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Review on NRQCD

Delve into the world of quarkonium with an in-depth look at NRQCD and EFT theories, their applications in collider physics, and the path to more evolved effective field theories. Explore the challenges and potential of quarkonium in understanding QCD, potential models, and radiative corrections.

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Review on NRQCD

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  1. Review on NRQCD A Look on Quarkonium EFT’s Apologies to everyone (and everything) not mentioned! EFT 2009, Valencia, 1-6 February 2009

  2. Outline • Introduction and the pre-NRQCD time • NRQCD: theory and applications at colliders • Path to more evolved EFT’s • New EFT’s: • Unstable particles EFT • Conclusions • pNRQCD • vNRQCD lattice Jonathan Flynn’s review talk Nora Brambilla finite T Miguel Escobedo EFT 2009, Valencia, 1-6 February 2009

  3. Quarkonium Discovery (1974) (1977) • very narrow resonances: Assuming QCD (asymptotic freedom) & states to be nonrelativistic bound states Appelquist, Politzer [1975] Brookhaven + SLAC [1974] De Rujula, Glashow [1975] • used methods familiar from nonrel. QM • helped to establish QCD EFT 2009, Valencia, 1-6 February 2009

  4. Quarkonium Since then quarkonia serve as • challenge to understand QCD • trigger mode Potential models • good description of masses, splittings, transitions • cannot be used for precise studies of QCD Problems with radiative corrections Appelquist, Dine, Muzinich [1977] • IR divergences in the static potential at 3 loops • IR divergences in NLO corrections to P-wave Barbieri, Caffo, Gatto, Remiddi [1980] color singlet model Soft divergences add up due to additional p-factor. Cuts contain short and long-distance contributions. EFT 2009, Valencia, 1-6 February 2009

  5. From a method to a theory Scales binding, kinetic energy hadronization energy production decay momentum inverse size Separation of short and long-distance modes. Effective Theory with m integrated out to treat decay.consistently. • Lagrangian for NRQED • Lagrangian for NRQCD • Lattice simulation with NRQCD • Resolution of IR-divergences in P-wave decays • NRQCD formalism for inclusive annihilation and Caswell, Lepage [1986] Lepage, Tacker [1988] Tacker, Lepage [1991] Bodwin, Braaten, Lepage [1992-1995] production of quarkonia EFT 2009, Valencia, 1-6 February 2009

  6. NRQCD Bodwin, Braaten, Lepage [1995] NRQCD: Local QFT constructed to reproduce low-energy modes of QCD large small Degrees of freedom • heavy quarks/antiquarks: Pauli spinors • soft gluon EFT 2009, Valencia, 1-6 February 2009

  7. NRQCD Bodwin, Braaten, Lepage [1995] Lagrangian … color singlet color octett EFT 2009, Valencia, 1-6 February 2009

  8. NRQCD color singlet color octett Symmetries • gauge invariant • Gallilei symmetry • spin symmetry • reparametrization/Poincaré invariance Luke, Manohar [1992] Manohar [1997] Brambilla, Gromes, Vairo [2003] EFT 2009, Valencia, 1-6 February 2009

  9. NRQCD color singlet color octett Power counting in v Standard v-counting EFT 2009, Valencia, 1-6 February 2009

  10. NRQCD color singlet color octett Matching P-wave decay QCD NRQCD IR-finite matching conditions EFT 2009, Valencia, 1-6 February 2009

  11. List of Applications • Spectroscopy on the lattice lattice session • Inclusive, electromagnetic, leptonic decays: • Radiative decays: • Exclusive decays • Total production rates, pT-distributions EFT 2009, Valencia, 1-6 February 2009

  12. production at the Tevatron Beneke, Krämer [1992] LO QCD ! analogous results: Braaten, Kniehl, Lee [1999] Cho, Leibovich [1995] EFT 2009, Valencia, 1-6 February 2009

