THE TENSOR AND THE SCALAR CHARGES OF THE NUCLEON FROM HADRON - - PowerPoint PPT Presentation

Instituto de Física, UNAM, Mexico

AURORE COURTOY

THE TENSOR AND THE SCALAR CHARGES

OF THE NUCLEON FROM HADRON PHENOMENOLOGY

partially based on Phys.Rev.Lett. 115 (2015) 162001

OUTLINE

How can hadronic physics help BSM search? Hadronic observables extraction Impact on β-decay observables

QCD FOR BSM

• Direct search
• Large-x PDF
• αs
• Indirect search
• Parity Violating DIS
• Beyond V-A interactions
• ...

HERE

can be sketched as

‟

h d

Γ

• ! u e−(pe)¯

νe(pν) i ⇥ [hP|¯ u Γ d|Ni] ”

ΒETA DECAY IN SM

N(pn) − → P(pp)e−(pe)¯ νe(pν)

Electroweak: V-A Proton structure: gV & gA

[Jackson et al., PR106]

BETA DECAY OBSERVABLES

• Neutron decay rate parameterized:

d3Γ = 1 (2π)5 G2

F |Vud|2

2 peEe (E0 − Ee)2 dEedΩedΩν ×ξ

• 1 + ape · pν

EeEν + bme Ee + sn

• A pe

Ee + B pν Eν + . . .

• Effective Hamiltonian for β-decay

➡

Lorentz low energy constants CS,P,V,A,T

➡

SM 1param λ=-CA/CV

➡

a(λ), A (λ), B (λ)

[Lee & Yang, PR104]

➡

sensitivity of neutron beta decay to new physics

• b=0 in SM
• B ⊂ bν =0 in SM

[Jackson et al., PR106]

BETA DECAY OBSERVABLES

• Neutron decay rate parameterized:

d3Γ = 1 (2π)5 G2

F |Vud|2

2 peEe (E0 − Ee)2 dEedΩedΩν ×ξ

• 1 + ape · pν

EeEν + bme Ee + sn

• A pe

Ee + B pν Eν + . . .

• [Lee & Yang, PR104]

➡

sensitivity of neutron beta decay to new physics

• b=0 in SM
• B ⊂ bν =0 in SM

b = 2 √ 1 − α2 1 + 3λ2

• Re

CS CV

• + 3λ2Re

CT CA

• this point, we already have a reasonably strong constraint

➡

b sensitive to scalar and tensor LEC

➡

same for bν

NEW PHYSICS IN δ

λ→pretty well known

SCALAR & TENSOR INTERACTIONS

from various processes

decay rate for super allowed 0+→0+ decay rate for beta decay (total, angular correlation in unpolarized & polarized parts) radiative pion decay

CV = CSM

V

+ δCV C′

V = CSM V

+ δC′

V

CA = CSM

A

+ δCA C′

A = CSM A

+ δC′

A

CS = δCS C′

S = δC′ S

CT = δCT C′

T = δC′ T .

Extract LEC

C

SM

V

= gV C

SM

A = −gA

Best constraints so far

−0.0026 < CT/CA < 0.0024

[Pattie et al., PRC88] [Hardy et al., PRC91]

@1σ

@95%CL

CS/CV = 0.0014(13)

Low energy

NEW FUNDAMENTAL INTERACTIONS

• Effective field theories for low energy

➡

New (heavy) dof integrated out

• Consider all Dirac bilinears for EW interactions

➡

1, γ5, γμ(1+γ5), σμν

➡

Define ``Wilson coefficient" for new interaction

High energy

New particles produced directly New particles hints

• in loops
• mediators of interaction
• ...

