Next-to-leading Order Contributions Research Articles

Back-to-back inclusive dijets in DIS at small x: Sudakov suppression and gluon saturation at NLO

Back-to-back dijet cross-sections in deeply inelastic scattering (DIS) at small xBj are suppressed by many-body multiple scattering and screening effects arising from gluon saturation at high parton densities. They are similarly sensitive in these kinematics to large Sudakov logarithms from soft gluon radiation. Uncovering novel physics in this DIS channel therefore requires understanding the interplay of the two phenomena. In this work, we compute the small xBj inclusive dijet DIS cross-section in back-to-back kinematics at next-to-leading order (NLO) in the Color Glass Condensate effective field theory (CGC EFT). Our result includes, for the first time, all real and virtual NLO contributions to the impact factor. These include all Sudakov double and single logarithm contributions, as well as all other finite mathcal{O} (αs) terms that contribute at this order. We demonstrate explicitly that resummations of small x and Sudakov logarithms can be performed simultaneously in the CGC EFT. This requires that the JIMWLK kernel for small x evolution of the Weizsäcker-Williams (WW) gluon distribution satisfies a kinematic constraint imposed by lifetime ordering of successive gluon emissions; the corresponding modifications to the kernel, corresponding to resummations of large double transverse logarithms, are precisely of the type required to stabilize JIMWLK evolution beyond leading logarithmicaccuracy. We compute the azimuthal harmonics of the NLO back-to-back distributions and show their sensitivity to both the unpolarized and linearly polarized WW gluon distributions. Finally, we discuss how TMD factorization is broken by an emergent saturation scale at small x.

Charmless two-body B meson decays in the perturbative QCD factorization approach* *Supported by the National Science Foundation of China (11805060, 11975112, 12105028, 12070131001, 11775117), the Joint Large-Scale Scientific Facility Funds of the NSFC and CAS (U1932110), the Natural Science Foundation of Jiangsu Province (BK20200980) and the National Key Research and Development Program of China (2020YFA0406400)

The perturbative quantum chromodynamics (PQCD) approach based on factorization has resulted in great achievements in the QCD calculation of hadronic B decays. By regulating the endpoint divergence by the transverse momentum of quarks in the propagators, one can perform the perturbation calculation for various diagrams, including annihilation type diagrams. In this paper, we review the current status of the PQCD factorization calculation of two-body charmless U decays up to next-to-leading order (NLO) QCD corrections. Two new power suppressed terms in the decaying amplitudes are also considered. Using universal input (non-perturbative) parameters, we collect the branching ratios and asymmetry parameters of all charmless two body B decays, which are calculated in the PQCD approach up to NLO. The results are compared with those of the QCD factorization approach, soft-collinear effective theory approach, and current experimental measurements. For most of the considered B meson decays, the PQCD results for branching ratios agree well with those of other approaches and experimental data. The PQCD predictions for the asymmetry parameters of many of the decay channels do not agree with those of other approaches but have better agreement with experimental data. The longstanding puzzle regarding the pattern of the direct CP asymmetries of penguin-dominated decays can be understood after the inclusion of NLO contributions in PQCD. The NLO corrections and power suppressed terms play an important role in color suppressed and pure annihilation type B decay modes. These rare decays are more sensitive to different types of corrections, providing an opportunity to examine the factorization approach with more precise experimental measurements.

Exclusive J/ψ photoproduction in ultraperipheral Pb+Pb collisions at the CERN Large Hadron Collider calculated at next-to-leading order perturbative QCD

We present the first next-to-leading-order (NLO) perturbative QCD (pQCD) study of rapidity-differential cross sections of coherent exclusive photoproduction of $J/\psi$ mesons in heavy-ion ultraperipheral collisions (UPCs) at the LHC, $d\sigma/dy(\text{Pb} + \text{Pb} \rightarrow \text{Pb} + J/\psi + \text{Pb})$. For this, we account for the photon-nucleon NLO cross sections at the forward limit, the $t$ dependence using a standard nuclear form factor, and the photon fluxes of the colliding nuclei. Approximating the generalized parton distributions with their forward-limit parton distribution functions (PDFs), we quantify the NLO contributions in the cross sections, show that the real part of the amplitude and quark-PDF contributions must not be neglected, quantify the uncertainties arising from the scale-choice and PDFs, and compare our results with ALICE, CMS and LHCb $J/\psi$ photoproduction data in Pb+Pb UPCs, exclusive $J/\psi$ photoproduction data from HERA, and LHCb data in p+p. The scale dependence in $d\sigma/dy(\text{Pb} + \text{Pb} \rightarrow \text{Pb} + J/\psi + \text{Pb})$ is significant, but we can find a scale-choice that reproduces the Pb+Pb UPC data both at 2.76 and 5.02 TeV collision energies. This process has traditionally been suggested to be a direct probe of nuclear gluon distributions. We show that the situation changes rather dramatically from LO to NLO: the NLO cross sections reflect the nuclear effects of both gluons and quarks in a complicated manner where the relative signs of the LO and NLO terms in the amplitude play a significant role.

