Feasibility of measuring the magnetic dipole moments of the charm baryons at the LHC using bent crystals
Received: May
Feasibility of measuring the magnetic dipole moments of the charm baryons at the LHC using bent crystals
A.S. Fomin 1 2 4 6 7
A.Yu. Korchin 1 2 4 6 7
A. Stocchi 1 2 6 7
O.A. Bezshyyko 1 2 3 6 7
L. Burmistrov 1 2 6 7
S.P. Fomin 1 2 4 6 7
I.V. Kirillin 1 2 4 6 7
L. Massacrier 1 2 6 7
A. Natochii 1 2 3 6 7
P. Robbe 1 2 6 7
W. Scandale 0 1 2 6 7
N.F. Shul'ga 1 2 4 6 7
0 CERN, European Organization for Nuclear Research , CH-1211 Geneva 23 , Switzerland
1 4 Svobody Sq. , 61022 Kharkiv , Ukraine
2 1 Akademicheskaya St. , 61108 Kharkiv , Ukraine
3 Faculty of Physics, Taras Shevchenko National University of Kyiv
4 School of Physics and Technology, V.N. Karazin Kharkiv National University
5 BP 34 , Rue Andre Ampere, 91898 Orsay Cedex , France
6 15 rue Georges CLEMENCEAU , 91406 Orsay , France
7 64/13 Volodymyrska St. , 01601 Kyiv , Ukraine
In this paper we revisit the idea of measuring the magnetic dipole moments of the charm baryons and, in particular, of c+ by studying the spin precession induced by the strong e ective magnetic eld inside the channels of a bent crystal. We present a detailed sensitivity study showing the feasibility of such an experiment at the LHC in the coming years.
Fixed target experiments; Polarization; Charm physics; Flavor physics
-
HJEP08(217)
Principle of measurement
Spin precession in a bent crystal. Master formulas
Basic principles of the angular analysis
The sensitivity studies
c+ production cross section:
Results of the sensitivity studies
c
Possible experimental setup for performing this experiment
Conclusions
A Aspects of formalism of the polarization precession
B Asymmetry parameter for decay of polarized
c+ to
C Details on de ection e ciency:
ang;
acc;
def
1 Introduction
2
3
4
5
2.1
2.2
3.1
3.2
3.3
3.4
3.5
3.6
1
Introduction
The magnetic dipole moment (MDM) of a particle is its fundamental characteristic that
determines the torque which particle experiences in an external magnetic eld. The MDMs
of many particles are presently known [1]. For electron the QED prediction agrees with
experimentally measured value up to very high precision. For muon the measurement of the
BNL E821 experiment [2] disagrees with the Standard Model prediction by 3{4 standard
deviations, which may suggest physics beyond the Standard Model. The disagreement for
the muon g
2 is the subject of many studies (see, e.g., review [3]). The MDM of the
-lepton has not been measured so far and is of great interest for testing calculations in
the Standard Model [4].
For hadrons, the MDMs are measured for the baryon octet with J P = 12 +. Historically,
reasonable agreement between the measured MDM and predictions of the quark model was
important to substantiate the constituent quark models of the hadrons.
{ 1 {
In general, the MDM of the spin- 12 particle is expressed as
where S~ = ~2~ , m is the particle mass, q is the particle electric charge, g is the
gyromagnetic factor. The value g = 2 corresponds to a Dirac particle without magnetic moment
anomaly. Usually, the MDM of baryons is measured in units of the nuclear magneton
N
e~=(2mpc) [1], where mp is the proton mass and e is the elementary charge.
It would be very important to measure the MDM of the charm baryons
c+(udc) and
c+(usc), which have not been measured so far because of their very short lifetime of the
of their structure [5{21]. As for the c+ baryon, majority of the calculations predict the
MDM and g-factor in the ranges
( c+)
N
= 0:37{0:42;
g( c+) = 1:80{2:05:
Thus, an experimental study of the MDM of heavy baryons can be useful to distinguish
between di erent theoretical approaches.
One of the motivations for measurement of the MDM of the heavy baryons is also
studying the MDM of the charm quark. If this quark behaves as a point-like Dirac particle,
then the corresponding gyromagnetic factor gc is equal or close to 2, while if the charm
quark has a composite structure we can expect a sizable deviation from this value.
In the quark model the MDM of the heavy baryon is expressed in terms of the MDMs
of the heavy and light quarks. In particular, for the charm baryons, the spin and avor
structure of the ground-state baryons c+ and c+ implies that (see, e.g., ref. [5])
( c+) = c
;
( c+) =
(2 u + 2 s
c) :
1
3
MDMs in eqs. (1.3) depend on the MDM of the charm quark. Let us consider
and take \e ective" mass of the c-quark mc = 1:6 GeV as suggested from the charmonia
spectroscopy [5]. Keeping explicitly the g-factor of the charm quark we can write
( c+)
N
= 0:39 gc ;
2
g( c+) = 1:91 gc :
2
For gc = 2 these values are consistent with eqs. (1.2).
For c+ one needs to specify also the masses of the light constituent quarks. Choosing
mu = 336 MeV and ms = 509 MeV, which reproduce MDMs of the baryon octet [22], one
obtains from (1.3)
( c+)
N
= 0:83
2
0:13 gc ; g( c+) = 4:37
0:69 gc ;
2
where the rst numbers in each quantity in (1.5) come from the u and s quarks, and the
second | from the c quark.
{ 2 {
(1.1)
(1.2)
(...truncated)