TMD phenomenology: from JLab to the LHC

Transcription

1 TMD phenomenology: from JLab to the LHC Andrea Signori Spatial and momentum tomography of hadrons and nuclei INT 17-3 Sept

2 TMD phenomenology at low and high energy Andrea Signori Spatial and momentum tomography of hadrons and nuclei INT 17-3 Sept

3 Outline I will present some research directions, in collaboration with: - J. Qiu, LDRD TMD team (JLab) - M. Grewal, Z. Kang (UCLA) - A. Bacchetta, G. Bozzi, M. Echevarria, C. Pisano, M. Radici (Pavia) - T. Kasemets, P. Mulders, M. Ritzmann (Nikhef) - J. Lansberg (IN2P3) 3

4 Outline I will touch different aspects related to phenomenology of TMDs at low and high energy: 1) TMDs and their evolution 2) relevance of the nonperturbative part 3) extractions from low energy data 4) predictions at high energy 5) computational tools 4

5 TMDs & their evolution References (intro and reviews) : - The 3D structure of the nucleon EPJ A (2016) 52 - J.C. Collins Foundations of perturbative QCD - material from the TMD collaboration summer school, e.g. : * P.J. Mulders lecture notes * A. Bacchetta s lecture notes * and all the other lecture notes/references on the webpage 5

6 quark TMD PDFs ij(k, P; S, T ) F.T. hpst j(0) U [0, ] i ( ) PSTi LF Quarks i i+ 5 P k T xp U f 1 h? 1 L g 1 h? 1L T f? 1T g 1T h 1, h? 1T LL f 1LL h? 1LL LT f 1LT g 1LT h 1LT, h? 1LT Sivers TMD PDF unpolarized TMD PDF TT f 1TT g 1TT h 1TT, h? 1TT bold : also collinear red : time-reversal odd (universality properties) 6 extraction of a quark not collinear with the proton encode all the possible spin-spin and spin-orbit correlation between the proton and its constituents

7 Status of TMD phenomenology Theory, data, fits : we are in a position to start validating the formalism quark pol. nucleon pol. U L T U f 1 h 1 L g 1L h 1L T f 1T g 1T h 1, h 1T Only first attempts Limited data, theory, fits Twist-2 TMDs see, e.g, Bacchetta, Radici, arxiv: Anselmino, Boglione, Melis, PRD86 (12) Echevarria, Idilbi, Kang, Vitev, PRD 89 (14) Anselmino, Boglione, D Alesio, Murgia, Prokudin, arxiv: Anselmino et al., PRD87 (13) Kang et al. arxiv: Lu, Ma, Schmidt, arxiv: Lefky, Prokudin arxiv: Barone, Boglione, Gonzalez, Melis, arxiv:

8 The frontier Nuclear Physics : - investigation of nucleon and nuclear structure and associated dynamics - observables of non-perturbative QCD - non-perturbative quark-gluon dynamics encoded in (TMD) PDFs and FFsNP High-Energy Physics : - precision physics, within and beyond the Standard Model - observables of perturbative QCD - assuming the knowledge of hadron structure NP HEP 8

9 W-term & TMDs W-term : transverse momentum resummation in terms of TMDs W (q T,Q)= Z d 2 b T (2 ) 2 eiq T b T W (bt,q) bt is the Fourier-conjugated variable of the (partonic and observed) transverse momenta W (b T,Q) F h 1 i (x 1,b T ; µ, 1 ) F h 2 j (x 2,b T ; µ, 2 ) Product of Fourier-transformed TMDs TMD evolution is multiplicative in bt space 9

10 W-term & TMDs FT of TMDs : F i (x, b T ; Q, Q 2 )= F i (x, b T,µˆb,µ 2ˆb) exp Z Q µˆb dµ µ F [ s (µ),q 2 /µ 2 ] Q 2 µ 2ˆb K(ˆbT ;µˆb) g K (b T ;{ }) Sudakov form factor : perturbative and nonperturbative contributions 10

