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Academic literature on the topic 'Renormalon'

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Published: 9 March 2023
Last updated: 10 March 2023

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Journal articles on the topic "Renormalon"

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LOEWE, M., and C. VALENZUELA. "THERMAL RENORMALONS IN SCALAR FIELD THEORY." Modern Physics Letters A 15, no. 18 (June 14, 2000): 1181–90. http://dx.doi.org/10.1142/s0217732300001481.

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In the framework of the scalar theory gϕ4, we explore the occurrence of thermal renormalons, i.e. temperature-dependent singularities in the Borel plane. The discussion of a particular renormalon type diagram at finite temperature, using Thermofield Dynamics, allows us to establish that these singularities actually get a temperature dependence. This dependence appears in the residues of the poles, the positions of the poles remain unchanged with temperature.
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Benitez-Rathgeb, Miguel A., Diogo Boito, André H. Hoang, and Matthias Jamin. "Reconciling the FOPT and CIPT Predictions for τ Hadronic Spectral Function Moments." EPJ Web of Conferences 274 (2022): 06005. http://dx.doi.org/10.1051/epjconf/202227406005.

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Recently it has been clarified by Hoang and Regner that the longstanding discrepancy between the CIPT and FOPT expansion approaches in αs determinations from the τ hadronic spectral function moments has been caused by an inconsistency of CIPT with the standard OPE approach. This inconsistency arises in the presence of IR renormalons in the underlying Adler function and is numerically dominated by the dimension-4 gluon condensate renormalon. In this talk we report on an approach to reconcile the CIPT based on a perturbative definition of a renormalon-free and scale-invariant gluon condensate scheme, called RF GC scheme. The scheme implies perturbative subtractions which eliminate the CIPT inconsistency for all practical applications of the τ hadronic spectral function moments. The scheme depends on the gluon condensate renormalon norm Ng as an independent input and on an IR subtraction scale R. We discuss three different approaches to determine Ng which yield consistent results and we apply the RF GC scheme in two full-fledged phenomenological αs determinations based on the truncated OPE and the duality violation model approach. In the RF GC scheme the long-standing CIPT-FOPT discrepancy problem is gone and the CIPT and FOPT αs determinations can be consistently combined.
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LEE, TAEKOON. "THE NATURE OF POWER CORRECTIONS IN LARGE-β0 APPROXIMATION." Modern Physics Letters A 19, no. 31 (October 10, 2004): 2371–76. http://dx.doi.org/10.1142/s0217732304015300.

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We investigate the nature of power corrections and infrared renormalon singularities in large-β0 approximation. We argue that the power correction associated with a renormalon pole singularity should appear at O(1), in contrast to the renormalon ambiguity appearing at O(1/β0), and give an explanation why the leading order renormalon singularities are generically poles.
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Takaura, Hiromasa. "Determination of HQET nonperturbative matrix elements with renormalon subtraction using Fourier transform." EPJ Web of Conferences 274 (2022): 03003. http://dx.doi.org/10.1051/epjconf/202227403003.

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As higher order perturbative series are available, it is becoming necessary to include nonperturbative effects in QCD calculations using the OPE. In order to systematically determine nonperturbative effects and to incorporate them into theoretical calculations, the renormalon problem should be resolved. We use a renormalon subtraction method utilizing Fourier transform to determine nonperturbative matrix elements of HQET, ⊼ and μ2π. This is the first determination performed with subtraction of the u = 1 renormalon.
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Vainshtein, A. I., and V. I. Zakharov. "Ultraviolet renormalon reexamined." Physical Review D 54, no. 6 (September 15, 1996): 4039–48. http://dx.doi.org/10.1103/physrevd.54.4039.

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Martinelli, Guido, Matthias Neubert, and Chris T. Sachrajda. "The invisible renormalon." Nuclear Physics B 461, no. 1-2 (February 1996): 238–58. http://dx.doi.org/10.1016/0550-3213(95)00613-3.

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Vainshtein, A. I., and V. I. Zakharov. "Ultraviolet-Renormalon Calculus." Physical Review Letters 73, no. 9 (August 29, 1994): 1207–10. http://dx.doi.org/10.1103/physrevlett.73.1207.

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Vainshtein, A. I., and V. I. Zakharov. "Ultraviolet-Renormalon Calculus." Physical Review Letters 75, no. 19 (November 6, 1995): 3588. http://dx.doi.org/10.1103/physrevlett.75.3588.

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Gambino, Paolo, and Alberto Sirlin. "Renormalon contributions to Δϱ." Physics Letters B 355, no. 1-2 (July 1995): 295–300. http://dx.doi.org/10.1016/0370-2693(95)00741-3.

