Andrea Signori. Andrea Signori VU / Nikhef

Transcription

1 Andrea Signori 12/20/13 Andrea Signori VU / Nikhef 1

2 Outline 1. Introduc?on 2. TMDs theory 3. TMDs phenomenology 12/20/13 Andrea Signori VU / Nikhef 2

3 Partons and hadrons 12/20/13 Andrea Signori VU / Nikhef 3

4 The parton model Rutherford experiment (1911) Inner structure of the atom 12/20/13 Andrea Signori VU / Nikhef 4

5 The parton model Rutherford experiment (1911) Inner structure of the atom Electron- Proton Deep Inelas?c ScaQering (ep DIS) SLAC/MIT 1960 e P! e 0 X e 0 X proton e 12/20/13 Andrea Signori VU / Nikhef 5

6 The parton model [Feynman, Bjorken] DIS experimental data are compa?ble with elas?c scaqering off pointlike, free, spin ½ par0cles Partons 12/20/13 Andrea Signori VU / Nikhef 6

7 The parton model Deep- inelas*c regime Q 2,!1 lim Q!1 S (Q) =0 QCD zeroth- order approxima?on This behavior jus?fies a posteriori the assump?on of free partons 12/20/13 Andrea Signori VU / Nikhef 7

8 Hadron structure 12/20/13 Andrea Signori VU / Nikhef 8

9 A (too) strong coupling Non perturba?ve regime 12/20/13 Andrea Signori VU / Nikhef 9

10 Hadrons in HEP lepton SIDIS lepton proton Drell-Yan lepton hadron proton proton antilepton electron l + l - to hadrons hadron proton pp to hadrons hadron positron hadron proton hadron 12/20/13 Andrea Signori VU / Nikhef 10

11 Soe physics Distribu?on func?on hadron! parton parton! hadron Fragmenta?on func?on 12/20/13 Andrea Signori VU / Nikhef 11

12 Collinear distribu?ons Distribu?on func?on P hadron! parton xp f a 1 (x) PDF k Fragmenta?on func?on parton! hadron k/z D a!h 1 (z) FF 12/20/13 Andrea Signori VU / Nikhef 12

13 Transverse- momentum- dependent distribu?ons Distribu?on func?on P hadron! parton xp f a 1 (x, k? ) TMD PDF D a!h 1 (z,p? ) parton! hadron TMD FF k Fragmenta?on func?on k/z 12/20/13 Andrea Signori VU / Nikhef 13

14 TMDs & co. Parton distribution functions (x) b T dependence k T dependence Transverse-momentum distributions (x, k ) Impact-parameter distributions (x, b ) 2D Fourier transform (b ) Generalized parton distributions (x, =0, T ) Wigner distributions (x, k, b ) 12/20/13 Andrea Signori VU / Nikhef 14

15 Access TMDs proton Drell-Yan lepton proton antilepton d f(x, k? ) f(x, k? ) 12/20/13 Andrea Signori VU / Nikhef 15

16 Access TMDs electron l + l - to hadrons hadron positron hadron d D(z,P? ) D(z,P? ) 12/20/13 Andrea Signori VU / Nikhef 16

17 Access TMDs lepton SIDIS lepton hadron proton d f(x, k? ) D(z,P? ) 12/20/13 Andrea Signori VU / Nikhef 17

18 The experimental side 12/20/13 Andrea Signori VU / Nikhef 18

19 TMDs - theory 12/20/13 Andrea Signori - VU/Nikhef 19

20 TMDs theory Unpolarized hadrons lepton SIDIS ` + P! `0 + h + X lepton hadron k k proton Tr M 2 12/20/13 Andrea Signori - VU/Nikhef 20

21 TMDs theory (z,p? )= D a 1(z,P 2?)+iH? 1 (z,p 2?) P µ? M h µ n 2 (x, k? )= f a 1 (x, k 2?)+ih? 1 (x, k 2?) kµ? M µ n /20/13 Andrea Signori - VU/Nikhef 21

22 TMDs theory Unpolarized SIDIS! (z,p? )= Fully unpolarized TMD fragmenta?on func?on (x, k? )= Fully unpolarized TMD distribu?on func?on D a 1(z,P 2?)+iH? 1 (z,p 2?) P µ? M h µ n 2 f a 1 (x, k 2?)+ih? 1 (x, k 2?) kµ? M µ n /20/13 Andrea Signori - VU/Nikhef 22

23 TMD PDFs quark pol. U L T nucleon pol. U f 1 h 1 L g 1L h 1L T f 1T g 1T h 1, h 1T Twist-2 TMDs And a similar scheme holds for FFs 12/20/13 Andrea Signori VU / Nikhef 23

24 Overview of theore?cal issues 1. Color gauge invariance 2. Universality of TMDs 3. Factoriza?on 4. Evolu?on with the energy scale 12/20/13 Andrea Signori VU / Nikhef 24

25 Color gauge invariance Tr M 2 k k Φ q ~ F.T. Proton ψ(x)ψ( y) Proton Not gauge Invariant..! 12/20/13 Andrea Signori VU / Nikhef 25

26 Color gauge invariance U(x,y): gauge link Tr M 2 k k Gauge Invariant..! Φ q ~ F.T. Proton ψ(x)u (x, y)ψ( y) proton 12/20/13 Andrea Signori VU / Nikhef 26

27 Color gauge invariance Tr M 2 k k Gauge link effect = Φ q ~ F.T. Proton ψ(x)u (x, y)ψ( y) proton Gauge Invariant..! 12/20/13 Andrea Signori VU / Nikhef 27

