Search

Polarized semi-inclusive deep-inelastic scattering (SIDIS) is a key process in the quest for a resolution of the proton spin puzzle. We present the complete results for the polarized SIDIS process at next-to-next-to-leading order (NNLO) in perturbative quantum chromodynamics. Our analytical results include all partonic channels for the scattering of polarized leptons off hadrons and a spin-averaged hadron identified in the final state. A numerical analysis of the NNLO corrections illustrates their significance and the reduced residual scale dependence in the kinematic range probed by the future Electron-Ion-Collider EIC., Comment: 6 pages, 2 figures; 1 ancillary file

We present the first results for the next-to-next-to leading order (NNLO) corrections to the semi-inclusive deep-inelastic scattering process in perturbative quantum chromodynamics. We consider the quark initiated flavor non-singlet process and obtain the complete contributions analytically at leading color. All relevant virtual and real emission Feynman diagrams have been computed using integration-by-parts reduction to master integrals and two approaches for their subsequent evaluation (parametric phase-space integration and method of differential equations). The numerical analysis demonstrates the significance of the NNLO corrections and their great impact on the reduction of the residual scale dependence., Comment: 6 pages, 1 figure; Ancillary file updated

We present the differential predictions for the rapidity distribution of pseudo-scalar Higgs boson through gluon fusion at the LHC. These results are obtained taking into account the soft-virtual (SV) as well as the next-to-soft virtual (NSV) resummation effects to next-to-next-to-leading-logarithmic ($\rm{\overline{NNLL}}$) accuracy and matching them to the approximate fixed order next-to-next-to-leading-order ($\rm{NNLO_A}$) computation. We perform the resummation in two dimensional Mellin space using our recent formalism \cite{Ajjath:2020lwb} by limiting ourselves to the contributions only from gluon-gluon ($gg$) initiated channels. The $\rm{NNLO_A}$ rapidity distribution of pseudo-scalar Higgs is obtained by applying a ratio method on the NNLO rapidity distribution of the scalar Higgs boson. We also present the first analytical results of $\rm{N^3LO}$ rapidity distribution of pseudo-scalar Higgs at SV+NSV accuracy. The phenomenological impacts of $\rm{{NNLO}_A+\overline{{NNLL}}}$ predictions for 13 TeV LHC are studied. We observe that, for $m_A$ =125(700) GeV, the SV+NSV resummation at $\rm{ \overline{NNLL}}$ level brings about 14.76\% (11.48\%) corrections to the $\rm{NNLO}_A$ results at the central scale value of $\mu_R=\mu_F=m_A$. Further, we find that the sensitivity to the renormalisation scale gets improved substantially by the inclusion of NSV resummed predictions at $\rm \overline{NNLL}$ accuracy., Comment: 64 pages, 6 figures

We present the analytic expressions for the color-planar contributions to the heavy-light form factors at three loops in perturbative QCD. These form factors play an important role in the precision predictions of various observables in top quark and flavour physics. We compute the master integrals using the method of differential equations. We perform the ultraviolet renormalization for all the appearing fields and parameters. The analytic results for the renormalized form factors are expressed in terms of generalized harmonic polylogarithms. We also study the Sudakov behaviour of these form factors in the asymptotic limit, which enables us to obtain the complete logarithmic three-loop and partial four-loop contributions., Comment: 72 pages; Ancillary Mathematica notebook (result.nb) attached

We present a framework for resumming the contributions from soft-virtual and next-to-soft virtual (NSV) logarithms. Numerical impact for these resummed predictions are discussed for the inclusive cross section for Drell-Yan di-lepton process up to next-to-next-to leading logarithmic accuracy, restricting to only diagonal partonic channels., Comment: 6 pages, 3 figures, presented by A. H. Ajjath at Diffraction and Low-x 2022, Corigliano Calabro, Italy, Sept. 24-30, 2022

We present the resumed predictions consisting of both soft-virtual(SV) as well as next-to-SV(NSV) threshold logarithms to all orders in perturbative QCD for the rapidity distribution of Higgs Boson till $\rm NNLO + \overline{NNLL}$ accuracy at LHC. Using our recent formalism\cite{Ajjath:2020lwb}, the resummation is carried out in the double Mellin space by restricting the NSV contributions only from diagonal $gg$ channel. We perform the inverse Mellin ransformation using the minimal prescription procedure and match it with the corresponding fixed order results. We do a detailed analysis of the numerical impact of the resummed result. The K-factor values at different logarithmic accuracy suggest that the prediction for the rapidity distribution converges and becomes more reliable at $\rm NNLO + \overline{NNLL}$ order. We further observed that the inclusion of resumed NSV contribution improves the renormalisation scale uncertainty at every order in perturbation theory. However, the uncertainty due to factorisation scale increases by the addition of resummed SV+NSV predictions to the fixed order rapidity distribution.

