To separate the energetic photons produced in hard scattering processes from those from other sources, measurements impose isolation requirements which restrict the hadronic radiation inside a cone around the photon. In this paper, we perform a detailed factorization analysis of the QCD effects associated with photon isolation. We show that for small cone radius $R$, photon isolation effects can be captured by a fragmentation function describing the decay of a parton into a photon accompanied by hadronic radiation. We compute this fragmentation function for different isolation criteria and solve the associated renormalization group equations to resum logarithms of $R$. For small isolation energy, the cone fragmentation function factorizes further, into collinear functions describing energetic quarks and gluons near the cone boundary and functions encoding their soft radiation emitted into the cone. Based on this factorization we also resum the non-global logarithms of the ratio of the photon energy and the isolation energy, so that we control all logarithmically enhanced terms in the cross section. Finally, we provide a simple formula to convert NNLO cross section results from smooth-cone isolation to fixed-cone isolation.
Models of Weakly Interacting Massive Particles (WIMPs) specified at the electroweak scale are systematically matched to effective theories at hadronic scales where WIMP-nucleus scattering observables are evaluated. Anomalous dimensions and heavy quark threshold matching conditions are computed for the complete basis of lowest-dimension effective operators involving quarks and gluons. The resulting QCD renormalization group evolution equations are solved. The status of relevant hadronic matrix elements is reviewed and phenomenological illustrations are given, including details for the computati…
The ultraviolet and rapidity divergences of transverse-momentum dependent parton distribution functions with lightlike and transverse gauge links is studied, also incorporating a soft eikonal factor. We find that in the light-cone gauge with $q^-$-independent pole prescriptions extra divergences appear which amount, at one-loop, to a cusp-like anomalous dimension. We show that such contributions are absent when the Mandelstam-Leibbrandt prescription is used. In the first case, the soft factor cancels the anomalous-dimension defect, while in the second case its ultraviolet-divergent part reduce…
Isolated photons at hadron colliders are defined by permitting only a limited amount of hadronic energy inside a fixed-size cone around the candidate photon direction. This isolation criterion admits contributions from collinear photon radiation off QCD partons and from parton-to-photon fragmentation processes. We compute the NNLO QCD corrections to isolated photon and photon-plus-jet production, including these two contributions. Our newly derived results allow us to reproduce the isolation prescription used in the experimental measurements, performing detailed comparisons with data from the …
We develop a model to compute high-energy reactions of hadrons and photons. The perturbative interaction is described by gluon exchange and the non-perturbative interaction by the stochastic vacuum model which leads to quark-confinement in dipoles via a string of color fields. We study the QCD structure of the dipole-dipole scattering in momentum space focussing especially on interactions between strings. We represent the string as a collection of stringless dipoles, show confinement effects in high-energy scattering and calculate unintegrated gluon distributions of hadrons and photons. In the…
We investigate the nuclear and the quark matter at finite real chemical potential ($μ_\mathrm{R}$) and low temperature from the viewpoint of the canonical sectors constructed via the imaginary chemical potential region. Based on the large $N_\mathrm{c}$ estimation, where $N_\mathrm{c}$ is the number of color, we can discuss the confinement-deconfinement nature at finite $μ_\mathrm{R}$ from the canonical sectors. We found the expectation that the sharp change of canonical sectors at $μ_\mathrm{R} \sim M_\mathrm{B}/N_\mathrm{c}$, where $M_\mathrm{B}$ is the lowest baryon mass, is happen in the l…
QCD at finite densities of heavy quarks is investigated using the density-of-states method. The phase factor expectation value of the quark determinant is calculated to unprecedented precision as a function of the chemical potential. Results are validated using those from a reweighting approach where the latter can produce a significant signal-to-noise ratio. We confirm the particle-hole symmetry at low temperatures, find a strong sign problem at intermediate values of the chemical potential, and an inverse Silver Blaze feature for chemical potentials close to the onset value: here, the phase …
We consider the production of prompt-photon pairs at the LHC and we report on a study of QCD radiative corrections up to the next-to-next-to-leading order (NNLO). We present a detailed comparison of next-to-leading order (NLO) results obtained within the standard and smooth cone isolation criteria, by studying the dependence on the isolation parameters. We highlight the role of different partonic subprocesses within the two isolation criteria, and we show that they produce large radiative corrections for both criteria. Smooth cone isolation is a consistent procedure to compute QCD radiative co…
We present an updated next-to-leading order analysis of the B -> X_s gamma branching ratio and photon spectrum, including consistently the effects of Fermi motion in the heavy-quark expansion. For the Standard Model, we obtain B(B -> X_s gamma) = (2.57+-0.26^{+0.31}_{-0.36}) * 10^{-4} for the integral over the high-energy part of the photon spectrum with E_gamma^{lab} > 2.2 GeV, where the first error reflects the uncertainty in the input parameters, and the second one the uncertainty in the calculation of Fermi motion. This prediction agrees with the CLEO measurement of the same quantity withi…
We present the NLO QCD corrections to diphoton plus jet production at hadron colliders. Our calculation includes contributions from the fragmentation of a hadronic jet into a highly energetic photon, and consequently allows the implementation of arbitrary infrared-safe photon isolation definitions. We compare different photon isolation criteria and perform a detailed study of the dependence of the diphoton plus jet cross section on the photon isolation parameters.
