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Arunima Bhattacharya

Publications and source records attributed to Arunima Bhattacharya.

At least 19 recordsLinked to original sources
arXiv2026

Higgs Boson Pair Production via Gluon Fusion: Higher-Order Corrections and Theoretical Uncertainties

In this contribution, the higher-order QCD and electroweak corrections to Standard Model Higgs boson pair production via the gluon-fusion mechanism, $gg\to hh$, are summarized and the different sources of theoretical uncertainty are assessed. The discussion includes finite top quark mass effects, matching to parton showers, approximate NNLO and N$^3$LO QCD corrections, NLO electroweak effects, and uncertainties associated with the top quark mass scheme and perturbative scale choices. In addition, we provide an updated state-of-the-art recommendation for the inclusive gluon-fusion Higgs boson pair production cross section and the corresponding Higgs boson pair invariant-mass distribution.

hep-ph↗
arXiv2026

Sharp partial regularity of Hamiltonian stationary and special Lagrangian graphs

We prove a sharp partial regularity result for Hamiltonian stationary Lagrangian Lipschitz submanifolds in arbitrary smooth almost K\"ahler manifolds: every weak solution of the corresponding equation is smooth away from a relatively closed singular set of Hausdorff dimension at most $n-5$. We show that the estimate is optimal by constructing a nonzero two-homogeneous viscosity solution \[ U\in C^{1,1}(\mathbb{R}^5)\setminus C^2(\mathbb{R}^5) \] of the phase-zero special Lagrangian equation, whose level sets on $\mathbb{S}^4$ are the leaves of Cartan's isoparametric foliation. Its gradient graph is a non-flat calibrated cone, real analytic away from the vertex. This also gives the first $C^{1,1}$ but non-$C^2$ solution of the special Lagrangian equation, and shows that the same dimensional estimate is sharp in the case of special Lagrangian graphs.

math.DG↗
arXiv2026

Nonuniqueness of solutions to the Lagrangian mean curvature equation

We resolve a question posed by Harvey and Lawson concerning the uniqueness of continuous viscosity solutions to the Dirichlet problem for the Lagrangian mean curvature equation on the unit ball with continuous boundary data. For every dimension $n\geq 2$, we construct a continuous phase $\psi \colon \overline{B_1}\to(-n\frac{\pi}{2},n\frac{\pi}{2})$ and continuous boundary data $g \colon \partial B_1\to \mathbb{R}$ for which the Dirichlet problem \[ \sum_{i=1}^n \arctan\lambda_i(D^2u)=\psi(x)\quad\text{in }B_1, \qquad u=g\quad\text{on }\partial B_1, \] admits a continuum of distinct continuous viscosity solutions.

math.AP↗
arXiv2026

Optimal Transport and Generalized Lagrangian Mean Curvature Flows on Kim-McCann Metrics

We express the mean curvature flow of Lagrangian submanifolds in pseudo-Riemannian manifolds endowed with the Kim-McCann-Warren metric within the framework of generalized mean curvature flow on Kim-McCann manifolds. While generalized mean curvature flow has been studied in Kähler geometry, our work shows that techniques from para-Kähler geometry arise naturally in the Kim-McCann setting. Using this perspective, we prove that the Lagrangian condition is preserved along the flow. By identifying generalized mean curvature flow with Lagrangian mean curvature flow, we show that the Ma-Trudinger-Wang regularity theory applies to this setting. In particular, the cross-curvature positivity condition of Kim-McCann yields smoothly converging flows of Lagrangian submanifolds. Under the cross-curvature condition, any Lagrangian submanifold avoiding the cut locus converges exponentially to a stationary submanifold, which locally arises as the graph of an optimal transport map. Our framework substantiates the analogy between special Lagrangian geometry in almost Calabi-Yau manifolds and optimal transport theory in the Kim-McCann setting. In particular, we show that Kim-McCann manifolds equipped with a para-holomorphic volume form serve as the natural counterpart to almost Calabi-Yau manifolds.