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DI CECIO, G., and G. PAFFUTI. "SOME PROPERTIES OF RENORMALONS IN GAUGE THEORIES." International Journal of Modern Physics A 10, no. 10 (April 20, 1995): 1449–63. http://dx.doi.org/10.1142/s0217751x95000693.

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We find the explicit operatorial form of renormalon type singularities in Abelian gauge theory. Local operators of dimension six take care of the first UV renormalon; nonlocal operators are needed for IR singularities. In the effective Lagrangian constructed with these operators nonlocal imaginary parts appearing in the usual perturbative expansion at large orders are canceled.
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Dissertations / Theses on the topic "Renormalon"

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Mirjalili, Abolfazl. "Scale dependence and renormalon-inspired resummations for some QCD observables." Thesis, Durham University, 2001. http://etheses.dur.ac.uk/3825/.

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Since the advent of Quantum Field Theory (QFT) in the late 1940's, perturbation theory has become one of the most successful means of extracting phenomenologically useful information from QFT. In the ever-increasing enthusiasm for new phenomenological predictions, the mechanics of perturbation theory itself have taken a back seat. It is in this light that this thesis aims to investigate some of the more fundamental properties of perturbation theory. In the first part of this thesis, we develop the idea, suggested by C.J.Maxwell, that at any given order of Feynman diagram calculation for a QCD observable all renormalization group (RG)-predictable terms should be resummed to all-orders. This "complete" RG-improvement (CORGI) serves to separate the perturbation series into infinite subsets of terms which when summed are renormalization scheme (RS)-invariant. Crucially all ultraviolet logarithms involving the dimensionful parameter, Q, on which the observable depends are resummed, thereby building the correct Q-dependence. We extend this idea, and show for moments of leptoproduction structure functions that all dependence on the renormahzation and factorization scales disappears provided that all the ultraviolet logarithms involving the physical energy scale Q are completely resummed. The approach is closely related to Grunberg's method of Effective Charges. In the second part, we perform an all-orders resummation of the QCD Adler D-function for the vector correlator, in which the portion of perturbative coefficients containing the leading power of b, the first beta-function coefficient, is resummed to all-orders. To avoid a renormalization scale dependence when we match the resummation to the exactly known next-to-leading order (NLO), and next-NLO (NNLO) results, we employ the Complete Renormalization Group Improvement (CORGI) approach , removing all dependence on the renormalization scale. We can also obtain fixed-order CORGI results. Including suitable weight-functions we can numerically integrate these results for the D-function in the complex energy plane to obtain so-called "contour-improved" results for the ratio R and its tau decay analogue Rr. We use the difference between the all-orders and fixed-order (NNLO) results to estimate the uncertainty in αs(M2/z) extracted from Rr measurements, and find αs(M2/z) = 0.120±0.002. We also estimate the corresponding uncertainty in a{Ml) arising from hadronic corrections by considering the uncertainty in R(s), in the low-energy region, and compare with other estimates. Analogous resummations are also given for the scalar correlator. As an adjunct to these studies we show how fixed-order contour-improved results can be obtained analytically in closed form at the two-loop level in terms of the Lambert W-function and hypergeometric functions.
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Pascalius, Lai Ho Shie. "N³LO-renormalon-inspired resummations and fully analytic infra-red freezing in perturbative QCD." Thesis, Durham University, 2013. http://etheses.dur.ac.uk/10570/.