28 Recent impact on Drell- Yan H H * Naive expectation for the cross section: d DY = 1 [ ] (x 1,p 1T )H [ ] X (x2,p 2T )H N c However: color is still entangled! The correct description is i d DY =Tr c hu [p 2 ] (x 1,p 1T )U [p 2 ]H U [p 1 ] (x 2,p 2T )U [p 1 ]H Buffing, Mulders, arxiv: [hep-ph]

29 PDFs: universality DIS lepton lepton We can extract PDFs from HERA data and use them for LHC data analysis! proton X proton Drell-Yan lepton proton antilepton 12/20/13 Andrea Signori VU / Nikhef 29

30 TMD PDFs: generalized universality DIS lepton lepton We can extract TMDs from HERA data and use them for LHC data analysis with caveat proton X proton Drell-Yan lepton Computable process dependence due to the presence of gauge- links proton antilepton 12/20/13 Andrea Signori VU / Nikhef 30

31 Factoriza?on breaking lepton SIDIS lepton proton Drell-Yan lepton hadron proton proton antilepton electron l + l - to hadrons hadron proton pp to hadrons hadron positron hadron proton hadron 12/20/13 Andrea Signori VU / Nikhef 31

32 Evolu?on f 1 (...,Q 2 ) S(Q) 6= 0 Interac0ng quarks and gluons: QCD framework 12/20/13 Andrea Signori VU / Nikhef 32

33 TMDs Phenomenology (SIDIS) 12/20/13 Andrea Signori VU / Nikhef 33

34 Gaussian TMDs Gaussian parametriza0on of TMD parts f a 1 (x, k 2?)=f a 1 (x) 1 hk 2? i exp k 2? hk 2? i /20/13 Andrea Signori - VU/Nikhef 34

35 Phenomenology lepton SIDIS lepton hadron proton 12/20/13 Andrea Signori VU / Nikhef 35

36 Gaussian TMDs Gaussian parametriza0on of TMD parts f a 1 (x, k 2?)=f a 1 (x) 1 hk 2? i exp k 2? hk 2? i hk 2?,ui = hk 2?,di = The same variance for all the flavors! /20/13 Andrea Signori - VU/Nikhef 36

37 Gaussianity and flavor dependence hp 2 T, upi 6= hp 2 T, downi 12/20/13 Andrea Signori VU / Nikhef 37

38 Unpolarized! pt,i partonic transverse momenta up quarks xi P down quarks a 2 2 D1 (z, P?, Q ) sea quarks collinear partonic momenta P pt,j photon proton momentum pt,l pt,m pt,k xm P xj P xk P xl P a 2 2 f1 (x, k?, Q ) Unpolarized! 12/20/13 Andrea Signori - VU/Nikhef 38

39 Flavor dependent TMDs Different Gaussian parametriza0ons of TMD parts f a 1 (x, k 2?)=f a 1 (x) 1 hk 2?,a i exp k 2? hk 2?,a i hk 2?,u v i6= hk 2?,d v i6= hk 2?,seai Simplified flavor dependence! /20/13 Andrea Signori - VU/Nikhef 39

40 Gaussian TMDs Gaussian parametriza0on of TMD parts D a!h 1 (z,p 2?)=D a!h 1 (z) 1 hp 2? i exp P 2? hp 2? i hp 2?,u! + i = hp 2?,u! i = hp 2?,u!K + i = The same variance for all the fragmenta?on processes /20/13 Andrea Signori - VU/Nikhef 40

41 Flavor- dependent TMDs Different Gaussian parametriza0on of TMD parts D1 a!h (z,p? )=D1 a!h 1 (z) hp?,a!h 2 i exp P 2? hp 2?,a!h i u, d, s Different combina?ons out of ±, K ± 12/20/13 Andrea Signori - VU/Nikhef 41

42 Gaussianity and flavour dependence lepton SIDIS lepton hp 2 T,upi, hp 2 T,downi, hp 2 T,seai hadron hk 2 T, unfi, hk 2 T, favi proton h + SIDIS/DIS(P 2 h?; x, z, Q 2 ) h 12/20/13 Andrea Signori VU / Nikhef 42

43 Fit procedure } 200 Monte Carlo fit Distribu?ons of best- values 12/20/13 Andrea Signori - VU/Nikhef 43

44 Results TMD PDFs GeV 2 hk 2?,seai =0.41 ± 0.16 hk 2?,d v i =0.30 ± hk 2?,u v i =0.36 ± Similar results hold for FFs! /20/13 Andrea Signori VU / Nikhef 44

45 Our recent work doi: / JHEP 11(2013)194 12/20/13 Andrea Signori - VU/Nikhef 45

46 Impact on HEP Difference of cross sec6ons Spin asymmetries Polarized TMDs A f( h, S) ~e ~ N / F f( h, S) ~e N ~ / F UU Pq e2 q TMD PDF q w TMD FF q P q e2 q f q 1 Dq 1 Unpolarized TMDs Poten?al influence on the extrac?on of polarized TMDs 12/20/13 Andrea Signori - VU/Nikhef 46

47 Impact on HEP Monte Carlo generators dealing with Intrinsic transverse momentum Herwig++ Gmc_trans ResBos 12/20/13 Andrea Signori - VU/Nikhef 47

48 Conclusions TMDs physics Theory Experiment Phenomenology 12/20/13 Andrea Signori VU / Nikhef 48

49 Conclusions TMDs physics Theory Have fun! Experiment Phenomenology 12/20/13 Andrea Signori VU / Nikhef 49