We present a formalism that sums up the soft-virtual (SV) and next-to-SV (NSV) diagonal contributions to inclusive colorless productions in hadron colliders to all orders in perturbative QCD. Using factorisation theorem, renormalisation group invariance and employing the transcendental structure of perturbative results, we show the exponential behavior of soft-collinear function. This allows us to predict certain SV and NSV terms to all orders from lower order information. We also present an integral representation for the coefficient functions which is suitable for Mellin $N$-space resummation., Comment: 7 pages. Shorter version of the paper with arxiv id 2006.06726. Accepted for publication as a Letter in Physical Review D

We present the differential predictions for the rapidity distribution of a pair of leptons through the Drell-Yan (DY) process at the LHC taking into account the soft-virtual (SV) as well as next-to-soft virtual (NSV) resummation effects in QCD perturbation theory to next-to-next-to-leading-order plus next-to-next-to-leading-logarithmic ($\rm{{NNLO+\overline{NNLL}}}$) accuracy. We perform the resummation in two dimensional Mellin space using our recent formalism \cite{Ajjath:2020lwb} by limiting ourselves to contributions only from quark anti-quark ($q \bar q$) initiated channels. The resummed corrections to the fixed order results are computed through a matched formula using the minimal prescription procedure. We find that the resummation at next-to-leading-logarithmic (next-to-next-to-leading-logarithmic) level brings about 3.98\% (1.24\%) corrections respectively to the NLO (NNLO) results at the central scale value of $q=M_Z$ for 13 TeV LHC. We also observe that the sensitivity to the renormalisation scale gets improved substantially by the inclusion of NSV resummed predictions at $\rm \overline{NNLL}$ accuracy. Further, the lack of quark gluon ($qg$) initiated contributions to NSV part in the $\rm \overline{NNLL}$ resummed predictions leaves large factorisation scale dependence indicating their importance at NSV level as we go to higher orders in perturbation theory., Comment: 21 pages, 9 figures, 7 tables. We have corrected some typos in equations 10,11, B3 and B6 and also added Eq 12 in this version

We present first results on the resummation of Next-to-Soft Virtual (NSV) logarithms for the threshold production of pseudoscalar Higgs boson through gluon fusion at the LHC. These results are presented after resumming the NSV logarithms of the kind ${\log}^{i}(1-z)$ to $\overline{\text{NNLL}}$ accuracy and matching them systematically to the fixed order NNLO cross-sections. These results are obtained using collinear factorization, renormalization group invariance and recent developments in the NSV resummation techniques. The phenomenological implications of these NSV resummed results for 13 TeV LHC are studied and it is observed that these NSV logarithms are quite large. We also evaluate theory uncertainties and find that the renormalization scale uncertainties get reduced further with the inclusion of NSV corrections at various orders in QCD. We further study the impact of QCD corrections on mixed scalar-pseudoscalar states for different values of the mixing angle $\alpha$., Comment: 29 pages, 8 figures, 3 tables

Through this article, we present the two-loop massless QCD corrections to the production of di-Higgs and di-pseudo-Higgs boson through quark annihilation in the large top quark mass limit. Within dimensional regularisation, we employ the non-anticommuting $\gamma_5$ and treat it under the Larin prescription. We discover the absence of any additional renormalisation, so-called contact renormalisation, that could arise from the short distance behaviour of two local operators. This finding is in corroboration with the operator product expansion. By examining the results, we discover the lack of similarity in the highest transcendentality weight terms between these finite remainders and that of a pair of half-BPS primary operators in maximally supersymmetric Yang-Mills theory. We need these newly computed finite remainders to calculate observables involving di-Higgs or di-pseudo-Higgs at the next-to-next-to-leading order. We implement the results to a numerical code for further phenomenological studies., Comment: 24 pages, 4 figures

We present the resummed predictions for inclusive cross section for the production of Higgs boson at next-to-next-to leading logarithmic ($\rm \overline {NNLL}$) accuracy taking into account both soft-virtual ($\rm SV$) and next-to SV ($\rm NSV$) threshold logarithms. We derive the $N$-dependent coefficients and the $N$-independent constants in Mellin-$N$ space for our study. Using the minimal prescription we perform the inverse Mellin transformation and match it with the corresponding fixed order results. We report in detail the numerical impact of $N$-independent part of resummed result and explore the ambiguity involved in exponentiating them. By studying the K factors at different logarithmic accuracy, we find that the perturbative expansion shows better convergence improving the reliability of the prediction at $\rm NNLO + \overline{NNLL}$ accuracy. For instance, the cross-section at $\rm NNLO + \overline{NNLL}$ accuracy reduces by $3.15\%$ as compared to the $\rm NNLO$ result for the central scale $\mu_R = \mu_F = m_H/2$ at 13 TeV LHC. We also observe that the resummed $\rm SV + NSV$ result improves the renormalisation scale uncertainty at every order in perturbation theory. The uncertainty from the renormalisation scale $\mu_R$ ranges between $(+8.85\% ,-10.12\%)$ at $\rm NNLO$ whereas it goes down to $(+6.54\% , - 8.32\%)$ at $\rm NNLO + \overline{NNLL}$ accuracy. However, the factorisation scale uncertainty is worsened by the inclusion of these NSV logarithms hinting the importance of resummation beyond $\rm NSV$ terms. We also present our predictions for $\rm SV + NSV$ resummed result at different collider energies., Comment: 51 pages, 6 Figures

