GPDs from charged current meson production in ep experiments Marat - PowerPoint PPT Presentation

GPDs from charged current meson production in ep experiments Marat Siddikov In collaboration with Ivan Schmidt Based on: PRD 96 (2017), 096006, PRD 95 (2017), 013004, PRD 91 (2015) 073002, PRD 89 (2014) 053001 PRD 87 (2013) 033008, PRD 86 (2012) 113018

Nucleon (hadron) structure Formidable theoretical problem (nonperturbative strongly interacting ¯ qqg ensemble) Parton distributions: concise descriptions of nonperturbative structure . Relations between parton distributions Factorization theorem k − 1 k + 1 2 ∆ 2 ∆ [Fig. by Markus Diehl] P − 1 2 ∆ P + 1 2 ∆ parton correlation function ∆ = 0 H ( k, P, ∆) f ( k, P ) � dk − parton correlation function ξ = 0 FT Bjorken kinematics H ( x, k , ξ, b ) H ( x, k , ξ, ∆ ) GTMD dk − W ( x, k , b ) � Wigner distribution Q 2 → ∞ , x B = const � d 2 k � d 2 k ξ = 0 FT H ( x, ξ, ∆ 2 ) � d 2 b H ( x, ξ, b ) GPD A ∼ C process ⊗ H target FT f ( x, z ) f ( x, k ) f ( x, b ) impact parameter Multiparton distributions � dx x n − 1 distribution TMD are suppressed in this � d 2 k ξ = 0 kinematics � n k =0 A nk (∆ 2 ) (2 ξ ) k � d 2 b � dx x n − 1 GFFs f ( x ) F n ( b ) F n (∆ 2 ) PDF form factor Constraints Helicity of partons/target might be flipped Positivity Each distribution depends on flavor Polynomiality

GPD extraction from DVCS (EIC white paper, 1212.1701) . Current DVCS data at colliders: 5 9 0 . 10 3 ZEUS- total xsec H1- total xsec ≤ 6 . ZEUS- d σ /dt H1- d σ /dt y 0 ≤ ≤ H1- A CU 1 y 0 . 0 Current DVCS data at fixed targets: 6 , . V 0 e ≤ G HERMES- A LT HERMES- A CU y 0 HERMES- A LU , A UL , A LL 4 1 HERMES- A UT Hall A- CFFs = s CLAS- A LU CLAS- A UL √ 10 2 Q 2 =100 GeV 2 C Q 2 (GeV 2 ) I E Planned DVCS at fixed targ.: 5 Q 2 =50 GeV 2 9 . COMPASS- d σ /dt, A CSU , A CST 0 ≤ JLAB12- d σ /dt, A LU , A UL , A LL y ≤ 1 Theoretically the cleanest, 0 . 0 V , e G best understood is DVCS 5 10 4 = s √ C I Interference with BH E ⇒ phase of the amplitude 1 Polarization asymmetries -4 -3 -2 -1 10 10 10 10 1 ⇒ separate H , E , ˜ H , ˜ E x Sensitive only to Kinematic coverage of DVCS experiments. f H f + O ( α s ) H g � e 2 H DVCS = DVMP may give access to GPD flavor structure, but theoretically is more complicated

Challenges in GPD extraction from pion production (CLAS) . 400 400 Tw-2 contribution is small, probes Q 2 =1.15 GeV 2 Q 2 =1.61 GeV 2 x B =0.13 x B =0.19 300 300 200 200 2 100 100 � � � { ˜ H , ˜ σ L ∼ E } ⊗ φ 2 ; π 0 0 � � -100 � -100 -200 -200 -300 V 2 ] -300 V 2 ] and underestimates significantly data 400 400 Q 2 =1.74 GeV 2 Q 2 =2.21 GeV 2 dσ/ dt [nb/ Ge dσ/ dt [nb/ Ge x B =0.28 x B =0.22 300 300 Dependence on azimuthal angle φ π be- 200 200 tween ee ′ and π p planes, should not ex- 100 100 0 0 -100 -100 ist in leading twist -200 -200 -300 -300 400 400 Q 2 =2.71 GeV 2 Q 2 =3.22 GeV 2 x B =0.34 x B =0.41 300 300 200 200 100 100 0 0 -100 -100 -200 -200 -300 -300 0 0.2 0.4 0.6 0.8 1 1.2 1.4 0 0.2 0.4 0.6 0.8 1 1.2 1.4 -t, GeV 2 -t, GeV 2 dQ 2 dx B dtd φ π = Γ( Q 2 , x B , E ) d 4 σ Signals that tw-3 contributions are ( σ T + ǫσ L 2 π pronounced + ǫ cos 2 φ π σ TT σ TT ∼ |{ H T , E T } ⊗ φ 3 ; π | 2 � + 2 ǫ ( 1 + ǫ ) cos φ π σ LT ) σ LT ∼ |{ H T , E T } ⊗ φ 3 ; π | 2 ⇒ This channel requires significantly larger Q 2 to access GPDs

