Resummation Of Large Logarithms Research Articles

Effective Field Theory for jet substructure in heavy ion collisions

I develop an Effective Field Theory (EFT) framework to compute jet substructure observables for heavy ion collision experiments. As an example, I consider dijet events that accompany the formation of a weakly coupled long lived Quark Gluon Plasma (QGP) medium in a heavy ion collision and look at an observable insensitive to jet selection bias: the simultaneous measurement of jet mass along with the transverse momentum imbalance between the jets that are groomed to remove soft radiation. Treating the jet as an open quantum system, I write down a factorization formula within the SCET (Soft Collinear Effective Theory) framework in the forward scattering regime. The physics of the medium is encoded in a universal soft field correlator while the jet-medium interaction is captured by a medium induced jet function. The factorization formula leads to a Lindblad type equation for the evolution of the reduced density matrix of the jet in the Markovian approximation. The solution for this equation allows a resummation of large logarithms that arise due to the final state measurements imposed while simultaneously summing over multiple incoherent interactions of the jet with the medium.

One-loop jet functions by geometric subtraction

In factorization formulae for cross sections of scattering processes, final-state jets are described by jet functions, which are a crucial ingredient in the resummation of large logarithms. We present an approach to calculate generic one-loop jet functions, by using the geometric subtraction scheme. This method leads to local counterterms generated from a slicing procedure; and whose analytic integration is particularly simple. The poles are obtained analytically, up to an integration over the azimuthal angle for the observable- dependent soft counterterm. The poles depend only on the soft limit of the observable, characterized by a power law, and the finite term is written as a numerical integral. We illustrate our method by reproducing the known expressions for the jet function for angularities, the jet shape, and jets defined through a cone or kT algorithm. As a new result, we obtain the one-loop jet function for an angularity measurement in e+e− collisions, that accounts for the formally power-suppressed but potentially large effect of recoil. An implementation of our approach is made available as the GOJet Mathematica package accompanying this paper.

Heavy-flavor PDF evolution and variable-flavor-number scheme uncertainties in deep-inelastic scattering

We consider a detailed account on the construction of the heavy-quark parton distribution functions for charm and bottom, starting from $n_f=3$ light flavors in the fixed-flavor number (FFN) scheme and by using the standard decoupling relations for heavy quarks in QCD. We also account for two-mass effects. Furthermore, different implementations of the variable-flavor-number (VFN) scheme in deep-inelastic scattering (DIS) are studied, with the particular focus on the resummation of large logarithms in $Q^2/m_h^2$, the ratio the virtuality of the exchanged gauge-boson $Q^2$ to the heavy-quark mass squared $m_h^2$. A little impact of resummation effects if found in the kinematic range of the existing data on the DIS charm-quark production so that they can be described very well within the FFN scheme. Finally, we study the theoretical uncertainties associated to the VFN scheme, which manifest predominantly at small $Q^2$.

Determination of \u03b1(Mz) from an hyperasymptotic approximation to the energy of a static quark-antiquark pair

We give the hyperasymptotic expansion of the energy of a static quark-antiquark pair with a precision that includes the effects of the subleading renormalon. The terminants associated to the first and second renormalon are incorporated in the analysis when necessary. In particular, we determine the normalization of the leading renormalon of the force and, consequently, of the subleading renormalon of the static potential. We obtain {Z}_3^F (nf = 3) = 2{Z}_3^V (nf = 3) = 0.37(17). The precision we reach in strict perturbation theory is next-to-next-to-next-to-leading logarithmic resummed order both for the static potential and for the force. We find that the resummation of large logarithms and the inclusion of the leading terminants associated to the renormalons are compulsory to get accurate determinations of {Lambda}_{overline{mathrm{MS}}} when fitting to short-distance lattice data of the static energy. We obtain {Lambda}_{overline{mathrm{MS}}}^{left({n}_f=3right)} = 338(12) MeV and α(Mz) = 0.1181(9). We have also MS found strong consistency checks that the ultrasoft correction to the static energy can be computed at weak coupling in the energy range we have studied.

The fully-differential gluon beam function at NNLO

The fully-differential beam function (dBF) is a universal ingredient in resummed predictions of hadron collider observables that probe the full kinematics of the incoming parton from each colliding proton — the virtuality and transverse momentum as well as the light-cone momentum fraction x. In this paper we compute the matching coefficients between the unpolarized gluon dBF and the usual parton distribution functions (PDFs) at the two-loop order. For observables probing both the virtuality and transverse momentum of incoming gluons, our results provide the part of the NNLO singular cross section related to collinear initial-state radiation, and are required for the resummation of large logarithms through N3LL. Further to this, the dBF is closely linked to the beam function appearing in a generalized version of threshold factorization, via a simple integration. By performing this integration for the two-loop gluon matching coefficients, we also obtain the corresponding quantities for the generalized threshold beam function.