We present the resummed predictions for inclusive cross section for Drell-Yan (DY) production up to next-to-next-to leading logarithmic ($\rm \overline{ NNLL}$) accuracy taking into account both soft virtual (SV) and next-to SV (NSV) threshold logarithms. We restrict ourselves to resummed contributions only from quark anti-quark ($q \bar q$) initiated channels. The resummation is performed in Mellin-$N$ space. We derive the $N$-dependent coefficients and the $N$-independent constants to desired accuracy for our study. The resummed results are matched through the minimal prescription procedure with the fixed order results. We find that the resummation, taking into account the NSV terms, appreciably increases the cross section while decreasing the sensitivity to renormalisation scale. \textcolor{black}{We observe that, at 13 TeV LHC energies, the SV+NSV resummation at $\rm \overline{ NLL} (\rm \overline{NNLL})$ gives about 8\% (2\%) corrections respectively to the NLO (NNLO) results for the considered $Q$ range: 150-3500 GeV}. In addition, the absence of quark gluon initiated contributions to NSV part in the resummed terms leaves large factorisation scale dependence indicating their importance at NSV level. We also study the numerical impact of $N$-independent constants and explore the ambiguity involved in exponetiating them. Finally we present our predictions for the neutral Drell-Yan process at various center of mass of energies., Comment: 60 pages, 13 Tables and 15 Figures

We present the general form of a universal soft-collinear distribution operator to compute the soft-virtual cross-section to next-to-next-to-next-to-next-to-leading order (N$^4$LO) in QCD for a process with any number of final state colorless particles in hadron colliders. By acting this universal operator on the pure virtual corrections, which need to be computed explicitly for a process, the soft-virtual cross-section can be obtained. The operator is constructed by exploiting the factorization and renormalization group evolution of amplitudes in QCD, and the universality of soft gluon contributions. We also provide the hard coefficient to perform the threshold resummation to next-to-next-to-next-to-leading logarithmic (N$^3$LL) accuracy. Furthermore, we present the approximate analytical results of the soft-virtual cross-sections at N$^4$LO and N$^3$LL for the Higgs boson production through gluon fusion and bottom quark annihilation, and also for the Drell-Yan production at the hadronic collider., Comment: 40 Pages

We present a systematic framework to study the threshold contributions of the differential rapidity distribution for the production of any number of colorless particles in the hadronic colliders. This has been achieved based on the universality structure of the soft enhancements associated with the real emissions, along with the factorization property of the differential cross section and the renormalization group invariance. In this formalism, we present a universal soft-collinear operator to compute the soft virtual differential cross section for a generic $2\rightarrow n$ scattering process up to next-to-next-to-next-to-next-to-leading order (N$^4$LO) in perturbative QCD. We also provide a universal operator to perform the threshold resummation to next-to-next-to-next-to-leading logarithmic (N$^3$LL) accuracy. We explicitly present the approximate analytical results of the rapidity distributions at N$^4$LO and N$^3$LL for the Higgs boson production through gluon fusion and bottom quark annihilation, and also for the Drell-Yan production at the hadronic collider. \textcolor{black}{We extend our framework to include the next to threshold contributions for the diagonal partonic channels., Comment: 27

We present a formalism that sums up both soft-virtual (SV) and next to SV (NSV) contributions to all orders in perturbative QCD for the rapidity distribution of any colorless particle produced in hadron colliders. We have exploited the factorization properties and the renormalisation group (RG) invariance of the differential cross-section to achieve this. Using the state-of-the-art multiloop and multileg results, we determine the complete NSV contributions to third order in strong coupling constant for the rapidity distributions for a pair of leptons in Drell-Yan and also for Higgs boson in gluon fusion as well as bottom quark annihilation. Using the integral representation of our all order $z$ space result, we show how the NSV contributions can be resummed in two-dimensional Mellin space., Comment: 6 Pages and 1 Table

We study the perturbative structure of threshold enhanced logarithms in the coefficient functions of deep inelastic scattering (DIS) and semi-inclusive $e^+e^-$ annihilation (SIA) processes and setup a framework to sum them up to all orders in perturbation theory. Threshold logarithms show up as the distributions $((1-z)^{-1} \log^i(1-z))_+$ from the soft plus virtual (SV) and as logarithms $\log^i(1-z)$ from next to SV (NSV) contributions. We use the Sudakov differential and the renormalisation group equations along with the factorisation properties of parton level cross sections to obtain the resummed result which predicts SV as well as next to SV contributions to all orders in strong coupling constant. In Mellin $N$ space, we resum the large logarithms of the form $\log^i(N)$ keeping $1/N$ corrections. In particular, the towers of logarithms, each of the form $a_s^n/N^\alpha \log^{2n-\alpha} (N), a_s^n/N^\alpha \log^{2n-1-\alpha}(N) \cdots $ etc for $\alpha =0,1$, are summed to all orders in $a_s$., Comment: 42 pages, 2 tables

