the notion of integrality (series with integer coefficients, or, more generally, globally bounded series) and the modularity of ODEs.

math-ph↗
arXiv2012

Ising n-fold integrals as diagonals of rational functions and integrality of series expansions: integrality versus modularity

We show that the n-fold integrals $χ^{(n)}$ of the magnetic susceptibility of the Ising model, as well as various other n-fold integrals of the "Ising class", or n-fold integrals from enumerative combinatorics, like lattice Green functions, are actually diagonals of rational functions. As a consequence, the power series expansions of these solutions of linear differential equations "Derived From Geometry" are globally bounded, which means that, after just one rescaling of the expansion variable, they can be cast into series expansions with integer coefficients. Besides, in a more enumerative combinatorics context, we show that generating functions whose coefficients are expressed in terms of nested sums of products of binomial terms can also be shown to be diagonals of rational functions. We give a large set of results illustrating the fact that the unique analytical solution of Calabi-Yau ODEs, and more generally of MUM ODEs, is, almost always, diagonal of rational functions. We revisit Christol's conjecture that globally bounded series of G-operators are necessarily diagonals of rational functions. We provide a large set of examples of globally bounded series, or series with integer coefficients, associated with modular forms, or Hadamard product of modular forms, or associated with Calabi-Yau ODEs, underlying the concept of modularity. We finally address the question of the relations between the notion of integrality (series with integer coefficients, or, more generally, globally bounded series) and the modularity (in particular integrality of the Taylor coefficients of mirror map), introducing new representations of Yukawa couplings.

math-ph↗
arXiv2012

Holonomic functions of several complex variables and singularities of anisotropic Ising n-fold integrals

Lattice statistical mechanics, often provides a natural (holonomic) framework to perform singularity analysis with several complex variables that would, in a general mathematical framework, be too complex, or could not be defined. Considering several Picard-Fuchs systems of two-variables "above" Calabi-Yau ODEs, associated with double hypergeometric series, we show that holonomic functions are actually a good framework for actually finding the singular manifolds. We, then, analyse the singular algebraic varieties of the n-fold integrals $ χ^{(n)}$, corresponding to the decomposition of the magnetic susceptibility of the anisotropic square Ising model. We revisit a set of Nickelian singularities that turns out to be a two-parameter family of elliptic curves. We then find a first set of non-Nickelian singularities for $ χ^{(3)}$ and $ χ^{(4)}$, that also turns out to be rational or ellipic curves. We underline the fact that these singular curves depend on the anisotropy of the Ising model. We address, from a birational viewpoint, the emergence of families of elliptic curves, and of Calabi-Yau manifolds on such problems. We discuss the accumulation of these singular curves for the non-holonomic anisotropic full susceptibility.

math-ph↗
arXiv2011

Diagonal Ising susceptibility: elliptic integrals, modular forms and Calabi-Yau equations

We give the exact expressions of the partial susceptibilities $χ^{(3)}_d$ and $χ^{(4)}_d$ for the diagonal susceptibility of the Ising model in terms of modular forms and Calabi-Yau ODEs, and more specifically, $_3F_2([1/3,2/3,3/2],\, [1,1];\, z)$ and $_4F_3([1/2,1/2,1/2,1/2],\, [1,1,1]; \, z)$ hypergeometric functions. By solving the connection problems we analytically compute the behavior at all finite singular points for $χ^{(3)}_d$ and $χ^{(4)}_d$. We also give new results for $χ^{(5)}_d$. We see in particular, the emergence of a remarkable order-six operator, which is such that its symmetric square has a rational solution. These new exact results indicate that the linear differential operators occurring in the $n$-fold integrals of the Ising model are not only "Derived from Geometry" (globally nilpotent), but actually correspond to "Special Geometry" (homomorphic to their formal adjoint). This raises the question of seeing if these "special geometry" Ising-operators, are "special" ones, reducing, in fact systematically, to (selected, k-balanced, ...) $_{q+1}F_q$ hypergeometric functions, or correspond to the more general solutions of Calabi-Yau equations.

