Diffractive Processes at Next-to-Leading Order in the Dipole Picture

In this thesis, we calculate diffractive processes at next-to-leading order (NLO) in the high-energy limit, with an emphasis on exclusive vector meson production and inclusive diffraction in deep inelastic scattering (DIS). Calculations in the high-energy limit can be done using the dipole picture, the basics of which are briefly reviewed. This includes using the color-glass condensate effective field theory to describe the nonperturbative dipole-target scattering amplitude which appears in practically all calculations in the dipole picture. The universality of the dipole-target scattering amplitude at NLO is shown numerically, in the sense that the same dipole-target scattering amplitude can be used to describe the data in both massless and massive quark production in inclusive DIS, and also in diffractive processes where exclusive vector meson production is considered. The analytical NLO calculations of exclusive vector meson production and inclusive diffraction in DIS are also explained. Exclusive vector meson production is calculated in the nonrelativistic limit for heavy mesons and the limit of large photon virtuality for light mesons. Also, the importance of including relativistic corrections to the heavy vector meson wave function in exclusive vector meson production is considered. For inclusive diffraction in DIS, we focus on the NLO corrections to the final state and show how the divergences cancel.Comment: PhD thesis, introductory par

Complete calculation of exclusive heavy vector meson production at next-to-leading order in the dipole picture

Exclusive production of transversely polarized heavy vector mesons in deep inelastic scattering at high energy is calculated at next-to-leading order accuracy in the Color Glass Condensate framework. In addition to the first QCD correction proportional to the strong coupling constant alpha(s), we systematically also include the first relativistic correction proportional to the heavy quark velocity squared v(2). When combined with our previously published results for longitudinal vector meson production at next-to-leading order accuracy, these results make phenomenological calculations of heavy vector meson production possible at the order O(alpha(s)v(0), alpha(0)(s)v(2)). When applied to J/phi and Upsilon production at HERA and at the LHC, a good agreement between the next-to-leading order calculations and experimental data is found. Additionally, we demonstrate that vector meson production can provide additional constraints compared to structure function analyses when the nonperturbative initial condition for the Balitsky-Kovchegov evolution equation is extracted.Peer reviewe

Exclusive production of light vector mesons at next-to-leading order in the dipole picture

Exclusive production of light vector mesons in deep inelastic scattering is calculated at next-to-leading order in the dipole picture in the limit of high photon virtuality. The resulting expression is free of any divergences and suitable for numerical evaluations. The higher-order corrections are found to be numerically important, but they can be mostly captured by the nonperturbative fit parameters describing the initial condition for the small-x evolution of the dipole scattering amplitude. The vector meson production cross section is shown to depend only weakly on the meson distribution amplitude and the factorization scale. We also present phenomenological comparisons of our result to the existing exclusive ?? and ?? production data from HERA and find an excellent agreement at high virtualities.Peer reviewe

Exclusive production of light vector mesons at next-to-leading order in the dipole picture

Exclusive production of light vector mesons in deep inelastic scattering is calculated at next-to-leading order in the dipole picture in the limit of high photon virtuality. The resulting expression is free of any divergences and suitable for numerical evaluations. The higher-order corrections are found to be numerically important, but they can be mostly captured by the nonperturbative fit parameters describing the initial condition for the small-x evolution of the dipole scattering amplitude. The vector meson production cross section is shown to depend only weakly on the meson distribution amplitude and the factorization scale. We also present phenomenological comparisons of our result to the existing exclusive ?? and ?? production data from HERA and find an excellent agreement at high virtualities.Peer reviewe

Exclusive heavy vector meson production at next-to-leading order in the dipole picture

We calculate exclusive production of a longitudinally polarized heavy vector meson at next-to-leading order in the dipole picture. The large quark mass allows us to separately include both the first QCD correction proportional to the coupling constant alpha(s), and the first relativistic correction suppressed by the quark velocity v(2). Both of these corrections are found to be numerically important in J/psi production. The results obtained are directly suitable for phenomenological calculations. We also demonstrate how vector meson production provides complementary information to structure function analyses when one extracts the initial condition for the energy evolution of the proton small-x structure. (C) 2021 The Author(s). Published by Elsevier B.V.Peer reviewe

Higher-order corrections to exclusive heavy vector meson production

We present results for higher-order corrections to exclusive $\mathrm{J}/\psi$ production. This includes the first relativistic correction of order $v^2$ in quark velocity, and next-to-leading order corrections in $\alpha_s$ for longitudinally polarized production. The relativistic corrections are found to be important for a good description of the HERA data, especially at small values of the photon virtuality. The next-to-leading order results for longitudinal production are evaluated numerically. We also demonstrate how the vector meson production provides complementary information to the structure functions for extracting the initial condition for the small-$x$ evolution of the dipole-proton scattering amplitude.Comment: Submission to SciPost, 6 pages, 2 figure