Next-to-leading order scalar contributions to μ→e conversion

Within a class of models in which lepton flavor violation is induced dominantly by scalar particle exchanges, we estimate the $\ensuremath{\mu}\ensuremath{\rightarrow}e$ conversion rate in several nuclei. We include next-to-leading order (NLO) terms in the one- and two-nucleon interactions in chiral effective theory, rectifying some incorrect results in the previous literature. We provide an uncertainty budget for the conversion rates and we find that NLO contributions affect the amplitudes at the level of $10%$, which could be larger than the uncertainty on the leading order couplings, dominated by the strange and nonstrange nucleon sigma terms. We study the implications of our results for testing Higgs-mediated charged lepton flavor violation (CLFV) in the future by combining results from various experimental searches, such as $\ensuremath{\mu}\ensuremath{\rightarrow}e$ conversion in multiple target nuclei and $\ensuremath{\mu}\ensuremath{\rightarrow}e\ensuremath{\gamma}$.

QCD pressure: Renormalization group optimized perturbation theory confronts lattice

The quark contribution to the QCD pressure, ${P}_{q}$, is evaluated up to next-to-leading order (NLO) within the renormalization group optimized perturbation theory (RGOPT) resummation approach. To evaluate the complete QCD pressure we simply add the perturbative NLO contribution from massless gluons to the resummed ${P}_{q}$. Despite this unsophisticated approximation our results for $P={P}_{q}+{P}_{g}$ at the central scale $M\ensuremath{\sim}2\ensuremath{\pi}T$ show a remarkable agreement with lattice predictions for $0.25\ensuremath{\lesssim}T\ensuremath{\lesssim}1\text{ }\text{ }\mathrm{GeV}$. We also show that by being imbued with RG properties, the RGOPT produces a drastic reduction of the embarrassing remnant scale dependence that plagues both standard thermal perturbative QCD and hard thermal loop perturbation theory applications.

NLO effects for Ω QQQ baryons in QCD Sum Rules * *Supported in part by the National Natural Science Foundation of China (11875071, 11975029) and the National Key Research and Development Program of China (2020YFA0406400)

We study the triply heavy baryons in the QCD sum rules by performing the first calculation of the next-to-leading order (NLO) contribution to the perturbative QCD part of the correlation functions. Compared with the leading order (LO) result, the NLO contribution is found to be very important to the . This is because the NLO not only results in a large correction but also reduces the parameter dependence, making the Borel platform more distinct, especially for the in the scheme, where the platform appears only at NLO but not at LO. Particularly, owing to the inclusion of the NLO contribution, the renormalization schemes ( and On-Shell) dependence and the scale dependence are significantly reduced. Consequently, after including the NLO contribution to the perturbative part in the QCD sum rules, the masses are estimated to be GeV for and GeV for , where the results are obtained at with errors including those from the variation of the renormalization scale μ in the range . A careful study of the μ dependence in a wider range is further performed, which shows that the LO results are very sensitive to the choice of μ whereas the NLO results are considerably better. In addition to the result, a more stable value, (4.75-4.80) GeV, for the mass is found in the range of , which should be viewed as a more relevant prediction in our NLO approach because of dependence.