11 W-term & TMDs FT of TMDs : F i (x, b T ; Q, Q 2 )= F i (x, b T,µˆb,µ 2ˆb) exp Z Q µˆb dµ µ F [ s (µ),q 2 /µ 2 ] Q 2 µ 2ˆb K(ˆbT ;µˆb) g K (b T ;{ }) Sudakov form factor : perturbative and nonperturbative contributions Collinear distribution (input) TMD distribution : Wilson coefficients and intrinsic part F i (x, b T ; µˆb,µ 2ˆb) = X C i/j (x, ˆb T ; µˆb,µ 2ˆb) f j (x; µˆb) F i,np (x, b T ; { }) j=q, q,g Nonperturbative parts defined in a negative way : observed-calculable 11

12 Phenomenology LHC... consolidate the formalism + extractions of TMDs new data predictions for unexplored/known effects in unexplored/known regions EIC... HIEPA 12

13 Phenomenology LHC... consolidate the formalism + extractions of TMDs - extraction of unpolarized quark TMDs : see talks by A. Bacchetta, A. Vladimirov - formalism for unpolarized gluon TMDs : see talks by S. Cotogno, C. Pisano, and next section new data predictions for unexplored/known effects in unexplored/known regions EIC... HIEPA 13

14 Phenomenology LHC... consolidate the formalism + extractions of TMDs predictions for unexplored/known effects in unexplored/known regions examples of predictions for known effects in known regions: - W qt-spectrum at LHC (quark TMDs) - Higgs qt-spectrum at LHC (gluon TMDs) 14

15 Phenomenology All kinematic regions (namely data) are important: some are more suited to constrain NP part of TMDs and their evolution, others to test the accuracy needed for TMD evolution LHC... consolidate the formalism + extractions of TMDs What is the best kinematic region to constrain the NP part of TMDs and what is the best region to be predictive? new data predictions for predictive power & nonperturbative input unexplored/known effects in unexplored/known regions EIC... HIEPA 15

16 Saddle point approximation Qiu-Zhang, Phys. Rev. D W (x 1,2,q T,Q)= = Z d 2 b T (2 ) 2 eiq T b T W (x1,2,b T,Q) Z dbt 2 b T J 0 (q T b T ) W (x 1,2,b T,Q) Z-boson production 10 b T J 0 (q T b T ) W (x 1,2,b T,Q) the idea is to calculate which b-region dominates the integral as a function of the kinematics b T -5 small-b region: computed in pqcd high-b region: need nonperturbative model

17 Saddle point approximation Qiu-Zhang, Phys. Rev. D let s look at the integrand at qt=0 to quantify the importance of the high bt region Z dbt W (x 1,2,q T =0,Q)= 2 b W T (x 1,2,b T,Q) d db T apple b T W (x1,2,b T,Q) b T =b sp =0 b T W (x1,2,b T,Q) from the Sudakov term higher Q smaller x 10 lower Q higher x 5 from DGLAP bsp bmax b T 17

18 Quark TMD PDF preliminary Grewal, Kang, Qiu, AS - in prep. We d like to check if the same statement holds for a single quark TMD PDF map the role of the NP contribution as a function of x and Q f(x, k T =0,Q)= Z dbt 2 b T f(x, b T,Q) accuracy : NLO and NLL 20 b T f(x, bt,q) high-q, small-x Q = Mw x = b T f(x, bt,q) high-q, high-x Q = Mw x = g2 = 0.2 g2 = 0.4 g2 = g2 = 0.2 g2 = 0.4 g2 = bmax b T bmax b T g2 = 0.4 integral +5% g2 = 0.2-7% g2 = % g2 = % g2 =

19 Quark TMD PDF preliminary Grewal, Kang, Qiu, AS - in prep. We d like to check if the same statement holds for a single quark TMD PDF map the role of the NP contribution as a function of x and Q f(x, f(x, k T bt =0,Q)= b T Z dbt 2 b f(x, T b T,Q) low-q, small-x Q = 3 GeV x = b T f(x, accuracy bt,q) : NLO and NLL low-q, high-x Q = 3 GeV x = g2 = 0.2 g2 = 0.4 g2 = g2 = 0.2 g2 = 0.4 g2 = bmax b T bmax b T g2 = 0.4 integral +24% g2 = % g2 = % g2 = % g2 =