EFT AT THE QUARK LEVEL

[Bhattarchaya et al., PRD85] [Cirigliano et al., NPB 830]

BETA DECAY IN EFT

SM 4-fermion interaction

L

(eff) = LSM +

X

i

1 Λ2

i

Oi

dj → uil−¯ νl

u d u d

→ ¯ Ldj →uiℓ− ¯

νℓ = −g2

2m2

W

Vij

• 1 + [vL]ℓℓij

¯ ℓLγµνℓL ¯ ui

Lγ µdj L + [vR]ℓℓij ¯

ℓLγµνℓL ¯ ui

Rγ µdj R

+ [sL]ℓℓij ¯ ℓRνℓL ¯ ui

Rdj L + [sR]ℓℓij ¯

ℓRνℓL ¯ ui

Ldj R

+ [tL]ℓℓij ¯ ℓRσµννℓL ¯ ui

Rσ µνdj L

• + h.c.,

Scalars

εS≣sL+sR

Tensor

εT≣tL

right

STANDARD MODEL

LEC IN TERMS OF HADRONIC × NEW INT.

CSM = GF √ 2 Vud (gV − gA)

CS = GF √ 2 Vud gS✏S CT = GF √ 2 Vud 4 gT ✏T

‟ ”

h d

Γ

• ! u e−(pe)¯

νe(pν) i ⇥ [hP|¯ u Γ d|Ni]

NEW BSM S & T INTERACTIONS

}

[Bhattarchaya et al., PRD85] [Cirigliano et al., NPB 830]

New LEC factorized into hadronic contribution & new EW interaction

|gT ✏T | < 6 · 10−4 |gS✏S| = 0.0014 ± 0.0013

@95%CL

@1σ

Precision with which the NEW COUPLINGS can be measured depend on the knowledge of hadronic charges

Isovector vector FF Isovector tensor FF

hP(pp, Sp)|¯ uγµd|N(pn, Sn)i = gV (t) ¯ uP γµuN + O( p t/M) hP(pp, Sp)|¯ uσµνd|N(pn, Sn)i = gT

• t, Q2

¯ uP σµνuN FORM FACTORS

t=(pn-pp)2 Q2 RGE scale

MATCHING AT HADRONIC LEVEL

Neutron Proton

hP(pp, Sp)|¯ uΓd|N(pn, Sn)i

⇓

When t→0, g(0)≡charge

Exist in hadronic physics

Fundamental charges for γμ & γμγ5 only

HADRONIC STRUCTURE

• Nonlocal matrix element for proton structure
• Parton Distribution Functions
• built from Lorentz symmetry from vectors at hand
• defined in Bjorken scaling
• nonperturbative objects
• 1st principle related to ``charges"

Structural charges for the others

Scalar & tensor charge accessible through sum rules of Parton Distributions

PDF AT LEADING TWIST

Lorentz structure Discrete symmetries Vectors at hand... To leading twist:

PDFs ⇒

f q

1 (x) ,

gq

1(x) ,

hq

1(x)

• Vector

Tensor

Dirac operator ⇒

Axial-vector

Kinematics of the Bjorken scaling Q2→∞ p.q→∞ Q2/2p.q≡x=finite

Charges ⇒

gV, gA, gT

Z 1

−1

dx huV −dV

1

(x) = gT

DEFINITION AND FACTORIZATION

ACCESS TO DISTRIBUTION FUNCTIONS

di-π, ...

Semi-inclusive processes

π, ...

Inclusive processes

π, ...

Exclusive processes

σ→ PDF×dσ σ→ PDF×dσ×Fragmentation Function

σ→ |Generalized PDF×H× Meson Amplitude|2

〉

θ sin

UT,p

φ sin

A

〈

x z ]

2

c [GeV/

hh

M

• 2

10

• 1

10 1

• 0.15
• 0.1
• 0.05

0.05 0.2 0.4 0.6 0.8

• 0.15
• 0.1
• 0.05

0.05

0.5 1 1.5 2

• 0.15
• 0.1
• 0.05

0.05

〉

θ sin

UT,d

φ sin

A

〈

• 2

10

• 1

10 1

• 0.15
• 0.1
• 0.05

0.05 0.2 0.4 0.6 0.8

• 0.15
• 0.1
• 0.05

0.05

0.5 1 1.5 2

• 0.15
• 0.1
• 0.05

0.05

2007 Proton Data 2002-4 Deuteron Data

(z, Mh)-dpdence determined by DiFF from Belle

[A.C., Bacchetta, Radici, Bianconi, Phys.Rev. D85]

x-dependence only from Transversity

[A.C., et al, PRL 2012, JHEP 2013, 2015]