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We make use of the recent calculation of d3 by Baikov, Chetrykin and Kuhn of N3LO QCD vacuum polarization to analyze the inclusive tau-decay ratio Rτ . We perform an all-orders resummation of the QCD Adler D function for the vector correlator, in which the part of perturbative coefficients containing the leading power of b, the first QCD beta-function equation coefficient, is resummed to all-orders. We match the resummation to the exactly known next-to-leading order (NLO), next-NLO (N2LO) and next-N2LO (N3LO) results, we employ the Complete Renormalization Group Improvement (CORGI) approach in which all RG-predictable ultra-violet logarithms are resummed to all-orders, removing all dependence on the renormalization scale. Hence the NLO, N2LO and N3LO CORGI result can be obtained and compared with the “leading b” all-orders CORGI result. Using an appropriate weight function, we can numerically integrate these results for the Adler D function in the complex energy plane to obtain so-called "contour-improved" results for the ratio Re+e− and its tau-decay analogue Rτ . A table showing the differences of αs(M2τ ) and αs(M2 Z) extracted from NLO, N2LO and N3LO CORGI as well as all-orders CORGI results were made, together with αS(M2τ) and αS(M2Z) extracted directly from Fixed-Order-Perturbation Theory at NLO, N2LO and N3LO. We also compared the ALEPH data for Rτ(s) with the all-orders CORGI result fitted at s = m2τ. We then go on to study the analyticity in energy of the leading one-chain term in a skeleton expansion for QCD observables. We show that by adding suitable non-perturbative terms in the energy regions Q2 > Λ2 and Q2 < Λ2 (where Q2 = Λ2 is the Landau pole of the one loop coupling), one can obtain an expression for the observables which is a holomorphic function of Q2, for which all derivatives are finite and continuous at Q2 = Λ2. This function is uniquely constrained by the requirement of asymptotic freedom, and the finiteness as Q2→0, up to addition of a non-perturbative holomorphic function. This full analyticity replaces the piecewise analyticity and continuity exhibited by the leading one-chain term itself. Using The Analytic Perturbation Theory (APT) Euclidean functions introduced by Shirkov and collaborators, we finally matched the equations K(L)PT +K(L)NP and U(L)PT + U(L)NP with a resummation of coefficients extracted from their Borel Transform multiplied by the APT Euclidean functions in the one loop case. For D(L)PT + D(L)NP , it is shown that it freezes to 2/b. Considering the GDH Sum Rule, we construct an analytic function which fits well with data from Jefferson Laboratory (JLab) for 0 < Q < 2GeV.
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LIMATOLA, GIOVANNI. "Infrared Linear Renormalons in Collider Processes." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2023. https://hdl.handle.net/10281/402371.

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Al fine di descrivere appropriatamente le osservabili studiate tramite collisori adronici e/o leptonici, risulta cruciale una corretta comprensione delle correzioni non perturbative (che si manifestano come correzioni di potenza), lineari nel rapporto tra una scala di energia non perturbativa e la scala caratteristica del processo. Utilizzando un modello abeliano ricerchiamo tali effetti nella distribuzione in momento trasverso di un bosone Z prodotto con un jet in collisioni adroniche, essendo questa una delle osservabili meglio misurate presso LHC. La presenza delle correzioni non perturbative di cui sopra impedirebbe di raggiungere la precisione sperimentale, anche considerando ordini superiori nello sviluppo perturbativo. Non avendo individuato alcuna correzione di questo tipo tramite tecniche semi numeriche, abbiamo scelto di adottare un approccio più rigoroso dal punto di vista teorico, fornendo una spiegazione attorno al manifestarsi di tali correzioni di potenza. Tale comprensione teorica è stata applicata allo studio delle variabili di shape in annichilazione $e^+e^-$, con particolare attenzione allo studio del C-parametro e del thrust, e ottenendo per tali osservabili una stima delle correzioni non perturbative nella regione dei tre jet per la prima volta. In tale lavoro è stata altresì ottenuta un'espressione fattorizzata per le correzioni non perturbative per alcune osservabili, con un termine dipendente dalla variazione dell'osservabile a seguito dell'emissione di un partone soffice, e un termine costante e universale, proporzionale al cosiddetto Milan factor. Tali osservabili sono ampiamente utilizzate al fine di estrarre valori della costante di interazione forte $\alpha_s$ e costituiscono il contesto ideale al fine di compiere studi di QCD perturbativa. È dunque estremamente importante ottenere stime affidabili delle correzioni non perturbative nell'intera regione di spazio delle fasi rilevante per i fit di $\alpha_s$.
Understanding leading non-perturbative corrections, showing up as linear power corrections, is crucial to properly describe observables both at lepton and hadron colliders. Using an abelian model, we examine these effects for the transverse momentum distribution of a $Z$ boson produced in association with a jet in hadronic collisions, that is one of the cleanest LHC observables, where the presence of leading non-perturbative corrections would spoil the chance to reach the current experimental accuracy, even considering higher orders in the perturbative expansion. As we did not find any such corrections exploiting semi-numerical techniques, we looked for a rigorous field-theoretical derivation of them, and explain under which circumstances linear power corrections can arise. We apply our theoretical understanding to the study of event-shape observables in $e^+e^-$ annihilation, focusing in particular on $C$-parameter and thrust, and obtaining for them an estimate of non-perturbative corrections in the three-jet region for the first time. We also derived a factorisation formula for non-perturbative corrections, with a term describing the change of the shape variable when a soft parton is emitted, and a constant universal factor, proportional to the so-called Milan factor. These observables are routinely used to extract the strong coupling constant $\alpha_s$ and they constitute an environment to test perturbative QCD. It is then extremely important to obtain reliable estimates of non-perturbative corrections in the whole kinematic region relevant for the $\alpha_s$ fits.
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FERRARIO, RAVASIO SILVIA. "Top-mass observables: all-orders behaviour, renormalons and NLO + Parton Shower effects." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2019. http://hdl.handle.net/10281/241087.