math-ph↗
arXiv2010

The Ising model: from elliptic curves to modular forms and Calabi-Yau equations

We show that almost all the linear differential operators factors obtained in the analysis of the n-particle contribution of the susceptibility of the Ising model for $\, n \le 6$, are operators "associated with elliptic curves". Beyond the simplest factors which are homomorphic to symmetric powers of the second order operator associated with the complete elliptic integral E, the second and third order differential operators can actually be interpreted as modular forms of the elliptic curve of the Ising model. A last order-four globally nilpotent operator is not reducible to this elliptic curve, modular forms scheme. It is shown to actually correspond to a natural generalization of this elliptic curve, modular forms scheme, with the emergence of a Calabi-Yau equation, corresponding to a selected $_4F_3$ hypergeometric function which can also be seen as a Hadamard product of the complete elliptic integral K, with a remarkably simple algebraic pull-back, the corresponding Calabi-Yau fourth-order differential operator having a symplectic differential Galois group SP(4,C). The associated mirror maps and higher order Schwarzian ODEs has an exact (isogenies) representation of the generators of the renormalization group, extending the modular group SL(2,Z) to a GL(2, Z) symmetry group.

math-ph↗
arXiv2010

Square lattice Ising model $\tildeχ^{(5)}$ ODE in exact arithmetic

We obtain in exact arithmetic the order 24 linear differential operator $L_{24}$ and right hand side $E^{(5)}$ of the inhomogeneous equation$L_{24}(Φ^{(5)}) = E^{(5)}$, where $Φ^{(5)} =\tildeχ^{(5)}-\tildeχ^{(3)}/2+\tildeχ^{(1)}/120$ is a linear combination of $n$-particle contributions to the susceptibility of the square lattice Ising model. In Bostan, et al. (J. Phys. A: Math. Theor. {\bf 42}, 275209 (2009)) the operator $L_{24}$ (modulo a prime) was shown to factorize into $L_{12}^{(\rm left)} \cdot L_{12}^{(\rm right)}$; here we prove that no further factorization of the order 12 operator $L_{12}^{(\rm left)}$ is possible. We use the exact ODE to obtain the behaviour of $\tildeχ^{(5)}$ at the ferromagnetic critical point and to obtain a limited number of analytic continuations of $\tildeχ^{(5)}$ beyond the principal disk defined by its high temperature series. Contrary to a speculation in Boukraa, et al (J. Phys. A: Math. Theor. {\bf 41} 455202 (2008)), we find that $\tildeχ^{(5)}$ is singular at $w=1/2$ on an infinite number of branches.

math-ph↗
arXiv2010

The saga of the Ising susceptibility

We review developments made since 1959 in the search for a closed form for the susceptibility of the Ising model. The expressions for the form factors in terms of the nome $q$ and the modulus $k$ are compared and contrasted. The $λ$ generalized correlations $C(M,N;λ)$ are defined and explicitly computed in terms of theta functions for $M=N=0,1$.

math-ph↗
arXiv2009

High order Fuchsian equations for the square lattice Ising model: $χ^{(6)}$

This paper deals with $\tildeχ^{(6)}$, the six-particle contribution to the magnetic susceptibility of the square lattice Ising model. We have generated, modulo a prime, series coefficients for $\tildeχ^{(6)}$. The length of the series is sufficient to produce the corresponding Fuchsian linear differential equation (modulo a prime). We obtain the Fuchsian linear differential equation that annihilates the "depleted" series $Φ^{(6)}=\tildeχ^{(6)} - {2 \over 3} \tildeχ^{(4)} + {2 \over 45} \tildeχ^{(2)}$. The factorization of the corresponding differential operator is performed using a method of factorization modulo a prime introduced in a previous paper. The "depleted" differential operator is shown to have a structure similar to the corresponding operator for $\tildeχ^{(5)}$. It splits into factors of smaller orders, with the left-most factor of order six being equivalent to the symmetric fifth power of the linear differential operator corresponding to the elliptic integral $E$. The right-most factor has a direct sum structure, and using series calculated modulo several primes, all the factors in the direct sum have been reconstructed in exact arithmetics.

math-ph↗
arXiv2009

A birational mapping with a strange attractor: Post critical set and covariant curves

We consider some two-dimensional birational transformations. One of them is a birational deformation of the Hénon map. For some of these birational mappings, the post critical set (i.e. the iterates of the critical set) is infinite and we show that this gives straightforwardly the algebraic covariant curves of the transformation when they exist. These covariant curves are used to build the preserved meromorphic two-form. One may have also an infinite post critical set yielding a covariant curve which is not algebraic (transcendent). For two of the birational mappings considered, the post critical set is not infinite and we claim that there is no algebraic covariant curve and no preserved meromorphic two-form. For these two mappings with non infinite post critical sets, attracting sets occur and we show that they pass the usual tests (Lyapunov exponents and the fractal dimension) for being strange attractors. The strange attractor of one of these two mappings is unbounded.

math-ph↗