GPDs from ρ L -mesons Probe unpolarized GPDs { H , E } ⊗ φ 2 ; π , smaller twist-3 contributions Challenge Vector meson wave function unknown • controlled by confinement (not SCSB), depends heavily on the model Popular phenomenological parametrizations: Boosted Gaussian WF AdS/CFT wave function f q ( x ) , f ¯ q ( x ) -unknown functions, everything except x and k ⊥ are free can be fixed from (hypothetical) parameters DIS on ρ -mesons Uncertainty in WF translates into significant uncertainty in . extraction of GPDs from this channel

Our suggestion Charged current π/ K -production can be used as a complementary source of information on GPDs V − A structure of interaction ⇒ access to unpolarized GPDs H , E • Relative contribution of higher twist corrections smaller Good knowledge of pion and kaon WF, closeness of DAs due to SU ( 3 ) f ⇒ can extract full flavor structure of GPD

Where such processes can be studied ? MINERvA@Fermilab Jefferson Laboratory Monochromatic beam, E e = 11 GeV Extremely large luminosity Luminosity L = 10 36 cm − 2 s − 1 Both ν µ and ¯ ν µ can be used Beam/target can be polarized Ongoing analysis of ν p → µ − π + p , ν p → µ + π − p in Bjorken kinematics ¯ UTFSM MINERvA group: J. Miller et al. Suggested process: ep → ν e π − p

Charged current studies in ep experiments Suggested process: ep → ν e π − p Kinematic coverage of JLAB Monochromatic beam, E e = 11 GeV Neutrino ν e momentum reconstructed via Luminosity L = 10 36 cm − 2 s − 1 momentum conservation Beam/target can be polarized p ν = p ′ + p π − p − p e -final hadrons are charged, kinematics resolution should be good. Variables x B , t , Q 2 are functions of pion and proton energies E π , E p and angle θ π p between π − and p t = 2 m p ( m p − E p ) − Q 2 = 2 m 2 p + m 2 π − 2 m p ( E π + E p ) + � � E 2 p − m 2 E 2 π − m 2 + 2 E π E p − 2 π cos θ π p p Q 2 x B = � � Q 2 + m 2 π + 2 E π E p − 2 E 2 p − m 2 E 2 π − m 2 π cos θ π p p

Cross-section in collinear factorization framework Coef. functions known up to NLO ( JETPL 80 , 226; EPJC 52 , 933 ) . Weak dependence on factorization scale for µ F � 3 GeV Scale choice: µ R = µ F = Q Estimates of NNLO corrections: µ R = µ F ∈ ( 0 . 5 , 2 ) Q NLO corrections increase all the cross-sections � 50% ⇒ NNLO corrections are needed ! NLO coefficient functions Sea quarks contribution W ± /Z W ± /Z W ± /Z W ± /Z W ± /Z π π π φ 2 ( z ) φ 2 ( z ) φ 2 ( z ) π π W ± /Z W ± /Z W ± /Z Gluons contribution (LO+NLO) π φ 2 ( z ) π π W ± /Z W ± /Z W ± /Z φ 2 ( z ) φ 2 ( z ) W ± /Z W ± /Z W ± /Z π π π π π π φ 2 ( z ) φ 2 ( z ) φ 2 ( z ) W ± /Z W ± /Z W ± /Z W ± /Z W ± /Z W ± /Z π π π π π π φ 2 ( z ) φ 2 ( z ) φ 2 ( z ) W ± /Z W ± /Z π π φ 2 ( z ) φ 2 ( z )

