Hi! This is **Taushif Ahmed!** Currently, I'm a **Research Associate** at **INFN Torino, University of Torino** in Italy. I worked as a **post-doctoral scientist at Max-Planck-Institute for Physics** at Munich in Germany from October 2018 to September 2020. I work on theorretical physics. Understanding the connection among various gauge theories from the perspective of transcendentality weight and infrared structures, making precise theoretical predictions through computing radiative corrections to scattering amplitudes and observables employing state-of-the-art techniques are my primary objectives. My primary focus is on maximally supersymmetric Yang-Mills theory, perturbative QCD and Electroweak theory.

- Theoretical Physics: Quantum Chromodynamics (QCD), Standard Model, \(\cal N\)=4 supersymmetric Yang-Mills
- Programming: FORM, Mathematica, C++, Fortran
- Integration-by-parts reduction packages: FiniteFlow, FIRE, Kira, Reduze, LiteRed
- Numerical integration: pySecDec
- Operating systems: Linux, MacOS
- Text editors: Vim, Emacs
- \(\LaTeX \), HTML

Production of the Higgs boson, H in association with a massive vector boson, V , i.e., the V H 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 mass- less 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 V H process in the five-flavour scheme. The com- putation 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 oppor- tunity 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.

*Taushif Ahmed, A. H. Ajjath, Long Chen, Prasanna K. Dhani, Pooja Mukherjee and V. Ravindran*

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 O1 and O2 are flavour and helicity blind configurations of supersymmetric descendant of the half-BPS and Konishi primary, respec- tively, and O3 is the energy-momentum tensor. The operators O1 and O2 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 the- ory and consequently, compute the quantum corrections to the corresponding dilatation operators. The highest transcendental (HT) weight terms of the FFs of O1 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 O2. FFs of the O3 exhibit identical behaviours to that of half-BPS, in concordance with the classical expectations. However, the three-point FFs of O3 violate the PMT while comparing with the corresponding quan- tity in the standard model, observed for the first time at the level of FF.

Under review

*Taushif Ahmed, Pulak Banerjee, Amlan Chakraborty, Prasanna K. Dhani and V. Ravindran*

We investigate the interaction of spin-2 fields with those of the 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 poten- tial observables. This sets the ground to investigate the phenomenological consequences of these interactions with spin-2 fields through more than one tensorial operator.

Phys.Rev. D95 (2017) no.3, 034035

*Taushif Ahmed, Pulak Banerjee, Prasanna K. Dhani, Prakash Mathews, Narayan Rana and V. Ravindran*

We present the first results on the third order corrections to on-shell form factor (FF) of the Kon- ishi operator in \(\cal N\) = 4 supersymmetric Yang-Mills theory using Feynman diagrammatic approach in modified dimensional reduction (DR) scheme. We show that it satisfies KG equation in 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.

Phys.Rev. D95 (2017) no.8, 085019

*Taushif Ahmed, Pulak Banerjee, Prasanna K. Dhani, Narayan Rana, V. Ravindran and Satyajit Seth*

Two-loop QCD correction to massive spin-2 Graviton decaying to q + \(\overline q\) + 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 di- mensional 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.

Eur.Phys.J. C76 (2016) no.12, 667

*Taushif Ahmed, Goutam Das, Prakash Mathews, Narayan Rana and V. Ravindran*

Thefirstresultsonthecompletenext-to-next-to-leadingorder(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 particu- lar, 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 mod- els, 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.

Eur.Phys.J. C77 (2017) no.1, 22

*Taushif Ahmed, Pulak Banerjee, Prasanna K. Dhani, M.C. Kumar, Prakash Mathews, Narayan Rana and V. Ravindran*

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 com- bining 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 or- der (N\(^3\)LO\(_A\) 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 (N3LL'). 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.