We present a framework that resums threshold enhanced large logarithms to all orders in perturbation theory for the production of a pair of leptons in Drell-Yan process and of Higgs boson in gluon fusion as well as in bottom quark annihilation. We restrict ourselves to contributions from diagonal partonic channels. These logarithms include the distributions $((1-z)^{-1} \ln^i(1-z))_+$ resulting from soft plus virtual (SV) and the logarithms $\ln^i(1-z)$ from next-to-SV (NSV) contributions. We use collinear factorisation and renormalisation group invariance to achieve this. The former allows one to define a Soft-Collinear (SC) function which encapsulates soft and collinear dynamics of the perturbative results to all orders in strong coupling constant. The logarithmic structure of these results are governed by universal infrared anomalous dimensions and process dependent functions of Sudakov differential equation that the SC satisfies. The solution to the differential equation is obtained by proposing an all-order ansatz in dimensional regularisation, owing to several state-of-the-art perturbative results available to third order. The $z$ space solutions thus obtained provide an integral representation to sum up large logarithms originating from both soft and collinear configurations, conveniently in Mellin $N$ space. We show that in $N$ space, tower of logarithms $a_s^n/N^\alpha \ln^{2n-\alpha} (N), a_s^n/N^\alpha \ln^{2n-1-\alpha}(N) \cdots $ etc for $\alpha =0,1$ are summed to all orders in $a_s$., Comment: 55 Pages, 3 Tables

We present the resummed predictions for inclusive cross-section for Drell-Yan (DY) production as well as onshell $Z,W^\pm$ productions at next-to-next-to-next-to leading logarithmic (N$^{3}$LL) accuracy. Using the standard techniques, we derive the $N$-dependent coefficients in the Mellin-$N$ space as well as the $N$-independent constants and match the resummed result through the minimal prescription matching procedure with that of existing next-to next-to leading order (NNLO). In addition to the standard $\ln N$ exponentiation, we study the numerical impacts of exponentiating $N$-independent part of the soft function and the complete $\bar{g}_0$ that appears in the resummed predictions in $N$ space. All the analytical pieces needed in these different approaches are extracted from the soft-virtual part of the inclusive cross section known to next-to-next-to-next-to leading order (N$^3$LO). We perform a detailed analysis on the scale and parton distribution function (PDF) variations and present predictions for the 13 TeV LHC for the neutral Drell-Yan process as well as onshell charged and neutral vector boson productions., Comment: 43 pages, 8 figures, 3 tables

We study the infrared (IR) structure of $SU(N) \times U(1)$ (QCD $\times$ QED) gauge theory with $n_f$ quarks and $n_l$ leptons within the framework of perturbation theory. In particular, we unravel the IR structure of the form factors and inclusive real emission cross sections that contribute to inclusive production of color neutral states, such as a pair of leptons or single W/Z in Drell-Yan processes and a Higgs boson in bottom quark annihilation, in Large Hadron Collider (LHC) in the threshold limit. Explicit computation of the relevant form factors to third order and the use of Sudakov's $K+G$ equation in $SU(N)\times U(1)$ gauge theory demonstrate the universality of the cusp anomalous dimensions ($A_I , I = q, b$). The abelianization rules that relate $A_I$ of $SU(N)$ with those from $U(1)$ and $SU(N)\times U(1)$ can be used to predict the soft distribution that results from the soft gluon emission subprocesses in the threshold limit. Using the latter and the third order form factors, we can obtain the collinear anomalous dimensions ($B_I$ ) and the renormalisation constant $Z_b$ to third order in perturbation theory. The form factors, the process independent soft distribution functions can be used to predict fixed and resummed inclusive cross sections to third order in couplings and in leading logarithmic approximation respectively., Comment: The updated version, which include corrected expression for beta function, mixed QCD-QED anomalous dimensions and soft-virtual parsonic cross section

We present a detailed study on the infrared structure of $\mathcal{N}=4$ SYM and its connection to QCD. Calculation of collinear splitting functions helps to understand the structure and thus one can get infrared safe cross sections. We also demonstrate the factorization property that soft plus virtual part of the cross section satisfies and through factorization, we calculate soft distribution function up to third order in perturbation theory. We show that the soft distribution function is process independent that includes operators as well as external legs. In addition to this we compare our findings against the known results in QCD through principle of maximum transcendentality (PMT). We extend our analysis further for the case of three-point form factors involving stress tensor and find that it violates the PMT while comparing with the corresponding quantity in the standard model, observed for the first time at the level of form factor., Comment: 10 pages, Contribution to the 14th International Symposium on Radiative Corrections (RADCOR2019), 9-13 September 2019, Palais des Papes, Avignon, France

We present the two-loop QCD corrections to the amplitude of the Higgs production associated with a $Z$ boson via the bottom quark-antiquark annihilation channel with a non-vanishing bottom-quark Yukawa coupling. The computation is performed by projecting the D-dimensional scattering amplitude directly onto a set of Lorentz structures related to the linear polarisation states of the $Z$ boson. We cross-check the finite remainders through a computation based on conventional form factor decomposition. We show that for physical observables, an ultimate D-dimensional form factor decomposition of amplitudes is not necessary which has a huge potential to simplify a multiloop computation. We compute numerically the resulting cross sections under the soft-virtual approximation to NNLO and find it three orders of magnitude smaller than that of the s-channel., Comment: 10 pages, 1 figure, Contribution to the 14th International Symposium on Radiative Corrections (RADCOR2019), 9-13 September 2019, Palais des Papes, Avignon, France