Initial Stages 2021

Exclusive vector meson production is a powerful process to probe the gluonic structure of protons and nuclei at small Bjorken-$x$, and it also makes it possible to study the geometry of the nuclei in the transverse plane. An accurate description of the process requires us to use a vector meson light front wave function that correctly represents the meson. Currently, the light front wave function is not fully understood and for heavy vector mesons the used light front wave functions are mostly either phenomenological or fully nonrelativistic. We present our recent work [1] where we develop a new method to compute a light front wave function for heavy vector mesons based on long distance matrix elements constrained by decay width analyses in the Non Relativistic QCD framework. Our approach provides a systematic expansion of the wave function in quark velocity. The first relativistic correction included in our calculation is found to be significant, and crucial for a good description of the HERA exclusive $J/\Psi$-production data. When looking at cross section ratios between nuclear and proton targets, the wave function dependence does not cancel out exactly. In particular, the fully nonrelativistic limit is found not to be a reliable approximation even in this ratio. The important role of the Melosh rotation to express the rest frame wave function on the light front is illustrated. [1] T. Lappi, H. Mäntysaari and J. Penttala, arXiv:2006.02830 [hep-ph], accepted for publication in Phys. Rev.

Heavy quarkonia in non-relativistic quantum chromodynamics

Quarkonium-hiukkaset ovat saman makulajin kvarkki-antikvarkkiparista muodostuvia sidottuja tiloja. Tässä työssä käydään läpi epärelativistiseksi kvanttiväridynamiikaksi kutsuttavaa efektiivistä kenttäteoriaa, jota voidaan käyttää raskaiden kvarkkien muodostamien quarkonium-hiukkasten kuvaamiseen. Teoriaa kuvaava Lagrangen funktio johdetaan alimmissa kertaluvuissa, ja sitä käytetään johtamaan eri operaattorien skaalautuminen kvarkin nopeuden suhteen. Skaalaussääntöjen avulla johdetaan tämän jälkeen arviot eri Fock-tilojen suuruuksille quarkoniumissa. Orbitaalista kvanttilukua L=0 vastaavien quarkonium-hiukkasten hajoamisleveydet kirjoitetaan potenssisarjana kvarkin nopeuden suhteen. Hajoamisleveyksien yhtälöissä esiintyy tuntemattomia vakioita, jotka esiintyvät myös quarkoniumin inklusiivisen tuoton vaikutusaloissa. Näiden tuntemattomien vakioiden yhteys quarkoniumin aaltofunktioon käydään myös läpi. Hajoamisleveyksien lausekkeista saatavia arvoja tutkitaan eri kertaluvuissa kvarkin nopeuden suhteen. Havaitaan, että potenssisarjan suppeneminen on hidasta ja riippuu hajoamisprosessista.Quarkonia are bound states of a quark-antiquark pair having the same flavour. In this work, we go through how the effective field theory of non-relativistic quantum chromodynamics (NRQCD) can be used to describe quarkonia formed by heavy quarks. The Lagrangian describing the theory is derived at lowest orders and used to determine the velocity-scaling of different operators. The velocity-scaling rules are then used to estimate contributions of different Fock states in quarkonia. We then describe the decay of S-wave quarkonia by writing the decay widths as power series in the velocity of the quark. The equations for the decay widths contain unknown constants that also appear in the inclusive cross sections of quarkonium production, and their connection to the quarkonium wave function is also shown. The results for the decay widths at different orders of the quark velocity are studied. It is found that the convergence of the power series is slow, with the convergence depending on the decay process