Eur.Phys.J. C76 (2016) no.12, 663

*Taushif Ahmed, Marco Bonvini, M.C. Kumar, Prakash Mathews, Narayan Rana, V. Ravindran, Luca Rottoli*

We present the first results on the production of pseudo-scalar through gluon fusion at the LHC to N3LO in QCD taking into account only soft gluon effects. We have used the effective Lagrangian that describes the coupling of pseudo-scalar with the gluons in the large top quark mass limit. We have used recently available quantities namely the three loop pseudo-scalar form factor and the third order universal soft function in QCD to achieve this. Along with the fixed order results, we also present the process dependent resummation coefficient for threshold resummation to N3LL in QCD. Phenomenological impact of these threshold N3LO corrections to pseudo-scalar production at the LHC is presented and their role to reduce the renormalisation scale dependence is demonstrated.

Eur.Phys.J. C76 (2016) no.6, 355

*Taushif Ahmed, Marco Bonvini, M.C. Kumar, Prakash Mathews, Narayan Rana, V. Ravindran, Luca Rottoli*

The coupling of a pseudo-scalar Higgs boson to gluons is mediated through a heavy quark loop. In the limit of large quark mass, it is described by an effective Lagrangian that only admits light degrees of freedom. In this effective theory, we compute the three- loop massless QCD corrections to the form factor that describes the coupling of a pseudo- scalar Higgs boson to gluons. Due to the axial anomaly, the pseudo-scalar operator for the gluonic field strength mixes with the divergence of the axial vector current. Working in dimensional regularization and using the ’t Hooft-Veltman prescription for the axial vector current, we compute the three-loop pseudo-scalar form factors for massless quarks and gluons. Using the universal infrared factorization properties, we independently derive the three-loop operator mixing and finite operator renormalisation from the renormalisation group equation for the form factors, thereby confirming recent results in the operator product expansion. The finite part of the three-loop form factor is an important ingredient to the precise prediction of the pseudo-scalar Higgs boson production cross section at hadron colliders. We discuss potential applications and derive the hard matching coefficient in soft-collinear effective theory.

*Taushif Ahmed, Thomas Gehrmann, Prakash Mathews, Narayan Rana and V. Ravindran*

Spin-2 fields are often candidates in physics beyond the Standard Model namely the models with extra-dimensions where spin-2 Kaluza-Klein gravitons couple to the fields of the SM. Also, in the context of Higgs searches, spin-2 fields have been studied as an alternative to the scalar Higgs boson. In this article, we present the complete three loop QCD radiative corrections to the spin-2 quark-antiquark and spin-2 gluon-gluon form factors in SU(N) gauge theory with nf light flavors. These form factors contribute to both quark-antiquark and gluon-gluon initiated processes involving spin-2 particle in the hadronic reactions at the LHC. We have studied the structure of infrared singularities in these form factors up to three loop level using Sudakov integro-differential equation and found that the anomalous dimensions originating from soft and collinear regions of the loop integrals coincide with those of the electroweak vector boson and Higgs form factors confirming the universality of the infrared singularities in QCD amplitudes.

*Taushif Ahmed, Goutam Das, Prakash Mathews, Narayan Rana and V. Ravindran*

The recent result on the third order correction to the Higgs boson production through gluon fusion by Anastasiou et al. [1] not only provides a precise prediction with reduced scale uncertain- ties for studying the Higgs boson properties but also establishes the reliability of the perturbative QCD. In this letter, we propose a novel approach to further reduce the uncertainty arising from the renormalization scale by systematically resumming the renormalization group (RG) accessible log- arithms to all orders in the strong coupling constant. Our numerical study based on this approach, demonstrates a significant improvement over the fixed order predictions.

*Taushif Ahmed, Goutam Das, M. C. Kumar, Narayan Rana and V. Ravindran*

We present threshold enhanced N3LO QCD corrections to inclusive Higgs production through bottom anti-bottom annihilation at hadron colliders using threshold resummed cross section. The resummed cross section is obtained using factorization prop- erties and Sudakov resummation of the inclusive cross section. We use the recent results on threshold N3LO corrections in QCD for Drell-Yan production and three loop QCD cor- rections to Higgs form factor with bottom anti-bottom quark to achieve this task. This is the first step towards the evaluation of complete N3LO result. We have numerically demonstrated the importance of such corrections at the LHC.