We present the first calculations of two-point two-loop form factors (FFs) with a two identical operators insertion in maximally supersymmetric Yang-Mills theory. In this article, we consider the supersymmetry protected half-BPS primary and unprotected Konishi operators. Unlike the FFs of a single operator insertion of the half-BPS primary, the FFs involving two half-BPS operators are found to contain lower transcendentality weight terms in addition to the highest ones. Moreover, in contrast to Sudakov FFs, the highest weight terms of the FFs of a double half-BPS no longer match with that of a double Konishi. We also find that the principle of maximal transcendentality, which dictates the presence of identical highest weight terms in the scalar FFs of half-BPS and quark/gluon FFs in QCD, does not hold true anymore for insertions of two identical operators. We discover the absence of any additional ultraviolet counterterm that could arise from the contact interaction between two composite operators., Comment: Published version, 7 pages, 2 figures, title changed, a new section on Regge and Collinear limit added

Production of the Higgs boson, $H$ in association with a massive vector boson, $V$, i.e., the $VH$ process, plays an important role in the explorations of Higgs physics at the Large Hadron Collider, both for a precise study of Higgs' Standard Model couplings and for probing New Physics. In this publication we present the two-loop corrections in massless quantum chromodynamics (QCD) to the amplitude of the Higgs production associated with a $Z$ boson via the bottom quark-antiquark annihilation channel with a non-vanishing bottom-quark Yukawa coupling, which is a necessary ingredient of the full next-to-next-to-leading-order QCD corrections to the $VH$ process in the five-flavour scheme. The computation is performed by projecting the D-dimensional scattering amplitude directly onto an appropriate set of Lorentz structures related to the linear polarisation states of the $Z$ boson. We provide analytic expressions of the complete set of renormalised polarised amplitudes in terms of polylogarithms of maximum weight four. To give an estimation of the size of contributions from amplitudes considered in this work, we compute numerically the resulting cross sections under the soft-virtual approximation. We also take the opportunity to make a dedicated discussion regarding an interesting subtlety appearing in the conventional form factor decomposition of amplitudes involving axial currents regularised in D dimensions., Comment: 40 pages, 5 figures and 1 table; references added, matched with the published version in JHEP

We compute the radiative corrections to the four-point amplitude $g+g \rightarrow A+A$ in massless Quantum Chromodynamics (QCD) up to order $a_s^4$ in perturbation theory. We used the effective field theory that describes the coupling of pseudo-scalars to gluons and quarks directly, in the large top quark mass limit. Due to the CP odd nature of the pseudo-scalar Higgs boson, the computation involves careful treatment of chiral quantities in dimensional regularisation. The ultraviolet finite results are shown to be consistent with the universal infrared structure of QCD amplitudes. The infrared finite part of these amplitudes constitutes the important component of any next to next to leading order corrections to observables involving pair of pseudo-scalars at the Large Hadron Collider., Comment: 18 pages, references updated, 2 figures added, 1-loop ancillary files included, 2-loop ancillary files are oversized for arXiv, available on request

We present next-to-next-to leading order (NNLO) quantum electrodynamics (QED) corrections to the production of the Higgs boson in bottom quark annihilation at the Large Hadron Collider (LHC) in the five flavor scheme. We have systematically included the NNLO corrections resulting from the interference of quantum chromodynamics (QCD) and QED interactions. We have investigated the infrared (IR) structure of the bottom quark form factor up to two loop level in QED and in QCD$\times$QED using K+G equation. We find that the IR poles in the form factor are controlled by the universal cusp, collinear and soft anomalous dimensions. In addition, we derive the QED as well as QCD$\times$QED contributions to soft distribution function as well as to the ultraviolet renormalization constant of the bottom Yukawa coupling up to second order in strong coupling and fine structure constant. Finally, we report our findings on the numerical impact of the NNLO results from QED and QCD$\times$QED at the LHC energies taking into account the dominant NNLO QCD corrections., Comment: 18 pages, 7 figures, 5 tables

Form factors are important ingredients to investigate the principle of maximal transcendentality (PMT) and to extract anomalous dimensions of local gauge invariant operators. In this article, we compute several two- and three-point FFs to three- and two-loops, respectively, for three different choices of local gauge invariant operators in ${\cal N}=4$ super Yang-Mills (SYM) theory. The operators ${\cal O}^1$ and ${\cal O}^2$ are flavour and helicity blind configurations of supersymmetric descendant of the half-BPS and Konishi primary, respectively, and ${\cal O}^3$ is the energy-momentum tensor. The operators ${\cal O}^1$ and ${\cal O}^2$ are composed of non-protected dimension-three (classical) fermionic and scalar components belonging to SU($2|3$) closed sub-sector of ${\cal N}=4$ SYM. We analyse the mixing among the non-protected fermionic and scalar components of these operators up to three-loops in perturbation theory and consequently, compute the quantum corrections to the corresponding dilatation operators. The highest transcendental (HT) weight terms of the FFs of ${\cal O}^1$ are found to be independent of the external on-shell states and, moreover, those are equal to that of half-BPS, however, this does not hold true for the FFs of ${\cal O}^2$. FFs of the ${\cal O}^3$ exhibit identical behaviours to that of half-BPS, in concordance with the classical expectations. However, the three-point FFs of ${\cal O}^3$ violate the PMT while comparing with the corresponding quantity in the standard model, observed for the first time at the level of FF., Comment: Substantial update of the contents, 36 pages, 1 figure