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In questa tesi ci concentriamo su alcuni aspetti teorici che concernono la determinazione della massa del quark top ($ m_t $), problema che persiste nell'essere altamente controverso. Generalmente, per misurare la massa del top, sono necessarie predizioni teoriche dipendenti da $m_t$. Il parametro $m_t$ coincide con la massa fisica, che è collegata alla massa nuda attraverso una procedura di rinormalizzazione. Sono possibili diversi schemi di rinormalizzazione per la massa e il più naturale sembra essere quello della massa polo. Tuttavia, nel caso di oggetti colorati, la massa polo contiene rinormaloni di origine infrarossa, i quali si manifestano come coefficienti che crescono fattorialmente, rovinando la convergenza delle serie perturbativa e portando ad ambigutá di ordine $\Lambda_{\rm QCD}$. D’altro canto, shemi di massa come l’$\overline{\rm MS}$ sono liberi da questi rinormaloni. Fortunatamente, l’ambiguitá rinormalonica sembra essere ben al di sotto dell’errore sistematico quotato per le misurazioni della massa polo. Pertanto questo tipo di determinazione è ancora affidabile. Nella prima parte della tesi studiamo la presenza di rinormaloni in osservabili che possono essere impiegate per la determinazione della massa del top. Consideriamo un modello semplificato per descrivere il processo $W^* \to t \bar{b} \to W b \bar{b}$. Il calcolo è eseguito nel limite in cui il numero di sapori dei quark leggeri $n_f$ è molto grande, utilizzando un nuovo metodo con cui è possibile valutare numericamente una generica osservabile all’ordine $\alpha_s(\alpha_s n_f)^n$ per ogni valore di $n$. Due sono le sorgenti di rinormaloni nelle nostre osservabile: l’uso della massa polo e la richiesta di tagli cinematici sui momenti dei jet. Per questo, predizioni ottenute nello schema polo sono comparate con quelle calcolate nello schema $\overline{\rm MS}$. Dalla nostra analisi risulta che la sezione d’urto senza tagli, se espressa in termini della massa $\overline{\rm MS}$, è libera da rinormaloni lineari, i quali appaiono però in ogni schema appena vengono introdotti dei tagli cinematici relativi al momento dei jet. Inoltre, la massa dei prodotti di decadimento del top è sempre affetta da rinormaloni lineari. L’energia del bosone $W$ ha un rinormalone in ogni schema nel limite in cui la larghezza di decadimento del top è zero, altrimenti, quando una larghezza finita è usata nel calcolo, tali rinormaloni sono assenti nello schema $\overline{\rm MS}$. Le determinazioni più precise della massa del top sono quelle dirette, ossia quelle basate sulla ricostruzione della cinematica dei prodotti di decadimento del top. Queste misure sono basate sull’uso di generatori di eventi Monte Carlo. I generatori che vengono utilizzati devono essere il più accurati possibili, onde evitare imprecisioni nella misura. A questo proposito, nella seconda parte della tesi confrontiamo diversi generatori NLO, implementati nel codice {\tt POWHEG BOX}, che differiscono per il livello di accuratezza impiegato nel descrivere il decadimento del top. Anche l’impatto dei programmi Monte Carlo che implementano la “parton shower”, e che quindi completano gli eventi generati da POWHEG BOX, è oggetto di studio in questa seconda parte della tesi. In particolare, noi ci focalizziamo sui programmi più usati, Pythia8.2 ed Herwig7.1, e presentiamo un metodo per interfacciarli a processi contenenti risonanze che possono emettere radiazione. Il paragone fra diversi generatori Monte Carlo che hanno formalmente lo stesso livello di accuratezza è infatti un passo obbligato verso una stima ragionevole dell’incertezza associata alla misurazione della massa del quark top.
In this thesis we focus on the theoretical subtleties of the top-quark mass ($m_t$) determination, issue which persists in being highly controversial. Typically, in order to infer the top mass, theoretical predictions dependent on $m_t$ are employed. The parameter $m_t$ is the physical mass, that is connected with the bare mass though a renormalization procedure. Several renormalization schemes are possible and the most natural seems to be the pole-mass one. However, the pole mass is not very well defined for a coloured object like the top quark. The pole mass is indeed affected by the presence of infrared renormalons. They manifest as factorially growing coefficients that spoil the convergence of the perturbative series, leading to ambiguities of order of $\Lambda_{\rm QCD}$. On the other hand, short-distance mass schemes, like the $\overline{\rm MS}$, are known to be free from such renormalons. Luckily, the renormalon ambiguity seems to be safely below the quoted systematic errors on the pole-mass determinations, so these measurements are still valuable. In the first part of the thesis, we investigate the presence of linear renormalons in observables that can be employed to determine the top mass. We considered a simplified toy model to describe $W^* \to t \bar{b} \to Wb \bar{b}$. The computation is carried out in the limit of a large number of flavours ($n_f$), using a new method that allows to easily evaluate any infrared safe observable at order $\alpha_s(\alpha_s n_f)^n$ for any $n$. The observables we consider are, in general, affected by two sources of renormalons: the pole-mass definition and the jet requirements. We compare and discuss the predictions obtained in the usual pole scheme with those computed in the $\overline{\rm MS}$ one. We find that the total cross section without cuts, when expressed in terms of the $\overline{\rm MS}$ mass, does not exhibit linear renormalons, but, as soon as selection cuts are introduced, jets-related linear renormalons arise in any mass scheme. In addition, we show that the reconstructed mass is affected by linear renormalons in any scheme. The average energy of the $W$ boson (that we consider as a simplified example of leptonic observable) has a renormalon in the narrow-width limit in any mass scheme, that is however screened at large orders for finite top widths, provided the top mass is in the $\overline{\rm MS}$ scheme. The most precise determinations of the top mass are the direct ones, i.e. those that rely upon the reconstruction of the kinematics of the top-decay products. Direct determinations are heavily based on the use of Monte Carlo event generators. The generators employed must be as much accurate as possible, in order not to introduce biases in the measurements. To this purpose, the second part of the thesis is devoted to the comparison of several NLO generators, implemented in the {\tt POWHEG BOX} framework, that differ by the level of accuracy employed to describe the top decay. The impact of the shower Monte Carlo programs, used to complete the NLO events generated by {\tt POWHEG BOX}, is also studied. In particular, we discuss the two most widely used shower Monte Carlo programs, i.e. {\tt Pythia 8.2} and \{\tt Herwig 7.1}, and we present a method to interface them with processes that contain decayed emitting resonances. The comparison of several Monte Carlo programs that have formally the same level of accuracy is, indeed, a mandatory step towards a sound estimate of the uncertainty associated with $m_t$.
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Miravitllas, Mas Ramon. "Asymptotic expansions, resurgence and large order behaviour of quantum chromodynamics." Doctoral thesis, Universitat Autònoma de Barcelona, 2019. http://hdl.handle.net/10803/667932.