Nonperturbative corrections to soft drop jet mass

We provide a quantum field theory based description of the nonperturbative effects from hadronization for soft drop groomed jet mass distributions using the soft- collinear effective theory and the coherent branching formalism. There are two distinct regions of jet mass mJ where grooming modifies hadronization effects. In a region with intermediate mJ an operator expansion can be used, and the leading power corrections are given by three universal nonperturbative parameters that are independent of all kinematic variables and grooming parameters, and only depend on whether the parton initiating the jet is a quark or gluon. The leading power corrections in this region cannot be described by a standard normalized shape function. These power corrections depend on the kinematics of the subjet that stops soft drop through short distance coefficients, which encode a perturbatively calculable dependence on the jet transverse momentum, jet rapidity, and on the soft drop grooming parameters zcut and β. Determining this dependence requires a resummation of large logarithms, which we carry out at LL order. For smaller mJ there is a nonperturbative region described by a one-dimensional shape function that is unusual because it is not normalized to unity, and has a non-trivial dependence on β.

BSM W W production with a jet veto

We consider the impact on W W production of the unique dimension-six operator coupling gluons to the Higgs field. In order to study this process, we have to appropriately model the effect of a veto on additional jets. This requires the resummation of large logarithms of the ratio of the maximum jet transverse momentum and the invariant mass of the W boson pair. We have performed such resummation at the appropriate accuracy for the Standard Model (SM) background and for a signal beyond the SM (BSM), and devised a simple method to interface jet-veto resummations with fixed-order event generators. This resulted in the fast numerical code MCFM-RE, the Resummation Edition of the fixed-order code MCFM. We compared our resummed predictions with parton-shower event generators and assessed the size of effects, such as limited detector acceptances, hadronisation and the underlying event, that were not included in our resummation. We have then used the code to compare the sensitivity of W W and Z Z production at the HL-LHC to the considered higher-dimension operator. We have found that W W can provide complementary sensitivity with respect to Z Z, provided one is able to control theory uncertainties at the percent-level. Our method is general and can be applied to the production of any colour singlet, both within and beyond the SM.

Polarization effects in standard model parton distributions at very high energies

We update the earlier work of refs. [1, 2] on parton distribution functions in the full Standard Model to include gauge boson polarization, non-zero input electroweak boson PDFs and next-to-leading-order resummation of large logarithms.

Precise prediction of the MSSM Higgs boson masses for low MA

Precise predictions for Higgs boson masses in the Minimal Supersymmetric Standard Model can be obtained by combining fixed-order calculations with effective field theory (EFT) methods for the resummation of large logarithms in case of heavy super-partners. This hybrid approach is implemented in the computer code FeynHiggs and has been applied in previous studies for calculating the mass of the lightest mathcal{C}mathcal{P} -even Higgs boson for low, intermediate and high SUSY scales. In these works it was assumed that the non-standard Higgs bosons share a common mass scale with the supersymmetric squark particles, leaving the Standard Model as the low-energy EFT. In this article, we relax this restriction and report on the implemention of a Two-Higgs-Doublet Model (THDM) as effective theory below the SUSY scale into our hybrid approach. We explain in detail how our EFT calculation is consistently combined with the fixed-order calculation within the code FeynHiggs. In our numerical investigation we find effects on the mass of the lightest mathcal{C}mathcal{P} -even Higgs boson h of up to 9GeV in scenarios with low MA, low tan β and high SUSY scales, when compared with previous versions of FeynHiggs. Comparisons to other publicly available pure EFT codes with a THDM show good agreement. Effects on the mass of the second lightest mathcal{C}mathcal{P} -even Higgs boson H are found to be negligible in the phenomenologically interesting parameter regions where H can be traded for h as the experimentally observed Higgs particle.