We present an accurate theoretical prediction for the production of Higgs boson through bottom quark annihilation at the LHC up to next-to-next-to-next-to leading order (N$^3$LO) plus next-to-next-to-next-to-leading logarithmic (N$^3$LL) accuracy. We determine the third order perturbative Quantum Chromodynamics (QCD) correction to the process dependent constant in the resummed expression using the three loop bottom quark form factor and third order quark soft distribution function. Thanks to the recent computation of N$^3$LO corrections to this production cross-section from all the partonic channels, an accurate matching can be obtained for a consistent predictions at N$^3$LO+N$^3$LL accuracy in QCD. We have studied in detail the impact of resummed threshold contributions to inclusive cross-sections at various centre-of-mass energies and also discussed their sensitivity to renormalization and factorization scales at next-to-next-to leading order (NNLO) matched with next-to-next-to leading logarithm (NNLL). At N$^3$LO+N$^3$LL, we predict the cross-section for different centre-of-mass energies using the recently available results in \cite{Duhr:2019kwi} as well as study the renormalization scale dependence at the same order., Comment: 19 pages, 4 figures, 2 tables

We present the first results on the two-loop massless QCD corrections to the four-point amplitude $b+\overline{b} \rightarrow H+H$ in the five flavor scheme, treating bottom quarks as massless. This amplitude is sensitive to the trilinear Higgs boson coupling. Our two-loop result for this amplitude constitutes of purely virtual contributions to the next-to-next-to-leading order QCD predictions for the production of a pair of Higgs bosons at the Large Hadron Collider. Using these two loop amplitudes and exploiting the universality of the soft contributions in perturbative QCD, we obtain the NNLO QCD effects in the soft plus virtual approximation. We find that the inclusion of higher order terms reduce the uncertainties resulting from the unphysical renormalisation and factorisation scales., Comment: 30 pages, 6 figures, 3 tables

We report our findings on the perturbative structure of ${\cal N}=4$ supersymmetric Yang-Mills (SYM) theory in the infrared sector by computing inclusive scattering cross sections of on-shell particles. We use half-BPS, energy-momentum tensor and Konishi operators to produce singlet states in the scattering processes to probe the soft and the collinear properties of the cross sections. By appropriately defining the infrared safe observables, we obtain collinear splitting functions up to second order in the perturbation theory. The splitting functions and the infrared finite cross sections demonstrate several interesting connections with those in the perturbative QCD. We also determine the process independent soft distribution function up to third order in the perturbation theory and show that it is universal {\it i.e.} independent of the operators as well as the external states. Interestingly, the soft distribution function in ${\cal N}=4$ SYM theory matches exactly with the leading transcendental part of the corresponding one in the QCD. This enables us to predict the third order soft plus virtual cross section for the production of the on-shell singlet states., Comment: 31 pages

We compute the two-loop massless QCD corrections to the four-point amplitude $g+g \rightarrow H+H$ resulting from effective operator insertions that describe the interaction of a Higgs boson with gluons in the infinite top quark mass limit. This amplitude is an essential ingredient to the third-order QCD corrections to Higgs boson pair production. We have implemented our results in a numerical code that can be used for further phenomenological studies., Comment: 3 figures

We present a formalism to resum large threshold logarithms to all orders in perturbative QCD for the rapidity distribution of any colorless particle at the hadron colliders. Using the derived resummed coefficients in two dimensional Mellin space, we present the rapidity distributions for the Higgs as well as for the Drell-Yan production to NNLO+NNLL accuracy at the LHC. The resummed distributions give stable prediction against the variation of unphysical renormalisation and factorisation scales in both the cases. Perturbative convergence is also improved with the inclusion of the resummed result., Comment: 8 pages, 7 figures, 1 table, talk presented at the Loops and Legs in Quantum Field Theory (LL2018)

In this article we have studied the transverse momentum distribution of the pseudo-scalar Higgs boson at the Large Hadron Collider (LHC). The small $\pt$ region which provides the bulk of the cross section is not accessible to fixed order perturbation theory due to the presence of large logarithms in the series. Using the universal infrared behaviour of the QCD we resum these large logarithms up to next-to-next-to-leading logarithmic (NNLL) accuracy. We observe a significant reduction in theoretical uncertainties due to the unphysical scales at NNLL level compared to the previous order. We present the $p_T$ distribution matched to NNLO$_A$+NNLL, valid for the whole $p_T$ region and provide a detailed phenomenological study in the context of both 14 TeV and 13 TeV LHC using different choices of masses, scales and parton distribution functions which will be useful for the search of such particle at the LHC in near future., Comment: 20 pages, 8 figures, 2 tables