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En les teories quàntiques de camps, les prediccions numèriques d’observables físics només es poden calcular amb expansions pertorbatives en potències de les constants d'acoblament, els paràmetres que determinen la força de les interaccions entre camps. Mentre que l’èxit predictiu de la teoria quàntica de camps no es pot negar, aquests càlculs pertorbatius estan plens de divergències. D’una banda, els coeficients de l’expansió pertorbativa es calculen a partir d’integrals de loops que són divergents la majoria de les vegades. Algunes d’aquestes divergències estan associades a termes no físics que es poden sostreure. En altres casos, s’aplica un procés de renormalització per cancelar aquestes divergències, però això suposa l'elecció d’un conveni teòric (escala i esquema) de la qual els observables físics no poden dependre. D’altra banda, un cop les integrals de loops han sigut renormalitzades, l’expansió resultant encara suma a una resposta infinita per tots els valors no nuls de la constant d'acoblament. Això succeeix perquè els coeficients de l’expansió creixent factorialment amb l’ordre. Tot i així, aquestes expansions es poden entendre com expansions asimptòtiques, que codifiquen el comportament de l’observable en el límit quan la constant d'acoblament s’acosta a zero, i l’observable es pot aproximar truncant l’expansió a un terme òptim. Aquest segon tipus de divergència no está limitat, de fet, a la teoria quàntica de camps, sinó que pot apareixer en diferents contextos de les matemàtiques i la física: per exemple, en expansions pertorbatives dels valors propis de l’energia d’un sistema de la mecànica quàntica, o com a solucions formals d’una equació diferencial. A la part I d’aquesta tesi, l’objecte principal d’estudi és la constant d'acoblament forta i les expansions pertorbatives d’observables físics a la quàntica chromodinàmica. Primer, discitum breument com les divergències de loops d’un gluó propagant-se a l’espai amb correccions quàntiques poden ser absorbides dins de la constant d'acoblament forta durant el procés de renormalització. Aquest procés, no obstant, implica el cost d’introduir dependències en l’escala i l’esquema dins la constant d'acoblament, per tant, aquesta no és un observable físic de la teoria. Això motiva una redefinició de la constant d'acoblament tal que la seva dependència en l’esquema es redueix a un sol paràmetre. Després utilitzem aquesta redefinició de la constant d'acoblament en anàlisis fenomenològics d’observables físics associats a dispersions electró-positró, i a la desintegració del Higgs i del tau en hadrons. Demostrem que eleccions apropiades d’aquest paràmetre d’esquema pot donar lloc a millores substancials de les prediccions pertorbatives d’aquests observables. A la part II, discutim les divergències d’expansions asimptòtiques en el context d’integrals de camí. Convencionalment, el mètode de la sumació de Borel asigna una resposta finita a les expansions divergents. Tot i així, la suma de Borel podria no contenir tota la informació d’una funció, perquè a aquesta li poden faltar correccions exponencialment petites. Llavors considerem una petita variació de la sumació de Borel, on una transformada de Borel generalitzada (una transformada de Laplace inversa) és seguida d’una transformada de Laplace direccionals. Aquestes eines ens permet donar, potser, millors respostes a problemes típics de la sumació de Borel, com la pèrdua de les correccions exponencials i les ambigüitats de la sumació de Borel. A més, definim ressurgència com una connexió entre la discontinuïtat d’una funció i els coeficients de la seva expansió asimptòtica. A partir d’aquesta definició, podem reduir el problema de ressurgència a un problema de correccions exponencials perdudes en les expansions asimptòtiques i podem relacionar diferents formes d’entendre la ressurgència que es troben a la literatura.
For realistic quantum field theories, numerical predictions of physical observables can only be calculated from perturbative expansions in powers of the couplings, the parameters that determine the strength of the field interactions. While the predictive success of quantum field theory is undeniable, these perturbative computations are plagued with divergences. On one hand, the coefficients of the perturbative expansion are computed from loop integrals that are divergent most of the times. Some of these divergences are associated with unphysical terms that can be subtracted. In other cases, a renormalisation procedure is applied to cancel these divergences, but this entails a choice of theoretical conventions (scale and scheme) which physical observables cannot depend on. On the other hand, once the loop integrals have been renormalised, the resulting expansion still sums to an infinite answer for all non-vanishing values of the coupling. This is due to the fact that the coefficients of the expansion grow factorially with the order. Still, these expansions can be understood as asymptotic expansions, which encode the limiting behaviour of the observable for small coupling, and whose truncation to an optimal term yields numerical approximations of the observable. This second kind of divergence is in fact not limited to quantum field theories, but it may arise in different contexts of mathematics and physics: for instance, in perturbative approximations to the energy eigenvalues of a quantum mechanic system, or in formal solutions to differential equations. In part I of this dissertation, the main object of study is the strong coupling constant and the perturbative expansions of physical observables in quantum chromodynamics. First, we briefly discuss how the loop divergence of the quantum corrected gluon propagator can be absorbed inside the strong coupling constant during the renormalisation. This process, however, comes at the cost of introducing scale and scheme dependences into the coupling, therefore it is not a physical observable of the theory. This motivates a coupling redefinition whose scheme dependence is reduced to a single parameter. We then use this coupling redefinition in phenomenological analysis of physical observables associated to electron-positron scattering, and to Higgs and tau decays into hadrons. We demonstrate that appropriate choices of this scheme parameter can lead to substantial improvements in perturbative predictions of these observables. In part II, we discuss the divergence of asymptotic expansions in the context of path integrals. Conventionally, the method of Borel summation assigns a finite answer to the divergent expansion. Still, the Borel sum might not encode the full information of a function, because it misses exponentially small corrections. We then consider a slight variation of the conventional Borel summation, in which a generalised Borel transform (an inverse Laplace transform) is followed by a directional Laplace transform. These tools allow us to give perhaps better answers to typical problems in Borel summation: missing exponential corrections and ambiguities in the Borel summation. In addition, we define resurgence as a connection between the discontinuity of a function and the coefficients of its asymptotic expansion. From this definition, we can reduce resurgence to the problem of missing exponential corrections in asymptotic expansions and correlate different approaches to resurgence found in the literature.
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Tafat, Sofiane. "Renormalons infrarouges et corrections de puissance en chromodynamique quantique." Paris 11, 2001. http://www.theses.fr/2001PA112328.