Determination of electric dipole transitions in heavy quarkonia using potential non-relativistic QCD

The electric dipole transitions with J = 0, 1, 2 and are computed using the weak-coupling version of a low-energy effective field theory named potential non-relativistic QCD (pNRQCD). In order to improve convergence and thus give firm predictions for the studied reactions, the full static potential is incorporated into the leading order Hamiltonian; moreover, we must handle properly renormalon effects and re-summation of large logarithms. The precision we reach is , where kγ is the photon energy, m is the mass of the heavy quark and v its velocity. Our analysis separates those relativistic contributions that account for the electromagnetic interaction terms in the pNRQCD Lagrangian which are v2 suppressed and those that account for wave function corrections of relative order v2. Among the last ones, corrections from 1/m and 1/m2 potentials are computed, but not those coming from higher Fock states since they demand non-perturbative input and are or suppressed, at least, in the strict weak coupling regime. These proceedings are based on the forthcoming publication [1].

Factorization, resummation and sum rules for heavy-to-light form factors

Precision calculations of heavy-to-light form factors are essential to sharpen our understanding towards the strong interaction dynamics of the heavy-quark system and to shed light on a coherent solution of flavor anomalies. We briefly review factorization properties of heavy-to-light form factors in the framework of QCD factorization in the heavy quark limit and discuss the recent progress on the QCD calculation of $B \to \pi$ form factors from the light-cone sum rules with the $B$-meson distribution amplitudes. Demonstration of QCD factorization for the vacuum-to-$B$-meson correlation function used in the sum-rule construction and resummation of large logarithms in the short-distance functions entering the factorization theorem are presented in detail. Phenomenological implications of the newly derived sum rules for $B \to \pi$ form factors are further addressed with a particular attention to the extraction of the CKM matrix element $|V_{ub}|$.

QCD corrections to [formula omitted] form factors from light-cone sum rules

We compute perturbative corrections to B→π form factors from QCD light-cone sum rules with B-meson distribution amplitudes. Applying the method of regions we demonstrate factorization of the vacuum-to-B-meson correlation function defined with an interpolating current for pion, at one-loop level, explicitly in the heavy quark limit. The short-distance functions in the factorization formulae of the correlation function involves both hard and hard-collinear scales; and these functions can be further factorized into hard coefficients by integrating out the hard fluctuations and jet functions encoding the hard-collinear information. Resummation of large logarithms in the short-distance functions is then achieved via the standard renormalization-group approach. We further show that structures of the factorization formulae for fBπ+(q2) and fBπ0(q2) at large hadronic recoil from QCD light-cone sum rules match that derived in QCD factorization. In particular, we perform an exploratory phenomenological analysis of B→π form factors, paying attention to various sources of perturbative and systematic uncertainties, and extract |Vub|=(3.05−0.38+0.54|th.±0.09|exp.)×10−3 with the inverse moment of the B-meson distribution amplitude ϕB+(ω) determined by reproducing fBπ+(q2=0) obtained from the light-cone sum rules with π distribution amplitudes. Furthermore, we present the invariant-mass distributions of the lepton pair for B→πℓνℓ (ℓ=μ,τ) in the whole kinematic region. Finally, we discuss non-valence Fock state contributions to the B→π form factors fBπ+(q2) and fBπ0(q2) in brief.

Precision calculations for supersymmetric Higgs bosons

Recent progress is presented on higher-order calculations for the mass spectrum of Higgs particles in the CP-conserving and CP-violating MSSM, covering diagrammatic two-loop calculations for neutral and charged Higgs bosons as well as all-order resummation of large logarithms arising from the strong and Yukawa coupling sectors.

Scale evolution of gluon TMDPDFs

By applying the effective field theory machinery we factorize the transverse momentum spectrum of Higgs boson production, where the main hadronic quantities are the gluon transverse momentum dependent parton distribution functions (TMDPDFs). We properly define those quantities, showing explicitly, in the case of an unpolarized hadron, that they are free from rapidity divergences, and extract their evolution properties. It turns out that the evolution for all eight (un-)polarized leading-twist gluon TMDPDFs is driven by the same evolution kernel, for which we derive the necessary ingredients to obtain a resummation of large logarithms at next-tonext-to-leading-logarithmic accuracy. We make predictions for the contribution of linearly polarized gluons to the Higgs boson qT -spectrum.

Effective field theory for Higgs boson plus jet production

We use an effective field theory (EFT) which includes all possible gluon-Higgs dimension-5 and dimension-7 operators to study Higgs boson plus jet production in next-to-leading order QCD. The EFT sheds light on the effect of a finite top quark mass as well as any Beyond-the-Standard Model (BSM) modifications of Higgs-gluon effective couplings. In the gluon channel, the accuracy of the heavy-top approximation for differential distributions arises from the non-interference between the helicity amplitudes of the G^3 h and G^2 h operators in the m_h < p_T limit at lowest order. One dimension-7 operator involving quark bilinears, however, contributes significantly at high p_T, and potentially offers a channel for seeing BSM effects. One-loop renormalization of these operators is determined, allowing resummation of large logarithms via renormalization group running. NLO numerical results at the LHC are presented, which include O(1/m_t^2) contributions in the SM limit.