We present here the first result on the three-loop gluon jet function in perturbative QCD. Using the three-loop coefficient functions [1,2] for deep-inelastic scattering via the exchange of a virtual photon that couples to quarks or a scalar that couples to gluons and employing the KG equation, renormalization group invariance and factorization theorem, we obtain both the quark and the gluon jet functions up to the three-loop level. The former agrees with the recent result [3]. These jet functions being universal ingredients for many collider and decay processes, will play an important role in the phenomenological studies at the Large Hadron Collider., Comment: 7 pages

We consider the production of pairs of lepton through the Drell-Yan process at the LHC and present the most accurate prediction on their rapidity distribution. While the fixed order prediction is already known to next-to-next-to-leading order in perturbative QCD, the resummed contribution coming from threshold region of phase space up to next-to-next-to-leading logarithmic (NNLL) accuracy has been computed in this article. The formalism developed in [1-3] has been used to resum large threshold logarithms in the two dimensional Mellin space to all orders in perturbation theory. We have done a detailed numerical comparison against other approaches that resum certain threshold logarithms in Mellin-Fourier space. Our predictions at NNLL level are close to theirs even though at leading logarithmic and next-to-leading logarithmic level we differ. We have also investigated the impact of these threshold logarithms on the stability of perturbation theory against factorisation and renormalisation scales. While the dependence on these scales does not get better with resummed results, the convergence of the perturbative series shows a better trend compared to the fixed order predictions. This is evident from the reduction in the K-factor for the resummed case compared to fixed order. We also present the uncertainties on the predictions resulting from parton distribution functions., Comment: 14 pages, 9 figures

We study the phenomenological impact of the interaction of spin-2 fields with those of the Standard Model in a model independent framework up to next-to-next-to-leading order in perturbative Quantum Chromodynamics. We use the invariant mass distribution of the pair of leptons produced at the LHC to demonstrate this. A minimal scenario where the spin-2 fields couple to two gauge invariant operators with different coupling strengths has been considered. These operators being not conserved show very different ultraviolet behaviour increasing the searches options of spin-2 particles at the colliders. We find that our results using the higher order quantum corrections stabilise the predictions with respect to renormalisation and factorisation scales. We also find that corrections are appreciable which need to be taken into account in such searches at the colliders., Comment: 24 pages, 15 figures

We present a formalism that resums threshold-enhanced logarithms to all orders in perturbative QCD for the rapidity distribution of any colorless particle produced in hadron colliders. We achieve this by exploiting the factorization properties and K+G equations satisfied by the soft and virtual parts of the cross section. We compute for the first time compact and most general expressions in two-dimensional Mellin space for the resummed coefficients. Using various state-of-the-art multiloop and multileg results, we demonstrate the numerical impact of our resummed results up to next-to-next-to-leading order for the rapidity distribution of the Higgs boson at the LHC. We find that inclusion of these threshold logs through resummation improves the reliability of perturbative predictions., Comment: (7 pages, 2 figures) This article is dedicated to the memory of Jack Smith

We present virtual contributions up to two loop level in perturbative Quantum Chromodynamic (QCD) to the decay of pseudo-scalar Higgs boson ($A$) to three gluons ($g$) and also to quark ($q$), anti-quark ($\overline q$) and a gluon. With appropriate crossing, they are well suited for predicting the differential distribution of $A$ in association with a jet in hadron colliders up to next-to-next-to-leading order (NNLO) in strong coupling constant and also for the subsequent decay of $A$ to hadrons. We use effective field theory approach to integrate out the top quarks in the heavy top limit. The resulting theory involves two pseudo-scalar composite operators describing the interaction of $A$ with gluons as well as with quark and anti-quark. We perform our computation in dimensional regularisation and use minimal subtraction ($\overline{MS}$) scheme to renormalise strong coupling constant as well as the composite operators. The ultraviolet (UV) finite amplitudes contain infrared (IR) divergences that are found to be in agreement with the predictions by Catani. For both the amplitudes namely $A \rightarrow g g g$ and $A \rightarrow q \overline q g$, the leading transcendental terms at one and two loops are found to be identical to those in a three point form factor (FF) of the half-BPS operator in ${\cal N}=4$ Supersymmetric Yang Mills (SYM) theory when the QCD color factors are adjusted in a specific way. We present our results in terms of harmonic polylogs well suited for further numerical study., Comment: 29 pages; two minor typographical errors in Eq. (A.3) and Eq. (A.4) are corrected

