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

k − 1

2∆

k + 1

2∆

P − 1

2∆

P + 1

2∆

H(k, P, ∆) H(x, k, ξ, ∆) H(x, ξ, ∆2) n

k=0 Ank(∆2) (2ξ)k

H(x, k, ξ, b) H(x, ξ, b) W(x, k, b) f(x, b) f(x, k) f(x) Fn(b) Fn(∆2) f(k, P) f(x, z)

• d2b
• d2b
• d2k
• d2k
• dk−
• dk−
• d2k
• dx xn−1

∆ = 0 ξ = 0 ξ = 0 ξ = 0 FT FT FT GTMD GPD TMD form factor GFFs PDF parton correlation function parton correlation function distribution impact parameter

• dx xn−1

Wigner distribution

Helicity of partons/target might be flipped Each distribution depends on flavor

[Fig. by Markus Diehl]

Factorization theorem

Bjorken kinematics Q2 → ∞, xB = const

A ∼ Cprocess ⊗ Htarget Multiparton distributions are suppressed in this kinematics

Constraints Positivity Polynomiality

GPD extraction from DVCS

(EIC white paper, 1212.1701)

Q2=100 GeV 2 Q2=50 GeV2

Planned DVCS at fixed targ.:

COMPASS- dσ/dt, ACSU, ACST JLAB12- dσ/dt, ALU, AUL, ALL

Current DVCS data at colliders:

ZEUS- total xsec ZEUS- dσ/dt H1- total xsec H1- dσ/dt H1- ACU

Current DVCS data at fixed targets:

HERMES- ALT HERMES- ACU HERMES- ALU, AUL, ALL HERMES- AUT Hall A- CFFs CLAS- ALU CLAS- AUL

1 10 10 2 10 3 10

• 4

10

• 3

10

• 2

10

• 1

1

x Q2 (GeV2)

E I C √ s = 1 4 G e V , . 1 ≤ y ≤ . 9 5 y ≤ . 6 y ≤ . 6 E I C √ s = 4 5 G e V , . 1 ≤ y ≤ . 9 5

Kinematic coverage of DVCS experiments.

.

Theoretically the cleanest, best understood is DVCS Interference with BH ⇒phase of the amplitude Polarization asymmetries ⇒ separate H, E, ˜ H, ˜ E Sensitive only to HDVCS =

• e2

f Hf + O(αs)Hg

DVMP may give access to GPD flavor structure, but theoretically is more complicated

Challenges in GPD extraction from pion production

(CLAS)

• 300
• 200
• 100

100 200 300 400

Q2=1.15 GeV2 xB=0.13

• 300
• 200
• 100

100 200 300 400

Q2=1.61 GeV2 xB=0.19

• 300
• 200
• 100

100 200 300 400

Q2=1.74 GeV2 xB=0.22

• 300
• 200
• 100

100 200 300 400

Q2=2.21 GeV2 xB=0.28

• 300
• 200
• 100

100 200 300 400 0.2 0.4 0.6 0.8 1 1.2 1.4

• t, GeV2

Q2=2.71 GeV2 xB=0.34

• 300
• 200
• 100

100 200 300 400 0.2 0.4 0.6 0.8 1 1.2 1.4

• t, GeV2

Q2=3.22 GeV2 xB=0.41 dσ/ dt [nb/ Ge V2] dσ/ dt [nb/ Ge V2]

d 4σ dQ2dxBdtdφπ = Γ(Q2, xB, E) 2π (σT + ǫσL +ǫ cos 2φπσTT +

• 2ǫ(1 + ǫ) cos φπσLT)

.

Tw-2 contribution is small, probes σL ∼

• {˜

H, ˜ E} ⊗ φ2;π

• 2

and underestimates significantly data Dependence on azimuthal angle φπ be- tween ee′ and πp planes, should not ex- ist in leading twist Signals that tw-3 contributions are pronounced σTT ∼ |{HT, ET} ⊗ φ3;π|2 σLT ∼ |{HT, ET} ⊗ φ3;π|2

⇒This channel requires significantly larger Q2 to access GPDs

GPDs from ρL-mesons

Probe unpolarized GPDs {H, E} ⊗ φ2;π, smaller twist-3 contributions

Challenge

Vector meson wave function unknown

• controlled by confinement (not SCSB), depends heavily on the model

Popular phenomenological parametrizations:

AdS/CFT wave function

fq(x), f¯

q(x)-unknown functions,

can be fixed from (hypothetical) DIS on ρ-mesons

Boosted Gaussian WF

everything except x and k⊥are free parameters 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

• f 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

Extremely large luminosity Both νµ and ¯ νµ can be used

Ongoing analysis of νp → µ−π+p,

¯ νp → µ+π−p in Bjorken kinematics

UTFSM MINERvA group: J. Miller et al.