S=−1 meson-baryon interaction and the role of isospin filtering processes

A study of the meson-baryon interaction in the $S=-1$ sector is performed, employing a chiral SU(3) lagrangian up to next-to-leading order (NLO) and implementing unitarization in coupled channels. The model is constrained by a large set of experimental data, paying a especial attention to processes that are sensitive to the NLO contributions, such as the $K^- p\to K^+\Xi^-, K^0\Xi^0$ reactions. The consideration of additional cross sections in single isospin channels, $K^-p\to \eta\Lambda, \eta\Sigma$, has been found to provide more homogeneous and reliable values of the low-energy constants, the stability of which has also been tested by the inclusion of explicit resonant terms. Predictions for new isospin filtering processes, like the $I=1$ $K^0_L p \to K^+ \Xi^0$ reaction that could be measured at the proposed secondary $K^0_L$ beam at Jlab, or the weak decay of the $\Lambda_b$ into a $J/\Psi$ and different meson-baryon pairs in $I=0$, available at LHCb, are presented. The measurement of such reactions would put valuable constraints on the chiral models describing the $S=-1$ meson-baryon interaction.

Constraining unintegrated gluon distributions from inclusive photon production in proton–proton collisions at the LHC

We compute the leading order (LO) qg→qγ and next-to-leading order (NLO) gg→qq¯γ contributions to inclusive photon production in proton–proton (p+p) collisions at the LHC. These channels provide the dominant contribution at LO and NLO for photon transverse momenta kγ⊥ corresponding to momentum fractions of x≤0.01 in the colliding protons. Our computations, performed in the dilute–dense framework of the Color Glass Condensate effective field theory (CGC EFT), show that the NLO contribution dominates at small-x because it is sensitive to k⊥-dependent unintegrated gluon distributions in both of the protons. We predict a maximal 10% modification of the cross section at low kγ⊥ as a direct consequence of the violation of k⊥-factorization. The coherence effects responsible for this modification are enhanced in nuclei and can be identified from inclusive photon measurements in proton–nucleus collisions. We provide numerical results for the isolated inclusive photon cross section for kγ⊥≤20 GeV in p+p collisions that can be tested in the future at the LHC.

NLO effects for doubly heavy baryons in QCD sum rules

With the QCD sum rules approach, we study the newly discovered doubly heavy baryon $\Xi_{cc}^{++}$. We analytically calculate the next-to-leading order (NLO) contribution to the perturbative part of $J^{P} = \frac{1}{2}^{+}$ baryon current with two identical heavy quarks, and then reanalyze the mass of $\Xi_{cc}^{++}$ at the NLO level. We find that the NLO correction significantly improves both scheme dependence and scale dependence, whereas it is hard to control these theoretical uncertainties at leading order. With the NLO contribution, the baryon mass is estimated to be $m_{\Xi_{cc}^{++}} = 3.66_{-0.10}^{+0.08} \text{~GeV}$, which is consistent with the LHCb measurement.

Diffractive scattering on the deuteron projectile in the NLO: triple interaction of reggeized gluons

High-mass diffractive production of protons on the deuteron target is studied in the next-to-leading order (NLO) of the perturbative QCD in the BFKL approach. The non-trivial part of the NLO contributions coming from the triple interactions of the exchanged reggeons is considered. Analytic formulas are presented and shown to be infrared free and so are ready for practical calculation.

Heavy flavor azimuthal correlations in cold nuclear matter

Background: It has been proposed that the azimuthal distributions of heavy flavor quark-antiquark pairs may be modified in the medium of a heavy-ion collision. Purpose: This work tests this proposition through next-to-leading order (NLO) calculations of the azimuthal distribution, $d\sigma/d\phi$, including transverse momentum broadening, employing $<k_T^2>$ and fragmentation in exclusive $Q \bar Q$ pair production. While these studies were done for $p+p$, $p + \bar p$ and $p+$Pb collisions, understanding azimuthal angle correlations between heavy quarks in these smaller, colder systems is important for their interpretation in heavy-ion collisions. Methods: First, single inclusive $p_T$ distributions calculated with the exclusive HVQMNR code are compared to those calculated in the fixed-order next-to-leading logarithm approach. Next the azimuthal distributions are calculated and sensitivities to $<k_T^2>$, $p_T$ cut, and rapidity are studied at $\sqrt{s} = 7$ TeV. Finally, calculations are compared to $Q \bar Q$ data in elementary $p+p$ and $p + \bar p$ collisions at $\sqrt{s} = 7$ TeV and 1.96 TeV as well as to the nuclear modification factor $R_{p {\rm Pb}}(p_T)$ in $p+$Pb collisions at $\sqrt{s_{NN}} = 5.02$ TeV measured by ALICE. Results: The low $p_T$ ($p_T < 10$ GeV) azimuthal distributions are very sensitive to the $k_T$ broadening and rather insensitive to the fragmentation function. The NLO contributions can result in an enhancement at $\phi \sim 0$ absent any other effects. Agreement with the data was found to be good. Conclusions: The NLO calculations, assuming collinear factorization and introducing $k_T$ broadening, result in significant modifications of the azimuthal distribution at low $p_T$ which must be taken into account in calculations of these distributions in heavy-ion collisions.