  13. production at the Tevatron Everything settled ? • proliferation of matrix element “can fit anything” • higher order v corrections • alternative power counting: • higher order radiative correction • factorization theorem NOT PROVEN Beneke [1997] Fleming, Rothstein, Leibovich [2000] Brambilla, Mereghetti, Vairo [2006] Artoisenet, Campbell, Lansberg, Maltoni, Tramontano [2007,2008] • NLO QCD for color-singlet channel • final state Sanchis-Lozano [1999] • intial state parton showers • intial state intrisic Kniehl, Kramer [1999] Petrelli [1999] Sridhar, Martin, Stirling [1999] Hagler, Kirschner, Schafer etal [2000] Not conclusive ! EFT 2009, Valencia, 1-6 February 2009

  14. Polarization CDF [2000] • channel dominant for large • fragmenting gluon on-shell, no spin-flip • transversely polarized for large Cho, Wise [1994] CDF [2007] EFT 2009, Valencia, 1-6 February 2009

  15. Bodwin, Garcia, Tormo, Lee [2008] Proof of factorization exists ! First theory predictions Experiments Braaten, Lee [2003, 2005] BELLE [2002, 2004] Liu, He, Chao [2002] BABAR [2005] Zhang, Gao, Chao [2006] • NLO QCD corrections: • relativistic corrections large: • corrections to wave functions from Gong, Wang [2008] Braaten, Lee [2003] Bodwin, Kang, Lee [2006] potential models in dim reg Bodwin, Lee, Yu [2008] • new predictions with corrections He, Fan, Chao [2007] EFT 2009, Valencia, 1-6 February 2009

  16. Paving the way … NRQCD sufficient to learn about short-distance dynamics of quarkonium processes, but difficult to use for studying their low-energy dynamics. Wish List: • unique & transparent power counting • simple rules for higher order computations • computations and matching using dim reg Labelle [1998] • separation of soft ( ) and ultrasoft ( ) modes necessary • inconsistency of NRQCD using dim reg for 2PI-diagrams • ultrasoft gluon field must be multi-pole expanded • effective action with two types of gluon fields • matching for bilinear sector from strict 1/m expansion (hard region) • soft gluons essential for correct RG-evolution Luke, Manohar [1997] Grinstein, Rothstein [1998] Luke, Savage [1998] Manohar [1997] Grieshammer [1998] EFT 2009, Valencia, 1-6 February 2009

  17. Threshold Expansion Task: Determine asymptotic expansion of Feynman diagrams for Beneke, Smirnov [1997] Momentum regions • separation of modes by Taylor-expanding in each region • computation in dim reg • unique v-counting of all contributions • not an EFT • allows for perturbative bound state computation in connection with EFT concepts • made bound state computations interesting to multi-loop community EFT 2009, Valencia, 1-6 February 2009

  18. Pineda, Soto [1998] pNRQCD Brambilla, Pineda, Soto, Vairo [2000] Primary aim: • start from NRQCD • integrate out soft modes at • potentials as Wilson coefficients Degrees of freedom • two renormalization scales: • static potential IR-finite (IR-div cancelled by S-O transition during matching) EFT 2009, Valencia, 1-6 February 2009

  19. Pineda, Soto [1998] pNRQCD Brambilla, Pineda, Soto, Vairo [2000] Primary aim: • start from NRQCD • integrate out soft modes at • potentials as Wilson coefficients Lamb-shift: EFT 2009, Valencia, 1-6 February 2009

  20. Pineda, Soto [1998] pNRQCD Brambilla, Pineda, Soto, Vairo [2000] Primary aim: • start from NRQCD • integrate out soft modes at • potentials as Wilson coefficients no perturbative matching Degrees of freedom • related CS and CO matrix elements to wave functions at the • connection of QCD to potential models Brambilla, Eiras, Pineda, Soto [2002] origin and moments of chromoelectric correlators EFT 2009, Valencia, 1-6 February 2009

  21. Luke, Manohar, Rothstein [1999] vNRQCD Manohar, Stewart [2000] Hoang, Stewart [2002] Primary aim: • separation of all low energy modes • account for correlation of all scales at all times • focus: • renormalization group scaling in velocity renormalization group Degrees of freedom EFT 2009, Valencia, 1-6 February 2009