By employing the perturbative QCD (PQCD) factorization approach, we calculated the branching ratios, CP-violating asymmetries, the longitudinal and transverse polarization fractions and other physical observables of the thirteen charmless hadronic $\bar{B}^0_s \to V V $ decays with the inclusion of all currently known next-to-leading order (NLO) contributions. We focused on the examination of the effects of all those currently known NLO contributions and found that: (a) for the measured decays $\bar{ B}_s^0 \to ϕϕ, K^{*0} ϕ,\bar K^{*0} K^{*0}$ and $ρ^0 ϕ$, the NLO contributions can provide $\s…
We present the next-to-leading order QCD corrections to the production of a photon pair in association with one or two jets. This class of processes constitutes an important background for Higgs physics at the LHC. For the one jet process we include photon fragmentation contributions and perform a comparison between different photon isolation criteria and various isolation parameters. The two jet calculation has been performed using a smooth cone isolation criterion. We find that the NLO QCD corrections are substantial and can lead to distortions of differential distributions.
In this paper we perform a comprehensive study of the four $B \to K \etap$ decays in the pQCD factorization approach. We calculate the CP-averaged branching ratios and CP-violating asymmetries of $B \to K\etap$ decays in the ordinary $η$-$\etar$, the $η$-$\etar$-$G$, and the $η$-$\etar$-$G$-$η_c$ mixing schemes. Besides the full LO contributions, all currently known NLO contributions to $B \to K \etap$ decays in the pQCD approach are taken into account. From our calculations and phenomenological analysis, we find the following. (a) The NLO contributions in general can provide significant enhan…
We consider the production of isolated prompt photons in hadronic collisions. We present a general discussion in QCD perturbation theory of the isolation criterion used by hadron collider experiments. The isolation criterion is implemented in a computer programme of the Monte Carlo type, which evaluates the production cross section at next-to-leading order accuracy in perturbative QCD. The calculation includes both the direct and the fragmentation components of the cross section, without any approximation of the dependence on the radius R of the isolation cone. We examine the scale dependence …
We propose a strategy to access the $q\bar{q}$ component of the $ρ$ resonance in lattice QCD. Through a mixed action formalism (overlap valence on domain wall sea), the energy of the $q\bar{q}$ component is derived at different valence quark masses, and shows a linear dependence on $m_π^2$. The slope is determined to be $c_1=0.505(3)\,{\rm GeV}^{-1}$, from which the valence $πρ$ sigma term is extracted to be $σ_{πρ}^{(\rm val)}=9.82(6)$ MeV using the Feynman-Hellman theorem. At the physical pion mass, the mass of the $q\bar{q}$ component is interpolated to be $m_ρ=775.9\pm 6.0\pm 1.8$ MeV, whi…
We present for the first time a model-independent anatomy of the ratio $\varepsilon'/\varepsilon$ in the context of the $ΔS = 1$ effective theory with operators invariant under QCD and QED and in the context of the Standard Model Effective Field Theory (SMEFT) with the operators invariant under the full SM gauge group. Our goal is to identify the new physics scenarios that are probed by this ratio and which could help to explain a possible deviation from the SM that is hinted by the data. To this end we derive a master formula for $\varepsilon'/\varepsilon$, which can be applied to any theory …
The use of the differential gluon structure function of the proton ${\cal F}(x,Q^{2})$ introduced by Fadin, Kuraev and Lipatov in 1975 is called upon in many applications of small-x QCD. We report here the first determination of ${\cal F}(x,Q^{2})$ from the experimental data on the small-x proton structure function $F_{2p}(x,Q^{2})$. We give convenient parameterizations for ${\cal F}(x,Q^{2})$ based partly on the available DGLAP evolution fits (GRV, CTEQ & MRS) to parton distribution functions and on realistic extrapolations into soft region. We discuss an impact of soft gluons on various obse…