20 The message - small-q and high-x: the region where the (quark) TMD PDF is most sensitive to the NP part (but also higher-twists, thresholds,...); data in this region are precious to constrain the NP part LHC... example: extractions of unpolarized quark TMDs (see Bacchetta, Vladimirov) consolidate example: the formalism formalism for + ηb,c production at the LHC or AFTER@LHC extractions of TMDs new data - high-q and small-x: the region where the formalism is most predictive and has less sensitivity to the NP corrections; example W production at LHC in this case, what is the actual impact of the NP part on physical observables? predictions for EIC... unexplored/known effects in unexplored/known regions HIEPA 20

21 ηb,c production at LHC (Some) References: - AS, PhD thesis - D. Boer, C. Pisano, arxiv: M.G. Echevarria, T. Kasemets, J.P. Lansberg, C. Pisano, AS - in preparation 21

22 gluon TMD PDFs f g 1 gluon TMDs ±1 ±1 ±1 ±1 f g 1 gluon TMDs pseudoscalar quarkonium production: pp b X pp c X M = 9.39 GeV M = 2.98 GeV (see also talk by C. Pisano week 4) d dq T U A U B M 2 unpolarized cross section at low transverse momentum for (pseudo)scalar state C[ f g/a 1 f g/b 1 ] ± C[ h?g/a 1 h?g/b 1 ] unpolarized gluons lin. polarized gluons 22

23 ηc production at LHC full transverse momentum spectrum: low qt matched with high qt region d /dqt [nb/gev] c production NP model b p min and b max s =7TeV R 0 2 = <y<4.5 LHCb Resummed Fixed-order Average preliminary q T [GeV] blue band: uncertainty from matching the matching is performed as a weighted average of the calculations at low and high transverse momentum the weights are related to the power corrections to TMD and collinear factorization: d dq T = 1 W + 2 Z 1 ((q T + m)/q)) 2, 2 (m/q T ) 2 23

24 ηc production at LHC full transverse momentum spectrum: low qt matched with high qt region d /dqt [nb/gev] c production NP model b p min and b max s =7TeV R 0 2 = <y<4.5 LHCb Resummed Fixed-order Average Scale uncertainty preliminary q T [GeV] blue band: uncertainty from matching grey band: scale uncertainty µ 2 i = i = µ 2ˆb, µ F.O. = m T fact. 2 variation and envelope 24

25 ηc production at LHC full transverse momentum spectrum: low qt matched with high qt region d /dqt [nb/gev] c production NP model b p min and b max s =7TeV R 0 2 = <y<4.5 LHCb Resummed Fixed-order Average Scale uncertainty NP uncertainty preliminary q T [GeV] blue band: uncertainty from matching grey band: scale uncertainty red band: nonpert. uncertainty apple a1 S NP ( b T )= 2 + a 2 2 ln Q2 b2 T ai = 0.5 GeV 2, var. 50%, envelope both for unpolarized and linearly polarized distributions the formalism is in good shape we need the data at low qt 25

26 W production at LHC References: - AS, PhD thesis - Bacchetta, Bozzi, Radici, Mulders, Ritzmann, AS - in preparation 26

27 Uncertainties - mass AS - PhD thesis sizable uncertainties from hadron structure associated to α s and NP evolution; no intrinsic transverse momentum 27

28 Nonperturbative effects AS - PhD thesis d Z/W ± dq T FT X i,j exp g ij b 2 T g ij hk 2 T i i + hk 2 T i j + soft gluons g comes from 2 TMD PDFs and controls the position of the peak P. Nadolsky /

29 Z vs W : flavor content AS - PhD thesis Z ū u Intrinsic kt effects have been measured on Z data and used to predict the W distribution, assuming they are the same for Z and W W + d u This reflects a flavor independent approach and might not be optimal because of the different flavor content: the intrinsic contributions are different in Z and W± production 29

30 Uncertainties - peak AS - PhD thesis the uncertainty including intrinsic transverse momentum is comparable in magnitude with the one associated to collinear PDFs 30

31 Event generators References: - M. Diefenthaler s talk - week 4 31

32 Study of Hadronization in NP and HEP LDRD:$$ started$in$fy17$ at$jlab' Correla0on$func0ons$$ of$tmd$factoriza0on$ Connec0on$between$NP$and$HEP' Pythia$MCEG$$ LUND$string$model$ Urgent'requirement$ MCEG$for$TMDs$ Understanding$of$hadroniza0on$process$ $ Unique'approach$Connec0on$between$hadroniza0on$ phenomena$in$np$and$hep.' $ By'doing'so:$ NP'Improve$theore0cal$framework$for$TMDs.$ HEP'Improve$hadroniza0on$models.$ 32