Jefferson Laboratory Monochromatic beam, Ee = 11 GeV Luminosity L = 1036cm−2s−1 Beam/target can be polarized Suggested process: ep → νeπ−p

Charged current studies in ep experiments

Kinematic coverage of JLAB Monochromatic beam, Ee = 11 GeV Luminosity L = 1036cm−2s−1 Beam/target can be polarized Suggested process: ep → νeπ− p Neutrino νe momentum reconstructed via momentum conservation pν = p′ + pπ − p − pe

• final hadrons are charged, kinematics

resolution should be good. Variables xB, t, Q2 are functions of pion and proton energies Eπ, Ep and angle θπp between π− and p

t = 2 mp (mp − Ep) −Q2 = 2m2

p + m2 π − 2mp (Eπ + Ep) +

+ 2EπEp − 2

• E 2

p − m2 p

• E 2

π − m2 π cos θπp xB = Q2 Q2 + m2

π + 2EπEp − 2

• E2

p − m2 p

• E2

π − m2 π cos θπp

Cross-section in collinear factorization framework

.

• Coef. functions known up to NLO (JETPL 80, 226; EPJC 52, 933)

Weak dependence on factorization scale for µF 3 GeV Scale choice: µR = µF = Q Estimates of NNLO corrections: µR = µF ∈ (0.5, 2)Q NLO corrections increase all the cross-sections 50% ⇒NNLO corrections are needed ! NLO coefficient functions

φ2(z) π W ±/Z φ2(z) π W ±/Z φ2(z) π W ±/Z φ2(z) π W ±/Z φ2(z) π W ±/Z φ2(z) π W ±/Z φ2(z) π W ±/Z φ2(z) π W ±/Z φ2(z) π W ±/Z φ2(z) π W ±/Z φ2(z) π W ±/Z φ2(z) π W ±/Z φ2(z) π W ±/Z φ2(z) π W ±/Z

Sea quarks contribution

π W ±/Z π W ±/Z

Gluons contribution (LO+NLO)

π W ±/Z π W ±/Z π W ±/Z π W ±/Z π W ±/Z π W ±/Z

Results for the e → νeM (NLO in αs)

1 2 3 4 5 6 7

dσ/dxBdQ2 (10−40 cm2/GeV2)

0.2 0.3 0.4 0.5 0.6 0.7 0.8

xB

ep → νeπ−p

Total Gluons only Ee=11 GeV Q2=2.5 GeV2 0.2 0.4 0.6 0.8 1.0

dσ/dxBdQ2 (10−40 cm2/GeV2)

0.3 0.4 0.5 0.6 0.7 0.8

xB

ep → νeπ−p

Total Gluons only Ee=11 GeV Q2=4 GeV2

.

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

dσ(H)/dσ(all)

0.2 0.3 0.4 0.5 0.6 0.7 0.8

ep → νeπ−p

Q2=2.5 GeV2 Q2=4 GeV2 Ee=11 GeV

Estimates were done with Kroll-Goloskokov parametrization Mostly sensitive to GPD Hu, Hd ( 80% of result). Gluons give minor contribution and slightly de- crease the cross-section (interference term q − g is negative)

Results for the e → νeM (NLO in αs)

0.05 0.1 0.15 0.2 0.25 0.3 0.35

dσ/dxBdQ2 (10−40 cm2/GeV2)

0.2 0.3 0.4 0.5 0.6 0.7 0.8

xB

ep → νeK−p

Total Gluons only Ee=11 GeV Q2=2.5 GeV2 0.5 1.0 1.5 2.0 2.5 3.0 3.5

dσ/dxBdQ2 (10−40 cm2/GeV2)

0.2 0.3 0.4 0.5 0.6 0.7 0.8

xB

en → νeπ−n

Total Gluons only Ee=11 GeV Q2=2.5 GeV2

.

0.5 1.0 1.5 2.0

dσ(Hi)/dσ(all)

0.2 0.3 0.4 0.5 0.6 0.7 0.8

ep → νeK−p

|H|2 |G|2 − (H∗G + G∗H) Ee=11 GeV Q2=2.5 GeV2

For K-mesons, suppression by an order of mag- nitude (Cabibbo forbidden), smaller statistics

• Sizeable negative contribution from interfe-

rence H∗G + G∗H For neutrons the cross-section is of the same order (∼ 40% less than in ep → νeπ−p), but kinematics reconstruction might be more difficult

Contaminations by twist-3 & Bethe-Heitler mechanisms

Twist-3 contributions Quark spin flip ⇒ probe transversity GPDs {HT, ET, ˜ HT, ˜ ET} ⊗ φ3;π Bethe-Heitler mechanism (diagram (b))

. e− νe W − π−

(a)

e− νe W − π− γ∗

(b)

formally is suppressed by αem kinematically is enhanced by Q2/

• t · α2

s(Q2)

• ≫ 1 in

Bjorken kinematics Both mechanisms generate azimuthal asymmetry d 4σ(tot) dt dQ2d ln ν dϕ = 1 2π d 3σ(DVMP) dt dQ2d ln ν ×

• 1 +
• n

(cn cos nϕ + sn sin nϕ)

• .

.