math.DG↗
arXiv2025

Higgs-Pair Production via Gluon Fusion: Top-Yukawa- and light-quark-induced electroweak Corrections

Gluon fusion, $gg\to HH$, is the dominant Higgs-pair production process at the Large Hadron Collider (LHC) and provides the first direct access to the trilinear Higgs self-interaction. The process is loop-induced, with the main contribution emerging from top-quark loops within the Standard Model. In the past, the QCD corrections have been calculated and found to increase the cross section significantly. With the anticipated accuracies achievable at the high-luminosity LHC (HL--LHC), the theoretical uncertainties will be of increased relevance to compete with the experimental precision at the level of less than 30\%. In this work, we take the next steps towards the determination of the complete electroweak corrections at next-to-leading order by calculating the full top-Yukawa and light-quark induced corrections. These corrections modify the cross section moderately in the kinematical regimes of interest.

hep-ph↗
arXiv2025

Doubling and the two-dimensional critical valued Lagrangian phase

In this paper, we establish interior Hessian and gradient estimates for the two-dimensional Lagrangian mean curvature equation when the phase changes signs, provided the gradient of the phase vanishes along its zero set. At the critical phase in two dimensions, the Jacobi inequality degenerates, preventing the use of higher-dimensional methods to obtain Hessian estimates. To address this difficulty, we introduce a modified doubling technique that applies to degenerate Jacobi inequalities and yields interior estimates.

math.AP↗
arXiv2025

Singularities of the Lagrangian mean curvature flow at the critical Lagrangian phase

We establish interior estimates for singularities of the Lagrangian mean curvature flow when the Lagrangian phase is critical, i.e., $|Θ|\geq (n-2)\tfracπ{2}$, and extend our results to the broader class of Lagrangian mean curvature type equations. Our gradient estimates require certain structural conditions, and we construct $C^α$ singular viscosity solutions to show that criticality of the phase is necessary, and that these conditions cannot be removed in dimension one. We also introduce a new method for proving $C^{2,α}$ estimates by exponentiating the arctangent operator into a concave one when $|Θ|\geq (n-2)\tfracπ{2}$ and $n>2$.

math.AP↗
arXiv2025

Optimal Regularity for Hölder continuous Hamiltonian Stationary Lagrangian graphs

In this paper, we establish optimal regularity for Hölder continuous Hamiltonian stationary Lagrangian graphs in $\mathbb{C}^n$. We prove that such a graph is smooth whenever its Hölder exponent is strictly larger than $\frac{1}{3}$ and the Lagrangian phase is supercritical, which yields semi-convexity of the potential. We establish the optimality of our result by constructing explicit singular solutions to the fourth order Hamiltonian stationary equation when the Hölder exponent of the graph is $\frac{1}{3}$. The singular solutions exist even under the strongest convexity assumption on the Lagrangian phase, namely the hypercritical phase, which enforces convexity of the potential. This presents a striking departure from the theory of special Lagrangian graphs.

math.AP↗
arXiv2025

Next to Soft Threshold Resummation for $VH$ Production

We study the threshold effects for the associated production of a Higgs boson with a massive vector boson $(V=Z,W)$ in the $q\bar{q} \rightarrow V^\star \rightarrow VH$ process at the LHC. By leveraging the universality of threshold logarithms and employing soft-virtual (SV) and next-to-soft virtual (NSV) resummation techniques, we compute threshold corrections to next-to-next-to-leading logarithmic accuracy. After matching the resummed predictions to the Next-to-Next-to-Leading order (NNLO) fixed order results, we present the invariant mass distribution to NNLO$+\overline{\text{NNLL}}$ accuracy in QCD for the current LHC energies and the total production cross sections. The $VH$ production channel is crucial for studying the couplings of the Higgs boson to the vector bosons $(W,Z)$ and understanding the mechanism of electroweak symmetry breaking. Precision measurements of this process help test the validity of the standard model (SM) and can reveal potential deviations indicating new physics.