Results for the e → ν e M (NLO in α s ) ep → ν e π − p ep → ν e π − p dσ/dx B dQ 2 (10 − 40 cm 2 /GeV 2 ) dσ/dx B dQ 2 (10 − 40 cm 2 /GeV 2 ) Total Total 7 Gluons only Gluons only 1.0 E e =11 GeV E e =11 GeV 6 Q 2 =2.5 GeV 2 Q 2 =4 GeV 2 0.8 5 4 0.6 3 0.4 2 0.2 1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.3 0.4 0.5 0.6 0.7 0.8 x B x B ep → ν e π − p . Estimates were done with Kroll-Goloskokov parametrization 0.9 0.8 Mostly sensitive to GPD H u , H d dσ ( H ) /dσ ( all ) 0.7 ( � 80 % of result). 0.6 Gluons give minor contribution and slightly de- 0.5 0.4 crease the cross-section (interference term q − g is 0.3 E e =11 GeV negative) 0.2 Q 2 =2.5 GeV 2 0.1 Q 2 =4 GeV 2 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Results for the e → ν e M (NLO in α s ) ep → ν e K − p en → ν e π − n dσ/dx B dQ 2 (10 − 40 cm 2 /GeV 2 ) dσ/dx B dQ 2 (10 − 40 cm 2 /GeV 2 ) Total Total 0.35 3.5 Gluons only Gluons only E e =11 GeV E e =11 GeV 0.3 3.0 Q 2 =2.5 GeV 2 Q 2 =2.5 GeV 2 0.25 2.5 0.2 2.0 0.15 1.5 0.1 1.0 0.05 0.5 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.2 0.3 0.4 0.5 0.6 0.7 0.8 x B x B ep → ν e K − p . For K -mesons, suppression by an order of mag- |H| 2 nitude (Cabibbo forbidden), smaller statistics |G| 2 2.0 • Sizeable negative contribution from interfe- − ( H ∗ G + G ∗ H ) dσ ( H i ) /dσ ( all ) rence H ∗ G + G ∗ H E e =11 GeV 1.5 Q 2 =2.5 GeV 2 For neutrons the cross-section is of the same order ( ∼ 40 % less than in ep → ν e π − p ), but kinematics 1.0 reconstruction might be more difficult 0.5 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Contaminations by twist-3 & Bethe-Heitler mechanisms Twist-3 contributions Quark spin flip ⇒ probe transversity GPDs { H T , E T , ˜ H T , ˜ E T } ⊗ φ 3 ; π Bethe-Heitler mechanism (diagram (b)) ν e ν e formally is suppressed by α em . kinematically is enhanced π − W − π − by Q 2 / t · α 2 s ( Q 2 ) � � ≫ 1 in W − e − e − γ ∗ Bjorken kinematics (a) (b) Both mechanisms generate azimuthal asymmetry � � d 4 σ ( tot ) d 3 σ ( DVMP ) dt dQ 2 d ln ν d ϕ = 1 � dt dQ 2 d ln ν × 1 + ( c n cos n ϕ + s n sin n ϕ ) 2 π n Use harmonics c n , s n to quantize the ef- . . fects of twist-3 and BH corrections

Contaminations by twist-3 & Bethe-Heitler mechanisms Generate azimuthal asymmetry, quantify effect in terms of angular harmonics � � d 4 σ ( tot ) d 3 σ ( DVMP ) dt dQ 2 d ln ν d φ = 1 � dt dQ 2 d ln ν × 1 + ( c n cos n φ + s n sin n φ ) 2 π n Twist-3 effects Bethe-Heitler mechanism . ep → ν e π − p ep → ν e π − p c 0 c 0 × 10 2 E e =11 GeV E e =11 GeV 0.4 c 1 c 1 × 10 2 Q 2 =4 GeV 2 0.5 Q 2 =4 GeV 2 s 1 s 1 × 10 2 0.2 ∆ ⊥ =0.1 GeV ∆ ⊥ =0.1 GeV c i , s i × 10 2 0.4 0.0 c i , s i -0.2 0.3 -0.4 0.2 -0.6 0.1 -0.8 0.3 0.4 0.5 0.6 0.7 0.8 0.3 0.4 0.5 0.6 0.7 x B x B In both cases the angular harmonics are small