Coherent μ−e conversion at next-to-leading order

We analyze next-to-leading order (NLO) corrections and uncertainties for coherent $\mu-e$ conversion . The analysis is general but numerical results focus on ${}^{27}\textrm{Al}$, which will be used in the Mu2E experiment. We obtain a simple expression for the branching ratio in terms of Wilson coefficients associated with possible physics beyond the Standard Model and a set of model-independent parameters determined solely by Standard Model dynamics. For scalar-mediated conversion, we find that NLO two-nucleon contributions can significantly decrease the branching ratio, potentially reducing the rate by as much as 50%. The pion-nucleon $\sigma$-term and quark masses give the dominant sources of parametric uncertainty in this case. For vector-mediated conversion, the impact of NLO contributions is considerably less severe, while the present theoretical uncertainties are comparable to parametric uncertainties.

Rho-pion transition form factors in the kT -factorization formalism revisited

We revisit the evaluations for the spacelike and timelike $\rho \pi$ transition form factors $F_{\rho\pi}(Q^2)$ and $G_{\rho\pi}(Q^2)$ with the inclusion of the the next-to-leading order (NLO) QCD contributions in the framework of the $k_T$ factorization theorem. The infrared divergence is regularized by the transversal momentum carried by external valence quarks, and ultimately absorbed into the meson wave functions. In the region of $ Q^2 \leqslant 2 \, \textrm{GeV}^2 $, where PQCD factorization apporach applicable, the NLO contribution can bring no larger than $ 35\%$ enhancement to the spacelike form factor $F_{\rho\pi}(Q^2)$. For the timelike form factor derived under the kinematic exchanging symmetry, this contribution is also under control when the momentum transfer squared is large enough. We also prolong our prediction into the small $Q^2$ region by taking the Lattice QCD results into account, and subsequently obtain the coupling $g_{\rho\pi\gamma} = G_{\rho\pi}(0)=0.596$.

Λ N → NN EFT potentials and hypertriton non-mesonic weak decay

The potential for the Λ N → NN weak transition, the main responsible for the non-mesonic weak decay of hypernuclei, has been developed within the framework of effective field theory (EFT) up to next-to-leading order (NLO). The leading order (LO) and NLO contributions have been calculated in both momentum and coordinate space, and have been organised into the different operators which mediate the N → NN transition. We compare the ranges of the one-meson and two-pion exchanges for each operator. The non-mesonic weak decay of the hypertriton has been computed within the plane-wave approximation using the LO weak potential and modern strong EFT NN potentials. Formally, two methods to calculate the final state interactions among the decay products are presented. We briefly comment on the calculation of the mesonic weak decay.

The NLO Chiral Lagrangian from the meson-baryon interaction in the S = −1 sector.

The present study consists of establishing the role played by the next-to-leading order (NLO) terms as well as the Born terms of a chiral SU(3) Lagrangian in the S = −1 meson-baryon interaction. This necessarily leads to the determination of the low energy constants present in the NLO contribution, which have not been fixed so far. In order to constrain them, we employ scattering data from the K−p interaction, paying a special attention to reactions and to isospin filtering processes such as . In addition, the stability and the accuracy of all the parameters involved in the model have been examined by means of the inclusion of high spin hyperonic resonances.

I = 2 ππ scattering phase shift from the HAL QCD method with the LapH smearing

Physical observables, such as the scattering phase shifts and the binding energies, calculated from the non-local HAL QCD potential do not depend on the sink operators used to define the potential. This is called the scheme independence of the HAL QCD method. In practical applications, the derivative expansion of the non-local potential is employed, so that physical observables may receive some scheme dependence at given order of the expansion. In this paper, we compare the $I=2$ $\pi\pi$ scattering phase shifts obtained in the point-sink scheme (the standard scheme in the HAL QCD method) and the smeared-sink scheme (the LapH smearing newly introduced in the HAL QCD method). Although potentials in different schemes have different forms as expected, we find that, for reasonably small smearing size, the resultant scattering phase shifts agree with each other if the next-to-leading order (NLO) term is taken into account. We also find that the HAL QCD potential in the point-sink scheme has negligible NLO term for wide range of energies, which implies a good convergence of the derivative expansion in this case, while the potential in the smeared-sink scheme has non-negligible NLO contribution. Implication of this observation to the future studies of resonance channels (such as the $I=0$ and $1$ $\pi\pi$ scatterings) with smeared all-to-all propagators is briefly discussed. All computations in this paper have been performed at the lattice spacing $a\simeq 0.12$ fm ($1/a \simeq 1.6$ GeV) on a $16^3\times 32$ lattice with the pion mass $m_\pi\simeq 870$ MeV.