33 Work plan FY17$ FY18$ FY19$ Publica6on:0DIS0in0Pythia80 +0TMD0observables0 Publica6on:0LUND0valida6on0 Publica6on:0Hadroniza6on0in0NP0and0HEP$ comparison$pythia8atmd$factoriza0on$ language$dic0onary$ Pythia8$with$spinAindependent$TMDs$ top- bottom approach: incorporate TMD effects in a fully exclusive event generator (Pythia 8) Spin,dependent0hadroniza6on$ Hadroniza0on$plugin$ user$model$for$ one$phenomenon$ rest$from$pythia8$ Incorporate$model$of$transA verse$spin$effects$into$pythia8$$ Anna$Mar0n$and$Albi$Kerbizi$ will$join$project$in$fy18$ 33

34 LDRD personnel (FY17) JLab Pythia Other Diefenthaler Joosten Experimentalists PI cobpi Melnitchouk Collins Theorists 34 Rogers Signori Sato Ethier Lönnblad Prestel cobpi

35 Conclusions and future developments - the relevance of the nonperturbative part of TMDs changes according to the kinematic region explored - we have extractions of unpolarized quark TMDs ; for gluons we are setting up the formalism (first calculation of full transverse momentum spectrum for η production at the LHC) - high-q & small-x is the region where the formalism is most predictive; even here, though, NP corrections leave sizable footprints in observables; see W production at the LHC - the EIC will be very helpful, since it will be able to provide new data ranging from low to high Q and from low to high x 35

36 Backup 36

37 The hadronic landscape Manifestation of hadron structure in scattering processes The European Physical Journal A Volume 52 / No 6 (June 2016) Nature is smooth : understand the link between TMDs & PDFs 37

38 quark TMD PDFs ij(k, P; S, T ) F.T. hpst j(0) U [0, ] i ( ) PSTi LF extraction of a quark not collinear with the proton courtesy A. Bacchetta 38

39 quark TMD PDFs ij(k, P; S, T ) F.T. hpst j(0) U [0, ] i ( ) PSTi LF Quarks i i+ 5 P k T xp U f 1 h? 1 L g 1 h? 1L T f? 1T g 1T h 1, h? 1T extraction of a quark not collinear with the proton LL f 1LL h? 1LL LT f 1LT g 1LT h 1LT, h? 1LT TT f 1TT g 1TT h 1TT, h? 1TT bold : also collinear red : time-reversal odd (generalized universality properties) 39

40 The frontier Nucleon tomography in momentum space: to understand how hadrons are built in terms of the elementary degrees of freedom of QCD High-energy phenomenology: to improve our understanding of high-energy scattering experiments and their potential to explore BSM physics A selection of open questions (formalism) : 1) How well do we understand collinear and TMD factorization? 2) How (well) can we match collinear and TMD factorization? 3) can we quantify factorization breaking effects? 4) how can we investigate gluon TMDs?... 40

41 The frontier Nucleon tomography in momentum space: to understand how hadrons are built in terms of the elementary degrees of freedom of QCD High-energy phenomenology: to improve our understanding of high-energy scattering experiments and their potential to explore BSM physics More open questions (phenomenology) : 1) what is the functional form of TMDs at low transverse momentum? 2) what is its kinematic and flavor dependence? 3) can we attempt a global fit of TMDs? 4) can we test the generalized universality of TMDs? 5) what s the impact of hadron structure on the high-energy physics processes? 41

42 W-term and TMDs Distribution for intrinsic transverse momentum (and its FT): F i,np (x, b T ; { }) a Gaussian? Soft gluon emission g K (b T ; { }) 42

43 W-term and TMDs Distribution for intrinsic transverse momentum (and its FT): Soft gluon emission F i,np (x, b T ; { }) a Gaussian? g K (b T ; { }) Separation of bt regions b max, b T +1 ˆbT (b T ; b min,b max ) b T, b min b T b max b min, b T 0 High bt limit : avoid Landau pole Low bt limit : recover fixed order expression 43