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L'étude des corrections non perturbatives en chromodynamique quantique (QCD) est un domaine de recherche trés actif ces dernières années, d'autant que la qualité des données expérimentales exige des prédictions théoriques de plus en plus précises. L'étude du comportement asymptotique des séries perturbatives permet de déduire la forme fonctionnelle des corrections de puissance. La contribution associée à l'intégration sur les petites impulsions est liée aux renormalons infrarouge. Cette démarche a donné lieu à des applications phénoménologiques trés intéressantes. Cependant sur le plan théorique cette approche n'est pas complètement satisfaisante, du fait que les renormalons infrarouge assurent d'une part l'universalité des corrections de puissance, ce qui suppose tacitement l'absence de contribution de twists élevés dues aux corrélations entre les quarks et les gluons dans les hadrons, et d'autre part ils ne peuvent pas expliquer la nature physique et la dynamique à grande distance. .
This thesis in theoretical elementary particle physics and specially in quantum chromodynamics. During my thesis I have been working on the problem of quantifying nonperturbative corrections to various QCD observables assiociated with the hadronization phenomenon. The hadronization corrections come from the interface of perturbative and perturbative and nonperturbative QCD dynamics and their study sheds some light into the confinement mechanism. One of the existing approaches to describe these corrections relies on the analysis of ambiguities of perturbative series to the QCD observables the so called infrared renormalons. This approach has many interesting phemenological applications and it hes been tested experimentally against aavaible data on the measurements of deviations of perturbative QCD predictions to various observables at LEP, Tevatron and DESY. The infrared renormalon approach has a number of limitations. Firstly, it does not tell us much about the origin of nonperturbative scale and underlying QCD dynamics. .
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Bauer, Clemens [Verfasser], and Gunnar S. [Akademischer Betreuer] Bali. "Numerical studies of QCD renormalons in high-order perturbative expansions / Clemens Bauer. Betreuer: Gunnar S. Bali." Regensburg : Universitätsbibliothek Regensburg, 2013. http://d-nb.info/1031130039/34.

