The Loop Corrections to the ParityViolating Elastic electron-proton
Scattering
Yu-Chun Chen
Institute of Physics, AS
Nov 29th 2008
Outline
Motivation
Parity-Violating asymmetry in the elastic
electron-proton scattering
Corrections to the Parity-Violating asymmetry
Partonic calculation
Results and discussion
Conclusion
Motivation
The implications of two-photon physics.
Rosenbluth separation
reduced cross section:
Include loop correction:
Polarization transfer
Parity-Violating asymmetry in the
elastic electron-proton scattering
An important observable to extract s form factors .
At tree level, parity violation in
elastic electron scattering is caused by
interference of the diagrams with the
single photon and single Z0-boson
exchange. The four-momentum q ≣ p’-p,
and Q2 ≣ -q2.
LO corrections：2 γ × 1 Z, 1 γ × γ Z, 1 γ × 2 Z, 1 γ × 2 W, …
The parity violating helicity asymmetry in elastic eN scattering
for a polarized lepton beam are defined by:
Assuming the distribution of u quarks in the proton is the same
as that of d quarks in the neutron(in SM), which gives：
The leading effect in elastic e-p scattering can be expressed as：
s content
Rosenbluth separation method (LT)
reduced cross section:
at a fix Q2, vary ε
( 1/ε= 1 +2(1+τ)tan2(θlab/2) )
Separation method for APV
Corrections to Parity-Violating
asymmetry
In the limit of Q2 =0, W.J. Marciano et al. (1983) gives:
The latest values for ρ and κ are 0.9876 and 1.0026,
respectively. (by W.-M. Yao (2006) ) These equations have been used
widely to extract the strange form factors, but physical ρ and κ
should depend on Q2 and θl with finite Q2.
To reduce theoretical uncertainty of the extraction of the
strange form factors, it is necessary to go beyond zero momentum
transfer approximation. One can use methods such as hadron
mechanism, GDPs etc, to calculate the LO correction to APV.
Including one-loop level diagrams, the parity asymmetry APV now
is written as： (up to order of 10-2)
The 1 γ × 2 γ term contributed from the corrections to the
total cross sections, and the rest terms contributed from the
corrections to the total parity violating cross sections.
The OPE and TPE diagrams contribute to the MPC.
The γZ, 2Z and 2W exchange contribute to the MPV.
Different model are used to calculate MPV and Mpc.
Partonic calculation
To estimate the corrections of APV, we start from calculating
the PV and PC amplitudes in elastic e-q scattering with massless
quarks by using handbag approximation.
• Main contributions comes from “handbag diagrams” at large Q2.
• “Cat’s ears” diagrams is important for getting over all IR divergence
correct.
hard scattering amplitude
l(k’)
l(k)
H
pq
l(k) + q(pq) → l(k’) + q(p’q)
exchange：2 γ , γ Z, 2 Z, 2W
p’q
SDirect and SCross
N(p1)
N(p2)
Value of these effective form factors in quark level can be gained
by loop integration.
IR div appear in those loop integration when one of exchange
boson is soft and with infinitesimal mass. This IR div part can
be cancelled by Bremsstrahlung contribution.
soft
soft
soft
soft
soft
soft
soft
Total soft effect is finite and only gives an overall factor to
all kinds of cross section, which does not contribute to APV. So
we taken out the soft contribution and only keeps the hard part.
Hard part in nucleon level (GPDs)
work in frame q+ = 0, nμ is a Sudakov vector ( n2 = 0, n . P = 1 )
handbag amplitude depends on GPD(x, ξ = 0, Q2), x=Pq+/P+
Sum over all quark states, and calculate PV and PC separatedly.
A,B & C can be defined by GPD integrals
“magnetic” GPD
“electric” GPD
“axial” GPD
Similarly, D,E & F can be defined by
form factor input corrected by TPE
neutron form factor
Kubon et al. (2002)
and Warren et al. (2003)
magnetic proton form factor
Brash et al. (2002)
electric proton form factor :
GE / GM of proton fixed from polarization data Gayou et al. (2002)
Results and discussion
The corrections contributed from TPE by using partonic model
-u > M2
Andrei V. Afanasev and Carl E. Carlson (2005)
TPE and γZ-exchange corrections to parity-violating asymmetry
1 γ × 2γ
1 Z × 2γ
all 2γ
γZ+all 2γ
2γ ∼same when Q2↗,
γZ ↘ when Q2↗,
Partonic
TPE and γZ-exchange corrections to parity-violating asymmetry
Hadronic
C.W.Kao (2008)
Partonic
The corrections contributed from ZZ+WW exchange by
using partonic model are close to γZ-exchange effect.
ZZ+WW corrections
All loop corrections
Results and discussion
•Do these box exchange give large corrections to APV?
A: Only few percent rise up in average and with 1~2% ε
dependence.
•Are these corrections important to extract s-content?
A: Yes! Few % correction for APV gives huge correction to A2.
δ0 -> GsM, δ(ε) -> GsE .
Results and discussion
•Can we use these correction to extract s-content form exp now?
A: Yes and no. We only have some single point at low Q2.
•Do any other correction gives same order effect?
A: Yes! It is very sensitive to the choice of the Form factors
input！
•How about Qweak constant?
A: Not so sensitive; have a test of Qweak constant in low Q2 limit,
but cant use GPD model at low Q2.
Conclusion
•Partonic calculation gives much larger corrections compare to
hadronic calculation results.
•ALL TBE exchange only have weak ε dependence, and TPE has
weak Q2 dependence when others have strong Q2 dependence.
•Small corrections to the APV is important when extracting scontent, but we still need to wait for future data.
•Two Z/W exchange is needed to get all loop corrections.
Thank you for listening
When the electron and nucleon interact by the exchange of one
photon, the eN →eN amplitude is given by :
When interact by the exchange of one Z boson, the amplitude is
given by :
with g the weak gauge coupling, θW the Weinberg angle, glV = -(1-4
sin2 θW), and glA = 1. the gauge coupling g is given by g sin θW = e.
where the three terms in the numerator are given by：
To extract the strange form factors from above equation, one
needs to make flavor decompositions of the form factors GγE,M
and GZE,M , which one can obtains in standard model：