Diffractive Processes at Next-to-Leading Order in the Dipole Picture

Diffraktiiviset prosessit ovat korkean energian rajalla sensitiivisiä kohdehiukkasen gluonijakaumalle, mistä johtuen niiden avulla voidaan tutkia kohdetta kvanttiväridynamiikan epälineaarisessa alueessa. Näiden epälineaaristen ilmiöiden odotetaan johtavan gluonisaturaatioon, jota voidaan kuvata luontevasti värilasikondensaatiksi kutsutun efektiivisen kenttäteorian avulla. Vaikka saatavilla olevassa kokeellisessa datassa onkin vahvoja viitteitä gluonisaturaatiosta, yksiselitteistä merkkiä saturaatiosta ei ole havaittu. Tämän vuoksi on tärkeää parantaa saturaatiolle sensitiivisten prosessien teoreettista ymmärrystä, jotta pystytään löytämään selkeitä eroja kvanttiväridynamiikan lineaarisen ja epälineaarisen alueen ennusteiden väillä. Diffraktiivisten prosessien laskeminen korkeammille kertaluvuille häiriöteoriassa on osa tätä kehitystä. Tässä väitöskirjassa lasketaan diffraktiivisia prosesseja korkean energian rajalla alinta seuraavassa kertaluvussa, ja näistä tarkastellaan erityisesti eksklusiivista vektorimesonituottoa sekä inklusiivista diffraktiota syvässä epäelastisessa sironnassa. Korkean energian rajalla laskuissa voidaan käyttää niin sanottua dipolikuvaa, jonka perusteet käydään lyhyesti läpi. Tähän kuuluu värilasikondensaattiteorian käyttäminen epäperturbatiivisen dipoliamplitudin kuvaamiseen, joka esiintyy oleellisesti kaikissa dipolikuvassa tehdyissä laskuissa. Dipoliamplitudin universaalius alinta seuraavassa kertaluvussa näytetään numeerisesti siinä mielessä, että samaa dipoliamplitudia voidaan käyttää sekä massattomien ja massallisten kvarkkien tuoton kuvaamiseen inklusiivisessa syvässä epäelastisessa sironnassa että diffraktiivisissa prosesseissa, joista tarkastellaan eksklusiivista vektorimesonituottoa. Eksklusiivisen vektorimesonituoton ja inklusiivisen diffraktion analyyttinen lasku alinta seuraavassa kertaluvussa käydään myös läpi. Näistä eksklusiivinen vektorimesonituotto lasketaan epärelativisella rajalla raskaiden mesonien tapauksessa ja suuren fotonin virtualiteetin rajalla kevyiden mesonien tapauksessa. Tämän lisäksi tarkastellaan relativististen korjausten tärkeyttä raskaiden mesonien aaltofunktioon tässä prosessissa. Inklusiivisen diffraktion tapauksessa keskitytään erityisesti alinta seuraavan kertaluvun korjauksiin lopputilassa sekä osoitetaan divergenssien kumoutuminen.Diffractive processes are very sensitive to the target’s gluon distribution in the highenergy limit, making them a good candidate for probing the target in the nonlinear region of quantum chromodynamics. The nonlinear effects are expected to eventually lead to gluon saturation which is naturally described in the color-glass condensate (CGC) effective field theory. While there are strong hints of gluon saturation in the currently available data, no unambiguous signal has been observed. It is then important to improve the theoretical understanding of processes sensitive to saturation to find a clear difference between predictions from the linear and nonlinear regions of QCD. This includes calculating diffractive processes beyond the leading order in perturbation theory. In this thesis, we calculate diffractive processes at next-to-leading order (NLO) in the high-energy limit, with an emphasis on exclusive vector meson production and inclusive diffraction in deep inelastic scattering (DIS). Calculations in the highenergy limit can be done using the dipole picture, the basics of which are briefly reviewed. This includes using the CGC effective field theory to describe the nonperturbative dipole-target scattering amplitude which appears in practically all calculations in the dipole picture. The universality of the dipole-target scattering amplitude at NLO is shown numerically, in the sense that the same dipole-target scattering amplitude can be used to describe the data in both massless and massive quark production in inclusive DIS, and also in diffractive processes where exclusive vector meson production is considered. The analytical NLO calculations of exclusive vector meson production and inclusive diffraction in DIS are also explained. Exclusive vector meson production is calculated in the nonrelativistic limit for heavy mesons and the limit of large photon virtuality for light mesons. Also, the importance of including relativistic corrections to the heavy vector meson wave function in exclusive vector meson production is considered. For inclusive diffraction in DIS, we focus on the NLO corrections to the final state and show how the divergences cancel

Charmonium-hiukkasen energiatilojen määrittäminen Cornellin potentiaalin avulla

Tämän tutkielman tarkoituksena on tutkia charmonium-hiukkasen energiatiloja Cornellin potentiaalin avulla. Potentiaalin parametrit määritetään kokeellisesti mitattujen energiatilojen ja hajoamisleveyksien avulla. Hajoamisleveyksille käytetään QCD:n häiriöteorian antamia lausekkeita. Parametrien ratkaisemista varten kirjoitetaan charmoniumin Schrödingerin yhtälö dimensiottomasta muodossa, jolloin Schrödingerin yhtälön ratkaiseminen on mahdollista tehdä numeerisesti. Aaltofunktion ja ominaisenergioiden numeerisessa ratkaisemisessa käytetään MATLAB-ohjelmaa. Ratkaistuilla parametrien arvoilla on laskettu charmoniumin alimpien energiatilojen massoja, jotka yleisesti ottaen noudattavat mitattujen ja muiden teoreettisten mallien antamien massojen arvoja. Tämän perusteella Cornellin potentiaali toimii hyvin charmoniumin karkeana mallina, jonka avulla voidaan selittää mitattujen energiatilojen rakennetta.The purpose of this thesis is to examine the energy states of the charmonium particle using the Cornell potential. The potential contains unknown parameters which have to be determined in order to use the potential. This is done by using the measured energy states and decay widths. The decay widths are made coincide with the theoretical values calculated from formulas given by perturbative QCD. In order to solve for the parameters, the Schrödinger equation for the charmonium particle is written in a dimensionless form allowing a numerical solution of the Schrödinger equation. The corresponding wave function and the eigenenergies are solved numerically using a MATLAB program. The solved parameter values are then used to calculate the masses of the lowest energy states. These masses generally agree with the measured values and the values calculated from other theoretical models. Based on this, the Cornell potential works well as a rough model for charmonium and can be used to explain the structure of the measured energy states