  22. Luke, Manohar, Rothstein [1999] vNRQCD Manohar, Stewart [2000] Hoang, Stewart [2002] Primary aim: • separation of all low energy modes • account for correlation of all scales at all times • focus: EFT 2009, Valencia, 1-6 February 2009

  23. Luke, Manohar, Rothstein [1999] vNRQCD Manohar, Stewart [2000] Hoang, Stewart [2002] Primary aim: • separation of all low energy modes • account for correlation of all scales at all times • focus: Velocity renormalization group for positronium: Manohar, Stewart [2000] • hyperfine splitting (reproduced): • decay rate (reproduced): • Lambshift (predicted): EFT 2009, Valencia, 1-6 February 2009

  24. RG-Evolution Energy correction inmuonic Hydrogenfrommassless electrons. Pineda [2001] Wilson coefficient of Darwin potential pNRQCD: vNRQCD: Matching 1) NRQCD/HQET: Evolution of Darwin op. soft ultrasoft 2) Matching: soft ultrasoft 3) pNRQCD: soft soft ultrasoft EFT 2009, Valencia, 1-6 February 2009

  25. RG-Evolution RG equation for S-wave production current at NLL order 2-Loop UV-divergences vNRQCD: Manohar, Stewart [2001] Presence of soft, usoft and potential essential at 3 loops for removal of subdivergences when mixed soft, usoft, potential UV-divergences appear. Hoang [2003] pNRQCD: Pineda [2001] Correlation of scales: EFT 2009, Valencia, 1-6 February 2009

  26. RG-Evolution CONS: Recorrelation of NRQCD-pNRQCD matching scale with pNRQCD renormalization scale for potential modes. pNRQCD: vNRQCD: Soft renormalization of soft multi-gluon operators requires consideration of an infinite set of soft operators Is there an even better formulated theory? vpNRQCD very pretty EFT 2009, Valencia, 1-6 February 2009

  27. Applications • spectrum computations (perturbation theory) • bottom and charm mass determinations • nonrelativistic sum rules • decay spectra • toponium physics, top threshold • top quark mass determination • ultraheavy colored particles (SUSY, little Higgs,.etc) EFT 2009, Valencia, 1-6 February 2009

  28. Top Threshold at the ILC EFT 2009, Valencia, 1-6 February 2009

  29. Top Threshold at the ILC EFT 2009, Valencia, 1-6 February 2009

  30. Top Threshold at the ILC [2001,2002,2003] Pineda, Signer [2007] EFT 2009, Valencia, 1-6 February 2009

  31. NRQCD for unstable quarks In the future we might face new ultraheavy colored particles • SUSY • little Higgs • extra dimensions form quarkonium-like bound states formation time lifetime top quark: NRQCD ideal to be an EFT for unstable heavy particles. Hoang, Reisser [2005] Hoang, Reisser, Ruiz [2008] Beneke, Falgari, Schwinn, Signer, Zangerighi [2007] expansion in v expansion in off-shellness EFT 2009, Valencia, 1-6 February 2009

  32. NRQCD for unstable quarks Assume sufficiently inclusive definition of the cross section to not upset v-counting Effects of instability Described in NRQCD by width, interference with background, background, experimental cuts complex Wilson coefficients and anomalous dimensions propagator EFT 2009, Valencia, 1-6 February 2009

  33. NRQCD for unstable quarks EFT 2009, Valencia, 1-6 February 2009

  34. NRQCD for unstable quarks EFT 2009, Valencia, 1-6 February 2009

  35. NRQCD for unstable quarks complex • accounts for interference of double and single resonant top final states • leads to the running of forward scattering operators • matching condition incorporates experimental cuts e.g. invariant mass cuts EFT 2009, Valencia, 1-6 February 2009

  36. Conclusions Practical: • many successful applications • some serious failures (not a failure of NRQCD) • v-expansion for charmonia could be problematic • many higher order computations still missing Conceptual: • significant progress in understanding of quarkonia production, decay and its internal dynamics • NRQCD on good hard ground • but more solid proofs of factorization for production needed • but conceptual developments are still needed to have a vpNRQCD I feel quite good, but not entirely happy. EFT 2009, Valencia, 1-6 February 2009

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