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Bunne, Tobias, and Per Iversen. "Avspecialisering som framgångskoncept för jämnare arbetsfördelning?" Thesis, University of Gävle, Department of Business Administration and Economics, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:hig:diva-20.

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The application of the LSS law and how the public organization (Municipality of Hudiksvall) later had to reform their organization to fit the new demands is the foundation to this master's thesis. An internal evaluation was performed due to this reorganisation process within the social care department (LSS unit). The aim was to investigate and evaluate if the reorganization resulted in a better working environment and if the work load (distribution of work) became more evenly divided between the different unit managing directors. The primary empirical information to this master's thesis is collected from that evaluation report. The main aim of this master’s thesis is to answer if the organisational choice between specialised or de-specialised working tasks has an effect (experienced and measured) on the level of stress among the unit managing directors. We have found that it is a question about moral stress rather than a question about stressed managing directors in general. In this thesis the definition of “moral stress” is the discrepancy between one persons ethical properties and the actions that person have to take due to appointed level of power and the responsibility that follows with this power. Our main recommendation is to find an organisational structure based on the premises of the LSS-law while at the same time attending to the problems of the more and more difficult working situation amongst the employees. This can be achieved by gaining approval for a new prioritizing order form the politicians, the clients, and the employees. Such a reformation process (Sw “omnormeringsprocess”) would imply less moral stress. If the managing directors have a basic employment as a generalist the working tasks will be more evenly divided amongst the employees. Teams of 5-7 employees that encompasses specially qualified generalist and that meets on a regular basis is essential to relieve pressure from colleagues. This is essential to be able to make the most out of the special knowledge of the directors. In the extension of this change the assistants should be included in the existing substitutes-pool and each assistant’s special competence should be clarified.

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Books on the topic "Renormalon"

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Vasiliev. Field Theory Renormaliz Critical Behaviour and Stochastic Dynamics. Taylor & Francis Group, 2002.

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Book chapters on the topic "Renormalon"

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Grozin, Andrey. "Renormalons in HQET." In Heavy Quark Effective Theory, 175–209. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-540-40977-9_9.

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Mankiewicz, L. "Phenomenology of Renormalons in Inclusive Processes." In New Non-Perturbative Methods and Quantization on the Light Cone, 209–12. Berlin, Heidelberg: Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/978-3-662-08973-6_24.

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Agaev, S. S. "Single Meson Photoproduction via Higher Twist Mechanism and IR Renormalons." In N* Physics and Nonperturbative Quantum Chromodynamics, 263–66. Vienna: Springer Vienna, 1999. http://dx.doi.org/10.1007/978-3-7091-6800-4_42.

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Korchemsky, G. P. "Recent Developments in the Theory Of Strong Interactions: Power Corrections and Renormalons." In Particle Physics: Ideas and Recent Developments, 245–66. Dordrecht: Springer Netherlands, 2000. http://dx.doi.org/10.1007/978-94-011-4128-4_10.