The quark beam function at two loops

In differential measurements at a hadron collider, collinear initial-state radiation is described by process-independent beam functions. They are the field-theoretic analog of initial-state parton showers. Depending on the measured observable they are differential in the virtuality and/or transverse momentum of the colliding partons in addition to the usual longitudinal momentum fraction. Perturbatively, the beam functions can be calculated by matching them onto standard quark and gluon parton distribution functions. We calculate the inclusive virtuality-dependent quark beam function at NNLO, which is relevant for any observables probing the virtuality of the incoming partons, including N-jettiness and beam thrust. For such observables, our results are an important ingredient in the resummation of large logarithms at N3LL order, and provide all contributions enhanced by collinear t-channel singularities at NNLO for quark-initiated processes in analytic form. We perform the calculation in both Feynman and axial gauge and use two different methods to evaluate the discontinuity of the two-loop Feynman diagrams, providing nontrivial checks of the calculation. As part of our results we reproduce the known two-loop QCD splitting functions and confirm at two loops that the virtuality-dependent beam and final-state jet functions have the same anomalous dimension.

Probing the low transverse momentum domain of Z production with novel variables

The measurement of the low transverse momentum region of vector boson production in Drell-Yan processes has long been invaluable to testing our knowledge of QCD dynamics both beyond fixed-order in perturbation theory as well as in the non-perturbative region. Recently the DØ collaboration have introduced novel variables which lead to improved measurements compared to the case of the standard Q T variable. To complement this improvement on the experimental side, we develop here a complete phenomenological study dedicated in particular to the new ϕ* variable. We compare our study, which contains the state-of-the-art next-to-next-to-leading resummation of large logarithms and a smooth matching to the full next-to-leading order $ \left( {\mathcal{O}\left( {\alpha_s^2} \right)} \right) $ result, to the experimental data and find excellent agreement over essentially the entire range of ϕ*, even without direct inclusion of non-perturbative effects. We comment on our findings and on the potential for future studies to constrain non-perturbative behaviour.

QCD predictions for new variables to study dilepton transverse momenta at hadron colliders

The D0 Collaboration has recently introduced new variables, aT and ϕ⁎ to more accurately probe the low QT domain of Z boson production at hadron colliders than had been previously possible through a direct study of the QT distribution. The comparison of such accurate data to precise theoretical predictions from QCD perturbation theory will yield important information on the ability of resummed QCD predictions as well as parton shower models to describe the low QT domain and should enable more stringent constraints on non-perturbative effects. In the present Letter we provide analytical predictions for the above mentioned variables, that contain resummation of large logarithms, including next-to-next-to-leading logarithmic (NNLL) terms, supplemented by exact O(αs2) next-to-leading order calculations from MCFM.

Resummation of large logarithms in γ*π0→ γ

In the collinear factorization of the form factor for the transition gamma*pi(0) -> gamma the hard part contains double log terms as In(2)x with x as the momentum fraction of partons from 0 to 1. A simple exponentiation for resummation leads to divergent results. We study the resummation of these In(2)x terms. We show that the In(2)x terms come partly from the light-cone wave function(LCWF) and partly from the form factor. We introduce a jet factor to factorize the In(2)x term in the form factor. To handel the In(2)x terms from the LCWF we introduce a nonstandard light-cone wave function(NLCWF) with the gauge links off the light-cone direction. An interesting relation between two wave function is found. With the introduced NLCWF and the jet factor we can re-factorize the form factor and obtain a new hard part which does not contain terms with In(2)x. Beside the renormalization scale p the introduced NLCWF and jet factor have extra scales to characterize their x-behaviors. Using the evolutions of the extra scales and the relation we can do the resummation perturbatively in sense that the LCWF is the only nonpertubative object in the resumed formula. Our results with some models of LCWF show that there is a significant difference between numerical predictions with the resummation and that without the resummation, and the resummed predictions can describe the experimental data.

Resummation of large logarithms within the method of effective charges

We show how the resummation of large logarithms can be incorporated into the method of effective charges. As an example this approach is applied to the event shape variables thrust and heavy-jet mass in e + e − annihilation. Whilst there are some problems with the behaviour of the effective charge in the two-jet region, smaller power corrections are required to fit the data compared to the standard approach.