44 Collinear and TMD factorization Let s consider a process with three separate scales: (SIDIS, Drell-Yan, e+e- to hadrons, pp to quarkonium,... ) hadronic mass scale QCD q T Q hard scale (related to the) transverse momentum of the observed particle The ratios QCD /Q QCD /q T q T /Q select the factorization theorem that we rely on. According to their values we can access different projections of hadron structure 44

45 Collinear and TMD factorization The key of phenomenology : emergence of TMD and collinear distributions from factorization theorems fixed Q, variable qt d /dq T q T Q fixed-order term collinear factorization A (x a ) B(x b ) collinear PDFs QCD Q relative error = O(ƛQCD/qT) q T degraded description 45

46 Collinear and TMD factorization The key of phenomenology : emergence of TMD and collinear distributions from factorization theorems fixed Q, variable qt d /dq T q T Q fixed-order term resummed term (W) TMD factorization collinear factorization A (x a ) B(x b ) collinear PDFs QCD Q q T A(x a, k Ta ) B(x b, k Tb ) TMD PDFs relative error = O(qT/Q) degraded description 46

47 Collinear and TMD factorization The key of phenomenology : emergence of TMD and collinear distributions from factorization theorems fixed Q, variable qt d /dq T q T Q Matching region fixed-order term resummed term (W) TMD PDFs TMD factorization degraded descriptions collinear factorization collinear PDFs QCD Q q T W, relative error = O(qT/Q) F.O., relative error = O(ƛQCD/qT) We need a prescription to deal with the region where both descriptions are not good 47

48 Collinear and TMD factorization The key of phenomenology : emergence of TMD and collinear distributions from factorization theorems fixed Q, variable qt d /dq T q T Q Matching region fixed-order term resummed term (W) TMD PDFs TMD factorization degraded descriptions collinear factorization collinear PDFs QCD The extraction of the nonperturbative (NP) part of TMDs is affected by the description of the whole qt range Q 48 Pheno: we are making progress q T Crucial, especially at low Q (e.g. JLab kinematics), where the regions shrink polarization?

49 W-term & TMDs W-term : transverse momentum resummation in terms of TMDs W (q T,Q)= Z d 2 b T (2 ) 2 eiq T b T W (bt,q) bt is the Fourier-conjugated variable of the (partonic and observed) transverse momenta Need a regularization to recover collinear factorization upon integration over qt: b T b T b min 1/Q =) Collins et al. PRD Z d 2 q T W (q T,Q) f h 1 i (x 1 ; µ) f h 2 j (x 2 ; µ) W (b T,Q) F h 1 i (x 1,b T ; µ, 1 ) F h 2 j (x 2,b T ; µ, 2 ) Product of Fourier-transformed TMDs TMD evolution is multiplicative in bt space 49

50 Quark TMD PDF Qiu-Zhang, Phys. Rev. D parameters: bmax, g1, g2, α g1 and α are fixed as a function of g2, bmax requiring continuity in bmax of the first and second derivative 50

51 ηc production at LHC d /dqt [nb/gev] log-average vs improved W+Y c production NP model b p min and b max s =7TeV R 0 2 = <y<4.5 LHCb Resummed Fixed-order Average Improved W+Y [30%] =1 =2 different preliminary q T [GeV] low-energy process Q = M(ηc) = 2.98 GeV bmin and bmax prescriptions smooth matching from W to FO - W dominates for qt < 1 GeV - FO dominates for qt > 3 GeV blue band: uncertainty from log-average matching red band: uncertainty from improved W+Y matching (larger) 51

52 TMD approach Philosophy : check if the structure of the IR divergencies is the same as in full QCD. If yes, the factorized form works as QCD, namely factorization is established virt,(1) no: It does not reproduce the physical (=QCD) result {H? same IR? f g/a 1 f g/b 1 } (1) virt yes: It reproduces the physical result and the hard part can be calculated by subtraction 52

53 Impact on Higgs physics G. Ferrera, talk at REF 2014, Antwerp, PDF uncertainties Intrinsic transverse momentum effects 53

54 Impact on Higgs physics G. Ferrera, talk at REF 2014, Antwerp, PDF uncertainties Intrinsic transverse momentum effects 53