TRIPTIC OF TARGET SPIN ASYMMETRY SIDIS PRODUCTION OF PION PAIRS @ COMPASS & HERMES

EXAMPLE OF DATA & EXTRACTION

TRANSVERSITY PDF

• Semi-inclusive processes
• eN→e π X Torino et

al

• eN→e (ππ) X Pavia et al
• Exclusive: eP→e π0 P GGL

[Goldstein et al, PRD 2015]

0.01 0.03 0.1 0.3 1

• 0.4
• 0.2

0.0 0.2 0.4 0.6 x x h1

uv

1σ error band from replicas @2.4 GeV2 PAVIA

Torino 2013 @2.4 GeV2 Kang et al central value

[Radici et al., JHEP 2015]

UNCERTAINTY & DATA RANGE

flexible functional form

0.0 0.2 0.4 0.01 0.10

x x h1

uV(x)-x h1 dV(x)/4 fit data HERMES data COMPASS

rigid functional form

0.0 0.2 0.4 0.01 0.10

x x h1

uV(x)-x h1 dV(x)/4 fit data HERMES data COMPASS

1 1

ROLE OF FUNCTIONAL FORM FOR FIT

MORE DATA

SOLUTIONS

1

Mh

0.25 0.5

x

0.025 0.05 0.075 0.1 0.125 0.15

AUT

sinφR

0.2

CLAS12 projection on proton target

• 0.1
• 0.08
• 0.06
• 0.04
• 0.02

AUT

sinφR

0.2 1

Mh

0.25 0.5

x

SoLID projection on neutron target 0.007 < x < 0.53

procedure repeated 100 times (until reproduce mean and std. deviation of original data)

mHx,z,PhT,Q2L, proton target

Xx\~0.15 XQ2\~2.9 GeV2

0.0 0.4 0.8 PhT 1 2 3

p-

0.27<z<0.30 0.38<z<0.48

x hu−u

1

(x)

x Pavia 15

JHEP1505 (2015) 123

+ MONTE CARLO LIKE FITTING

?

ISOVECTOR TENSOR CHARGE

ge gT = δuv−δdv.

Pavia flexible 0.125

• ‡

‡

Ú

Ê

Ù Ï

¯

1 2 3 4 5 6 7 0.4 0.6 0.8 1.0 1.2 du-dd HQ2 = 4 GeV2L

WITH MONTE CARLO LIKE FITTING

for gT = 0.81 ± 0.44 % confidence level.

In Fig. 11, the at Q2 = 4 GeV2 We compare it wi

LATTICE RESULTS PRESENT TINY ERRORS W.R.T. HADRONIC EXTRACTIONS HERE TESTING GROUND FOR LATTICE QCD CALCULATIONS

Various Lattice QCD results

0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.5 1.0 1.5 2.0 x ∆h1

uvxh1 uvx

0.0 0.2 0.4 0.6 0.8 1.0 0.5 1.0 1.5 x ∆h1

uvxh1 uvx

FUTURE

• GGL depends on new JLab data
• Pavia depends on new JLab data
• Torino depends on TMD evolution +new JLab data

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.0 0.5 1.0 1.5 2.0 x ∆h1

uvxh1 uvx

Ye et al.,1609.02449 Courtoy et al, PRL 115

rigid flex extra-flex

xBj= 0.2, Q2= 1.5 GeV2

* p o p'

u = 0.91!0.08, d = -0.12 u = 0.6, d = -0.12 u = 1.4, d = -0.12

• t (GeV2)