Precision measurements of diphoton distributions at the LHC display some tension with theory predictions, obtained at next-to-next-to-leading order (NNLO) in QCD. We revisit the theoretical uncertainties arising from the approximation of the experimental photon isolation by smooth-cone isolation, and from the choice of functional form for the renormalisation and factorisation scales. We find that the resulting variations are substantial overall, and enhanced in certain regions. We discuss the infrared sensitivity at the cone boundaries in cone-based isolation in related distributions. Finally,…
We first examine the scaling argument for a renormalization-group (RG) analysis applied to a system subject to the dimensional reduction in strong magnetic fields, and discuss the fact that a four-Fermi operator of the low-energy excitations is marginal irrespective of the strength of the coupling constant in underlying theories. We then construct a scale-dependent effective four-Fermi interaction as a result of screened photon exchanges at weak coupling, and establish the RG method appropriately including the screening effect, in which the RG evolution from ultraviolet to infrared scales is s…
By employing the perturbative QCD (PQCD) factorization approach, we made a systematic investigation for the CP-averaged branching ratios and the CP-violating asymmetries of the thirteen $\bar{B}^0_s \to PP $ decays ( here $P=(π,K, η, η^{\prime})$) with the inclusion of all currently known next-to-leading order (NLO) contributions, and compared our results with the measured values or the theoretical predictions from other different approaches. We focused on the examination of the effects of the NLO contributions and found the following points: (a) for $\bar{B}_s^0 \to (K^0 \bar{K}^0, K^+ K^-, η…
In this paper, we will make systematic calculations for the branching ratios and the CP-violating asymmetries of the twenty one $\bar{B}^0_s \to PV $ decays by employing the perturbative QCD (PQCD) factorization approach. Besides the full leading-order (LO) contributions, all currently known next-to-leading order (NLO) contributions are taken into account. We found numerically that: (a) the NLO contributions can provide $\sim 40\%$ enhancement to the LO PQCD predictions for ${\cal B}(\bar{B}_s^0 \to K^0 \bar{K}^{*0})$ and $ {\cal B}(\bar{B}_s^0 \to K^{\pm}K^{*\mp})$, or a $\sim 37\% $ reductio…
We calculate the CP-averaged branching ratios and CP-violating asymmetries for the two-body charmless hadronic decays $Λ_b \to p π, pK$ in the perturbative QCD (pQCD) approach to lowest order in $α_s$. The baryon distribution amplitudes involved in the factorization formulae are considered to the leading twist accuracy and the distribution amplitudes of the proton are expanded to the next-to-leading conformal spin (i.e., "P" -waves), the moments of which are determined from QCD sum rules. Our work shows that the contributions from the factorizable diagrams in $Λ_b \to p π, pK$ decays are much …
Using next-to-leading-log calculations of Higgs production and hadronic two photon production, a signal and background study in the intermediate mass range of the Higgs boson is done for $\sqrt{s}=$ 40 and 14 TeV. The effects of realistic cuts, including photon isolation, are examined.
I present a definition of the cross section for the production of an isolated photon plus $n$ jets which only depends upon direct photon production, and it is independent of the parton-to-photon fragmentation contribution. This prescription, based on a modified cone approach which implements the isolation condition in a smooth way, treats in the same way quarks and gluons and can be directly applied to experimental data in hadron-hadron, photon-hadron and $\epem$ collisions. The case of several, isolated photons in the final state can also be dealt with in the very same way.
The cross section for photoproduction of an isolated prompt photon in association with a jet is studied in Next-to-Leading Order. The kinematics are those appropriate for the DESY $ep$ collider HERA. The effects on the cross section of various experimental cuts including isolation cuts on the photon is examined. Comparisons with the ZEUS preliminary data using two parametrizations of the photon structure function is made, and good agreement is found. The data is not yet precise enough to make a distinction between various models for the photon structure function.