Production ofHHHandHHV(V=γ,Z)at the hadron colliders

We consider the production of two Higgs bosons in association with a gauge boson or another Higgs boson at the hadron colliders. We compute the cross sections and distributions for the processes $ p p \to H H H $ and $H H Z$ within the standard model. In particular, we compute the gluon-gluon fusion one-loop contributions mediated via heavy quarks in the loop. It is the leading order contribution to $ p p \to H H H $ process. To the process $ p p \to H H Z $, it is next-to-next-to-leading-order (NNLO) contribution in QCD coupling. We also compare this contribution to the next-to-leading-order (NLO) QCD contribution to this process. The NNLO contribution can be similar to NLO contribution at the Large Hadron Collider (LHC), and significantly more at higher center-of-mass energy machines. We also study new physics effects in these processes by considering $ttH, HHH, HHHH, HZZ$, and $HHZZ$ interactions as anomalous. The anomalous couplings can enhance the cross sections significantly. The $gg \to HHH$ process is specially sensitive to anomalous trilinear Higgs boson self-coupling. For the $gg \to HHZ$ process, there is some modest dependence on anomalous $HZZ$ couplings.

Towards next-to-leading order corrections to the heavy quark potential in the effective string theory

We present our calculation of the non-relativistic corrections to the heavy quark-antiquark potential up to leading and next-to-leading order (NLO) via the effective string theory (EST). Full systematics of effective field theory (EFT) are discussed in order for including the NLO contribution that arises in the EST. We also show how the number of dimensionful parameters arising from the EST are reduced by the constraints between the Wilson coeffcients from non-relativistic EFTs for QCD.

The chiral S = −1 meson–baryon interaction with new constraints on the NLO contributions

We present a study of the S=−1 meson–baryon interaction, employing a chiral SU(3) Lagrangian up to next-to-leading order (NLO) and implementing unitarization in coupled channels. The parameters of the model have been fitted to a large set of experimental scattering data in different two-body channels, to threshold branching ratios, and to the precise SIDDHARTA value of the energy shift and width of kaonic hidrogen. In contrast to other groups, we have taken into consideration the K−p→K+Ξ−,K0Ξ0 reaction data, since we found in a previous work to be especially sensitive to the NLO parameters of the chiral Lagrangian. In the present work we also include the Born terms, which usually have very little effect, and find them to be non-negligible in the K−p→KΞ channels, correspondingly causing significant modifications to the NLO parameters. We furthermore show that the importance of the Born terms becomes more visible in the isospin projected amplitudes of the K−p→KΞ reactions. The measurement of processes that filter single isospin components, like the KL0p→K+Ξ0 reaction that could be measured at the proposed secondary KL0 beam at Jlab, would put valuable constraints on the chiral models describing the meson–baryon interaction in the S=−1 sector.

Exclusive J/ψ and ϒ photoproduction and the low x gluon

We study exclusive vector meson photoproduction, with or ϒ, at next-to-leading order (NLO) in collinear factorisation, in order to examine what may be learnt about the gluon distribution at very low x. We examine the factorisation scale dependence of the predictions. We argue that, using knowledge of the NLO corrections, terms enhanced by a large can be reabsorbed in the LO part by a choice of the factorisation scale. (In these exclusive processes ξ takes the role of Bjorken-x.) Then, the scale dependence coming from the remaining NLO contributions has no enhancements. As a result, we find that predictions for the amplitude of ϒ production are stable to within about ±15%. This will allow data for the exclusive process at the Large Hadron Collider (LHC), particularly from LHCb, to be included in global parton analyses to constrain the gluon parton distribution function (PDF) down to Moreover, the study of exclusive photoproduction indicates that the gluon density found in the recent global PDF analyses is too small at low x and low scales.