The Role of Heavy Quarks in Light Hadron Fragmentation. HUGS Manuel Epele Instituto de Física La Plata

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1 The Role of Heavy Quarks in Light Hadron Fragmentation. In collaboration with C. A. Garcia Canal and R. Sassot HUGS 2016 Jefferson Lab, Newport News, Virginia June, 2016

2 Outline Fragmentation Functions and Global Analyses Heavy Quark Mass Effects and General Mass Schemes General Mass Global Analysis Summary

3 Fragmentation functions (FF) and Global Analyses Hadroproduction in scattering processes begins with the excitation of free partonic states (quarks and gluons). e + γ q D H i H Fragmentation: excited partons group together into hadrons through a non perturbative mechanism. e q First stages can be described in a perturbative theory (pqcd): partonic cross sections ˆσ i (x, Q). The final partonic state of the type i is excited. Q is the energy scale of the process. x is center of mass momentum fraction carried by the parton The probability of producing the hadron H from a parton i is measured by FFs: D H i (y, Q). y is the momentum fraction of the parton i carried by the H hadron ˆσ i

4 The QCD prediction for the cross section of production of H. dσ dz (Q) = ˆσ i (Q) Di H (Q) i=q, q,g Can be measured. Convolution in the Mellin sense. QCD tells us how fragmentation functions evolve in the energy scale: Altarelli - Parisi equations. ( ) d Dqi d ln(q 2 = ( ) ( ) Pqi q j P qi g Dqj (1) ) D g P gqj P gg D g j Extraction of fragmentation functions by performing a QCD global analysis. Propose a parametrization for the fragmentation functions at an initial scale. Evolve to some experiment energy scale through the Altarelli - Parisi equations. Compute cross section predictions as a fucntion of the unknown parameters. Obtain best parameter values by minimizing a χ 2 function. Fragmentation functions are universal quantities. All available experimental data set types are used: - semi inclusive electron-positron annihilation (SIA) - semi inclusive deep inelastic scattering (SIDIS) - proton-proton collisions

5 Heavy Quark Mass Effects and General Mass Schemes Cross section calculation at zero mass variable flavour number () scheme: dσ = ˆσ i ZM (Q) Di ZM (Q) (2) dz i=q,h,g functions evolve through the standard zero mass evolution equations. D ZM i Cross section calculation at a massive (M) scheme: M dσ = ˆσ i M (Q, m h ) Di M (Q) + ˆσ h M dz (Q, m h) Dh M (3) i=q,g αs n ln(q/m h ) k Light flavour Di M equations. D M h functions evolve through the standard zero mass evolution are decoupled of the QCD evolution. Large logarithmic contributions can be factorised systematically: ˆσ i M (Q, m h ) ˆσ j ZM (Q) A ji (Q/m h ) (4) m h 0 j=q,g,h

6 The best of the two worlds: general mass variable flavour number scheme (). dσ = ˆσ j GM (Q, m h ) Dj GM (Q) (5) dz i=q,g,h ˆσ i M (Q, m h ) A 1 ij (Q/m h ) i=q,g,h D GM i functions evolve through the standard zero mass evolution equations. To ensure continuity across the threshold is necessary to impose matching condition: Dj GM (m h ) = A ji (1) Di M (m h ) i=q,g,h The scheme is not unique. We can emphasize massive-like behaviour if: ˆσ j GM ˆσ j GM* = (1 f (Q)) ˆσ j M + f (Q) ˆσ j GM f (Q) (6) Alternatively, we can emphasize massless-like behaviour if: ˆσ GM j ˆσ GM* j = (1 f (Q)) ˆσ GM j Any power-like choice for f (Q) is equally valid. Q 2m h 0 f (Q) Q 1 + f (Q) ˆσ ZM j (7)

7 General Mass Global Analysis Experimental data sets used: - SIA (ALEPH, BABAR, BELLE, DELPHI, OPAL, SLD, TPC) - SIDIS (COMPASS, HERMES) - proton-proton collisions (PHENIX, STAR, ALICE) Only SIA partonic cross section were computed in the. Best results were obtained with a mass dependent scheme, specifically: emphasize the massive behaviour of the charm flavour emphasize the massless behaviour of the bottom flavour experiment # data TOTAL χ 2 : No significant improvement with more sophisticated Q-dependence than f (Q) = 1 2m h /Q.

8 Better agreement between lower energy data sets (Belle, Babar) and theory is obtained for the general mass scheme. 0.1 Belle: (data - theory)/theory BaBar: ( Q 10 GeV experiment data # data type in fit N i χ 2 N i χ 2 BaBar incl Belle incl scheme scheme relative exp. error relative e There is also a considerable improvement in the description of data from experiments at a higher energy scale. Q = 91.2 GeV experiment data # data 0 type in fit N i χ 2 N i χ 2 Opal incl scheme 15.9 Sld incl scheme 9.5 uds tag relative exp. error c tag b tag Belle: (data - theory)/theory z z BaBar: (data - theory)/theory scheme scheme relative exp. error z 0.

9 Extracted fragmentation functions: zd π+ i (z) zd π+ i (z) u + u s + s u = d c + c gluon 0.2 Q = 4 GeV Q = 4 GeV zd π+ i (z) zd π+ i (z) u + u s + s u = d c + c gluon b + b 0.2 Q = M Z Q = M Z z 1 z 1 Most noticeable difference in the charm distribution. No change for the bottom: suppressed at Belle and Babar, no mass effects at M Z. No change in the light flavors: fixed mostly by SIDIS.

10 Summary A determination of the fragmentation probabilities required a scheme sensitive to the heavy flavour dynamics. Heavy quark dependence is specially relevant in the single inclusive electron-positron annihilation into pions. Impact of the mass correction in SIDIS and proton-proton corrections into pions is needed to be evaluated.