We describe the calculation of the next-to-next-to-leading order (NNLO) QCD corrections to isolated photon and photon-plus-jet production, and discuss how the experimental hadron-level photon definition and isolation criteria can be approximated in the theoretical parton-level calculation. The NNLO corrections lead to a considerable reduction of the theory uncertainty on the predictions, typically to less than five per cent, and enable an improved description of experimental measurements from ATLAS and CMS.
We discuss the isolation of prompt photons in hadronic collisions by means of narrow isolation cones and the QCD computation of the corresponding cross sections. We reconsider the occurence of large perturbative terms with logarithmic dependence on the cone size and their impact on the fragmentation scale dependence. We cure the apparent perturbative violation of unitarity for small cone sizes, which had been noticed earlier in next-to-leading-order (NLO) calculations, by resumming the leading logarithmic dependence on the cone size. We discuss possible implications regarding the implementatio…
We present a complete order $α_s$ analysis of the process $p p\to γγ+ X$ with polarized initial states, previously studied by us with leading order structure functions. We include in our calculation new sets of parton densities evolved in NLO QCD, such as those of Gehrmann and Stirling and of Glück et al., which incorporate the new anomalous dimensions of Mertig and Van Neerven in the evolution equation. A detailed phenomenological analysis is also given which includes the photon isolation. Our results indicate that the asymmetries, although not very large, should be substantial enough at RHIC…
The NLO QCD calculation for the photoproduction of the isolated photon with a large pT at the HERA ep collider is presented. The single resolved photon contribution and the QCD corrections of order alpha_s to the Born term are consistently included. The NNLO contributions, the box and the double resolved photon subprocesses, are sizeable and are taken into account in addition. The importance of the isolation cut, as well as the influence of other experimental cuts on pT and final photon rapidity distributions are discussed in detail. The investigation of the renormalization scale dependence is…
The NLO QCD calculation for the photoproduction of the isolated photon with a large $p_T$ at the HERA $ep$ collider is presented. The single resolved photon contribution and the QCD corrections of order $α_s$ to the Born term are consistently included. The sizeable NNLO contributions, the box and the double resolved photon subprocesses, are taken into account in addition. The importance of the isolation cut, as well as the influence of other experimental cuts on the p_T and rapidity eta_gamma distributions are discussed in detail. Results are compared with experimental data and with the differ…
A second order, $O(α^2_s)$, calculation in perturbative quantum chromodynamics of the two particle inclusive cross section is presented for the reaction $p +\bar{p}\rightarrow γ+ c + X$ for large values of the transverse momentum of the prompt photon and charm quark. The combination of analytic and Monte Carlo integration methods used here to perform phase-space integrations facilitates imposition of photon isolation restrictions and other selections of relevance in experiments. Differential distributions are provided for various observables. Positive correlations in rapidity are predicted.
We discuss different approaches to photon isolation in fixed-order calculations and present a new next-to-next-to-leading order (NNLO) QCD calculation of $R_{13/8}^γ$, the ratio of the inclusive isolated photon cross section at 8 TeV and 13 TeV, differential in the photon transverse momentum, which was recently measured by the ATLAS collaboration.