hep-ph↗
arXiv2025

Variational integrals on Hessian spaces: partial regularity for critical points

We develop regularity theory for critical points of variational integrals defined on Hessian spaces of functions on open, bounded subdomains of $\mathbb{R}^n$, under compactly supported variations. The critical point solves a fourth order nonlinear equation in double divergence form. We show that for smooth convex functionals, a $W^{2,\infty}$ critical point with bounded Hessian is smooth provided that its Hessian has a small bounded mean oscillation (BMO). We deduce that the interior singular set of a critical point has Hausdorff dimension at most $n-p_0$, for some $p_0 \in (2,3)$. We state some applications of our results to variational problems in Lagrangian geometry. Finally, we use the Hamiltonian stationary equation to demonstrate the importance of our assumption on the a priori regularity of the critical point.

math.AP↗
arXiv2024

Optimal regularity for Lagrangian mean curvature type equations

We classify regularity for Lagrangian mean curvature type equations, which include the potential equation for prescribed Lagrangian mean curvature and those for Lagrangian mean curvature flow self-shrinkers and expanders, translating solitons, and rotating solitons. Convex solutions of the second boundary value problem for certain such equations were constructed by Brendle-Warren 2010, Huang 2015, and Wang-Huang-Bao 2023. We first show that convex viscosity solutions are regular provided the Lagrangian angle or phase is $C^2$ and convex in the gradient variable. We next show that for merely Hölder continuous phases, convex solutions are regular if they are $C^{1,β}$ for sufficiently large $β$. Singular solutions are given to show that each condition is optimal and that the Hölder exponent is sharp. Along the way, we generalize the constant rank theorem of Bian and Guan to include arbitrary dependence on the Legendre transform.

math.AP↗
arXiv2024

Radiative corrections and threshold resummed predictions to pseudoscalar Higgs boson production in QCD

This thesis studies the pseudoscalar Higgs boson production via gluon fusion in the EFT framework in a CP-conserving model. First, it presents the di-pseudoscalar Higgs boson production cross-section via gluon fusion till NNLO with the results valid for the pseudoscalar Higgs boson of MSSM and 2HDM with small tan $β$ by adjusting the top Yukawa coupling. We have used dimensional regularization to regulate the UV and IR divergences while carefully treating the Levi-Civita tensor and $γ_5$. Unlike the amplitudes involving a pair of scalar Higgs bosons, we do not need UV contact counter terms. We used Catani's predictions to factorize the IR singularities, and our IR poles agreed with Catani's predictions. Our results are essential for studies on producing a pair of pseudoscalar Higgs bosons at the LHC up to NNLO accuracy. This thesis also includes the next-to-soft-virtual (NSV) resummed corrections to $\overline{\text{NNLL}}$ accuracy, which are also matched to the NNLO cross-sections for a pseudoscalar Higgs boson production via gluon fusion. These NSV corrections are potentially significant compared to the conventional soft-virtual (SV) logarithms. We have estimated the uncertainties due to the choice of various PDFs and those due to the renormalization and factorization scales. The scale uncertainties show improvement for renormalization scale variation only, which suggests that NSV contributions from other parton channels and beyond NSV contributions in the gluon fusion channel are necessary for improved stability. We also studied the production cross-sections for mixed scalar-pseudoscalar states and their impact on QCD cross-sections for different values of the mixing angle $α$. The study indicates the necessity of improving the precision results for the pseudoscalar Higgs boson up to an order comparable to that of the scalar Higgs boson.

hep-ph↗
arXiv2024

The CR-Volume of Horizontal Submanifolds of Spheres

We study an analog in CR-geometry of the conformal volume of Li-Yau. In particular, to submanifolds of odd-dimensional spheres that are Legendrian or, more generally, horizontal with respect to the sphere's standard CR-structure we associate a quantity that is invariant under the CR-automorphisms of the sphere. We apply this concept to a corresponding notion of Willmore energy.

math.DG↗