A fast and accurate method for perturbative resummation of transverse momentum-dependent observables

We propose a novel strategy for the perturbative resummation of transverse momentum-dependent (TMD) observables, using the $q_T$ spectra of gauge bosons ($\gamma^*$, Higgs) in $pp$ collisions in the regime of low (but perturbative) transverse momentum $q_T$ as a specific example. First we introduce a scheme to choose the factorization scale for virtuality in momentum space instead of in impact parameter space, allowing us to avoid integrating over (or cutting off) a Landau pole in the inverse Fourier transform of the latter to the former. The factorization scale for rapidity is still chosen as a function of impact parameter $b$, but in such a way designed to obtain a Gaussian form (in $\ln b$) for the exponentiated rapidity evolution kernel, guaranteeing convergence of the $b$ integral. We then apply this scheme to obtain the $q_T$ spectra for Drell-Yan and Higgs production at NNLL accuracy. In addition, using this scheme we are able to obtain a fast semi-analytic formula for the perturbative resummed cross sections in momentum space: analytic in its dependence on all physical variables at each order of logarithmic accuracy, up to a numerical expansion for the pure mathematical Bessel function in the inverse Fourier transform that needs to be performed just once for all observables and kinematics, to any desired accuracy.Comment: 60 pages + Appendices, 16 Figures v.2, Accepted in JHEP, discussion added on low-qT limit, other minor clarifications made and typos correcte

Probing Transverse-Momentum Dependent Evolution With Groomed Jets

We propose an observable which involves measuring the properties (transverse momentum $p_{h\perp}$ and energy fraction $z_h$) of an identified hadron inside a groomed jet. The jet is identified with an anti-kT/CA algorithm and is groomed by implementing the modified mass drop procedure with an energy cut-off parameter $z_{cut}$. The transverse momentum of the hadron inside the jet is measured with respect to the groomed jet axis. We obtain a factorization theorem in the framework of Soft Collinear Effective Theory (SCET), to define a Transverse Momentum Dependent Fragmenting Jet Function (TMDFJF). The TMDFJF is factorized into collinear and collinear soft modes by matching onto SCET$_+$. We resum large logarithms in $E_J/p_{h\perp}$, where $E_J$ is the ungroomed jet energy, to NLL accuracy and apply this formalism for computing the shape of the $p_{h\perp}$ distribution of a pion produced in an $e^+ +e^-$ collision. We observe that the introduction of grooming makes this observable insensitive to non-global logarithms and particularly sensitive to non-perturbative physics of the transverse momentum dependent evolution at low values of $p_{h\perp}$, which can be probed in the variation of the cut-off parameter $z_{cut}$ of the groomer. We discuss how this observable can be used to distinguish between non-perturbative models that describe universal TMD evolution and provide a window into the three dimensional structure of hadrons.Comment: 23 pages, 4 figure

Impact of Cost Sharing Levels on Adherence to Controller Drugs and Consequent Outcomes among Asthma Patients

Prescription drug cost sharing is an effective tool to reduce the excessive drug consumption. However, many times it could have a negative impact on the drug utilization especially in case of chronic conditions. Chronic conditions such as asthma require appropriate utilization of controller medication to keep the inflammation and symptoms under control. Literature on asthma drug utilization has consistently reported underuse of controller drugs among asthma patients. The present study attempted to investigate the impact of prescription drug cost sharing levels on the controller adherence among the privately insured asthma population with moderate persistent asthma. The study also analyzed the relationship between adherence and asthma related health services utilization outcomes. A retrospective analysis using the MarketScan administrative claims database was conducted for the years 2000 and 2001. Asthma patients that were stepped up to dual controller therapy in the study period and had no diagnosis for COPD or other respiratory conditions were included in the study. Study participants were also required to be in the age range of 5-65 and continuously enrolled in the health plan for the entire study period. Multivariate regression analysis using SAS 9.1 was performed to analyze the relationship between cost sharing levels and controller adherence. Linear probabilistic models were built to analyze the relationship between adherence and asthma related health services utilization. A total of 1447 patients met the study criteria. The overall association between cost sharing and adherence was significantly negative. The drop in adherence to Inhaled Corticosteroids (ICS) with respect to cost sharing was greater after the patients were stepped to the dual controller therapy. Comparison of subgroups that used ICS+ LABA and ICS + LTRA revealed that the subjects ICS+LTRA subgroup are slightly more sensitive to the out of pocket costs. The analysis of adherence and health services utilization showed mixed results with reduction in ER visits but no association of hospital stay and SAB use. Cost sharing levels had a negative impact on utilization of controller drugs. In terms of ICS adherence pre and post index periods, it can be concluded that the increased cost burden affected significantly even though the need to be adherent was increased. Based on the sub group analysis in the post-index period between the two add-on options, ICS + LTRA subgroup was more sensitive to the price changes. Adherence to controller regimen had a negative impact on ER visits however the data did not provide evidence in case of hospitalizations and SAB use

Radiative corrections for factorized jet observables in heavy ion collisions

I look at the renormalization of the medium structure function and a medium induced jet function in a factorized cross section for jet substructure observables in Heavy Ion collisions. This is based on the formalism developed in \cite{Vaidya:2020lih}, which uses an Open quantum system approach combined with the Effective Field Theory(EFT) for forward scattering to derive a factorization formula for jet observables which work as hard probes of a long lived dilute Quark Gluon Plasma(QGP) medium. I show that the universal medium structure function that captures the observable independent physics of the QGP has both UV and rapidity anomalous dimensions that appear due to medium induced Bremsstrahlung. The resulting Renormalization Group(RG) equations correspond to the BFKL equation and the running of the QCD coupling respectively. I present the first results for the numerical impact of resummation using these RG equations on the mean free path of the jet in the medium. I also briefly discuss the prospects of extending this formalism for a short lived dense medium.Comment: 35 pages, 8 Figure

The Higgs Transverse Momentum Distribution at NNLL and its Theoretical Errors

In this letter, we present the NNLL-NNLO transverse momentum Higgs distribution arising from gluon fusion. In the regime $p_\perp\ll m_H$ we include the resummation of the large logs at next to next-to leading order and then match on to the $\alpha_s^2$ fixed order result near $p_\perp \sim m_h$. By utilizing the rapidity renormalization group (RRG) we are able to smoothly match between the resummed, small $p_\perp$ regime and the fixed order regime. We give a detailed discussion of the scale dependence of the result including an analysis of the rapidity scale dependence. Our central value differs from previous results, in the transition region as well as the tail, by an amount which is outside the error band. This difference is due to the fact that the RRG profile allows us to smoothly turn off the resummation.Comment: 23 pages, 10 figure