The cross section for inclusive prompt photon production with polarized hadron beams is calculated at order $αα_s^2$ using the phase space slicing or analytic/Monte Carlo method. Isolation cuts are placed on the photon and the results are compared to a previous fully analytic calculation. Numerical results for the isolated cross section are presented for for $\vec{p}\vec{p}\rightarrow γ+X$ at RHIC center-of-mass energies with plausible isolation parameters using the most modern polarized parton densities evolved in next-to-leading order QCD. The perturbative stability of the asymmetries and sc…
Initial- and final-state rescattering, neglected in the parton model, have a profound effect in QCD hard-scattering reactions, predicting single-spin asymmetries, diffractive deep inelastic scattering, diffractive hard hadronic reactions, the breakdown of the Lam Tung relation in Drell-Yan reactions, and nuclear shadowing and non-universal antishadowing--leading-twist physics not incorporated in the light-front wavefunctions of the target computed in isolation. I also discuss the use of diffraction to materialize the Fock states of a hadronic projectile and test QCD color transparency, and ano…
Results for the first test of the ``crude'' QCD continuum model, commonly used in QCD Sum Rule analyses, are presented for baryon correlation functions. The QCD continuum model is found to effectively account for excited state contributions to the short-time regime of two-point correlation functions and allows the isolation of ground state properties. Confusion in the literature surrounding the physics represented in point-to-point correlation functions is also addressed. These results justify the use of the ``crude'' QCD continuum model and lend credence to the results of rigorous QCD Sum Rul…
We present a full next-to-leading order (NLO) QCD corrections to diphoton production at the hadron colliders in both standard model and ADD model. The invariant mass and rapidity distributions of the diphotons are obtained using a semi-analytical two cut-off phase space slicing method which allows for a successful numerical implementation of various kinematical cuts used in the experiments. The fragmentation photons are systematically removed using smooth-cone-isolation cuts on the photons. The NLO QCD corrections not only stabilise the perturbative predictions but also enhance the production …
The next-to-leading-order electroweak corrections to $pp\to l^+l^-/\barνν+γ+X$ production, including all off-shell effects of intermediate Z bosons in the complex-mass scheme, are calculated for LHC energies, revealing the typically expected large corrections of tens of percent in the TeV range. Contributions from quark-photon and photon-photon initial states are taken into account as well, but their impact is found to be moderate or small. Moreover, the known next-to-leading-order QCD corrections are reproduced. In order to separate hard photons from jets, both a quark-to-photon fragmentation…
We discuss effects induced by beyond leading order contributions to photon pair production. We point out that next to leading order contributions to the fragmentation component of the signal lead to a change in the shape of distributions. This is already mildly visible in present Tevatron data though stringent isolation criteria tend to suppress the fragmentation component considerably. We expect the effect to be experimentally confirmed in future data samples with higher statistics which would serve as a precision test for QCD.
We compute the QCD corrections to the gluon fusion subprocess gg to gamma gamma, which forms an important component of the background to the search for a light Higgs boson at the LHC. We study the dependence of the improved pp to gamma gamma X background calculation on the factorization and renormalization scales, on various choices for photon isolation cuts, and on the rapidities of the photons. We also investigate ways to enhance the statistical significance of the Higgs signal in the di-photon channel.
An event generator for diphoton ($γγ$) production in hadron collisions that includes associated jet production up to two jets has been developed using a subtraction method based on the LLL subtraction. The parton shower (PS) simulation to restore the subtracted divergent components involves both QED and QCD radiation, and QED radiation at very small $Q^{2}$ are simulated by referring to a fragmentation function (FF). The PS/FF simulation has the ability to enforce the radiation of a given number of energetic photons. The generated events can be fed to PYTHIA to obtain particle (hadron)-level e…
I illustrate how to define an isolated-photon cross section which is independent of the parton-to-photon fragmentation contribution, it is infrared safe to all orders in perturbative QCD, and it is exclusive in the kinematical variables of the photon and of the accompanying jets. This isolation prescription is applicable to any kind of polarized or unpolarized hard collisions. It can also be used without any modifications in the case of two or more isolated photons in the final state. I present results for one-photon production in hadronic collisions, and I compare them with existing results o…
It is usually assumed -- following the parton model -- that the leading-twist structure functions measured in deep inelastic lepton-proton scattering are simply the probability distributions for finding quarks and gluons in the target nucleon. In fact, gluon exchange between the outgoing quarks and the target spectators effects the leading-twist structure functions in a profound way, leading to diffractive leptoproduction processes, shadowing and antishadowing of nuclear structure functions, and target spin asymmetries, physics not incorporated in the light-front wavefunctions of the target co…
The theoretical description of photon production at particle colliders combines direct photon radiation and fragmentation processes, which can not be separated from each other for definitions of photon isolation used in experimental measurements. The theoretical description of these processes must account for collinear parton-photon configurations, retaining the dependence on the photon momentum fraction, and includes the parton-to-photon fragmentation functions. We extend the antenna subtraction method to include photon fragmentation processes up to next-to-next-to-leading order (NNLO) in QCD…
Techniques to compute hadron properties from lattice QCD rely upon the limit of long time separation. For baryons, the signal-to-noise problem often restricts one to time separations that are not ideally long, and for which couplings to excited states can obstruct the isolation of ground-state baryon properties. We consider excited-state contamination in nucleon two- and three-point functions. Using chiral perturbation theory, we determine couplings to pion-nucleon and pion-delta excited states. In two-point functions, these contributions are small, in accordance with general properties of the…