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Ellis, John, Einan Gardi, Marek Karliner, and Mark A. Samuel. "Pade Approximants, Borel Transform, And Renormalons: The Bjorken Sum Rule as a Case Study." In Neutrino Mass, Dark Matter, Gravitational Waves, Monopole Condensation, and Light Cone Quantization, 309–18. Boston, MA: Springer US, 1996. http://dx.doi.org/10.1007/978-1-4899-1564-1_28.

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"Renormalons." In QCD as a Theory of Hadrons, 315–28. Cambridge University Press, 2004. http://dx.doi.org/10.1017/cbo9780511535000.035.

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"Renormalons." In QCD as a Theory of Hadrons, 315–28. Cambridge University Press, 2023. http://dx.doi.org/10.1017/9781009290296.040.

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BENEKE, M., and V. M. BRAUN. "RENORMALONS AND POWER CORRECTIONS." In At The Frontier of Particle Physics, 1719–73. WORLD SCIENTIFIC, 2001. http://dx.doi.org/10.1142/9789812810458_0036.

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Mueller, Al H. "RENORMALONS AND PHENOMENOLOGY IN QCD." In A Passion for Physics, 137–42. WORLD SCIENTIFIC, 1985. http://dx.doi.org/10.1142/9789811219207_0019.

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DAVID, F. "The Operator Product Expansion and Renormalons: A Comment." In Current Physics–Sources and Comments, 508–19. Elsevier, 1990. http://dx.doi.org/10.1016/b978-0-444-88597-5.50070-3.

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Conference papers on the topic "Renormalon"

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Beneke, M. "Renormalon phenomenology: Questions and directions." In The 5th international workshop on deep inelastic scattering and QCD. American Institute of Physics, 1997. http://dx.doi.org/10.1063/1.53696.

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Bauer, Clemens, and Gunnar Bali. "Hunting the static energy renormalon." In The XXVIII International Symposium on Lattice Field Theory. Trieste, Italy: Sissa Medialab, 2011. http://dx.doi.org/10.22323/1.105.0221.

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Broadhurst, David, and Michael Borinsky. "Taming a resurgent ultra-violet renormalon." In Loops and Legs in Quantum Field Theory. Trieste, Italy: Sissa Medialab, 2022. http://dx.doi.org/10.22323/1.416.0013.

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CONTRERAS, C. "DETERMINATION OF THE B-MASS USING RENORMALON CANCELLATION." In Proceedings of the Fifth Latin American Symposium. WORLD SCIENTIFIC, 2006. http://dx.doi.org/10.1142/9789812773951_0036.

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Williamson, Alexander R. "Renormalon analysis of heavy-light exclusive B decays." In THEORETICAL HIGH ENERGY PHYSICS: MRST 2001: A Tribute to Roger Migneron. AIP, 2001. http://dx.doi.org/10.1063/1.1435655.

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Takaura, Hiromasa. "$a_S$ determination from static QCD potential with renormalon subtraction." In alphas-2019: Workshop on precision measurements of the QCD coupling constant. Trieste, Italy: Sissa Medialab, 2019. http://dx.doi.org/10.22323/1.365.0025.

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SUMINO, Y. "RENORMALON CANCELLATION AND PERTURBATIVE QCD POTENTIAL AS A COULOMB+LINEAR POTENTIAL." In Proceedings of the International Conference. WORLD SCIENTIFIC, 2004. http://dx.doi.org/10.1142/9789812702845_0015.

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Hoang, Andre, Diogo Boito, Matthias Jamin, Christoph Regner, and Miguel Benitez-Rathgeb. "Inclusive tau hadronic decay rate in a renormalon-free gluon condensate scheme." In Loops and Legs in Quantum Field Theory. Trieste, Italy: Sissa Medialab, 2022. http://dx.doi.org/10.22323/1.416.0016.

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GOMEZ, CESAR. "RENORMALONS AND FRACTIONAL INSTANTONS." In Proceedings of the Fifth International Workshop. WORLD SCIENTIFIC, 2004. http://dx.doi.org/10.1142/9789812702562_0009.

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Belitsky, A. V. "Renormalons in exclusive meson electroproduction." In INTERSECTIONS OF PARTICLE AND NUCLEAR PHYSICS: 8th Conference CIPANP2003. AIP, 2004. http://dx.doi.org/10.1063/1.1664310.

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Reports on the topic "Renormalon"

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Rathsman, J. Conformal expansions and renormalons. Office of Scientific and Technical Information (OSTI), February 2000. http://dx.doi.org/10.2172/753292.

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