We present three point form factors (FF) in ${\cal N}=4$ Super Yang Mills theory for both the half-BPS and the Konishi operators at two loop level in the `t Hooft coupling using Feynman diagrammatic approach. We have chosen on shell final states consisting of $g \phi \phi$ and $\phi \lambda \lambda$, where $\phi,\lambda, g$ are scalar, Majorana fermion and gauge fields respectively. The computation is done both in the modified dimensional reduction as well as in the four dimensional helicity scheme. We have studied the universal structure of infrared (IR) singularities in these FFs using Catani's IR subtraction operators. Exploiting the factorisation property of the IR singularities and following BDS like ansatz for the IR sensitive terms in FFs, we determine the finite remainders of them. We find that the finite remainders of FFs of the half-BPS for both the choices of final states give not only identical results but also contain terms of uniform transcendentality of weight two and four at one and two loop levels, respectively. In the case of the Konishi operator, the finite remainders depend on the external states and do not exhibit uniform transcendentality. However, surprisingly, the leading transcendental terms for $g \phi \phi$ agree with that of the half-BPS. We have demonstrated the role of on shell external states for the FFs in the context of maximum transcendentality principle., Comment: 37 pages

We investigate the interaction of spin-2 fields with those of Standard Model in a model independent framework. We have considered interactions where the spin-2 fields couple to two sets of gauge invariant tensorial operators that are not conserved unlike the energy momentum tensor with different coupling strengths. Such interactions not only change the ultraviolet behaviour of the couplings but also expand the scope of the searches of spin-2 particles at the colliders. We present all the relevant renormalisation constants up to three loop level in QCD and also the form factors that contribute to potential observables. This sets the ground to investigate the phenomenological consequences of these interactions with spin-2 fields through more than one tensorial operator., Comment: 24 pages, Journal version

We present the first results on the third order corrections to on-shell form factor (FF) of the Konishi operator in ${\cal N}=4$ supersymmetric Yang-Mills theory using Feynman diagrammatic approach in modified dimensional reduction ($\overline {DR}$) scheme. We show that it satisfies KG equation in $\overline {DR}$ scheme while the result obtained in four dimensional helicity (FDH) scheme needs to be suitably modified not only to satisfy the KG equation but also to get the correct ultraviolet (UV) anomalous dimensions. We find that the cusp, soft and collinear anomalous dimensions obtained to third order are same as those of the FF of the half-BPS operator confirming the universality of the infrared (IR) structures of on-shell form factors. In addition, the highest transcendental terms of the FF of Konishi operator are identical to those of half-BPS operator indicating the probable existence of deeper structure of the on-shell FF. We also confirm the UV anomalous dimensions of Konishi operator up to third order providing a consistency check on the both UV and universal IR structures in ${\cal N}=4$., Comment: 7 pages

Two-loop QCD correction to massive spin-2 Graviton decaying to $q ~ + ~ \bar{q}~ + ~g$ is presented considering a generic universal spin-2 coupling to the SM through the conserved energy-momentum tensor. Such a massive spin-2 particle can arise in extra-dimensional models. The ultraviolet and infrared structure of the QCD amplitudes are studied. In dimensional regularisation, the infrared pole structure is in agreement with Catani's proposal, confirming the universal factorization property of QCD amplitudes, even with the spin-2 tensorial coupling. This computation now completes the full two-loop QCD corrections for the production of a spin-2 in association with a jet., Comment: 37 pages, references updated

The first results on the complete next-to-next-to-leading order (NNLO) Quantum Chromodynamic (QCD) corrections to the production of di-leptons at hadron colliders in large extra dimension models with spin-2 particles are reported in this article. In particular, we have computed these corrections to the invariant mass distribution of the di-leptons taking into account all the partonic subprocesses that contribute at NNLO. In these models, spin-2 particles couple through the energy-momentum tensor of the Standard Model (SM) with the universal coupling strength. The tensorial nature of the interaction and the presence of both quark annihilation and gluon fusion channels at the Born level make it challenging computationally and interesting phenomenologically. We have demonstrated numerically the importance of our results at the Large Hadron Collider (LHC) energies. The two loop corrections contribute an additional 10\% to the total cross section. We find that the QCD corrections are not only large but also important to make the predictions stable under renormalisation and factorisation scale variations providing an opportunity to stringently constrain the parameters of the models with a spin-2 particle., Comment: 51 pages, 17 figures

We consider the production of a pseudo-scalar particle $A$ at the LHC, and present accurate theoretical predictions for its inclusive cross section in gluon fusion. The prediction is based on combining fixed-order perturbation theory and all-order threshold resummation. At fixed order we include the exact next-to-next-to-leading order (NNLO) plus an approximate next-to-next-to-next-to-leading order (N$^3$LO$_{\rm A}$) which is based on the recent computation at this order for the scalar case. We then add threshold resummation at next-to-next-to-next-to leading logarithmic accuracy (N$^3$LL$^\prime$). Various forms of threshold resummation are considered, differing by the treatment of subleading terms, allowing a robust estimate of the theoretical uncertainties due to missing higher orders. With particular attention to pseudo-scalar masses of $200$ GeV and $750$ GeV, we also observe that perturbative convergence is much improved when resummation is included. Additionally, results obtained with threshold resummation in direct QCD are compared with analogous results as computed in soft-collinear effective theory, which turn out to be in good agreement. We provide precise predictions for pseudo-scalar inclusive cross section at $13$ TeV LHC for a wide range of masses. The results are available through updated versions of the public codes ggHiggs and TROLL., Comment: 14 pages, 7 figures, 1 table. Now includes a more precise assessment of the uncertainty on the approximate N3LO. Final version accepted by EPJC