*Taushif Ahmed, M. K. Mandal, Narayan Rana and V. Ravindran*

Exclusive observables involving Higgs boson in association with jets are often well suited to study the Higgs boson properties. They are rates involving cuts on the final state jets or differential distributions of rapidity, transverse momentum of the observed Higgs boson. While they get dominant contributions from gluon initiated partonic subpro- cesses, it is important to include the subdominant ones coming from other channels. In this article, we study one such channel namely the Higgs production in association with a jet in bottom anti-bottom annihilation process. We compute relevant amplitude H → b+b+g up to two loop level in QCD where Higgs couples to bottom quark through Yukawa coupling. We use projection operators to obtain the coefficients for each tensorial structure appearing in this process. We have demonstrated that the renormalized amplitudes do have the right infrared structure predicted by the QCD factorization in dimensional regularization. The finite parts of the one and two loop amplitudes are presented after subtracting the infrared poles using Catani’s subtraction operators.

*Taushif Ahmed, Maguni Mahakhud, Prakash Mathews, Narayan Rana and V. Ravindran*

We present the threshold N3LO perturbative QCD corrections to the rapidity distributions of dileptons in the Drell-Yan process and Higgs boson in gluon fusion. Sudakov resummation of QCD amplitudes, renormalization group invariance, and the mass factorization theorem provide useful guidelines to obtain them in an elegant manner. We use various state of the art three loop results that have been recently available to obtain these distributions. For the Higgs boson, we demonstrate numerically the importance of these corrections at the LHC.

Phys.Rev.Lett. 113 (2014) 212003

*Taushif Ahmed, M. K. Mandal, Narayan Rana and V. Ravindran*

The recent computation on the full threshold contributions to Higgs boson production at next- to-next-to-next-to-leading order (N\(^3\)LO) in QCD contains valuable information on the soft gluons resulting from virtual and real emission partonic subprocesses. We use those from the real emissions to obtain the corresponding soft gluon contributions to Drell-Yan production and determine the missing \(\delta\)(1 − z) part of the N\(^3\)LO. The numerical impact of threshold effects demonstrates the importance of our results in the precision study with the Drell-Yan process at the LHC.

Phys.Rev.Lett. 113 (2014) no.11, 112002

*Taushif Ahmed, Maguni Mahakhud, Narayan Rana and V. Ravindran*

We present the third order virtual QCD corrections to the process h \(\rightarrow\) g+g+g due to interference of born and two-loop amplitudes, where h is a massive spin-2 particle and g is the gluon. We assume that the SM fields couple to h through the SM energy momentum tensor. Our result constitutes one of the ingredients to full NNLO QCD contribution to production of a massive spin-2 particle along with a jet in the scattering process at the LHC. In particular, this massive spin-2 could be a KK mode of a ADD graviton in large extra dimensional model or a RS KK mode in warped extra dimensional model or a generic massive spin-2. In addition, it provides an opportunity to study the ultraviolet and infrared structures of QCD amplitudes involving tensorial coupling resulting from energy momentum operator. Using dimensional regularization, we find that infrared poles of this amplitude are in agreement with the proposal by Catani confirming the factorization property of QCD amplitudes with tensorial insertion.

*Taushif Ahmed, Maguni Mahakhud, Prakash Mathews, Narayan Rana and V. Ravindran*

We present a detailed study on the infrared structure of 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.

*Taushif Ahmed, Pulak Banerjee, Amlan Chakraborty, Prasanna K. Dhani, V. Ravindran and Satyajit Seth*

14th International Symposium on Radiative Corrections (RADCOR2019), 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.

