Transcript pylos2004 - Demokritos

Neutrino Cross Sections at
HERA and Beyond
ISVHECRI
September 10, 2004
Mary Hall Reno
Neutrino Energy Ranges
TeV
PeV
EeV
Water Cherenkov
TD, GZK neutrinos
Radio
AGN, GRB
Acoustic
EAShowers
Air Fluorescence
Mary Hall Reno
Outline
• Review the neutrino cross section and important
features.
• Pre-HERA, what did we know?
• Implications of HERA measurements of the structure
functions.
• Beyond….
Mary Hall Reno
Neutrino cross sections
• Neutrino cross section
depends on the usual
variables:
k
q  k k'
q  Q
2
2
2
Q
x
2P  q
y  P  q / P  k  ( E  E ') / E(lab frame )
Mary Hall Reno
k’
Charged Current Scattering
2G ME
d

dx dy

2
2
F
2
 M

2


xq
(
x
,
Q
)

xq
(
x
,
Q
)(1

y
)
 2
2  
 Q  MW 
2
W
cross section grows like
E at low energies
parton distribution
functions
W-boson propagator
At high energies, Q dependence is important in pdf and
propagator
M2
Q 2 ~ M W2 and x ~
Mary Hall Reno
W
M N E
Q Dependence
sea quark dominated
• QCD evolution of PDFs:
importance in neutrino
cross sections first
pointed out by Andreev,
Berezinsky and Smirnov,
Phys. Lett. 84B (1979).
“Earth is opaque”
Using old PDFs: CTEQ3
(post-HERA) and EHLQ
(pre-HERA).
no QCD evolution
Fig: Gandhi et al. 1995 (GQRS95)
Mary Hall Reno
half the cross
section
x dependence
5
3
10
10
Mary Hall Reno
10
1
Fig: GQRS 95
Average Q
Mary Hall Reno
Measurements
Energy of incident particle:
neutrino energies up to 350 GeV.
HERA ep scattering, equivalent energy of
~54 TeV.
(x,Q) for ultrahigh-energy neutrino
scattering are not measured.
Mary Hall Reno
Muon neutrino and antineutrino CC cross
section
[0
30 || 50 GeV
PDG, Hagiwara et al,
Phys Rev D66 (2002)
Mary Hall Reno
350]
Kinematic Reach
HERA
Eequiv
54 TeV , y  1
xy (2ME )  Q 2  x  105  Q 2
Fixed Target
E  350 GeV , y  1
3
x  1.6 10  Q
2
Plot from Zeus public
plots database.
Mary Hall Reno
PDFs pre-HERA
Eichten et al. Rev. Mod. Phys.1984,
focus on SSC. Also Duke and Owens.
Mary Hall Reno
Pre-HERA Parametrizations
e.g.,Duke and Owens (1984), Eichten,
Lane, Hinchliffe and Quigg (1984)
EHLQ 1984 
xus ( x, Q0 )  0.185(1  x)
2
7.12
 xd s
xg ( x, Q0 )  (1.75  15.575 x)(1  x)
2
xg and xq are initially constant in x at low x.
Mary Hall Reno
6.03
“Evolution” of PDFs
•LO analysis improved to NLO
analysis
•quark and gluon distributions
rise at small x for Q>a few GeV.
Mary Hall Reno
“Evolution” of PDFs
•CTEQ6 – Pumplin et al., JHEP
(2002) is part of a series of
CTEQ analyses.
•Martin et al.: series of analyses
MRST, HMRS, KMRS, MRS.
•Gluck, Reya and Vogt:
dynamical parton distribution
functions.
•not actually measuring
the pdfs at this value –
DGLAP evolution….
Mary Hall Reno
HERA CC and NC Measurements
Zeus Collab, Eur. Phys. J. C 32, 1 (2003)
H1 Collab, Eur. Phys. J. C 30, 1 (2003)
x  102
Mary Hall Reno
CC Cross Sections-UHE Extrapolations
DGLAP extrapolations: power law
and double leading log approx.
Numerous calculations: Quigg, Reno & Walker (1986), McKay & Ralston (1986), Frichter, McKay
& Ralston (1995), Gandhi et al. (1996,1998), Gluck, Kretzer & Reya (1999)
Mary Hall Reno
Theory Issues
BFKL=Balitsky, Fadin,
Kuraev & Lipatov
transition region
BFKL
ln 1/x
non-perturbative
saturation
Deep Inelastic Scattering Devenish &
Cooper-Sarkar, Oxford (2004)
DGLAP
ln Q
Mary Hall Reno
DGLAP=Dokshitzer,
Gribov, Lipatov, Altarelli
& Parisi
Small-x extrapolations
DGLAP evolution of parton distribution
functions: small-x evolution dominated by gluon
g  qq
Sea quarks dominate the cross section.
xg ( x, Q0 ) ~ A x