Use harmonics cn, sn 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 4σ(tot) dt dQ2d ln ν dφ = 1 2π d 3σ(DVMP) dt dQ2d ln ν ×

• 1 +
• n

(cn cos nφ + sn sin nφ)

• Twist-3 effects

.

0.1 0.2 0.3 0.4 0.5

ci, si

0.3 0.4 0.5 0.6 0.7

xB

ep → νeπ−p

c0 c1 s1 Ee=11 GeV Q2=4 GeV2 ∆⊥=0.1 GeV

Bethe-Heitler mechanism

• 0.8
• 0.6
• 0.4
• 0.2

0.0 0.2 0.4

ci, si × 102

0.3 0.4 0.5 0.6 0.7 0.8

xB

ep → νeπ−p

c0 × 102 c1 × 102 s1 × 102 Ee=11 GeV Q2=4 GeV2 ∆⊥=0.1 GeV

In both cases the angular harmonics are small

How do such events look like in lab frame?

Kinematic reconstruction Need only energies Eπ, Ep and angle θπp

t = 2 mp (mp − Ep) −Q2 = 2m2

p + m2 π − 2mp (Eπ + Ep) +

+ 2EπEp − 2 | pπ| | pp| cos θπp xB = Q2 Q2 + m2

π + 2EπEp − 2 |

pp| | pπ| cos θπp | pi| =

• E 2

i − m2 i

Luminosity L = 1035cm−2s−1⇒∼ 6 π−/day in Bjorken kinematics (green region) Angles of interest: (0.3 θπp 0.8) rad

• smaller angles lead to small Wπp 2 GeV

(resonance region)

• larger angles lead to small Q2 2.5 GeV

.

Cuts to eliminate backgrounds

Pion misidentification as electron Elastic scattering e−p → e−p Neutrino energy Eν distribution after Bjorken regime cuts in e−p → νeπ−p

2 4 6 8 0.05 0.10 0.15 Eν, GeV ρ(Eν), GeV-1 Cuts Q2>2.5 GeV2, W>2GeV imposed

For elastic scattering ”Eν” ≡ 0 ⇒Additional cut Eν > 1 GeV allows to get rid of elastic background Multihadron photoproduction e−p → Xπ−p

p p′ e e′ π+ π−

Missing (“neutrino”) momentum squared:

p2

ν =

• i=undetected

pi 2 ≥

• i=undetected

mi 2

In case of true CCDVMP p2

ν = m2 N − Q2 + 2Ee (Ep + Eπ − mN)

− 2

• E 2

e − m2 e (pp,z + pπ,z) ≡ m2 ν (... eV)2

⇒Cut p2

ν < m2 π to eliminate this background

Extension to ρ−

L CC-production

DAs of π− vs. ρ−

L

Leading twist: Quark structure differs from pion only by γ5:

φ2;π(u) ∼

• dz ei(2u−1)z
• ¯

ψ(0)γ+γ5ψ(z)

• π
• φ(L)

2;ρ(u) ∼

• dz ei(2u−1)z
• ¯

ψ(0)γ+ψ(z)

• ρL
• e → e M case

γ5 ⇒sensitivity to different GPD sets,

ρL : (H, E)

• p′| ¯

ψ(0)γ+ψ(z)|p

• π :
• ˜

H, ˜ E

• p′| ¯

ψ(0)γ+γ5ψ(z)|p

• e → νe M case

sensitivity to exactly the same GPDs:

γ5γµ (1 − γ5) = γµ (1 − γ5) Charged current, asymptotic DA

• For φ2;π(u) = φ(L)

2;ρ(u) = 6u(1 − u) in the

leading twist A(tw−2,asy)

e→νeρ−

L

= A(tw−2,asy)

e→νeπ−

Charged Current, realistic DA In the leading twist meson DA enters as a multiplicative factor φ−1

2;M =

• du φ2;M(u)

u ⇒ dσ(tw−2)

e→νeρ−

L

dσ(tw−2)

e→νeπ−

=

• φ−1

2;ρL

φ−1

2;π

2 = const

• any (xB, Q2, t)-dependence of this

ratio⇒twist-three effects

Summary

Charged current Deeply Virtual Pion Production can be used as an additional source

• f information on proton structure (its GPDs)
• Can be studied at νp and ep experiments thanks to large luminosity of modern

experiments.

• Cross-section dominated by unpolarized GPDs H, E ; expect smaller

contamination by higher twist and Bethe-Heitler corrections.

• Need to impose cuts in (missing) neutrino energy Eν 1 GeV and (missing)

invariant mass (m2

ν m2 π) to suppress backgrounds

Summary

Charged current Deeply Virtual Pion Production can be used as an additional source

• f information on proton structure (its GPDs)
• Can be studied at νp and ep experiments thanks to large luminosity of modern

experiments.

• Cross-section dominated by unpolarized GPDs H, E ; expect smaller

contamination by higher twist and Bethe-Heitler corrections.

• Need to impose cuts in (missing) neutrino energy Eν 1 GeV and (missing)

invariant mass (m2

ν m2 π) to suppress backgrounds

T HANK YOU FOR YOUR AT T ENT ION!