*Taushif Ahmed, A. H. Ajjath, Long Chen, Prasanna K. Dhani, Pooja Mukherjee and V. Ravindran*

14th International Symposium on Radiative Corrections (RADCOR2019), Palais des Papes, Avignon, France

In the limit of large top quark mass, using an effective Lagrangian that only admits light degrees of freedom we compute the three-loop QCD corrections to the quark and gluon form factors of a pseudo-scalar Higgs boson. Using the universal infrared factorisation properties, the three-loop operator mixing and finite operator renormalisation are re-derived thereby confirming the results in the operator product expansion. We find that our findings are consistent with the anomaly equation. We derive the hard matching coefficient in soft-collinear effective theory in order to perform the matching of the SCET-based resummation onto the full QCD calculation up to the three loop order.

*Taushif Ahmed, Thomas Gehrmann, Prakash Mathews, Narayan Rana and V. Ravindran*

Loops and Legs in Quantum Field Theory - LL 2016, Leipzig, Germany

INFN Torino, Turin, Italy

Group of Simon Badger

Max-Planck-Institute for Physics (Werner Heiserberg Institute), Munich, Germany

Group of Johannes Henn

Johannes Guttenberg University of Mainz, Germany

Group of Johannes Henn

Karlsruhe Institute of Technology, Germany

Group of Matthias Steinhauser (and Johannes Henn from Mainz)

The Institute of Mathematical Sciences, Chennai, India

Advisor: V.Ravindran

Harish-Chandra Research Institute, Allahabad, India

Advisor: V.Ravindran

Doctoral Thesis

- QCD Radiative Corrections to Higgs Physics

Oct 2010 - Sept 2013

Harish-Chandra Research Institute, Allahabad, India

Master Thesis

- Spin Coherent State through Path Integral & Semi-Classical Physics
- Unruh Effect
- Intrinsic Parity of Neutral Pion
- Dirac and Majorana Neutrino
- The Anti-proton
- Classical Analogy of Fano Interference

Adv: Rajesh Gopakumar

Adv: Ashoke Sen

Adv: Biswarup Mukhopadhyaya

Adv: Biswarup Mukhopadhyaya

Adv: Biswarup Mukhopadhyaya

Adv: Ashok Mohapatra

Aug 2007 - Jul 2010

St. Xavier's College, Kolkata, India

Bachelor Thesis

- General Relativistic Spin Precision of Binary Pulsars

Adv: N. D. Hari Dass

Aug 2001 - Jul 2007

Al-Ameen Mission, Howrah, India

- Harish-Chandra Research Institute, India
- The Institute of Mathematical Sciences, India
- Indian Institute of Science, India
- The Inter-University Centre for Astronomy and Astrophysics, India
- National Centre for Radio Astrophysics, India
- Indian Institute of Astrophysics, India
- S. N. Bose National Centre For Basic Sciences, India

All India score 97.85 percentile

All India rank 67

One of the National Toppers

**Seminars (Selected)**

- Ph.D. defence, The Institute of Mathematical Sciences, Chennai, India, 2016: QCD Radiative Corrections to Higgs Physics
- Seminar at University of Buffalo, USA, 2016 Pseudo-Scalar Form Factors at 3-loop in QCD
- Seminar at Various Universities in Europe, 2015 Threshold Corrections to DY and Higgs at N\(^3\)LO QCD
- Seminar at Harish-Chandra Research Institute, India, 2014 Two Loop QCD Corrections To Massive Spin-2 Resonance \(\rightarrow\) 3-gluons

**Teaching Assistant in Advanced QFT, Spring 2015 and 2016**

**Lecture Notes**

- Advanced QFT, Fall 2014, Harish-Chandra Research Institute, Rajesh Gopakumar Handwritten lecture notes (partial) taken by me
- Advanced QFT, Fall 2012, Harish-Chandra Research Institute, Ashoke Sen Handwritten lecture notes taken by me

**Useful webpages**