A

UTsins

• 0.3
• 0.2
• 0.1

0.1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

NOW WITH gT± σgT AND

TENSOR INTERACTION AS OF NOW

PNDME LHPC RQCD Single hadron FF Dihadron FF DVMP

|gT ✏T | < 6 · 10−4

we find....

gT

New PNDME: gT =0.987(51)(20) [PRD94] NME compatible results [1611.07452] Ye et al.: gT =0.64±0.021 (Q2=2.4GeV2)

★ HESSIAN PROPAGATION

• Usual error propagation

★ MONTE CARLO APPROACH

• N replicas of data within xσ gaussian noise

★ SCATTER PLOT

• 2+ D
• Random generation of allowed values within xσ

★ RFIT METHOD

• Theoretical param anywhere within [a-σa, a+σa] only
• ther params as usual

★ ...

ERROR TREATMENT

σ2

f =

X

a,b ∈ params

∂f ∂a covab ∂f ∂b

∆χ2 = 1

with here

f ± σf = X%CL × fi, i = 1, · · · N

X = 68, 90, 95, ... −2 ln Lcalc({ycalc}) ≡ 0, ∀ ycalc,i ∈ [ycalc,i ± δycalc,i] ∞,

• therwise

NOW WITH gT± σgT AND

TENSOR INTERACTION AS OF NOW

|gT ✏T | < 6 · 10−4

Rfit method:

Pavia 2015 1D for <εT> only

• present: |εT| < 0.00162
• compared to

Naviliat-Cuncic & González-Alonso: |εT| < 0.0013

Monte Carlo approach:

• with gS = 1.02 ± 0.11

from González-Alonso and Martin Camalich, PRL 112

• with gT = 0.81 ± 0.44

from Pavia 15

• to be compared to <gT>=0.839(357)

from GGL & Pavia 15

εT vs. εS plane from b0+ and b

NEW SCALAR-TENSOR

1σ errors

• Hessian in blue & pink
• Rfit method in red
• Scatter plot in blue

Warning: not a global fit

• ϵ

ϵ

CLAS collaboration

• S. Pisano et al., to be published

A.C. et al. 1405.7659

DIHADRON ASYMMETRY FOR UNPOLARIZED TARGET INVOLVING SCALAR PDF (subleading)

CAN WE DO THE SAME FOR SCALAR CHARGE?

SCALAR CHARGE related to e(x=0) lots of things to think of...

■ ■ ■ ▲ ▲ ▲

• ■

• ()

Spectator χQSM Bag

WORTH MENTIONING

HADRONIC MATRIX ELEMENTS RELATED TO OUTSTANDING QCD QUESTIONS STRUCTURE OF HADRONS→CONFINEMENT, CHIRAL SYMMETRY,...

CONCLUSIONS

Evaluation of bounds for BSM tensor interaction

➡ from hadronic matrix elements extracted from experiments ➡ as opposed to lattice calculations

★ Hadronic uncertainties are still very large ★ However, competitive results expected from future hadronic experiments ★ Complementarity +testing of lattice results

FUTURE OF BETA DECAY OBSERVABLES

• Neutron decay rate parameterized:
• Nab collaboration plans to measure b, term sensitive to CS and CT with precision of

10^-3

• abBA collaboration (and others) plans to measure A and B angular coefficients for

polarized neutrons, B is also sensitive to CS and CT with precision of 10^-3

d3Γ = 1 (2π)5 G2

F |Vud|2

2 peEe (E0 − Ee)2 dEedΩedΩν ×ξ

• 1 + ape · pν

EeEν + bme Ee + sn

• A pe

Ee + B pν Eν + . . .

SCALE OF NEW PHYSICS

Redefinition of "new" scale

effective coupling (rescaled) but underlying mechanism not known

GF = g2/(4 √ 2m2

W)

✏i ∝ m2

W/Λ2 i

where mW enters through