 xg ( x, Q) ~ x ,  (~ 0.2)
e.g.,Ellis, Kunszt & Levin (1994)
Mary Hall Reno
Extrapolations-DGLAP
for
~0
This is the extrapolation for EHLQ. Requires
double leading log approximation:
2
2
1/ 2

xg ( x, Q ) ~ A exp  B(ln(Q / Q0 )ln( x0 / x)) 
2
Gribov, Levin & Ryskin, Phys. Rep. 100 (1983)
Mary Hall Reno
CC Cross Sections Revisited
DGLAP extrapolations: power law
and double leading log approx.
all power law
extrapolations
DLA
vs.
power
law
Numerous calculations: Quigg, Reno & Walker (1986), McKay & Ralston (1986), Frichter, McKay
& Ralston (1995), Gandhi et al. (1996,1998), Gluck, Kretzer & Reya (1999)
Mary Hall Reno
More small-x extrapolations
LO BFKL, sum leading ln(1/x) (LL(1/x))
Multiple gluon emissions at small-x predict

xf ( x, Q) ~ x  
LL(1/x): OK (0.5), NLL(1/x): wrong sign, for fixed
s
Fadin & Lipatov, Camici & Ciafaloni
Recent work by Altarelli, Ball & Forte; Ciafaloni, Colferai, Salam
& Stasto on ln(1/x) resummation with running coupling, Kutak
and Stasto including saturation effects.
Mary Hall Reno
BFKL/DGLAP vs DGLAP
BFKL evolution matched to
DGLAP accounting for some
subleading ln(1/x), running
coupling constant,matched to
GRV parton distribution functions
Kwiecinski, Martin & Stasto, PRD
59 (1999)093002
Mary Hall Reno
Saturation effects
Saturation due to high gluon density at small x
(recombination effects)
g-g cross section
gluons/unit
rapidity
s
Q
2
xg ( x, Q )  R
Estimate of scale:
Qs
MW
2
Qs
for
2
size of
proton disk
2
4
1 GeV  (10 / x)
2
x 10
Mary Hall Reno
17
0.3
First Guess
Contours of constant
cross section for
E  1012 GeV
saturation region
MHR, Sarcevic, Sterman, Stratmann & Vogelsang, hep-ph/0110235
Mary Hall Reno
CC Cross Sections
KMS: Kwiecinski, Martin &
Stasto, PRD56(1997)3991;
KK: Kutak & Kwiecinski,
EPJ,C29(2003)521
more realistic
screening,
incl. QCD
evolution
Golec-Biernat & Wusthoff
model (1999), color dipole
interactions for screening.
Mary Hall Reno
Other results
L  (  N N A )
1
Fiore et al. PRD68 (2003),
with a soft non-perturbative
model and approx QCD
evolution.
Note: J. Jalilan-Marian, PRD68
(2003) suggests that there are
enhancements to the cross
section due to high gluon
density effects; enhancements
also in Gazizov et al. astroph/0112244.
factor ~2
Machado, hep-ph/0311281,
color dipole with BFKL/DGLAP.
Mary Hall Reno
Upward- vs. Downward-going UHE
neutrinos
11
10 GeV
air shower probability per
incident tau neutrino:
Upward Air Showers (UAS)
with different energy
thresholds, and Horizontal
Air Showers (HAS)
KMS and KK cross sections
Kusenko & Weiler, PRL 88(2002)
Mary Hall Reno
Small x at high energies?
•LHC will give the opportunity to measure small x values
at Q equal to the W boson mass, but still not as low as
we need to go. Look at the continuing story of pdfs,
small x and theory meets experiment.
Small x for lower energies?
• Perturbative cross sections – e.g. for charm-anticharm
and bottom-antibottom. This has implications for prompt
neutrino fluxes from the semileptonic decays of charmed
quarks. (See Stasto et al.)
Mary Hall Reno