Probing hadron structure from hard processes Hiroyuki Kawamura (KEK) “New Hadrons” Workshop 2010 Feb. 28 2011 @ RIKEN

Hard Processes Internal structure of hadrons can be probed by processes with large momentum transfer (“hard process”). Hard scale ↔ quarks & gluons inside hadrons. Inclusive & Initial Inclusive & Final DIS e+ e- → h + X h e e+ ↔ ↔ h PDF e- FF Exclusive & Initial /Final Exclusive & Decay Form Factor B → l nu gamma π π ↔ B ↔ LC wavefunction LC wavefunction

QCD Factorization Inclusive Exclusive = factorization of hard and soft QCD dynamics Inclusive Calculable DIS = PDFs Theoretically easy to handle ,,, (Proof by O.P.E. ) Exclusive “End-point singularity” Information of w.f. is relevant even to show factorization. More elaborate setup needed. Brodsky & Lepage etc.

Global analysis of FFs Inclusive hadron production Factoriziation Data In collaboration with Hirai, Kumano, Saito Inclusive hadron production Factoriziation Data Calculable

Fragmentation function h ≈ probability density of a → h with mom. fraction z a DGLAP equation ↔ scale dep. Time-like splitting function ─ matrix form in flavor singlet channel HKNS07

HKNS07 results Mainly determined by LEP1 data at the Z mass. Large uncertainties in gluon & sea quark components. ─ Can be reduced by mixing effects through evolution ─ High precision data from BELLE are crucial !! Data will be released soon.

Small-z problems for FF de Florian, Stratmann, Vogelsang (‘98) (1) Time-like splitting functions Moch, Vogt (‘07) Double log corrections at each order of perturbation. Negative cross section at some value of z. log z resummation using angular ordering (color coherence) are known up to next-to leading order (MLLA). ─ Difficult to unify the evolutions in the small-z and intermediate region. Albino, Kniehl, Kramer, Ochs (‘04) Albino, Kniehl, Kramer (’04, ‘06)

(2) Hadron mass effect Unity at production threshold Important for Belle data. for K. “Rescaled” variable : There are still other power corrections (higher twist corr.). Naïve solution Set a lower limit : Conventionally, For BELLE data

FFs for Partonic structure can be explored by the shape of FFs. Hirai, Kumano, Oka, Sudoh (‘08) Partonic structure can be explored by the shape of FFs. Tetraquark picture s-sbar picture soft (disfavored) hard (favored) Peak positions & 2nd moments Large uncertainty  no definite conclusion Data from Belle or Belle II are desirable.

Summery Internal structure of hadrons can be probed from hard processes. ─ Non-perturbative functions (PDFs, FFs, etc.) defined via “QCD Factorization” ↔ Internal structure of hadrons ─ Well-defined quantities extracted from experimental data. We are preparing for a new global fit of fragmemtation functions with the first Belle data is coming soon. ─ First high precision data at low → Impacts on ─ Small-z problems : timelike splitting functions,hadron mass effects, higher twist effects etc. Towards exploring internal structure of exotic hadrons ─ Fragmentation functions, exclusive production, decays with HQET

Fragmentation function Operator definition DGLAP equation Time-like splitting function